Yeah, I made a comment on a Wings of Pegasus video, where he was using pitch analysis to work out whether auto-tune was being applied to a vocalist's performance - and he was comparing it to Freddie Mercury's vocals, who was infamously good at perfectly pitching his voice. And the point I made was that auto-tune - at least out of the box - will be "correcting" vocal performances to Equal Temperament. So, weirdly, what the software could well be doing is taking a perfectly pitched Just Intonation tuning... and then de-tuning it to be slightly wrong to match Equal Temperament. That auto-tune could, with the best singers, actually be making their performance worse. Adding in "beating" that actually wasn't originally there in the live performance. I mentioned this because I also noticed that - understandably so - his pitch analysis software (you can get it on Android, so I took a look for myself as well) analyses pitch in - you guessed it - Equal Temperament. So when analysing these vocal performances, you could see even the best singers seemingly being just slightly out. Being just slightly below or above the pitch lines. But, ah, this was why I commented. Was Freddie Mercury actually consistently pitching himself just shy of "correct" tuning, as per Equal Temperament, or was he, in fact, always perfectly hitting Just Intonation tuning, but because the pitch analysis software (and auto-tune, for the vocal performance he was comparing it to) is fixed to Equal Temperament, it's wrongly saying that Just Intonation is "slightly out of tune"? But, of course, the truth is that Just Intonation is "perfect" tuning, and what it's actually registering there is that Equal Temperament is the thing that's always "just slightly out of tune". But it is a mad thought - particularly with the prevalence of pitch correction / auto-tune in modern recording - that all these vocal performances are being forced to be "slightly wrong" to match Equal Temperament, when they could well have been (probably were, because, as you noted, this is how singers tune themselves, listening out for "beating") exactly on the nose in Just Intonation. That recording studios and labels are so obsessed with creating "the perfect product" that they are very possibly - with the best singers - actually degrading their live vocal performance to something worse than it actually originally was? (Except Adele. The pitch analysis software shows it - she never uses auto-tune or pitch correction. A shame, though, because probably only a singer of her quality and repute is able to carry enough clout with the record label to insist "no auto-tune". A surprising one, in the analysis by Wings of Pegasus, is that Michael Bublé - or Mickey Bubbles, as I prefer to call him - is actually pitch corrected on his albums. This is kind of weird, as the guy has done enough live performances - that are provably not corrected - to know that, no, he does not need that "assistance". But I don't know... do modern studio engineers just kind of automatically apply "auto-tune" to vocals without telling the artist? That it's now such a routine part of recording, it happens without thought to whether it's appropriate or needed to do so? Like, is Bublé even aware that they've done this to his performance? Or does he just "leave it to the engineers" and they just do it as a matter of course, out of habit, these days?)
@@klaxoncow It's unlikely to add beating unless there are multiple voices being sung at the same note with the same intonation. It's an issue in choirs because of so many people trying to sing the same note, but is less of an issue in a performance with just a single singer, and might actually fix beating that exists, particularly if the singer is doubling an instrument that is 12-tet tuned and they try to sing justly (unlikely to happen if they're singing / playing at the same time, but hey, you never know). And you seem to be assuming that just intonation is better or is "correct" when there really is no basis for assuming either of those things.
I'm a flute player, who has to learn early, how to adjust the tuning constantly. Even changes brought upon heat or cold of the room adjusted your tuning . Many wood wind players are always aware of "being in tune". Thank you for this video
Thanks. I played trumpet. We'd play a note before a concert and the band master would tell us to push or pull part of the instrument in or out. Never even considered it would change during a concert unless I hit it by accident. Brass must be less susceptible than woodwinds. But then no one told me you could breathe into the horn slowly and the note would emerge. That probably means the note isn't exact.
This is why in Indian classical music, each "note" is not a specific frequency, but a range of frequencies so they can be justly intoned in different harmonic contexts.
@@placeholdier For an artist I would look to Ravi Shankar or his daughter Anoushka. But generally if you just search for raga composers, there are very many.
@@placeholdier do you want instrumental or vocal? Some recommendations: Instrumental: raag bihag by Nikhil baneejee or Ravi Shankar Vocals: raga bhoop by Kishori Amonkar or raag nand by kumar gandharva. Hope this helps!
Wow, the thought put into this and the amount of info crammed into this short of a video is crazy. I respect that and keep making videos because i learn so much about music because of it.
Right?? I watched that Jacob Collier video from the start awhile ago and I was like "Ok this guy talks in music and i cant understand" but this was MUCH easier to grasp (parts at least, still learning the basics!)
I remember an interview with Tom Sholz of Boston, where he mentioned that he always tunes his guitar a bit flat (10 cents, I think he said) so that he can play with the temperament of the notes on the fly using finger pressure. So there are options even for fretted instruments.
@ghost mall yea, it does make sense if you're playing barred chords or just soloing with fretted notes or something and you want to match things both above and below equal temperament. It just seems unwieldy to me, but hey, who am I to argue with Tom Sholz? Guitar isn't even my primary instrument and he's a famous (and fantastic) guitarist!
Interesting. While watching the video I was wondering if a top guitarist could adjust their finger position within a fret to affect the sound. Does this mean that they could?
Something about that intro to Scar Tissue always sounded off to me. But not in an unpleasant way, or one I could put into words. Now it makes sense, and shows just how trained our ears are in the traditional tuning. Thanks for noting that song.
For synths and DAW use, there is Hermode tuning. A adaptive tuning system that will tune every note on the fly. Hermode might already be in your DAW as Cubase and Logic Pro both have this standard available. Some synths (e.g. older Waldorf and newer Virus models) have this build in too.
@@tibitoth_hu If you look up Hermode tuning there is a good explanation of how it works online. Including a in depth discussion of the algorithm behind it all. And plenty of example audio files. The original version used pitch bend messages to achieve the micro tuning. Using the Roland interpretation of "OMNI ON, MONO" mode to "fake" polyphonic pitch bend. This uses a one voice per channel setup and was intended for controlling midi synths from a midi guitar. Not sure if the modern Hermode versions build into Cubase or Logic still use the same trick. An other approach would be to manipulate micro tuning parameters on the fly using CC.
So glad you brought up Hermode! I use it in my Logic Pro DAW. I'm a little oversensitive to Equal Temperament and I consider it a godsend. As a guitarist,I can't resist constantly tweaking the tuning depending on key..D Major drives me up the wall otherwise. The overwhelming number of alternate temperaments with software also,to accommodate ethnic instruments,is amazing. I'm sure Hermode and microtonal possibilities will be increasingly refined in the near future.
This explains why when I tune my guitar by ear and play whats sounds to me like an in tune e chord, but when playing some other chords after, my ears think a string is still out of tune. Great video!
This is something that fretted instrument players just have to learn to play around. You choose your intervals to match the song (like you said "playing Am at the 5th fret") and making slight string bends to justly tune chords & solos that use more than one string. Every time you bend a string in a solo you're most likely pitching it up to a justly tuned position. It eventually becomes second nature.
Not to mention that, if you tune each string relative to the last to just intonation, the high e is really flat, about a syntonic comma (81:80, 21.5 cents)
Dear David, Your capability of explaining complex matters in a very simple and understandable yet thorough way is just impressive. Rarely have I seen a video bringing to the point the problem of temperament as easily as that one.
A song that goes from one justly intoned key to another with smooth transitions would probably sound like a Barbershop Harmony arrangement. In Barbershop Harmony we often change the chord prior to one of those awkward shifts to another key into a transitional chord or inversion so that the two sections transition easily with it all being in just intonation. This technique is often called a swipe.
That last piece composed by David made me the same effect as when I'm having a conversation and suddenly we change room. The musical/conversational information is there, yet at the transition between chords/doors, it takes a very discreet and quick moment for my brain to re-adjust.
Excellent video! I’ve been into Microtonality since 1977, and since I recently got my Lumatone a few months ago, I’ve been (finally!) able to play in 31TET (31 equal steps per octave rather than the usual 12). It’s kinda wild for the M3 to sound rock-solid, dead-on Just, and the P5 to sound a little … unsettled. However, the 31TET P5 is ~2.5 better in-tune than 12TET’s M3, so it’s only slightly unsettled-sounding.
This is so wildly helpful. My greatest struggle with learning about music is the inherent "why" of the choices and traditions that we have. Thank you SO much for making these, you make things so much more understandable!
I'm an electrical engineer and we study harmonics in the voltage/currents (Fourier and all that stuff). I remember that in order to have even harmonics the function must be asymmetric. So if we have a tone with a fundamental and an octave higher harmonic like in the example, the sound wave form is not symmetrical. I wouldn't have expected this
@@althealligator1467 It means that the positive and negative parts of the sound wave (which is a pressure wave),or, equivalently, the movement of the string in a string instrument,are not symmetric about the X (0) axis..
Yet again, a truly masterfully done piece of content. I'm beginning to wonder if this is all you or you have a large staff of professors and composers coming up with these things. Truly, I don't know how you could have explained it any better - I've seen others try. Of the many channels I've seen, it dawns on me that yours is the only one where I've gone back and listened a second and third time just for the enjoyment and not because I couldn't hear, see or understand the first time round.
To further complicate things, the harmonics on a string instrument are a bit higher-pitched than the actual integer ratios due to the stiffness of the strings. Since the sensation of consonance derives at least in part from two notes having the same harmonic frequencies, this would mean that consonant notes would not necessarily have simple rational frequency ratios.
@@DavidBennettPiano Some early electronic keyboards had tones that were too pure to sound natural so effects like Leslie speakers or reverb were needed. Some ran them through guitar amps or effects like chorus to mimic flaws we're used to with traditional instruments. The physics of round instruments like gongs dictate that upper harmonics cannot be what Western music is used to from long thin sound generators like strings or organ pipes.
Yes and it changes with ratios of string width to length or how the ends are held. It's why a Ukelele has different sound to a harp and why some guitar genres tune low to sound more deathly.
Not only that, but also the very act of plucking/bowing/etc a string actually makes the string go a bit sharp in tuning because the tension on the string increases a bit for a short time, and if the string-tension increases the tuning of the string goes sharp.
2:15 actually, a glass being dinged with a spoon is very likely to have some significant inharmonic overtones. generally, 1-dimensional systems like air columns and strings resonate harmonically, while 2-dimensional systems like cymbals, plates, or glasses resonate at least partially in non-integer ratios. but we're usually not doing harmony on a drum kit.
David Bennett's RUclips channel is my favorite music theory channel BY FAR, and this video is a great example of why. I have been playing and studying music for more than sixty years and thought I knew just about everything there was to know about just versus equal temperament tuning. Boy, was I wrong. I learned more about it in twenty minutes watching David than I learned over the years from dozens of music teachers and books.
I am an amateur when it comes to music and your videos not only open the world of theory understandably, it also teaches me how to play songs while recognizing patterns. Thank you so much David for helping me!
I worked out equal temperament as a teenager back in the 80s. I grew up playing sax where you have to adjust constantly, but picked up guitar at 13. This was before digital tuners and you had to use your ears to find the best compromise. I also studied Bach and was introduced to the well tempered clavier, plus had a physics teacher who explained the 12th root of two!. I was truly in the right place at the right time. Understanding this has shaped my life as a musician and guitar tech. This is a great video, but also check out Howard Goodall's "big bang" episode about equal temperament. It is excellent. The piece at the end sounds so strange to our equally tempered ears. "Uncanny" is a great description. It actually made me feel slightly anxious! I wonder what JS would have made of it... Keep up the great content mate.
Excellent as always: a very clear presentation of a potentially confusing subject. If I were to quibble, I’d say that the title is a bit misleading, since while one could argue that an instrument is only “in tune” if it’s in tune with itself, thus requiring just intonation, the typical use of the phrase “in tune” means to be in tune with other instruments, and hence almost always in A440 12-TET. But I know it’s a constant battle with the RUclips algorithm, so a bit of benign quasi-clickbait is understandable! It’s also questionable whether being perfectly in tune and free of beating is desirable. A single, pure, unwavering tone sounds flat and thin, so musicians, producers and sound designers use all sorts of techniques to introduce variation and richness, often through detuning: ensembles of players, double-tracking vocals, detuned analogue VCOs, chorus pedals etc. Also, while the harmonic series might be baked into mathematics, it’s not baked into the universe. It’s a simplified mathematical model of one-dimensional vibration, and works pretty well for thin plucked strings or vibrating air columns, but doesn’t quite capture the richness of many instruments. Even the bass strings of pianos are thick enough that their harmonics deviate noticeably from the integer ratios of the harmonic series, adding to the complexity that we know and love about pianos. Two and three dimensional vibrations such as those in bells and drums have highly inharmonic spectra, and I wonder whether that has led to some musical traditions (e.g. gamelan) being less obsessed with trying to fix the mathematical impossibilities of Pythagorean tuning than Western culture has been.
Great video, very interesting. There is a trick to play in just intonation on a guitar with an adjustable bridge for intonation. You have to shift all saddles, or the complete bridge slightly to the right (or left on a left handed guitar), so all strings, when fretted, are a bit flat. Then you can bend the string to get exactly the pitch that you want. This is only suited for playing a monophonic melody. Playing chords will hurt your ears.
I have a good ear, and I bought the tools and tuned my own piano. I used my ear, and the strobe, and it came out well, but I found myself frustrated a bit with the outcome. There is nuance to tuning that comes with knowledge and experience, and if I want a beautifully tuned piano, I suppose I will have to call the professional.
After playing a lot of funky-blues stuff, I discovered the harmonic series which led me into creating music using overtone singing, jaw-harps, overtone flutes. This video is excellent, super clear! Understanding the relation between harmonics and temperaments can unlock many doors for both musicians and listeners. Another good book I'd recommend is: Temperament: How Music Became a Battleground for the Great Minds of Western Civilization , by Stuart Isacoff (2001)
10:38 sounds out of tune for two reasons: 1) people exposed solely to 12-TET aren't used to anything but quasi-Pythagorean melodic intervals which approximate the Pythagorean half-step (256/243) and the major whole tone (9/8), which are both derived from perfect fifths, and so larger semitones (16/15) and smaller whole tones (10/9) derived from the 5th harmonic will sound melodically out of tune to them, because they don't recognize them; 2) the Bb was in fact out of tune in this case, because the effect was overexaggerated for the purpose of the demonstration. It's sharper than the actual 5-limit Bb by around 2/3 of a comma (around 15 cents).
To quote Science Officer Spock, "Fascinating." ...especially hearing the juxtaposed measures of different tunings. Brings to mind your compositions in 24-TET: suddenly, an unexpected pitch! As an experienced mandolin-neglecter, I can report that some fretted instruments, especially those with short scale lengths, love to self-adjust their own intonation right in the middle of being played. I call it the ill-temperament.
Your piece at the end was so strange to hear. Some of the chords were simply beautiful; more pure than any I've probably ever heard before. But then certain notes (especially the chromatic ornaments, as you said) were strangely off. I would have liked to heared it played in even temperament for comparison.
I love learning the science behind this! When I was in college and mostly singing a capella choral pieces and then would come home to our just-tuned piano to play or sing along, I would always feel like something was slightly wrong.
This is the perfect analogue to Andrew Huang's outstanding video on the Harmonic Series 2 years ago. Several of the specific points Andrew mentioned at the end of his discussion as things to look into further are addressed here in great style. Brilliant work David! Will be using this with my Music Theory students.
Perfectly clear and understandable explanation of the tuning problem! Nevertheless I am wondering why digital pianos couldn't easily retune the notes for each key - it's possible to tune to C-major or F# major in perfect tuning. Just not both keys at the same time. 17:15 oops, my objection was too early. :-)
I'm curious how you chose the key center for each of the pitches that weren't A (assuming you went with A440). Did you just use the 12TET frequency for each root note and then tune the rest justly? I wonder if you could make it sound less wonky by tuning the next key center based on the melody, even if that means starting and ending on a different tuning for A. I remember hearing about a looping vocal piece that is specifically written to get sharper and sharper when using just intonation between chords, but I can't for the life of me find the name of it.
I wish I could have linked to this when I saw a YT vid about how to choose the right guitar strings to prevent the G being out of tune. I knew this was a misconception, and my Comment about how tuning strings by harmonics, i.e. Justly, and tuning strings by fretting, will always come to a clash at the G/B 4-fret non-just interval. I got a bigger-than-usual response to one of my comments, mostly positive.
Good video. Can I share a tip? Microtonal tuning differences are much easier to hear with raw sawtooth waves than with a piano sound. Just thought I'd mention it...
Great video! I've been using sweetened tuning on my acoustic guitar in studio recording for some time. I'll do multiple takes where each take favours a couple of chords that sound best, with the others sounding okay but a little off. Then repeat as necessary where another set of chords sound best. After all the takes are done, I'll comp together all the best bits where chords sound the best. The key is making sure one is really consistent with the rhythm of each take. I tried explaining this to my band mates who didn't really hear it at first (it drove me nuts hearing certain chords sounding out); this video is the best explanation I've seen! Cheers! 😃 👍
One thing I really like about this video is that you correctly explained the difference between a tuning and a temperament. A lot of people mistakenly think the two concepts are the same, but _they’re not synonymous_ : All temperaments are tunings, but not all tunings are temperaments. A temperament is a system of adjustments from whole-number ratios, most famously (as you clearly demonstrated) to allow a single tuning to be usable in more than one key. So, Just Intonation is a tuning, but not a temperament. However, for the record, at 6:25 this video implies that Pythagorean is a temperament. It’s not because it uses exact whole-number frequency ratios, just not the preferable ones for triadic harmony.
I gotta say I’ve been binge watching your videos which is crazy since I’ve always hated trying to learn music theory as a self taught guitarist. You’ve really made appreciating music theory possible, thank you for the outstanding content!
David you are such a breath of fresh air. Thank you for explaining these concepts to us. I always fell like I’ve come away as a better musician after watching your videos!! MAY God richly bless you in all that you do.
What a fantastic video, thank you! When I was learning fretless banjo I asked a fiddle player friend how she managed. "Actually" she said, "The hardest thing is once you've got it, most instruments sound out of tune to you!"
I wonder if you could use something like pitch correction software to identify the chord being played and fix the tuning not to 12TET but to Just Intonation. It should be fairly straightforward to write a simple synth that does that, I might give it a go.
I've been curious about that too! I think in order for it to work, the software would have to identify the tonic note of the chord... which in many cases would be easy, but at times could be tricky.
@@moi01887 there would be several ways to do it, though, because the root note of each chord could be tuned differently depending on prior harmonic context. And then what about inversions? The root note wouldn't necessarily be the most important. There would be really no "correct" tuning.
People already do this manually. Watch Adam Neely's video on 7 Levels of Jazz Harmony, level 7 is just that. As cool as the idea is, it doesn't really sound good (you can still like it of course), as the simplicity of the overall tuning and the consistency of each note are sacrificed, so it sounds all over the place, and, oddly enough, out of tune; the thing with music is that context matters, which is why resolutions from dissonant to consonant intervals and music as a whole even work in the first place. You remember the pitches that came before, so justly intonating each chord this way makes each chord sound disconnected, out of tune. 12TET really is the single best compromise for tuning, specifically because it's even. Edit: Or the piece at the end of the video
Good luck dealing with inversions and chord extensions. Just intonation is nice for creating pleasing intervals in reference to a single note, but is in no way a musical system capable of dealing with the types of things done in western music.
David, as usual, a fascinating video which had my brain mangled until, that is, you arrived at ‘tempered tuning’, then it all fell into place. Also, is it (at all) interesting that the albums that leapt out at me from the 08:00 frame(s) were ‘Buddy Holly’ and ‘The Chirping Crickets’ - even before ‘Sgt Pepper’, ‘Hard Days Night’ etc, etc. despite my being a (rabid) Beatle (and, of course, Buddy Holly) fan. Must be my age, I guess… old fart. 😬 Your videos are incredibly entertaining and thought provoking.
You discovered the Fender Rhodes sound @13:05. Thats when the beating comes out of the left then the right speaker with each pulse. But in general even temperament makes the major 7th interval suffer when resolving to the tonic (or key) As in 'ti - Do' - as the 'ti' note always seems a bit flat. In 4 part stringed chamber music one can experience the best tonalities music offers.
15:30 I don't want to sound like a nerd but I'm pretty sure with Pedal Lap Steel guitars you're able to adjust the tuning of the string in real time, although I do not know to what degree it allows.
Thank you for shedding the light on one of the most fundamental and interesting topic of music theory and history! Awaiting impatiently for other temperaments! And please, more audio examples are desired 👍
I'm a pedal steel guitar player and have two tunings I use depending on which guitar I'm playing. The first tuning is just intonation for my Emmons Original Push Pull. Each string and pedal is adjusted using Hz, ie 445, 430. The second tuning is a slightly modified version of the 12 tone standard with some changes adjusted by +/- a few cents and I use it on my modern Mullens all pull guitar. I'm always at odds with the guitar player over who's out of tune. I found the best way to resolve it is to make sure we're not both playing in the same range. An octave makes all the difference in the world.
For your song at the end, I assume the best thing to do would be to slowly change the intonation rather than adjusting it abruptly. (similar to Collier's half-sharp movement) Also, check out Anna Von Hausswolff's album All Thoughts Fly which was all done on a 1/4 comma mean tone organ.
Well, the harmonic series can be easily understood with a guitar for example. If you rest your finger on the 12th fret (half of the string) and play it, you have a one-octave harmonic, a perfect fifth (thirteenth avtually) harmonic on fret 7 (thirf part of the string), and a two-octave harmonic on fret 5 (fourth part of the string)
I think the harmonic series is more easily understood as being... twice the fundamental, three times the fundamental, four times the fundamental, five times the fundamental and so forth. It's just integer multiples of the fundamental frequency. That's what's really going on there. But then you can translate this into musical intervals and note that, yeah, that's octave, fifth, fourth, major 3rd, minor 3rd. And then you can also understand where, ultimately, these intervals come from. As our ears / brains are listening out for harmonics. Because if two sounds are occurring at the same time, how does the brain know which frequencies relate to which sound? To be able to interpret that all those particular frequencies go together as "a dog bark" and all those other frequencies go together as "the neighbour talking next door". Because what our brain does is listen out for the harmonics. It picks up 220Hz, 440Hz, 660Hz, 880Hz, 1100Hz, 1320Hz, etc. and then, ah, those all go together, as those are harmonics of the fundamental 220Hz. So the brain hears all of those frequencies as one sound... of a particular timbre. But another sound - happening at the same time - is pitched at, say, 345Hz. All of its harmonics are different. So that's how the brain can say "all these frequencies go together as one sound, and all these other frequencies go together as a different sound". And we can, therefore, differentiate sounds and, for example, understand what someone is saying to us, even though there's traffic noise and dog barks and other sounds also happening at the same time. Because our brains have this means - via grouping things together in their harmonic series - to pull out individual sounds from a big cacophony of frequencies that could be happening at the same time. And now we've actually kind of evolutionarily explained music. Our brains need the harmonic series to separate out different sounds, when multiple sounds are happening at the same time. That's the evolutionary "survival advantage" for you. Why it even exists in the first place. But then we can see that music is essentially what's known as "super-stimulation" of this mechanism. By having instruments dance around on this harmonic series - coinciding with each other, conflicting with each other, in an elaborate dance of frequencies - this is, in essence, driving that part of the brain wild. We're giving it one hell of a "puzzle" of harmonic frequencies to solve. We're over-stimulating that part of the brain. Overloading it. And I guess this is like, you know, solving a crossword puzzle or getting the answers right on a TV quiz. You get a little dopamine hit - a burst of "happy chemicals" to the brain - for solving the puzzle. Again, the evolutionary reason is simple: reward good behaviour with a chemical "buzz" and we'll want to do good things more often, to enjoy the "happy chemical" hit. The ultimate expression of this evolutionary system being, you know, the orgasm. It's a evolutionary reward for propagating your genes (evolution hasn't yet adapted to the invention of the condom yet... shh, don't tell it, or it might have to adapt its strategy in many, many thousands of years), so you get a big flood of "happy chemicals" to the brain - the orgasm. And it works, right? This makes sex feel awesome, so you totally want to do it again. While music is not quite "better than sex" (okay, some people might want to debate that one), you can see that it's a similar mechanism. Music presents this overload to our brains - a big frequency puzzle to be solved - and when we solve the puzzle, evolution's prepared a nice little dopamine reward for you to say "well done", and to encourage us to keep being clever at solving these puzzles (a puzzle that does, at its root, come from a "survival instinct" origin, as differentiating sounds - the sound of the wind, from the sound of a hungry wolf that's about to attack you - would have had plenty of evolutionary utility for our cavemen ancestors). The harmonic series, in fact, unlocks it all. Why humans respond to music. What its evolutionary advantage would have been to develop in the first place. Where the intervals - and, thus, chords - come from. Why we love listening to music. It's all in there. Because of the convenient physics that if a string can vibrate at 220Hz, then it can also neatly vibrate at 440Hz, 660Hz or any neat integer multiple of the fundamental frequency. So that provides the brain with "one little trick to differentiate sounds from each other", and music has been riding this hard - in "overload" mode - ever since.
Except that the 19th fret (12+7) doesn't divide the string in 1/3 - 2/3, because only the octaves are just intonated. When you touch the string lightly above a fret corresponding to the harmonic series of the open string, then play the string and release the finger to create that typical harmonic sound, the node of vibration of the string will be slightly off the fret (unless it is one or 2 octaves) because the string will accommodate itself to the "simple fraction" ratio.
One interesting aspect of the beating phenomenon is that it doesn't actually rely on physical interference between the two waves -- that is, if you stick one of the pitches in JUST one ear and another pitch in the other ear, the beating will emerge strictly in *your brain* (termed a "binaural beat")
As a trumpeter born with way too sensitive ears (no perfect pitch but I hear much more than I'm good with) and playing in one of my country's best concert bands, being trained on this every rehearsal, this explained a lot to me. I just CAN'T with keyboard-insyruments, the 3rds and 7ths are... killing me! Every rehearsal our conductor tells us to find out which function our respective tones have in the chord, and we have to adjust them to make the chord sound calm (no beating. I didn't know it was called that, thank you!!) all tones together. It's quite a job and you should be practising a lot to know exactly where the right tone is belonging to the right chord at every time, not having to adjust it after you've already started playing it. Thank you David, for explaining to me I'm not totally crazy, I'm just born that way that I can actually hear and FEEL these small differences. (They're scratching my ears and my brain in a very annoying way)
As a guitarist, a huge thank you for sharing your knowledge and talents with the musical community. This explains why slight note bends and dips on fretted instruments can sound much more tastful
Thank you very much for this brilliant video. Just to add a little layer as to the tuning of pianos: the higher notes are also a bit “spread” to increase the brilliance of the sound. So one really understands that the “right” tuning of a piano is really an art.
There is a video on RUclips by a classical guitar player that shows a classical guitar with movable partial frets and how if he plays in tune in C( or its relative minor) by moving the frets , he can't play in any other key for precisely the reasons you indicated here; he also demonstrates how the adjusted tuning in C sounds so much better . It is like your video , quite interesting and quite eye opening.
I was fascinated by this topic as a student of electrical engineering and music theory in college in the 80s. I've been programming synths as a hobby since then, on everything from 8086 PCs to modern DSPs. I've also programmed tuners, including piano tuners. If you take a step or two into the topic of temperament, you tend to be dissatisfied with limitations of fixed tuning and look for the purity of perfectly just tuned intervals. This will often lead one to believe that there is some kind of mystical magic that happens when you adhere perfectly to Pythagorean integer ratios of frequencies. As you approach that, some very interesting and psycho-acoustically potent things happen. This has been demonstrated beautifully by Jacob Collier and others. But digitally, you CAN make it absolutely perfect. When you do, you find that it sounds awful. This isn't because there's a mystical optimal very close but not exactly at integer ratios of frequencies. It's something else. 1. We don't experience musical frequencies in time. Our brains don't work that fast. We experience them in a one-dimensional space on the sensor element in our ear, the cochlea, in a way that's similar to the way we perceive light on the two-dimensional space of the retina. We can hear a tone going on and off about as fast as we can see a light flashing on and off. 2. When sound is produced by playing a single note with a real physical device such as a string, vocal cord or bell for example, the overtones are not at exact multiples of the fundamental. The harmonics of a single note on the best piano you can buy are out of tune with one another. In the case of a string, the shorter and fatter it is, the more pronounced this phenomenon becomes. 3. The pitch of the fundamental and overtones of a note played on a physical instrument typically depend fairly strongly on how loudly the note is played. This can be seen easily when tuning the low strings on a guitar using a strobe tuner or something similar. Generally, the louder, the sharper. 4. Beating occurs when two tones (i.e., overtones) with nearly equal but different frequencies are sounded. Since the overtones of a single note don't overlap with the fundamental or with one another, beats don't result from the overtones being out of tune relative to the fundamental. Harmonics that are out of tune, within reason, don't sound dissonant if there are no other harmonics from other notes or instruments being generated near that frequency. There is nothing for them to compete with or beat against. 5. When tuning a 12-string guitar, perfectly matching the frequencies of each of the string pairs will make it sound like a six string. Very slightly detuning them accentuates the richness, complexity and presence of the tone. It also increases sustain. Detuning them further makes it sound like a honkytonk piano. The key point: It's not the mathematical purity of just tuned harmony that makes it sound good. Although there's more to it, the way the overlapping tones/overtones from various notes, voices and instruments DANCE WITH ONE ANOTHER (interact with one another) produces much of the "harmoniousness" of a given harmony. If overtones are doing exactly the same thing (sounding at exactly the same frequency), they're not dancing, they're just speaking redundantly. When tones/overtones interact independently, with their own identity and information content, at slightly different frequencies, the brain's spatial interpretive mechanisms are engaged in ways that might not necessarily be perceived as position or motion in three-dimensional space but involve the activation of neural pathways used to interpret the physical/spatial presence of a sound source. In my view, we should understand this spectral dance of harmony in a quantitative way and design digital instruments to expressively exploit this understanding. This, I think, will lead to music that is liberated from the 12-tone scale yet even more richly harmonious with a broader range of chord structures, music that can be designed/composed in a purely mathematical sense, rather than being derived from the limited framework offered by mechanical contraptions and their legacy.
Wow, extraordinary. What you say about harmony needing to dance makes SUCH sense. If it isn't dancing then, it actually feels dead; there is no musical conversation. Thank you SO much for your detailed and helpful response. We use Music to harmonise the soul (our ego) and so we naturally avoid unharmonious sounds because they fail to liberate the ego from an inner state of ego-dissonance. The ego is initially bodily, hence dance (or any human movement in response) is our 1st reaction to music in its role as soul-therapy. Music is temporal which means it must celebrate harmony as a life (not death) force. Harmonious perfection equals death. You can however so see why the so-called "perfect" intervals extensively used in late medieval polyphony, actually feel more joyously alive than a ghastly (ego upsetting) 3rd?
Another brilliant video. Thanks! When I attempt to explain this stuff to a friend or customer (I'm a piano tuner/technician) they usually just get even more confused. ... An interesting followup might be about how a piano tuner tunes by ear. It's all about hearing the beats where the partials of two notes should coincide but they don't. Tuners use those beat speeds of all the intervals to arrive at equal temperament. To make things more complicated, piano strings are not perfectly harmonic and the tuner needs to compensate for that, which makes a piano even more "out of tune"!
actually, i and some others, including Sevish, have started saying "ed2" instead of "tet" or "edo", and the reason for that is because you can replace "2" with any other interval, "2" refers to octave in this case so "12ed2" would translate to "12 equal divisions of the octave", this format actually really helps with tunings like wendy carlos tunings that are based on the fifth, wendy carlos alpha would be refered to as 9ed3/2, bohlen pierce would be 13ed3! however, "tet" also works too, but i think its important to also bring up "edo" and "ed2" as some of us who create microtonal songs use other acronyms and names for "divisions of the octave". great video by the way! speaking of tonality, you could try and find some tracks using different tuning systems and such, not just microtonality, but tuning systems distant from 12ed2, for example desert island rain by Sevish uses a completely different scale not possible in 12ed2, although im sure it'd be pretty difficult finding other examples that arent electronic... 😅
I experimented with temperament methods a few years ago, while developing a synth based on a very small 8bit chip and what worked quite well for me was using just fifths and octaves to get all the coefficients. A1 *3 => E2 /2 => E1 *3 => B2 /2 => B1 *3 => F#2 ... and so on. (The chip couldn't multiple nor divide and *3 /2 can be done easily using binary shifts). Nice video anyway.
Good video. Tuning a guitar is always an exercise in "close enough." When you get the open strings perfectly in tune according to the tuner and 12TET, try playing a bunch of spicy chords, especially up the neck, and you'll find dissonance where it doesn't belong. The tuner is only a starting point. Using octaves, natural harmonics, and relating every string to every other string, you can usually make tiny adjustments to find a point where the average ear finds all the intervals pleasing and nothing sounds noticeably off. What the tuner says at that point will vary somewhat from one instrument to the next.
I've been playing the guitar for over 50 years. When I was learning, there was no such thing as electronic tuners. One of the first lessons was how to tune your guitar by ear, by tuning, usually the 'A' string, with either a pitch pipe or tuning fork. I think it is too easy to rely on an electronic tuner.
True Temperament guitars are fretted to maintain 12TET down to the 24th fret. In exchange for that you get a guitar that looks like the frets are made out of random twigs you found on the forest floor :P
That's why it's important to adjust the neck and the bridge height so that the string-to-fret distance is according to specification. If the strings are too far away from the fretboard, when you press a string down the speaking length of the string, therefore the pitch, is a little bit off, and it gets worse the higher up on the fretboard you go. I have a cheap student electric guitar and it was amazing how much better it sounded after I adjusted the neck tension just a little bit.
@@davidbstang116 Well, yeah. But that’s only part of the equation. What you found is that a proper set-up will make it much easier to achieve “close enough.”
Great video, thanks! What is the keyboard instrument illustrated top right at 9:00 ? By the way it is worth mentioning guitar string bending as improvisational tool to sharp up a bit melodic phrases. And the "fluid piano" is a fascinating acoustic instrument allowing to set or improvise temperament and pitch for a performance, opening up eastern repertoire or experimental intervals for piano players. In both cases it's not a systemical "solution" but it shows how the ear of the player can guide the performance for certain intervals and note pitching, just like it is for violin players.
At 17:12 if musicians want to use just temperament in a bar or two in the studio and then go to equal temperament, that is fine, but it should be noted in the sheet music. I like to think of sheet music as "source code" just like we write for computers. Source code is FULL of comments for the human but the computer does not use. I think we need new notation, hey music has been evolving for centuries, and with MIDI you can step on a for switch and swap just/equal temperament on the fly. We didn't have this live before the 1980s (only in a studio that is not real time). I am thinking Studio Guitar Astring[-14cent]_____________________________ |
I absolutely loved this video! You’ve shed light on so many of the foundational aspects of music and sound. I found this incredibly informative and insightful. Thanks :)
This was very educational. I’ve been playing guitar for 40 years, and you may have just explained why I always find my guitar is out of tune after tuning it. For the last 20 years or so, I have used a digital or pedal tuner, then play an open “cowboy” D chord, then adjust the G B E strings by ear until it sounds good.
Great video! Only thing is I don't understand your point at 17:57. If you tuned to just tuning relative to A major, would all intervals not be justly tuned as long as you stay in the key of A major?
I used to keep a guitar in my workplace (about 50 years ago) to play during breaks. Tuning was always an issue. One day a guy who sang in a barber shop group tuned my guitar to open A. The guitar rang like a bell - it sounded perfect (in that key).
David, thank you very much for such a great video! To put all the necessary information about TET and reasons for its implementation in a such concise and straight to the point manner is a super great work! I wish I could give 10 likes to this video!
I play the piano and I come from the good ol' Amiga days when I was using OctaMED and playing all the great melodies from my favourite games (Turrican II, Impossamole, Shadow of the Beast, Lotus Esprite Turbo Challenge 2) on the computer keyboard For me, mentally, playing the piano is just pressing the right buttons at the right time. An easy mental barrier to get over. After watching your video it has cemented my opinion that the Violin is the hardest instrument to learn/play. Fascinating vid and I've really starting to enjoy your compositions at the end. Thank you.
As a player of keyboards and fretted instruments, I never realized how hard it truly is for string, wind and horn players I play with to be constantly adjusting pitches until this video. Hats off to you David for the wealth of info and that said, kudos to those non-fixed-tuning players!! 🙂
I was trying to explain this to my friend when he asked how a speaker can reproduce every single sound of nature if it is just a bunch if metal with a magnet inside. His question was very smart actually, it's amazing how perfectly a speaker can reproduce the sound of the sea, or some birds singing,to give and example.
Perfectly reproduce the *vibrations* of the sea and birds *as we perceive them*. Speakers are amazing, but they are mechanically doing exactly what our eardrums do (in reverse). Plus speakers don't have to exactly reproduce the original vibrations, they only have to reproduce in a way that we will perceive as accurate.
@@noonehere0987 not really. I know how it works, what amazes me is that in this day and age we don't bother to realize how many incredible things we use daily
Actually, as a very seasoned guitar player myself, there are 2 ways to intonate your strings individually on a guitar, however you can only pitch up and not down. The first and most obvious way is just bending the strings but for harmonic purposes this may be much too inaccurate. The second way is one that most people dont know actually makes a difference and its something they teach you NOT to do when learning guitar, and thats pressing the frets down harder, or pressing them in different spots. If you bottom out a mid fret on the low E string it can amount to maybe a 30 cent change in pitch upwards. As well, if you slide your finger up and down a fret while playing a note, youll notice that it changes pitch up and down as well.
Brass players have to constantly listen to the ensemble around them. Fortunately, some instruments can be tuned on the fly with the tuning slides (trombones are obvious, but trumpets can also be tuned on the fly with the slides as well.) That said, it's not always possible (or desirable) to use slides(F horns, baritones, etc.), so we learn how to "lip up" or "lip down" a note using our embouchure. It takes lots of practice. You can be playing a unison note within a section and you'll hear the beats then all of a sudden they disappear, as each player adjusts either their lip position or even how much air they're putting through the horn. Quite fun when you get it right, and obnoxious when it's wrong.
I wonder how a person with perfect pitch deals with the different tuning systems? Does it drive them crazy if they hear one over the other being accustomed to one system their whole life? That would be an interesting deep dive video
@ghost mall perfect pitch isn't relative to any tuning, but the absolute pitch (frequency) of each note. If you meet a person with perfect pitch in the Western World and ask them to sing a G for example, they'll probably sing an equal tempered G. Their perfect pitch isn't based on 12TET, but they learned the note _names_ according to 12TET. They'll still be better than you at just intonation though lol
You don't need to have perfect pitch to get rattled by off tuning. Otherwise, why are the rest of us listening to this video (sorry, for me, you tube is only for listening to) ?
Great video! I always wondered to what extent violinists, vocalists, etc used just intonation. One thing I'll add is, during guitar solos, it's amazingly common to hit a major-3rd double stop on the G+B strings and then bend the lower note up slightly. It was a huge revelation to me when I realized this was effectively achieving just intonation on the fly.
I might be late mentioning this, not having read through all the comments, but I recommend doing a RUclips search for micro-fretted guitars, ie a small fret for each string in the right position for just intonation. The comparisons with TET are very obvious. The same guy also uses elastic bands as frets which he can move slightly to create just tuning but only in a given key or two. As I became a more experience guitar player (nearly 70 now) I became more and more intolerant of the consequences of using either conventional tuning from the fifth fret (fourth G to B) or electronic tuners. The guitar tech at Hank's guitar shop in Denmark St, London, told me his secret about 30 years ago. It is to tune from the D, 12th fret harmonic to the B, third fret. You then do a sequence of 5th to 7th fret tuning, but adjust the A to D relationship so that the A is slightly flat with a slow beat of maybe four beats a second. That usually gets you into a far better compromise tuning than any other I've come across. Anyone got any others? The clip of Voces8 reminds me that during lockdown, their second tenor, Blake, did a very good live-stream talking about all of this with examples of a capella singing where a clear beat could be heard through TETish tuning or, when you get everyone properly in tune, all the other harmonics are prompted and clear notes, not being sung, ring out. Fantastic. Sorry to ramble on - this stuff interests me!! Great channel, David.
4:20 Not quite 14%, as it should be compared to the A not the next semitone. The equal tempered major 3rd is 400 cent apart, but should be 386 in just intonation. So the C# is 3.6% too high.
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Yeah, I made a comment on a Wings of Pegasus video, where he was using pitch analysis to work out whether auto-tune was being applied to a vocalist's performance - and he was comparing it to Freddie Mercury's vocals, who was infamously good at perfectly pitching his voice.
And the point I made was that auto-tune - at least out of the box - will be "correcting" vocal performances to Equal Temperament.
So, weirdly, what the software could well be doing is taking a perfectly pitched Just Intonation tuning... and then de-tuning it to be slightly wrong to match Equal Temperament.
That auto-tune could, with the best singers, actually be making their performance worse. Adding in "beating" that actually wasn't originally there in the live performance.
I mentioned this because I also noticed that - understandably so - his pitch analysis software (you can get it on Android, so I took a look for myself as well) analyses pitch in - you guessed it - Equal Temperament.
So when analysing these vocal performances, you could see even the best singers seemingly being just slightly out. Being just slightly below or above the pitch lines.
But, ah, this was why I commented.
Was Freddie Mercury actually consistently pitching himself just shy of "correct" tuning, as per Equal Temperament, or was he, in fact, always perfectly hitting Just Intonation tuning, but because the pitch analysis software (and auto-tune, for the vocal performance he was comparing it to) is fixed to Equal Temperament, it's wrongly saying that Just Intonation is "slightly out of tune"? But, of course, the truth is that Just Intonation is "perfect" tuning, and what it's actually registering there is that Equal Temperament is the thing that's always "just slightly out of tune".
But it is a mad thought - particularly with the prevalence of pitch correction / auto-tune in modern recording - that all these vocal performances are being forced to be "slightly wrong" to match Equal Temperament, when they could well have been (probably were, because, as you noted, this is how singers tune themselves, listening out for "beating") exactly on the nose in Just Intonation.
That recording studios and labels are so obsessed with creating "the perfect product" that they are very possibly - with the best singers - actually degrading their live vocal performance to something worse than it actually originally was?
(Except Adele. The pitch analysis software shows it - she never uses auto-tune or pitch correction. A shame, though, because probably only a singer of her quality and repute is able to carry enough clout with the record label to insist "no auto-tune".
A surprising one, in the analysis by Wings of Pegasus, is that Michael Bublé - or Mickey Bubbles, as I prefer to call him - is actually pitch corrected on his albums. This is kind of weird, as the guy has done enough live performances - that are provably not corrected - to know that, no, he does not need that "assistance". But I don't know... do modern studio engineers just kind of automatically apply "auto-tune" to vocals without telling the artist? That it's now such a routine part of recording, it happens without thought to whether it's appropriate or needed to do so? Like, is Bublé even aware that they've done this to his performance? Or does he just "leave it to the engineers" and they just do it as a matter of course, out of habit, these days?)
Top quality and thoughtful content as ever David, ^oo^
@@bernardthedisappointedowl6938 thanks!
@@klaxoncow It's unlikely to add beating unless there are multiple voices being sung at the same note with the same intonation. It's an issue in choirs because of so many people trying to sing the same note, but is less of an issue in a performance with just a single singer, and might actually fix beating that exists, particularly if the singer is doubling an instrument that is 12-tet tuned and they try to sing justly (unlikely to happen if they're singing / playing at the same time, but hey, you never know).
And you seem to be assuming that just intonation is better or is "correct" when there really is no basis for assuming either of those things.
I love your channel thank you!
My respect for instrumentalists using non-fretted instruments just went up massively
ngl ive been playing violin for 5 years and I've never even done this conciously
Especially confusing learning where to put your fingers but if you know your music theory, have a good ear, and practice you can figure it out.
Exactly
My thoughts for years
But wait, wind players do this too(?)
I'm a flute player, who has to learn early, how to adjust the tuning constantly. Even changes brought upon heat or cold of the room adjusted your tuning . Many wood wind players are always aware of "being in tune". Thank you for this video
Thanks!
Interesting. How do you adjust it on a flute ?
@@tanguydelooz2881 Embouchure
@@tanguydelooz2881 Lip position on the mouthpiece and air support are the 2 main ways.
Thanks. I played trumpet. We'd play a note before a concert and the band master would tell us to push or pull part of the instrument in or out. Never even considered it would change during a concert unless I hit it by accident. Brass must be less susceptible than woodwinds. But then no one told me you could breathe into the horn slowly and the note would emerge. That probably means the note isn't exact.
This is why in Indian classical music, each "note" is not a specific frequency, but a range of frequencies so they can be justly intoned in different harmonic contexts.
And it's funny because obviously violin players in Western 12TET music do this instinctively. But it's not notated in any way by our musical system.
Care to share some example of indian classical music? :)
@@placeholdier For an artist I would look to Ravi Shankar or his daughter Anoushka. But generally if you just search for raga composers, there are very many.
@@placeholdier do you want instrumental or vocal? Some recommendations:
Instrumental: raag bihag by Nikhil baneejee or Ravi Shankar
Vocals: raga bhoop by Kishori Amonkar or raag nand by kumar gandharva.
Hope this helps!
I’ve been trying to explain that to my students for years, but your video just nailed it. Thanks, David!
😊😊😊
Wow, the thought put into this and the amount of info crammed into this short of a video is crazy. I respect that and keep making videos because i learn so much about music because of it.
Right?? I watched that Jacob Collier video from the start awhile ago and I was like "Ok this guy talks in music and i cant understand" but this was MUCH easier to grasp (parts at least, still learning the basics!)
I remember an interview with Tom Sholz of Boston, where he mentioned that he always tunes his guitar a bit flat (10 cents, I think he said) so that he can play with the temperament of the notes on the fly using finger pressure. So there are options even for fretted instruments.
Open strings: "You can't do this to me... YOU KNOW HOW MUCH I SACRIFICED?!"
That destroys open chords, and you can adjust the temperament anyways if you're playing because there is no preferred reference pitch.
@ghost mall yea, it does make sense if you're playing barred chords or just soloing with fretted notes or something and you want to match things both above and below equal temperament. It just seems unwieldy to me, but hey, who am I to argue with Tom Sholz? Guitar isn't even my primary instrument and he's a famous (and fantastic) guitarist!
Musicians always have BS tales like this. It's not likely to be true.
Interesting. While watching the video I was wondering if a top guitarist could adjust their finger position within a fret to affect the sound. Does this mean that they could?
Something about that intro to Scar Tissue always sounded off to me. But not in an unpleasant way, or one I could put into words. Now it makes sense, and shows just how trained our ears are in the traditional tuning. Thanks for noting that song.
For synths and DAW use, there is Hermode tuning. A adaptive tuning system that will tune every note on the fly. Hermode might already be in your DAW as Cubase and Logic Pro both have this standard available. Some synths (e.g. older Waldorf and newer Virus models) have this build in too.
is it cpu friendly or does it make ur pc a jet engine xd
@@doinky4345 Its just midi data. Very little cpu power needed.
@@ezion67 So does midi support microtonality? That's new to me
@@tibitoth_hu If you look up Hermode tuning there is a good explanation of how it works online. Including a in depth discussion of the algorithm behind it all. And plenty of example audio files.
The original version used pitch bend messages to achieve the micro tuning. Using the Roland interpretation of "OMNI ON, MONO" mode to "fake" polyphonic pitch bend. This uses a one voice per channel setup and was intended for controlling midi synths from a midi guitar.
Not sure if the modern Hermode versions build into Cubase or Logic still use the same trick. An other approach would be to manipulate micro tuning parameters on the fly using CC.
So glad you brought up Hermode! I use it in my Logic Pro DAW. I'm a little oversensitive to Equal Temperament and I consider it a godsend. As a guitarist,I can't resist constantly tweaking the tuning depending on key..D Major drives me up the wall otherwise. The overwhelming number of alternate temperaments with software also,to accommodate ethnic instruments,is amazing. I'm sure Hermode and microtonal possibilities will be increasingly refined in the near future.
This explains why when I tune my guitar by ear and play whats sounds to me like an in tune e chord, but when playing some other chords after, my ears think a string is still out of tune. Great video!
Yes, guitar is interesting in that it’s not only using an imperfect tuning, but the fret intonation is also somewhat imperfect.
@@clipsmasterproductions7479 and that's why true temperament frets (the squiggly frets) exist lol
This is something that fretted instrument players just have to learn to play around. You choose your intervals to match the song (like you said "playing Am at the 5th fret") and making slight string bends to justly tune chords & solos that use more than one string. Every time you bend a string in a solo you're most likely pitching it up to a justly tuned position. It eventually becomes second nature.
It is rare to hear an in tune guitar, sadly. Or at least, if your ears are sensitive, you often feel guitar as the rough stuff.
Not to mention that, if you tune each string relative to the last to just intonation, the high e is really flat, about a syntonic comma (81:80, 21.5 cents)
Can I just say this is the best plugged sponsorship ever XD Great video as usual!
Thanks!!
As a violinist who plays both guitar and piano, this is the video explanation I needed to help others understand the subtlety, thank you!
Dear David,
Your capability of explaining complex matters in a very simple and understandable yet thorough way is just impressive.
Rarely have I seen a video bringing to the point the problem of temperament as easily as that one.
A song that goes from one justly intoned key to another with smooth transitions would probably sound like a Barbershop Harmony arrangement. In Barbershop Harmony we often change the chord prior to one of those awkward shifts to another key into a transitional chord or inversion so that the two sections transition easily with it all being in just intonation. This technique is often called a swipe.
Wow good point
that's very interesting!
I wrote of this exact concept but from my violin background.
Ah, that wonderful "Barber of Seville"?
That last piece composed by David made me the same effect as when I'm having a conversation and suddenly we change room. The musical/conversational information is there, yet at the transition between chords/doors, it takes a very discreet and quick moment for my brain to re-adjust.
Haha great analogy. Love it. The acoustical space literally changes mid-conversation
Brilliant analogy because it lit. describes a mood change which can only happen through time and space.
Excellent video! I’ve been into Microtonality since 1977, and since I recently got my Lumatone a few months ago, I’ve been (finally!) able to play in 31TET (31 equal steps per octave rather than the usual 12). It’s kinda wild for the M3 to sound rock-solid, dead-on Just, and the P5 to sound a little … unsettled. However, the 31TET P5 is ~2.5 better in-tune than 12TET’s M3, so it’s only slightly unsettled-sounding.
This is so wildly helpful. My greatest struggle with learning about music is the inherent "why" of the choices and traditions that we have. Thank you SO much for making these, you make things so much more understandable!
Coming from a math background, I never fully understood why the harmonic series was called that. Now it actually makes sense
😃
I'm an electrical engineer and we study harmonics in the voltage/currents (Fourier and all that stuff). I remember that in order to have even harmonics the function must be asymmetric. So if we have a tone with a fundamental and an octave higher harmonic like in the example, the sound wave form is not symmetrical. I wouldn't have expected this
@@joseluisblanco8074 symmetrical in what way? I just had my first day of musicology, so I'm interested
not me thinking you meant math rock 😭
@@althealligator1467 It means that the positive and negative parts of the sound wave (which is a pressure wave),or, equivalently, the movement of the string in a string instrument,are not symmetric about the X (0) axis..
As others have mentioned you just have a knack for explaining things in a way that makes them very easy to understand
Yet again, a truly masterfully done piece of content. I'm beginning to wonder if this is all you or you have a large staff of professors and composers coming up with these things.
Truly, I don't know how you could have explained it any better - I've seen others try. Of the many channels I've seen, it dawns on me that yours is the only one where I've gone back and listened a second and third time just for the enjoyment and not because I couldn't hear, see or understand the first time round.
To further complicate things, the harmonics on a string instrument are a bit higher-pitched than the actual integer ratios due to the stiffness of the strings. Since the sensation of consonance derives at least in part from two notes having the same harmonic frequencies, this would mean that consonant notes would not necessarily have simple rational frequency ratios.
That’s true. It’s called Inharmonicity and makes an already impossible task even harder!
@@DavidBennettPiano Some early electronic keyboards had tones that were too pure to sound natural so effects like Leslie speakers or reverb were needed. Some ran them through guitar amps or effects like chorus to mimic flaws we're used to with traditional instruments. The physics of round instruments like gongs dictate that upper harmonics cannot be what Western music is used to from long thin sound generators like strings or organ pipes.
Yes and it changes with ratios of string width to length or how the ends are held. It's why a Ukelele has different sound to a harp and why some guitar genres tune low to sound more deathly.
Not only that, but also the very act of plucking/bowing/etc a string actually makes the string go a bit sharp in tuning because the tension on the string increases a bit for a short time, and if the string-tension increases the tuning of the string goes sharp.
Fascinating. Interesting how few folk have got this far. I hate being as sensitive to tuning as I am and I don't even have perfect pitch..
It is the best explanation I have ever heard and seen about tuning in my life! Thank you!
I'd heard about this before but never really grasped the full implications of equal temperament/just intonation until watching this. Excellent work.
2:15 actually, a glass being dinged with a spoon is very likely to have some significant inharmonic overtones. generally, 1-dimensional systems like air columns and strings resonate harmonically, while 2-dimensional systems like cymbals, plates, or glasses resonate at least partially in non-integer ratios. but we're usually not doing harmony on a drum kit.
David Bennett's RUclips channel is my favorite music theory channel BY FAR, and this video is a great example of why. I have been playing and studying music for more than sixty years and thought I knew just about everything there was to know about just versus equal temperament tuning. Boy, was I wrong. I learned more about it in twenty minutes watching David than I learned over the years from dozens of music teachers and books.
12TET is all well and good but the "close enough for rock 'n' roll" temperament usually works for me.
Excellent video, the best one I've seen on tuning.
Thanks 😀
I am an amateur when it comes to music and your videos not only open the world of theory understandably, it also teaches me how to play songs while recognizing patterns. Thank you so much David for helping me!
I worked out equal temperament as a teenager back in the 80s. I grew up playing sax where you have to adjust constantly, but picked up guitar at 13. This was before digital tuners and you had to use your ears to find the best compromise. I also studied Bach and was introduced to the well tempered clavier, plus had a physics teacher who explained the 12th root of two!. I was truly in the right place at the right time. Understanding this has shaped my life as a musician and guitar tech.
This is a great video, but also check out Howard Goodall's "big bang" episode about equal temperament. It is excellent.
The piece at the end sounds so strange to our equally tempered ears. "Uncanny" is a great description. It actually made me feel slightly anxious! I wonder what JS would have made of it... Keep up the great content mate.
Digital tuners were around in the 80s may have been pricey though.
Excellent as always: a very clear presentation of a potentially confusing subject. If I were to quibble, I’d say that the title is a bit misleading, since while one could argue that an instrument is only “in tune” if it’s in tune with itself, thus requiring just intonation, the typical use of the phrase “in tune” means to be in tune with other instruments, and hence almost always in A440 12-TET. But I know it’s a constant battle with the RUclips algorithm, so a bit of benign quasi-clickbait is understandable! It’s also questionable whether being perfectly in tune and free of beating is desirable. A single, pure, unwavering tone sounds flat and thin, so musicians, producers and sound designers use all sorts of techniques to introduce variation and richness, often through detuning: ensembles of players, double-tracking vocals, detuned analogue VCOs, chorus pedals etc. Also, while the harmonic series might be baked into mathematics, it’s not baked into the universe. It’s a simplified mathematical model of one-dimensional vibration, and works pretty well for thin plucked strings or vibrating air columns, but doesn’t quite capture the richness of many instruments. Even the bass strings of pianos are thick enough that their harmonics deviate noticeably from the integer ratios of the harmonic series, adding to the complexity that we know and love about pianos. Two and three dimensional vibrations such as those in bells and drums have highly inharmonic spectra, and I wonder whether that has led to some musical traditions (e.g. gamelan) being less obsessed with trying to fix the mathematical impossibilities of Pythagorean tuning than Western culture has been.
Thank you for this interesting comment.
super cool video 🔥
Thank you David for your videos. They are so clear and packed with information. You're a natural born teacher.
Great video, very interesting.
There is a trick to play in just intonation on a guitar with an adjustable bridge for intonation. You have to shift all saddles, or the complete bridge slightly to the right (or left on a left handed guitar), so all strings, when fretted, are a bit flat. Then you can bend the string to get exactly the pitch that you want. This is only suited for playing a monophonic melody. Playing chords will hurt your ears.
Really nice composition there at the end, David.
I have a good ear, and I bought the tools and tuned my own piano. I used my ear, and the strobe, and it came out well, but I found myself frustrated a bit with the outcome. There is nuance to tuning that comes with knowledge and experience, and if I want a beautifully tuned piano, I suppose I will have to call the professional.
After playing a lot of funky-blues stuff, I discovered the harmonic series which led me into creating music using overtone singing, jaw-harps, overtone flutes. This video is excellent, super clear!
Understanding the relation between harmonics and temperaments can unlock many doors for both musicians and listeners.
Another good book I'd recommend is: Temperament: How Music Became a Battleground for the Great Minds of Western Civilization , by Stuart Isacoff (2001)
I’m so glad more people are talking about this recently.
10:38 sounds out of tune for two reasons: 1) people exposed solely to 12-TET aren't used to anything but quasi-Pythagorean melodic intervals which approximate the Pythagorean half-step (256/243) and the major whole tone (9/8), which are both derived from perfect fifths, and so larger semitones (16/15) and smaller whole tones (10/9) derived from the 5th harmonic will sound melodically out of tune to them, because they don't recognize them; 2) the Bb was in fact out of tune in this case, because the effect was overexaggerated for the purpose of the demonstration. It's sharper than the actual 5-limit Bb by around 2/3 of a comma (around 15 cents).
To quote Science Officer Spock, "Fascinating." ...especially hearing the juxtaposed measures of different tunings. Brings to mind your compositions in 24-TET: suddenly, an unexpected pitch!
As an experienced mandolin-neglecter, I can report that some fretted instruments, especially those with short scale lengths, love to self-adjust their own intonation right in the middle of being played. I call it the ill-temperament.
This is an interesting problem. I wonder how Spock, or any Vulcan, would have addressed the problem?
Your piece at the end was so strange to hear. Some of the chords were simply beautiful; more pure than any I've probably ever heard before. But then certain notes (especially the chromatic ornaments, as you said) were strangely off. I would have liked to heared it played in even temperament for comparison.
I love learning the science behind this! When I was in college and mostly singing a capella choral pieces and then would come home to our just-tuned piano to play or sing along, I would always feel like something was slightly wrong.
This is the perfect analogue to Andrew Huang's outstanding video on the Harmonic Series 2 years ago. Several of the specific points Andrew mentioned at the end of his discussion as things to look into further are addressed here in great style. Brilliant work David! Will be using this with my Music Theory students.
Perfectly clear and understandable explanation of the tuning problem!
Nevertheless I am wondering why digital pianos couldn't easily retune the notes for each key - it's possible to tune to C-major or F# major in perfect tuning. Just not both keys at the same time.
17:15 oops, my objection was too early. :-)
I'm curious how you chose the key center for each of the pitches that weren't A (assuming you went with A440). Did you just use the 12TET frequency for each root note and then tune the rest justly? I wonder if you could make it sound less wonky by tuning the next key center based on the melody, even if that means starting and ending on a different tuning for A. I remember hearing about a looping vocal piece that is specifically written to get sharper and sharper when using just intonation between chords, but I can't for the life of me find the name of it.
Are you talking about Bendetti's Puzzle? Adam Neely did a video on it.
Don't string players and voice use Pythagorian tuning (5ths) for the melody (horizontal) and Just Intonation for the harmony (vertical)?
Comma pump?
"I will be doing a video on historical temperaments in the future"
Time traveller confirmed! No wonder he looks so young.
I wish I could have linked to this when I saw a YT vid about how to choose the right guitar strings to prevent the G being out of tune. I knew this was a misconception, and my Comment about how tuning strings by harmonics, i.e. Justly, and tuning strings by fretting, will always come to a clash at the G/B 4-fret non-just interval. I got a bigger-than-usual response to one of my comments, mostly positive.
Good video. Can I share a tip? Microtonal tuning differences are much easier to hear with raw sawtooth waves than with a piano sound. Just thought I'd mention it...
Great video! I've been using sweetened tuning on my acoustic guitar in studio recording for some time. I'll do multiple takes where each take favours a couple of chords that sound best, with the others sounding okay but a little off. Then repeat as necessary where another set of chords sound best. After all the takes are done, I'll comp together all the best bits where chords sound the best. The key is making sure one is really consistent with the rhythm of each take. I tried explaining this to my band mates who didn't really hear it at first (it drove me nuts hearing certain chords sounding out); this video is the best explanation I've seen! Cheers! 😃 👍
One thing I really like about this video is that you correctly explained the difference between a tuning and a temperament. A lot of people mistakenly think the two concepts are the same, but _they’re not synonymous_ : All temperaments are tunings, but not all tunings are temperaments.
A temperament is a system of adjustments from whole-number ratios, most famously (as you clearly demonstrated) to allow a single tuning to be usable in more than one key. So, Just Intonation is a tuning, but not a temperament.
However, for the record, at 6:25 this video implies that Pythagorean is a temperament. It’s not because it uses exact whole-number frequency ratios, just not the preferable ones for triadic harmony.
I gotta say I’ve been binge watching your videos which is crazy since I’ve always hated trying to learn music theory as a self taught guitarist. You’ve really made appreciating music theory possible, thank you for the outstanding content!
The piece at the end is absolutely mesmerising, love it!
David you are such a breath of fresh air. Thank you for explaining these concepts to us. I always fell like I’ve come away as a better musician after watching your videos!! MAY God richly bless you in all that you do.
What a fantastic video, thank you!
When I was learning fretless banjo I asked a fiddle player friend how she managed.
"Actually" she said, "The hardest thing is once you've got it, most instruments sound out of tune to you!"
I wonder if you could use something like pitch correction software to identify the chord being played and fix the tuning not to 12TET but to Just Intonation. It should be fairly straightforward to write a simple synth that does that, I might give it a go.
I've been curious about that too! I think in order for it to work, the software would have to identify the tonic note of the chord... which in many cases would be easy, but at times could be tricky.
@@moi01887 there would be several ways to do it, though, because the root note of each chord could be tuned differently depending on prior harmonic context. And then what about inversions? The root note wouldn't necessarily be the most important. There would be really no "correct" tuning.
People already do this manually. Watch Adam Neely's video on 7 Levels of Jazz Harmony, level 7 is just that.
As cool as the idea is, it doesn't really sound good (you can still like it of course), as the simplicity of the overall tuning and the consistency of each note are sacrificed, so it sounds all over the place, and, oddly enough, out of tune; the thing with music is that context matters, which is why resolutions from dissonant to consonant intervals and music as a whole even work in the first place. You remember the pitches that came before, so justly intonating each chord this way makes each chord sound disconnected, out of tune.
12TET really is the single best compromise for tuning, specifically because it's even.
Edit: Or the piece at the end of the video
Good luck dealing with inversions and chord extensions. Just intonation is nice for creating pleasing intervals in reference to a single note, but is in no way a musical system capable of dealing with the types of things done in western music.
Apparently that's a thing, called Hermode Tuning.
Another superb video David!
David, as usual, a fascinating video which had my brain mangled until, that is, you arrived at ‘tempered tuning’, then it all fell into place.
Also, is it (at all) interesting that the albums that leapt out at me from the 08:00 frame(s) were ‘Buddy Holly’ and ‘The Chirping Crickets’ - even before ‘Sgt Pepper’, ‘Hard Days Night’ etc, etc. despite my being a (rabid) Beatle (and, of course, Buddy Holly) fan.
Must be my age, I guess… old fart. 😬
Your videos are incredibly entertaining and thought provoking.
As a Canadian I pronounce Tune as "Two-ne" where I hear you sounds like "T'chu-une" with the English accent :D Great video!
I really like the piano piece at the end of the video. It almost seems like the chord changes are easier to hear and they resonate a lot more clearly
You discovered the Fender Rhodes sound @13:05. Thats when the beating comes out of the left then the right speaker with each pulse. But in general even temperament makes the major 7th interval suffer when resolving to the tonic (or key) As in 'ti - Do' - as the 'ti' note always seems a bit flat. In 4 part stringed chamber music one can experience the best tonalities music offers.
15:30 I don't want to sound like a nerd but I'm pretty sure with Pedal Lap Steel guitars you're able to adjust the tuning of the string in real time, although I do not know to what degree it allows.
This has blown my mind any you explain these highly complex ideas so clearly, thank you!
Thank you for shedding the light on one of the most fundamental and interesting topic of music theory and history! Awaiting impatiently for other temperaments! And please, more audio examples are desired 👍
Maybe there should be some kind of least-squares technology where you stick in the sheet music and it optimizes the temperament.
I'm a pedal steel guitar player and have two tunings I use depending on which guitar I'm playing. The first tuning is just intonation for my Emmons Original Push Pull. Each string and pedal is adjusted using Hz, ie 445, 430. The second tuning is a slightly modified version of the 12 tone standard with some changes adjusted by +/- a few cents and I use it on my modern Mullens all pull guitar. I'm always at odds with the guitar player over who's out of tune. I found the best way to resolve it is to make sure we're not both playing in the same range. An octave makes all the difference in the world.
For your song at the end, I assume the best thing to do would be to slowly change the intonation rather than adjusting it abruptly. (similar to Collier's half-sharp movement)
Also, check out Anna Von Hausswolff's album All Thoughts Fly which was all done on a 1/4 comma mean tone organ.
Well, the harmonic series can be easily understood with a guitar for example. If you rest your finger on the 12th fret (half of the string) and play it, you have a one-octave harmonic, a perfect fifth (thirteenth avtually) harmonic on fret 7 (thirf part of the string), and a two-octave harmonic on fret 5 (fourth part of the string)
I think the harmonic series is more easily understood as being... twice the fundamental, three times the fundamental, four times the fundamental, five times the fundamental and so forth.
It's just integer multiples of the fundamental frequency. That's what's really going on there.
But then you can translate this into musical intervals and note that, yeah, that's octave, fifth, fourth, major 3rd, minor 3rd.
And then you can also understand where, ultimately, these intervals come from.
As our ears / brains are listening out for harmonics. Because if two sounds are occurring at the same time, how does the brain know which frequencies relate to which sound? To be able to interpret that all those particular frequencies go together as "a dog bark" and all those other frequencies go together as "the neighbour talking next door".
Because what our brain does is listen out for the harmonics. It picks up 220Hz, 440Hz, 660Hz, 880Hz, 1100Hz, 1320Hz, etc. and then, ah, those all go together, as those are harmonics of the fundamental 220Hz. So the brain hears all of those frequencies as one sound... of a particular timbre.
But another sound - happening at the same time - is pitched at, say, 345Hz. All of its harmonics are different. So that's how the brain can say "all these frequencies go together as one sound, and all these other frequencies go together as a different sound".
And we can, therefore, differentiate sounds and, for example, understand what someone is saying to us, even though there's traffic noise and dog barks and other sounds also happening at the same time. Because our brains have this means - via grouping things together in their harmonic series - to pull out individual sounds from a big cacophony of frequencies that could be happening at the same time.
And now we've actually kind of evolutionarily explained music. Our brains need the harmonic series to separate out different sounds, when multiple sounds are happening at the same time. That's the evolutionary "survival advantage" for you. Why it even exists in the first place.
But then we can see that music is essentially what's known as "super-stimulation" of this mechanism. By having instruments dance around on this harmonic series - coinciding with each other, conflicting with each other, in an elaborate dance of frequencies - this is, in essence, driving that part of the brain wild.
We're giving it one hell of a "puzzle" of harmonic frequencies to solve. We're over-stimulating that part of the brain. Overloading it.
And I guess this is like, you know, solving a crossword puzzle or getting the answers right on a TV quiz. You get a little dopamine hit - a burst of "happy chemicals" to the brain - for solving the puzzle.
Again, the evolutionary reason is simple: reward good behaviour with a chemical "buzz" and we'll want to do good things more often, to enjoy the "happy chemical" hit.
The ultimate expression of this evolutionary system being, you know, the orgasm. It's a evolutionary reward for propagating your genes (evolution hasn't yet adapted to the invention of the condom yet... shh, don't tell it, or it might have to adapt its strategy in many, many thousands of years), so you get a big flood of "happy chemicals" to the brain - the orgasm. And it works, right? This makes sex feel awesome, so you totally want to do it again.
While music is not quite "better than sex" (okay, some people might want to debate that one), you can see that it's a similar mechanism.
Music presents this overload to our brains - a big frequency puzzle to be solved - and when we solve the puzzle, evolution's prepared a nice little dopamine reward for you to say "well done", and to encourage us to keep being clever at solving these puzzles (a puzzle that does, at its root, come from a "survival instinct" origin, as differentiating sounds - the sound of the wind, from the sound of a hungry wolf that's about to attack you - would have had plenty of evolutionary utility for our cavemen ancestors).
The harmonic series, in fact, unlocks it all.
Why humans respond to music. What its evolutionary advantage would have been to develop in the first place. Where the intervals - and, thus, chords - come from. Why we love listening to music. It's all in there. Because of the convenient physics that if a string can vibrate at 220Hz, then it can also neatly vibrate at 440Hz, 660Hz or any neat integer multiple of the fundamental frequency. So that provides the brain with "one little trick to differentiate sounds from each other", and music has been riding this hard - in "overload" mode - ever since.
Except that the 19th fret (12+7) doesn't divide the string in 1/3 - 2/3, because only the octaves are just intonated. When you touch the string lightly above a fret corresponding to the harmonic series of the open string, then play the string and release the finger to create that typical harmonic sound, the node of vibration of the string will be slightly off the fret (unless it is one or 2 octaves) because the string will accommodate itself to the "simple fraction" ratio.
@@adb012 I didn't know that. Pretty interesting. Thanks!
Well illustrated, excellent video!
Thank you!!
One interesting aspect of the beating phenomenon is that it doesn't actually rely on physical interference between the two waves -- that is, if you stick one of the pitches in JUST one ear and another pitch in the other ear, the beating will emerge strictly in *your brain* (termed a "binaural beat")
As a trumpeter born with way too sensitive ears (no perfect pitch but I hear much more than I'm good with) and playing in one of my country's best concert bands, being trained on this every rehearsal, this explained a lot to me.
I just CAN'T with keyboard-insyruments, the 3rds and 7ths are... killing me!
Every rehearsal our conductor tells us to find out which function our respective tones have in the chord, and we have to adjust them to make the chord sound calm (no beating. I didn't know it was called that, thank you!!) all tones together.
It's quite a job and you should be practising a lot to know exactly where the right tone is belonging to the right chord at every time, not having to adjust it after you've already started playing it.
Thank you David, for explaining to me I'm not totally crazy, I'm just born that way that I can actually hear and FEEL these small differences. (They're scratching my ears and my brain in a very annoying way)
I’m glad you found my video helpful 😃😃
@@DavidBennettPiano guess I won't be needing the psych ward after all! 🤣
As a guitarist, a huge thank you for sharing your knowledge and talents with the musical community. This explains why slight note bends and dips on fretted instruments can sound much more tastful
Thank you very much for this brilliant video. Just to add a little layer as to the tuning of pianos: the higher notes are also a bit “spread” to increase the brilliance of the sound. So one really understands that the “right” tuning of a piano is really an art.
There is a video on RUclips by a classical guitar player that shows a classical guitar with movable partial frets and how if he plays in tune in C( or its relative minor) by moving the frets , he can't play in any other key for precisely the reasons you indicated here; he also demonstrates how the adjusted tuning in C sounds so much better . It is like your video , quite interesting and quite eye opening.
I was fascinated by this topic as a student of electrical engineering and music theory in college in the 80s. I've been programming synths as a hobby since then, on everything from 8086 PCs to modern DSPs. I've also programmed tuners, including piano tuners. If you take a step or two into the topic of temperament, you tend to be dissatisfied with limitations of fixed tuning and look for the purity of perfectly just tuned intervals. This will often lead one to believe that there is some kind of mystical magic that happens when you adhere perfectly to Pythagorean integer ratios of frequencies. As you approach that, some very interesting and psycho-acoustically potent things happen. This has been demonstrated beautifully by Jacob Collier and others. But digitally, you CAN make it absolutely perfect. When you do, you find that it sounds awful. This isn't because there's a mystical optimal very close but not exactly at integer ratios of frequencies. It's something else.
1. We don't experience musical frequencies in time. Our brains don't work that fast. We experience them in a one-dimensional space on the sensor element in our ear, the cochlea, in a way that's similar to the way we perceive light on the two-dimensional space of the retina. We can hear a tone going on and off about as fast as we can see a light flashing on and off.
2. When sound is produced by playing a single note with a real physical device such as a string, vocal cord or bell for example, the overtones are not at exact multiples of the fundamental. The harmonics of a single note on the best piano you can buy are out of tune with one another. In the case of a string, the shorter and fatter it is, the more pronounced this phenomenon becomes.
3. The pitch of the fundamental and overtones of a note played on a physical instrument typically depend fairly strongly on how loudly the note is played. This can be seen easily when tuning the low strings on a guitar using a strobe tuner or something similar. Generally, the louder, the sharper.
4. Beating occurs when two tones (i.e., overtones) with nearly equal but different frequencies are sounded. Since the overtones of a single note don't overlap with the fundamental or with one another, beats don't result from the overtones being out of tune relative to the fundamental. Harmonics that are out of tune, within reason, don't sound dissonant if there are no other harmonics from other notes or instruments being generated near that frequency. There is nothing for them to compete with or beat against.
5. When tuning a 12-string guitar, perfectly matching the frequencies of each of the string pairs will make it sound like a six string. Very slightly detuning them accentuates the richness, complexity and presence of the tone. It also increases sustain. Detuning them further makes it sound like a honkytonk piano.
The key point: It's not the mathematical purity of just tuned harmony that makes it sound good. Although there's more to it, the way the overlapping tones/overtones from various notes, voices and instruments DANCE WITH ONE ANOTHER (interact with one another) produces much of the "harmoniousness" of a given harmony. If overtones are doing exactly the same thing (sounding at exactly the same frequency), they're not dancing, they're just speaking redundantly. When tones/overtones interact independently, with their own identity and information content, at slightly different frequencies, the brain's spatial interpretive mechanisms are engaged in ways that might not necessarily be perceived as position or motion in three-dimensional space but involve the activation of neural pathways used to interpret the physical/spatial presence of a sound source.
In my view, we should understand this spectral dance of harmony in a quantitative way and design digital instruments to expressively exploit this understanding. This, I think, will lead to music that is liberated from the 12-tone scale yet even more richly harmonious with a broader range of chord structures, music that can be designed/composed in a purely mathematical sense, rather than being derived from the limited framework offered by mechanical contraptions and their legacy.
Wow, extraordinary. What you say about harmony needing to dance makes SUCH sense. If it isn't dancing then, it actually feels dead; there is no musical conversation. Thank you SO much for your detailed and helpful response. We use Music to harmonise the soul (our ego) and so we naturally avoid unharmonious sounds because they fail to liberate the ego from an inner state of ego-dissonance. The ego is initially bodily, hence dance (or any human movement in response) is our 1st reaction to music in its role as soul-therapy. Music is temporal which means it must celebrate harmony as a life (not death) force. Harmonious perfection equals death. You can however so see why the so-called "perfect" intervals extensively used in late medieval polyphony, actually feel more joyously alive than a ghastly (ego upsetting) 3rd?
Miss the video the weekend, thanks for all the amazing content!
Another brilliant video. Thanks! When I attempt to explain this stuff to a friend or customer (I'm a piano tuner/technician) they usually just get even more confused. ... An interesting followup might be about how a piano tuner tunes by ear. It's all about hearing the beats where the partials of two notes should coincide but they don't. Tuners use those beat speeds of all the intervals to arrive at equal temperament. To make things more complicated, piano strings are not perfectly harmonic and the tuner needs to compensate for that, which makes a piano even more "out of tune"!
actually, i and some others, including Sevish, have started saying "ed2" instead of "tet" or "edo", and the reason for that is because you can replace "2" with any other interval, "2" refers to octave in this case so "12ed2" would translate to "12 equal divisions of the octave", this format actually really helps with tunings like wendy carlos tunings that are based on the fifth, wendy carlos alpha would be refered to as 9ed3/2, bohlen pierce would be 13ed3!
however, "tet" also works too, but i think its important to also bring up "edo" and "ed2" as some of us who create microtonal songs use other acronyms and names for "divisions of the octave".
great video by the way! speaking of tonality, you could try and find some tracks using different tuning systems and such, not just microtonality, but tuning systems distant from 12ed2, for example desert island rain by Sevish uses a completely different scale not possible in 12ed2, although im sure it'd be pretty difficult finding other examples that arent electronic... 😅
What a well-made video. The violin sample at 10:22 for example.
I experimented with temperament methods a few years ago, while developing a synth based on a very small 8bit chip and what worked quite well for me was using just fifths and octaves to get all the coefficients. A1 *3 => E2 /2 => E1 *3 => B2 /2 => B1 *3 => F#2 ... and so on. (The chip couldn't multiple nor divide and *3 /2 can be done easily using binary shifts). Nice video anyway.
Good video. Tuning a guitar is always an exercise in "close enough." When you get the open strings perfectly in tune according to the tuner and 12TET, try playing a bunch of spicy chords, especially up the neck, and you'll find dissonance where it doesn't belong. The tuner is only a starting point. Using octaves, natural harmonics, and relating every string to every other string, you can usually make tiny adjustments to find a point where the average ear finds all the intervals pleasing and nothing sounds noticeably off. What the tuner says at that point will vary somewhat from one instrument to the next.
I've been playing the guitar for over 50 years. When I was learning, there was no such thing as electronic tuners. One of the first lessons was how to tune your guitar by ear, by tuning, usually the 'A' string, with either a pitch pipe or tuning fork. I think it is too easy to rely on an electronic tuner.
True Temperament guitars are fretted to maintain 12TET down to the 24th fret. In exchange for that you get a guitar that looks like the frets are made out of random twigs you found on the forest floor :P
That's why it's important to adjust the neck and the bridge height so that the string-to-fret distance is according to specification. If the strings are too far away from the fretboard, when you press a string down the speaking length of the string, therefore the pitch, is a little bit off, and it gets worse the higher up on the fretboard you go. I have a cheap student electric guitar and it was amazing how much better it sounded after I adjusted the neck tension just a little bit.
@@davidbstang116 Well, yeah. But that’s only part of the equation. What you found is that a proper set-up will make it much easier to achieve “close enough.”
👍
Great video, thanks! What is the keyboard instrument illustrated top right at 9:00 ? By the way it is worth mentioning guitar string bending as improvisational tool to sharp up a bit melodic phrases. And the "fluid piano" is a fascinating acoustic instrument allowing to set or improvise temperament and pitch for a performance, opening up eastern repertoire or experimental intervals for piano players. In both cases it's not a systemical "solution" but it shows how the ear of the player can guide the performance for certain intervals and note pitching, just like it is for violin players.
At 17:12 if musicians want to use just temperament in a bar or two in the studio and then go to equal temperament, that is fine, but it should be noted in the sheet music. I like to think of sheet music as "source code" just like we write for computers. Source code is FULL of comments for the human but the computer does not use. I think we need new notation, hey music has been evolving for centuries, and with MIDI you can step on a for switch and swap just/equal temperament on the fly. We didn't have this live before the 1980s (only in a studio that is not real time).
I am thinking
Studio
Guitar
Astring[-14cent]_____________________________
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The "strange" chord changes in the sample piece meant beautifully spiced strangeness to my ears. Pretty satisfying.
I absolutely loved this video! You’ve shed light on so many of the foundational aspects of music and sound. I found this incredibly informative and insightful. Thanks :)
Glad you enjoyed it!
This was very educational. I’ve been playing guitar for 40 years, and you may have just explained why I always find my guitar is out of tune after tuning it. For the last 20 years or so, I have used a digital or pedal tuner, then play an open “cowboy” D chord, then adjust the G B E strings by ear until it sounds good.
Great video! Only thing is I don't understand your point at 17:57. If you tuned to just tuning relative to A major, would all intervals not be justly tuned as long as you stay in the key of A major?
great video David! thanks!
Thank you!
I used to keep a guitar in my workplace (about 50 years ago) to play during breaks. Tuning was always an issue. One day a guy who sang in a barber shop group tuned my guitar to open A. The guitar rang like a bell - it sounded perfect (in that key).
Ah ha! That fab guy, the Barber of Seville, surely?
David, thank you very much for such a great video!
To put all the necessary information about TET and reasons for its implementation in a such concise and straight to the point manner is a super great work!
I wish I could give 10 likes to this video!
Thanks Peter!
I play the piano and I come from the good ol' Amiga days when I was using OctaMED and playing all the great melodies from my favourite games (Turrican II, Impossamole, Shadow of the Beast, Lotus Esprite Turbo Challenge 2) on the computer keyboard
For me, mentally, playing the piano is just pressing the right buttons at the right time. An easy mental barrier to get over.
After watching your video it has cemented my opinion that the Violin is the hardest instrument to learn/play.
Fascinating vid and I've really starting to enjoy your compositions at the end. Thank you.
Eh, violin's not so hard. I'd say a trumpet is considerably harder.
@@noonehere0987
Definitely seems harder to use your face to blow a raspberry through a brass tube.
As a player of keyboards and fretted instruments, I never realized how hard it truly is for string, wind and horn players I play with to be constantly adjusting pitches until this video. Hats off to you David for the wealth of info and that said, kudos to those non-fixed-tuning players!! 🙂
I was trying to explain this to my friend when he asked how a speaker can reproduce every single sound of nature if it is just a bunch if metal with a magnet inside.
His question was very smart actually, it's amazing how perfectly a speaker can reproduce the sound of the sea, or some birds singing,to give and example.
Perfectly reproduce the *vibrations* of the sea and birds *as we perceive them*. Speakers are amazing, but they are mechanically doing exactly what our eardrums do (in reverse). Plus speakers don't have to exactly reproduce the original vibrations, they only have to reproduce in a way that we will perceive as accurate.
@@kurtjuday6937 yes, just the harmonics that make the timbre iconic
When you understand what sound is, it becomes a bit less amazing.
@@noonehere0987 not really. I know how it works, what amazes me is that in this day and age we don't bother to realize how many incredible things we use daily
That piece at the end sounds incredible. Maybe you could do a half tuning on the awkward transitions
Re: 8:33 - I first heard the justly tuned M3 as flat at first. Now I know why that is!
Don't know if he talked about this in the video. But sitars are actually tuned in just intonation since they're tuned and played in a certain key
Actually, as a very seasoned guitar player myself, there are 2 ways to intonate your strings individually on a guitar, however you can only pitch up and not down. The first and most obvious way is just bending the strings but for harmonic purposes this may be much too inaccurate. The second way is one that most people dont know actually makes a difference and its something they teach you NOT to do when learning guitar, and thats pressing the frets down harder, or pressing them in different spots. If you bottom out a mid fret on the low E string it can amount to maybe a 30 cent change in pitch upwards. As well, if you slide your finger up and down a fret while playing a note, youll notice that it changes pitch up and down as well.
as someone who listens to a lot of 31tet music the just intonation piece at the end just sounded really peaceful, and not weird at all
Brass players have to constantly listen to the ensemble around them. Fortunately, some instruments can be tuned on the fly with the tuning slides (trombones are obvious, but trumpets can also be tuned on the fly with the slides as well.) That said, it's not always possible (or desirable) to use slides(F horns, baritones, etc.), so we learn how to "lip up" or "lip down" a note using our embouchure. It takes lots of practice. You can be playing a unison note within a section and you'll hear the beats then all of a sudden they disappear, as each player adjusts either their lip position or even how much air they're putting through the horn. Quite fun when you get it right, and obnoxious when it's wrong.
I wonder how a person with perfect pitch deals with the different tuning systems? Does it drive them crazy if they hear one over the other being accustomed to one system their whole life? That would be an interesting deep dive video
@ghost mall perfect pitch isn't relative to any tuning, but the absolute pitch (frequency) of each note. If you meet a person with perfect pitch in the Western World and ask them to sing a G for example, they'll probably sing an equal tempered G. Their perfect pitch isn't based on 12TET, but they learned the note _names_ according to 12TET.
They'll still be better than you at just intonation though lol
You don't need to have perfect pitch to get rattled by off tuning. Otherwise, why are the rest of us listening to this video (sorry, for me, you tube is only for listening to) ?
Great video! I always wondered to what extent violinists, vocalists, etc used just intonation. One thing I'll add is, during guitar solos, it's amazingly common to hit a major-3rd double stop on the G+B strings and then bend the lower note up slightly. It was a huge revelation to me when I realized this was effectively achieving just intonation on the fly.
slide players will often angle the slide to slightly lower the b string note to achieve the same result
I might be late mentioning this, not having read through all the comments, but I recommend doing a RUclips search for micro-fretted guitars, ie a small fret for each string in the right position for just intonation. The comparisons with TET are very obvious. The same guy also uses elastic bands as frets which he can move slightly to create just tuning but only in a given key or two. As I became a more experience guitar player (nearly 70 now) I became more and more intolerant of the consequences of using either conventional tuning from the fifth fret (fourth G to B) or electronic tuners. The guitar tech at Hank's guitar shop in Denmark St, London, told me his secret about 30 years ago. It is to tune from the D, 12th fret harmonic to the B, third fret. You then do a sequence of 5th to 7th fret tuning, but adjust the A to D relationship so that the A is slightly flat with a slow beat of maybe four beats a second. That usually gets you into a far better compromise tuning than any other I've come across. Anyone got any others? The clip of Voces8 reminds me that during lockdown, their second tenor, Blake, did a very good live-stream talking about all of this with examples of a capella singing where a clear beat could be heard through TETish tuning or, when you get everyone properly in tune, all the other harmonics are prompted and clear notes, not being sung, ring out. Fantastic. Sorry to ramble on - this stuff interests me!! Great channel, David.
4:20 Not quite 14%, as it should be compared to the A not the next semitone. The equal tempered major 3rd is 400 cent apart, but should be 386 in just intonation. So the C# is 3.6% too high.