this video is what made me realize how special non-equal tempered scales are. Thank you. You've inspired me (along with a math discovery i just made) to make my own! TLDR: I learned about the harmonic mean, and realized how you can use it to construct scales using the 'reflection' concept discussed in the video, along with the arithmetic mean (average). These scales are very very close to 12-TET. So I discovered how if you take 4 different means of an octave interval, you can get very close to the 5-8 chromatic scale degrees. Eg, we have 440 Hz (A5), and 880 Hz (A6). If you take the harmonic mean, you get a perfect 4th. (D5) The geometric mean, you get the 6th chromatic note (Eb5), in perfect 12-TET tuning. The arithmetic mean (aka, the average), yields a perfect 5th (E5). And the Root mean squared seems coincidental, but it actually supports this hypothesis i have. It yields a very close approximation to (F5). (440*sqrt(2.5) = 695.70 Hz). In this case, we did these 4 means for f vs 2f (440 & 880Hz). But if you do this for 4f, 8f, and 16f, you can fill out most of the chromatic scale. Just use the reflection concept like in the video and keep dividing by 2. You will see a shocking number of candidates. Strangely, RMS almost always yeilds a 'hit'. Ie, you always get a ratio very close to the 12-TET scale ratios compared to the root. While this seems obvious for powers of 2, the same thing occurs for most integers. So, most of the chromatic scale can be found with taking these different means using f vs f*2^n. Many yeild very nice rational ratios. Most of the scale can be constructed using only the harmonic and arithmetic means. But seeing the geometric and RMS constantly get soooo close to others is what I'm curious about. I haven't found a satisfying way to get the 'missing spots' (ie, 3rd and 9th chromatic note). The 9th one is close to the harmonic mean of f vs 5f. The 3rd note (harmonic minor) eludes me. For now, i have justified it as a 'quarter octave', which is the same definition in 12-TET. Which feels like cheating, except further 'so close'-ratios are found when doing means of f vs 2^(n+0.5) (where n is an integer). Very interesting. Welp, that's my book report. More exploration is needed. Making scales using that reflection concept is very liberating. Really makes you wanna explore the possibilities. 🤔
Best music theory education channel, hands down. Every explanation is well motivated and intuitive, which is a rarity in music education. I've seen no one else explain the "why" of music theory so clearly
"It´s not instruction, it´s insight" This is so good. I always looked for the underlying Physics of Music explained like this. You explained it extremly well, on the point, clever and efficent(Also just the right amount of foreseeing possible Confusion of the viewer as well as things he already could know and skip)
I actually wrote a paper for my musicology final, discussing why the perfect fifth is responsible for 12 tone. I've basically touched a lot on the universal nature of the perfect fifth, lol.
This might be the best video i've seen of this subject. I've played the guitar since I was a kid and only recently started wondering about the "why's: "why the name octave?", "why 12 notes", how things developed in music, and so on. It's like I could not advance in music theory anymore without understanding all of these stuff. And in fact there are still some gaps in the whole basic history of notes/harmonic series/scale that I haven't figured out yet. For example, after reading and watching some videos, I've figured out the basics of the beginning of music, strings vibrations, Pythagoras, wave lenght, frequency, harmonic series, waves that are consonant and sound good to our years. But to get from this to the next step (understading the construction of scales) I'm not sure I understood properly. Apparently the harmonic series (simple ratios="easy" math=good to our ears) is the root of the rest of the stuff (scales, chords; melody and harmony), but I couldn't get the "logical path" from intervals appearing in the harmonic series (physical relations regarding wave lenght and frequencies) to the origin/construction of scales. Maybe I can understand the pentatonic scale (because the first overtones of the harmonic series have these ratio that are "simple" and produce consonant intervals, so it makes sense that everywhere in the world people use these intervals, because our ears perceive as consonant and pleasant), but the 7-scale or the 12-scale, I still don't get it. Maybe I have to watch that part at 9:58 over and over again, because 9/5 and 15/8 don't seem "simple ratios"...it still seems arbitrary for me. And i find interesting to see how many ways people try to explain this subject. The most fascinating for me is to try to reconstruct how things evolved from Pythagoras observations of strings to scales and then finally talking about "octaves" or "fifths" (i'm saying this because i've seen many videos talking about octaves and fifths as if they were a "given", like obvious names that shouldn't be explained in a context). Anyway, i'm just thinking out loud. It's too much stuff and my brain is exploding. I'm almost getting spiritual thinking that 12 is a mysterious number in nature, because it appears everywere. Thanks a lot for this video.
Finally helped me understand Just Intonation, and there was so much I never even thought to ask. This is easily the best educational channel on youtube, you should be a teacher. Seriously, I wish there was someone like you for every subject.
Your breakdowns of something that normally isn't easy to explain, is amazing! You've taken a difficult topic and made it clear in a fun, fast and brilliant way. Love the "simplified" animations too. Thank you so much. I'm donating for sure! (Just did a test donation, will send more if it worked)
You're an absolute reference for me, not only on understanding of music theory, but also on how to explain it. I recommend your videos as much as I can. I also watch them often to memorize how you explain the different subjects. I really admire your work and hope it will get as famous as it should.
Amazing set of explanations. I had wondered about 12 tone system for ages but never really looked into it. Thanks, YT, for actually recommending a useful video.
When 6, 12, 30, and 60 show up it usually means simple ratios are nearby. Simple ratios are also why we have a 60, 60, 24 system for time. Same thing with binary and the powers of 2.
actually thats not necessarily whats going on here. 12tet being so composite is kind of a coincidence. for example 6tet actually completely misses 3/2. 19tet, 31tet, and 41tet all offer remarkable consonance while not being composite at all! when you divide an octave equally, you're doing it logarithmically, because that is how we perceive pitch. composite-ness and consonance arent necessary related.
In band our teacher would always tell us to bend the pitch of the third down because it's so sharp in equal temperament. It makes the I chord ring so purely
In this video and others like it by other RUclips creators such as 12tone or David Bennett piano, you excellently explain why we have a chromatic scale as well as the pros and cons. One question I hadn't thought of until recently is somewhat phrased "Why these 12 notes?" For example we know that 440 Hz is "A" and then everything else is a relative frequency from that. But how did "A" become standardized at 440? It's only in relatively recent times that oscilloscopes, frequency analyzers or other such equipment could determine that frequency. Traditionally at the beginning of an orchestra performance, the first violin plays an "A" and everyone else in the orchestra tunes to that pitch. A cappella singers often use a pitch pipe to get them on key at the beginning of a song. But again… How do we know that that first violin or the pitch pipe is actually accurate. When were the standards for notes established so that if you heard a concert in one venue or another or even between performances of the same artists, how did you know that they were on pitch according to some established standard?
In terms of the choice of 440, it is indeed arbitrary. There is some interesting history behind it; there used to be an amazing video on the subject on youtube but I can't find it anymore. And now youtube is swamped by dumb "440 vs 432" videos making it even harder to find good summaries. For a basic summary you could try "Why is A 440 Hz?" by Walk that Bass: ruclips.net/video/GwWXDwqgWjo/видео.html
Hey, awesome video. Can you do a video explaining different historical 12 tone tuning systems and why they might be better than 12-tet for certain pieces in certain keys? I wonder if there is a better tuning system of om playing in say, C major, where I don't need to worry about key changes? If we are playing only Bach for instance, what's the best tuning system to use? I know there is a lot of debate on which tuning system is best for Bach. I'd love to hear your input, especially in video format with the helpful visualizations.
Thanks for the suggestion! -- it's a little too far out of my area for me to seriously contemplate making, though. Have you searched around a bit for existing videos? I feel like it may be pretty well covered already, but I admit that I haven't looked very hard.
You should be able to get a grant from NEA, or some music teachers group. Very well done, and I would recommend it to anyone who challenges or questions the 12 tone system.
I like the way you graphically show the simple frequency ratios and their relationship to the root and octave. It’s also interesting that the ‘fifth’ at 3/2 the root is itself a 4/3 interval up to the octave, which in turn is a ‘fourth’ interval. As you point out, the fourth and the fifth are nearly perfect with the choice of 12 notes per octave. It’s fascinating with choice of 12 that each half-step interval mathematically becomes 2^(-12), or the twelfth root of two. Just under 6% higher frequency than the half-step below.
Love the explanation. I just struggled to see some of the tonal graphs on my phone screen. I remember from my astronomy days that photo negatives of Astrophotography were used to spot faint objects because our eyes are more sensitive to subtle changes in light objects than dark ones. I'm sure there are analogous affects in sound.
Thank you for the video. Was there any study involving the measuring of perception of consonance and dissonance in the animal world (using dogs, cats, horses, domestic animals, etc)? It would be interesting to see it. Being a part time dog trainer, I noticed something: when using normal or a bit harsher voice (deliberately more dissonant), dogs pay more attention to it, look straight in the eyes. Such voice is good to tell the dog it is time to execute a command. But when using a more falsetto-like "singing voice" when praising the dog, which I believe involves more consonant sounds, the dogs react to that with enthusiasm and expects cuddling and a reward. Dissonant - alert and attention; consonant - award and relaxation.
I'm not sure... I'm purely speculating here, but it seems clear that many animals have perceptual abilities of pitch similar to us (given the similar structure of cochlea and the evolutionary value of hearing pitch, not to mention plenty of research confirming it) and while I've not heard of a study about consonance/dissonance in particular, I'd be surprised if an animal like a dog couldn't tell a difference between a pure tone and a tone with inharmonic overtones (e.g. howl vs growl).
I guess my issue is from early on, when you talk about consonant intervals, in particular the "most consonant intervals" - you use this (and the idea of "consonant" and "simple ratios" being somehow equivalent or at least closely related) as these become fundamental to your argument. I would say that the whole range of intervals from somewhat smaller than 6/5 (slightly bigger than 9/8) to at least 4/3 are all fundamentally consonant, the rational and irrational ones included. To my ears, what is conventionally called a "third" (major, minor, anything in between) sounds just as consonant, and probably more so, than the 3/2 ratio of the perfect fifth, so I don't see why you single out the 3/2 ratio as "more" consonant. If you look at the graph at 6:50, and try and equate amplitude to perceived consonance, then 8/5, 5/3, 14/8 (7/4) and 15/8 are all quieter (and hence more "dissonant") than the bottom of the dip between 7/5 and 3/2 - conversely, the entire range between 1/1 and 9/8 is louder than anything between 9/8 and 2/1, which correlating amplitude to "consonance" would imply that the range of intervals from unison to the major second are the most "consonant" of intervals, far more consonant that any 3rds, 4ths or 5ths - patent nonsense. So I'm not sure what relevance the study of the pitch content of human speech has on the supremacy of the 12-note octave.
Thanks for your thoughts -- We're agreed that consonance is a pretty important part of my overall thesis here (not that I invented these ideas, of course.) People have their own experience of consonance, and there's certainly wide variation, but as mentioned in the video there is a remarkably clear overall pattern across people from all over the world when it comes to consonance. E.g. 3/2 is certainly more consonant (for humans in general, if not yourself) than something between a major and minor third. I'd suggest checking out the links in the video description under "nuances of consonance" for some theories about it. It's not a simple question, for sure, and the simple ratios shouldn't be automatically assumed to be consonant just because the math is pretty, but it has been shown through a lot of experimentation that there is truly something to it. (And certainly the proliferation around the world of tonal systems that utilize these intervals isn't mere cultural accident.) In terms of the graph at 6:50, I'd note that the harmonic series will naturally drop in amplitude as the frequency increases, which of course is why the graph curves down as it goes to the right. As far as I understand it, the authors are not arguing (nor was I using the graph to argue) that their data comprehensively explain the origin of consonance, just that the presence of these intervals in human speech is a provocative explanation for why our hearing system may be so keyed into them. I think I do see your point: that one would expect the higher frequency harmonics to be less relevant (and therefore less consonant) if they are so much quieter in speech, but perhaps the same mechanisms that key us into the lower harmonics have the effect of sensitizing us to the upper harmonics, or there are other subtleties we're not incorporating. I don't think the graph is a conclusive proof of anything, and I certainly don't think the question of the 12 tone scale system is a totally closed case.
@@CaseyConnor "I'd note that the harmonic series will naturally drop in amplitude as the frequency increases" - except if you look at the dynamic graph at 4:48, this doesn't appear to be true for musical notes; the fundamental and the first six overtones are all roughly equal in volume - the 5th and 6th overtones in particular (D5 and F5) have amplitudes as high as the fundamental; although the 7th overtone (G5) is noticeably quieter, the 8th overtone (A5) has the same amplitude as the 3rd overtone (G4) and bigger than the 2nd overtone (D4). The "Biological Rationale for Musical Consonance" is interesting (I'd come across it before) but the studies they report which get people to rank 12TET intervals in terms of dissonance are problematic, as they say nothing about the relative perceived consonance/dissonance of two intervals (are they very close, or widely different?) because they are based only on ranking (is the difference in consonance between a major and a minor 3rd the same as the difference in consonance between a major second and a minor second? They are both adjacent intervals in terms of ranking) and also, the comparisons are simply too coarse, with only 13 intervals in an octave. It would be far more interesting to create relative dissonance curves measuring intervals at 10 cent granularity, rather than 100 cent granularity (so 121 intervals in an octave rather than 13). One interesting thing is that the perfect fifth (700 cents), according to the studies, is *more* consonant than the major 3rd (400 cents); the diminished fifth (tritone - 600 cents) is *less* consonant than the major 3rd (400 cents). There must therefore be an interval somewhere between 600 and 700 cents which is _exactly_ as consonant as the major 3rd (400 cents).
I find it intriguing that in the graph at 6:48, the flat 7th is a harmonic 7th (a ratio of 7/4 or 1.75) instead of one of the "just minor sevenths" which are closer to the minor 7th in 12-TET (16/9 [1.777...], which is two stacked perfect 4ths or the inversion of the major second, 9/8; or 9/5 [1.8], which is a stacked perfect fifth and minor third and is still closer to the ratio we get using 12-TET, ~1.7818 [The actual ratio would be 1:2^(10/12).] ).
Sidenote: at 13:54, do you remember which just interval you used? Seems like it would have to be 9/5 since it was sharper than the 12-TET note, but any particular reason?
Yeah I wonder if the authors of that paper just picked out an even ratio near the peak, or if the resolution of their data is sufficient to distinguish between 7/4 and 9/5 and it clearly pointed to 7/4. Either way, 7/4 seems intuitively like it might be the more "naturally consonant" interval, just based on the smaller denominator (though apparently subjective consonance is not quite as simple as that).
@@zozzy4630 It would have been 9/5, yeah. those intervals came from some version of just intonation I was working from (I don't recall where I got it off-hand). I leaned towards systems with simpler intervals (e.g. 9/5 instead of 16/9) because I wasn't trying to build a just intonation scale that was most compatible with 12-TET and modulation and so on, rather I was trying to be "true" to the J.I. idea of each interval being as consonant as possible. Maybe I should have gone with 7/4, but 9/5 seemed more common, IIRC. In other words, no: there was no particular reason, just some loose impressions. :-)
1:14 Octet means eight in Latin language, that is where octave word comes from. Since there are 7 notes + 1 repeatitive (root) note in an octave interval which makes 8 in total.
@@AFRoSHEENT3ARCMICHAEL69 Ik this is like 3 months late, but October used to be the 8th month. (Sept)ember (Oct)ober (Nov)ember (Dec)ember. Then the romans screwed up the calendar by adding January and February, and now those names lost their meaning
@@danielcohen2657 According to wikipedia July and August were originally named Quintilis and Sextilis before being renamed to honor Julius and Augustus en.wikipedia.org/wiki/Roman_calendar
Thank you. I'm studying music by myself, as a hobby. Your channel helped me immensely. I have one question though. Why the C major scale is so ubiquitous? Why we named all the notes and intervals after it? Is this just history and traditions, or there is something fundamentally "good" about it?
Maxim Salnikov history and tradition. I'm not qualified to give the particulars, bit that's the gist. IIRC there are good googleable answers on the net. Glad you liked the videos!
Love your channel - new subscriber! I just wanted to give you my 2-cents worth for the tuning of a pure fifth from a 12-TET 5th. 😄🎹 Oooh, don't know if this is too esoteric for your channel, but I'd love to see a similar take (your explanations are so very clear!) on tempered scales, like 1/4-comma meantone, 1/5-comma meantone, Valotti, and Werkmeister temperaments - etc. (Who's afraid of the Big Bad Wolf Chord?) 🐺
When you played that interval at 3:12 I insantly thought of the song "NF - Remember This", I checked it and indeed it is exactly the same :) And I didnt listen to this song for over a month for sure!
Conclusion: 7 times the simplest interval (the octave) is pretty close to 12 times the next-simplest interval (the perfect fifth), so we just lowball the perfect fifth a little bit and say it’s exact. This system, 12-tone equal temperament, has the nice side effect that the other simple intervals are reasonably close to notes in here.
Thanks for this great video - like others who have commented, I have been searching for an explanation as clear as yours for a long time. Donation made. Are you able to provide an explanation for what seems to me to be the natural next question? Viz: why does the "Tone, Tone, Semitone, Tone, Tone, Tone, Semitone" sequence for selecting 8 from the 12 tones on the scale make sense? Is it that this selection picks out the 8 tones that are most consonant?
Thanks Daniel, and thanks for the donation! This is a great question. Broadly speaking, the questions of "how many tones in an average scale chosen from the 12 tones" and "which scale out of the 12 tones is likely to be most common" are very influenced by cultural history, but I think a case could be made that there would be a tendency towards something in the neighborhood of 5-9 notes in a scale, for many of the same reasons that are described in this video as applying to the overall tonal system: more tones in a played scale means greater precision required of instrument construction, higher demands on the musician and listener to discriminate pitches, more opportunities for dissonance, etc. Too few tones in a scale means less opportunities for expression. 5-9 seems to be a rough middle ground that works for our monkey brains. As to which tones to select, I'd guess that consonance/dissonance plays a big role. You start with the octave; the fourth and fifth kind of demand a seat at the table. Past that, you pick notes that aren't too close together, are roughly evenly spaced, and which work well in combination with each other. I'm not sure if anyone has proven that the major scale is the most consonant possible collection of notes, but if you add a constraint that you want the fifth of each note in the scale to also be in the scale (i.e. construct the scale using a circle of fifths) then the major scale is as close as you can get (all the notes but the seventh have their fifth in the scale). From this analysis, the root mode of the major scale (AKA the major scale) doesn't have any special claim over the other modes. AFAIK the preference of this mode as the "major scale" over, say, the mixolydian mode (or any of the others, at least the ones with a natural fourth and fifth interval off the root present in the scale), is just an accident of history.
because the consonant 3/2 is the most important one and assuming the number of notes in an octave is an even value, the minimum number of notes in an octave can be calculated with this formula: log(2)/log((3/2)/sqrt(2))=11.76 (approximately 12) by the way now i think that notes are not required to be at an equal distance from each other and they can be just the following ratios to sound good (not using more than 5 as denominator): 1, 6/5, 5/4, 4/3, 7/5, 3/2, 8/5, 5/3, 7/4 (mising ratio in the video), 9/5.
amazing video. I wonder if a digital instrument could be designed that automatically retunes itself to mathematically perfect ratios (rather than even temperament) as it is played?
Yes! It has been done, though the specific vendor escapes me now. Jacob Collier demonstrates it in some video somewhere... I wish I could dig it up. It might be an instrument for Kontakt, I'm not sure, but the idea is exactly as you suggest: as you play, the software is analyzing and guessing the key and so forth, and automatically adjusting chord tunings to cleaner intervals as you go. I think it's a really interesting idea and I hope it gains some more traction. It's not always obvious what the correct adjustment would be: even in a given chord you could argue one way or the other depending on how the intervals stack up. And in a dynamic piece of music what the next chord coming up will be will influence how you tune the current chord, etc, but that doesn't mean it's not worth trying!
I wondered about this too. An alien could find the compromises that "are ok" for humans unacceptable. There could be completely different evolutionary pressures for hearing. Not even earthly other animals seem to care much for human music.
A não ser que você vá pedir para uma capivara analisar sua música. Se eu não importo com a música que estamos produzindo eu vou me importar com a música de quem? do pássaro que está cantando lindamente aqui fora?? Isso se chama aprendizado ou você coloca o lá 440Hz que o autotune te deu hoje e Aceita isso aí. Pelo seu comentário digo que sua frequência não é a música.
@caseyconnor have you tried to space the 12 tones by 2^(i/12)? So that we have a logarithmic spacing between the notes. By this spacing the difference is much less then the even spacing. the good with sounding the ratios 2^(i/12) 1,000 1,000 1,067 1,059 1,125 1,122 1,200 1,189 1,250 1,260 1,333 1,335 1,400 1,414 1,500 1,498 1,600 1,587 1,667 1,682 1,800 1,782 1,875 1,888 2,000 2,000
Thanks -- what you describe is in fact the "even spacing" -- remember that the notes shown on screen are shown on a logarithmic scale (this is done because pitch perception is itself logarithmic, or at least roughly so. See around 1:45 for the note on that.) 12TET, the "even spacing" as described in this video, is indeed generated via 2^(i/12) just as you describe. So unless I have misunderstood you, you have invented 12TET on your own! :-)
@@CaseyConnor thanks for your answer! :) indeed I searched for frequencies of musical notes and figured that the ratios are exactly 2^(i/12)... so I just misunderstood even spacing for 1 + i/12 :) haha I guess that I invented it for myself from a misunderstanding... actually from this perspective of logarithmic perception, I interpret the ratios 3/2, 8/5 etc. as accidentally close to the evenly spaced logarithmic ratios, which probably mark the real pleasing ratios for our perception.
Why is 3/2 (1.5) slightly past the middle between 1 and 2? Shouldnt it be halfway? I know you have it right, my brain is just running in circles trying to rationalize this
@@bigbirdmusic8199 yes, exactly - that's the implication of 1:46, that linear points on the scale are skewed a little sure to the logarithmic(ish) nature of pitch perception.
Thanks for answering the most basic question! Was confused why nobody answered this in these music theory tutorials. Okay, now what's up with these # notes? Why is it called A, A#, B, C, C#, D, D#, E, F, F#, G, G# and not just A, B, C, D, E, F, G, H, I, J, K, L instead?
Have you watched my "music theory distilled" series? Maybe start there... the precise historical reasons I'm not super clear on myself, but basically there is a naming bias towards the C major scale. There are arguments to be made that other naming systems would be more logical or intuitive. As far as I know the one we use is a mixture of logic and historical happenstance.
@@CaseyConnor Yes, I found the playlist. Thanks for it! I now can connect all these parts of music theory much better. Helps a lot to get a more scientific explanation. 👍
So sounds in nature are generally not dissonant? That's fascinating. I was under the impression that musical notes were just a specific fine tuning of sound for a purpose. I wasn't aware that natural sounds also have a tendency to avoid dissonance.
Hmmm... what timestamp (if there is one) are you replying to, exactly? I might have phrased something poorly. I would say that "dissonance" is a bit of a loaded term, with ties to human psychoacoustics, but that to exist it requires a certain degree of specificity in the sound. E.g. the sound of wind is not usually considered dissonant even though it has plenty of (uncorrelated) frequencies present in it that 'conflict' with each other, but two unnaturally-pure sine tones at a strange interval to each other would be called dissonant. So I would say that most natural sounds are dissonant, pedantically speaking, just because noise in general doesn't involve particular relationships between frequencies, but it's a bit of a stretch since we don't perceive them that way because they aren't feeding us much specific pitch information. Presumably birds and many other animals making a noise experience evolutionary pressure to create sounds that are unusual or distinct in some fashion, e.g. not just noise like wind, rustling plants, splashing water, simple thuds, etc, and that leads to sounds that have particular pitches or rhythmic components to them. Said another way, sounds with less "acoustic entropy" become markers for intelligence, intention, or just presence of a life form. As far as those sounds being dissonant or not, I'm not sure I would make a claim that they tend not to be dissonant overall, but in at least some cases (e.g. human speech, bird songs) the ratio of overtones tend to fall into consonant patterns. And consonance does show up a lot in physics, e.g. frequencies generating overtones of themselves in vibrating bodies, such as in a plucked string or blown flute, and physics also govern the sound-producing organs in birds and humans, so, perhaps I should have said "animal-produced sounds tend to have some in-built consonance due to the means of production, but not necessarily consonance from moment to moment.)
At 4:25 you say "There are other pitches with simple ratios as well, but these are the most consonant." But what makes them consonant? Cause I thought simple ratios are what made them consonant. What paper did you get it from? Need something to cite lolol
Having a simple ratio does tend to make a combination consonant, but consonance is a matter of degree, so the degree of consonance depends on the particular ratio. Perceptual consonance is a complex topic... there are a few links in the video description to papers and such (under "Nuances of consonance".) The particular ratios I used come from various places, but if you check the links in the description you will find a few mentioned in there.
"Consonant" means it sounds with it. You have one tone with his harmonics. To create a scale, we used the second harmonic, the first one won't work. To create a harmony, we used the harmonics. This is how it started.
@@CaseyConnor When you use more than one oscillator, you can ie. set the 2nd to n octave(s) lower or higher. And/or you can more or less slightly detune them to obtain certain "effects". @Mike Parmer: yes!
Kind of like when a violinist vibrates it's fingers on a string to detune it slightly, or the "chorus effect" on electronic instruments.it makes the note pass through the tempered tuning even if the instrument is stretched tuning.
15 :16 This graph is really great. I tried something interesting in Sonic Pi. I wrote a script to play a minor chord and shift the 3rd tone gradually upward to the major chord, the result changed along with it. With this tech, it allows me to modify the power of the emotion. This might be useful, since when we make music on computer, we don't need to worry about the instrument. It means ,if an octave is separated into more fragments, we might control the music more exquisitely. This might be extremely useful when making piano music on computer. let ms(minor second) = 2 to 1/12 == 1.059463 ms to 3 == 1.1892 ms to 4 == 1.259921 ms to 4 - ms to 3 == 0.0707139 6 / 5 == 1.2 ( 6 / 5 - ms to 3 ) / ( ms to 4 - ms to 3 ) == 0.01079/ 0.0707139 == 0.1526274 == 1/6.55. What if we separate an octave into 12*7or 12*8 fragments?
Consistent overtones appear naturally in analog acoustics (especially humans) and desire to land in these positions because the 12-tone scale comes straight from the amazing designer of music, and of everything: ALMIGHTY GOD.
Freaking wow 😮😱 yeah your videos definitely help me I was struggling with sharps and flats your video was so effective I don't need to look chord chart 🤔🎹
This is the best explanation of this subject I've ever seen, thank you
hey it's the machine learning guy
agreed
man I didn't expect to see you around here ! it's nice ! :)
Couldn’t have said it better myself
this video is what made me realize how special non-equal tempered scales are. Thank you. You've inspired me (along with a math discovery i just made) to make my own!
TLDR: I learned about the harmonic mean, and realized how you can use it to construct scales using the 'reflection' concept discussed in the video, along with the arithmetic mean (average). These scales are very very close to 12-TET.
So I discovered how if you take 4 different means of an octave interval, you can get very close to the 5-8 chromatic scale degrees. Eg, we have 440 Hz (A5), and 880 Hz (A6).
If you take the harmonic mean, you get a perfect 4th. (D5)
The geometric mean, you get the 6th chromatic note (Eb5), in perfect 12-TET tuning.
The arithmetic mean (aka, the average), yields a perfect 5th (E5).
And the Root mean squared seems coincidental, but it actually supports this hypothesis i have. It yields a very close approximation to (F5). (440*sqrt(2.5) = 695.70 Hz).
In this case, we did these 4 means for f vs 2f (440 & 880Hz). But if you do this for 4f, 8f, and 16f, you can fill out most of the chromatic scale. Just use the reflection concept like in the video and keep dividing by 2. You will see a shocking number of candidates.
Strangely, RMS almost always yeilds a 'hit'. Ie, you always get a ratio very close to the 12-TET scale ratios compared to the root. While this seems obvious for powers of 2, the same thing occurs for most integers.
So, most of the chromatic scale can be found with taking these different means using f vs f*2^n. Many yeild very nice rational ratios. Most of the scale can be constructed using only the harmonic and arithmetic means. But seeing the geometric and RMS constantly get soooo close to others is what I'm curious about.
I haven't found a satisfying way to get the 'missing spots' (ie, 3rd and 9th chromatic note). The 9th one is close to the harmonic mean of f vs 5f. The 3rd note (harmonic minor) eludes me. For now, i have justified it as a 'quarter octave', which is the same definition in 12-TET. Which feels like cheating, except further 'so close'-ratios are found when doing means of f vs 2^(n+0.5) (where n is an integer). Very interesting.
Welp, that's my book report. More exploration is needed. Making scales using that reflection concept is very liberating. Really makes you wanna explore the possibilities. 🤔
Best music theory education channel, hands down. Every explanation is well motivated and intuitive, which is a rarity in music education. I've seen no one else explain the "why" of music theory so clearly
"It´s not instruction, it´s insight" This is so good. I always looked for the underlying Physics of Music explained like this. You explained it extremly well, on the point, clever and efficent(Also just the right amount of foreseeing possible Confusion of the viewer as well as things he already could know and skip)
I'm writing a math report for my high school IB report that's due tomorrow, and you just saved my ass.
I’ve been looking for this video ever since I started to learn the piano 15 years ago, but never knew it. Thank you!
I actually wrote a paper for my musicology final, discussing why the perfect fifth is responsible for 12 tone. I've basically touched a lot on the universal nature of the perfect fifth, lol.
Look into "Comma of Pythagoras" Fifths bear no connection to octaves or semitones. which is why he keeps "bending" here.
Okay! Now this makes more sense :)
Thank you so much for making these videos buddy!
9:40 The most concise and well layed-out 12-tet (and just int.) explanation I've ever seen!
This might be the best video i've seen of this subject. I've played the guitar since I was a kid and only recently started wondering about the "why's: "why the name octave?", "why 12 notes", how things developed in music, and so on. It's like I could not advance in music theory anymore without understanding all of these stuff. And in fact there are still some gaps in the whole basic history of notes/harmonic series/scale that I haven't figured out yet. For example, after reading and watching some videos, I've figured out the basics of the beginning of music, strings vibrations, Pythagoras, wave lenght, frequency, harmonic series, waves that are consonant and sound good to our years. But to get from this to the next step (understading the construction of scales) I'm not sure I understood properly. Apparently the harmonic series (simple ratios="easy" math=good to our ears) is the root of the rest of the stuff (scales, chords; melody and harmony), but I couldn't get the "logical path" from intervals appearing in the harmonic series (physical relations regarding wave lenght and frequencies) to the origin/construction of scales. Maybe I can understand the pentatonic scale (because the first overtones of the harmonic series have these ratio that are "simple" and produce consonant intervals, so it makes sense that everywhere in the world people use these intervals, because our ears perceive as consonant and pleasant), but the 7-scale or the 12-scale, I still don't get it. Maybe I have to watch that part at 9:58 over and over again, because 9/5 and 15/8 don't seem "simple ratios"...it still seems arbitrary for me. And i find interesting to see how many ways people try to explain this subject. The most fascinating for me is to try to reconstruct how things evolved from Pythagoras observations of strings to scales and then finally talking about "octaves" or "fifths" (i'm saying this because i've seen many videos talking about octaves and fifths as if they were a "given", like obvious names that shouldn't be explained in a context). Anyway, i'm just thinking out loud. It's too much stuff and my brain is exploding. I'm almost getting spiritual thinking that 12 is a mysterious number in nature, because it appears everywere. Thanks a lot for this video.
Finally helped me understand Just Intonation, and there was so much I never even thought to ask. This is easily the best educational channel on youtube, you should be a teacher. Seriously, I wish there was someone like you for every subject.
Very good video. I really like your way of explaining things!
Your breakdowns of something that normally isn't easy to explain, is amazing! You've taken a difficult topic and made it clear in a fun, fast and brilliant way. Love the "simplified" animations too. Thank you so much. I'm donating for sure! (Just did a test donation, will send more if it worked)
I'm impressed by how long you managed to hold that G note.
39 seconds
You're an absolute reference for me, not only on understanding of music theory, but also on how to explain it. I recommend your videos as much as I can. I also watch them often to memorize how you explain the different subjects.
I really admire your work and hope it will get as famous as it should.
Thanks! So glad you find it valuable. :-)
your music theory videos are the best i have seen so far.
Amazingly well put together! Thank you for making this!
Sir, this was an excellent explanation of a topic that has rattled my brain since I was a teen. Thank you so much for such great insight!
Amazing set of explanations. I had wondered about 12 tone system for ages but never really looked into it. Thanks, YT, for actually recommending a useful video.
When 6, 12, 30, and 60 show up it usually means simple ratios are nearby. Simple ratios are also why we have a 60, 60, 24 system for time. Same thing with binary and the powers of 2.
actually thats not necessarily whats going on here. 12tet being so composite is kind of a coincidence. for example 6tet actually completely misses 3/2. 19tet, 31tet, and 41tet all offer remarkable consonance while not being composite at all!
when you divide an octave equally, you're doing it logarithmically, because that is how we perceive pitch.
composite-ness and consonance arent necessary related.
Another wonderful piece of information, thanks!
In band our teacher would always tell us to bend the pitch of the third down because it's so sharp in equal temperament. It makes the I chord ring so purely
Nice! Yeah, it can be tuned down 14 cents. Unless it's a minor third, in which case it goes up 16. :-)
In this video and others like it by other RUclips creators such as 12tone or David Bennett piano, you excellently explain why we have a chromatic scale as well as the pros and cons.
One question I hadn't thought of until recently is somewhat phrased "Why these 12 notes?" For example we know that 440 Hz is "A" and then everything else is a relative frequency from that. But how did "A" become standardized at 440? It's only in relatively recent times that oscilloscopes, frequency analyzers or other such equipment could determine that frequency.
Traditionally at the beginning of an orchestra performance, the first violin plays an "A" and everyone else in the orchestra tunes to that pitch. A cappella singers often use a pitch pipe to get them on key at the beginning of a song.
But again… How do we know that that first violin or the pitch pipe is actually accurate. When were the standards for notes established so that if you heard a concert in one venue or another or even between performances of the same artists, how did you know that they were on pitch according to some established standard?
In terms of the choice of 440, it is indeed arbitrary. There is some interesting history behind it; there used to be an amazing video on the subject on youtube but I can't find it anymore. And now youtube is swamped by dumb "440 vs 432" videos making it even harder to find good summaries. For a basic summary you could try "Why is A 440 Hz?" by Walk that Bass: ruclips.net/video/GwWXDwqgWjo/видео.html
This is one of the best videos of this topic I have ever seen. Perfectly tempered explanation.
This needs to go viral. Can the RUclips algorithm take a hint and promote this way more?
As a music theory teacher myself, I'll recommend this to my students. Amazing work in this channel!
This video is exactly what I was looking for. Thank you for making the understanding of this topic so much easier!
This is the best explanation on youtube. Even for a complete beginner like me, I understand everything in the video. Very informative.
This is so clear and exact at the same time. Thank you!
Thanks for this. This is the most useful video on the subject that I've seen. Keep it up - this really helped.
Very clearly explained, with minimal math and maximum visuals.
Good stuff, really happy to see you are continuing to make content
Hey, awesome video. Can you do a video explaining different historical 12 tone tuning systems and why they might be better than 12-tet for certain pieces in certain keys? I wonder if there is a better tuning system of om playing in say, C major, where I don't need to worry about key changes? If we are playing only Bach for instance, what's the best tuning system to use? I know there is a lot of debate on which tuning system is best for Bach. I'd love to hear your input, especially in video format with the helpful visualizations.
Thanks for the suggestion! -- it's a little too far out of my area for me to seriously contemplate making, though. Have you searched around a bit for existing videos? I feel like it may be pretty well covered already, but I admit that I haven't looked very hard.
You should be able to get a grant from NEA, or some music teachers group. Very well done, and I would recommend it to anyone who challenges or questions the 12 tone system.
I like the way you graphically show the simple frequency ratios and their relationship to the root and octave. It’s also interesting that the ‘fifth’ at 3/2 the root is itself a 4/3 interval up to the octave, which in turn is a ‘fourth’ interval. As you point out, the fourth and the fifth are nearly perfect with the choice of 12 notes per octave. It’s fascinating with choice of 12 that each half-step interval mathematically becomes 2^(-12), or the twelfth root of two. Just under 6% higher frequency than the half-step below.
Really good explanation!
many thanks, grazie mille , namaste , your work helps me understand and helps me go through depression
a lot of love for you!
The way you see music is very different. Love it!
Thank you for your good work.
Thank you so much for this! Your videos are just awesome
Love the explanation. I just struggled to see some of the tonal graphs on my phone screen. I remember from my astronomy days that photo negatives of Astrophotography were used to spot faint objects because our eyes are more sensitive to subtle changes in light objects than dark ones. I'm sure there are analogous affects in sound.
So much good information. Thank you!
Very well done. Congrats!
alhamdulillah, one of the bestest videos regarding to my questions.
The best explanation of this subject! Thanks!!
Just enough information. Not so much I get lost, not so little it's dumbed-down. As a lifelong musician with no maths perception, I thank you.
Best video I have found, finally understanding things clearly
Thank you for the video. Was there any study involving the measuring of perception of consonance and dissonance in the animal world (using dogs, cats, horses, domestic animals, etc)? It would be interesting to see it. Being a part time dog trainer, I noticed something: when using normal or a bit harsher voice (deliberately more dissonant), dogs pay more attention to it, look straight in the eyes. Such voice is good to tell the dog it is time to execute a command. But when using a more falsetto-like "singing voice" when praising the dog, which I believe involves more consonant sounds, the dogs react to that with enthusiasm and expects cuddling and a reward. Dissonant - alert and attention; consonant - award and relaxation.
I'm not sure... I'm purely speculating here, but it seems clear that many animals have perceptual abilities of pitch similar to us (given the similar structure of cochlea and the evolutionary value of hearing pitch, not to mention plenty of research confirming it) and while I've not heard of a study about consonance/dissonance in particular, I'd be surprised if an animal like a dog couldn't tell a difference between a pure tone and a tone with inharmonic overtones (e.g. howl vs growl).
Gooood loord! My mind is about to explode couse its not get used to handle the amount of flawless powerfull revelation in such a tiny amount of time.
Fantastic video!
You are doing a great work.
I guess my issue is from early on, when you talk about consonant intervals, in particular the "most consonant intervals" - you use this (and the idea of "consonant" and "simple ratios" being somehow equivalent or at least closely related) as these become fundamental to your argument.
I would say that the whole range of intervals from somewhat smaller than 6/5 (slightly bigger than 9/8) to at least 4/3 are all fundamentally consonant, the rational and irrational ones included. To my ears, what is conventionally called a "third" (major, minor, anything in between) sounds just as consonant, and probably more so, than the 3/2 ratio of the perfect fifth, so I don't see why you single out the 3/2 ratio as "more" consonant.
If you look at the graph at 6:50, and try and equate amplitude to perceived consonance, then 8/5, 5/3, 14/8 (7/4) and 15/8 are all quieter (and hence more "dissonant") than the bottom of the dip between 7/5 and 3/2 - conversely, the entire range between 1/1 and 9/8 is louder than anything between 9/8 and 2/1, which correlating amplitude to "consonance" would imply that the range of intervals from unison to the major second are the most "consonant" of intervals, far more consonant that any 3rds, 4ths or 5ths - patent nonsense. So I'm not sure what relevance the study of the pitch content of human speech has on the supremacy of the 12-note octave.
Thanks for your thoughts -- We're agreed that consonance is a pretty important part of my overall thesis here (not that I invented these ideas, of course.) People have their own experience of consonance, and there's certainly wide variation, but as mentioned in the video there is a remarkably clear overall pattern across people from all over the world when it comes to consonance. E.g. 3/2 is certainly more consonant (for humans in general, if not yourself) than something between a major and minor third. I'd suggest checking out the links in the video description under "nuances of consonance" for some theories about it. It's not a simple question, for sure, and the simple ratios shouldn't be automatically assumed to be consonant just because the math is pretty, but it has been shown through a lot of experimentation that there is truly something to it. (And certainly the proliferation around the world of tonal systems that utilize these intervals isn't mere cultural accident.)
In terms of the graph at 6:50, I'd note that the harmonic series will naturally drop in amplitude as the frequency increases, which of course is why the graph curves down as it goes to the right. As far as I understand it, the authors are not arguing (nor was I using the graph to argue) that their data comprehensively explain the origin of consonance, just that the presence of these intervals in human speech is a provocative explanation for why our hearing system may be so keyed into them. I think I do see your point: that one would expect the higher frequency harmonics to be less relevant (and therefore less consonant) if they are so much quieter in speech, but perhaps the same mechanisms that key us into the lower harmonics have the effect of sensitizing us to the upper harmonics, or there are other subtleties we're not incorporating.
I don't think the graph is a conclusive proof of anything, and I certainly don't think the question of the 12 tone scale system is a totally closed case.
@@CaseyConnor "I'd note that the harmonic series will naturally drop in amplitude as the frequency increases" - except if you look at the dynamic graph at 4:48, this doesn't appear to be true for musical notes; the fundamental and the first six overtones are all roughly equal in volume - the 5th and 6th overtones in particular (D5 and F5) have amplitudes as high as the fundamental; although the 7th overtone (G5) is noticeably quieter, the 8th overtone (A5) has the same amplitude as the 3rd overtone (G4) and bigger than the 2nd overtone (D4).
The "Biological Rationale for Musical Consonance" is interesting (I'd come across it before) but the studies they report which get people to rank 12TET intervals in terms of dissonance are problematic, as they say nothing about the relative perceived consonance/dissonance of two intervals (are they very close, or widely different?) because they are based only on ranking (is the difference in consonance between a major and a minor 3rd the same as the difference in consonance between a major second and a minor second? They are both adjacent intervals in terms of ranking) and also, the comparisons are simply too coarse, with only 13 intervals in an octave. It would be far more interesting to create relative dissonance curves measuring intervals at 10 cent granularity, rather than 100 cent granularity (so 121 intervals in an octave rather than 13).
One interesting thing is that the perfect fifth (700 cents), according to the studies, is *more* consonant than the major 3rd (400 cents); the diminished fifth (tritone - 600 cents) is *less* consonant than the major 3rd (400 cents). There must therefore be an interval somewhere between 600 and 700 cents which is _exactly_ as consonant as the major 3rd (400 cents).
Excellent video, well done!
I find it intriguing that in the graph at 6:48, the flat 7th is a harmonic 7th (a ratio of 7/4 or 1.75) instead of one of the "just minor sevenths" which are closer to the minor 7th in 12-TET (16/9 [1.777...], which is two stacked perfect 4ths or the inversion of the major second, 9/8; or 9/5 [1.8], which is a stacked perfect fifth and minor third and is still closer to the ratio we get using 12-TET, ~1.7818 [The actual ratio would be 1:2^(10/12).] ).
Sidenote: at 13:54, do you remember which just interval you used? Seems like it would have to be 9/5 since it was sharper than the 12-TET note, but any particular reason?
Yeah I wonder if the authors of that paper just picked out an even ratio near the peak, or if the resolution of their data is sufficient to distinguish between 7/4 and 9/5 and it clearly pointed to 7/4. Either way, 7/4 seems intuitively like it might be the more "naturally consonant" interval, just based on the smaller denominator (though apparently subjective consonance is not quite as simple as that).
@@zozzy4630 It would have been 9/5, yeah. those intervals came from some version of just intonation I was working from (I don't recall where I got it off-hand). I leaned towards systems with simpler intervals (e.g. 9/5 instead of 16/9) because I wasn't trying to build a just intonation scale that was most compatible with 12-TET and modulation and so on, rather I was trying to be "true" to the J.I. idea of each interval being as consonant as possible. Maybe I should have gone with 7/4, but 9/5 seemed more common, IIRC. In other words, no: there was no particular reason, just some loose impressions. :-)
Excellent. Just excellent explanations.
Really good explanation 👍👍
That explains a feeling I sometimes have while playing guitar, that notes don't always totally blend together even though I'm tuned.
Correct. Standard guitar tuning/frets are only 'near enough' for convenience.
see: ruclips.net/video/D8EjCTb88oA/видео.html
Very good... i learned a lot here. You explain well. I'm a blues guitarist so I bend strings a lot.
Extremely interesting. Always wondered about this. My mind is blown!
1:14 Octet means eight in Latin language, that is where octave word comes from. Since there are 7 notes + 1 repeatitive (root) note in an octave interval which makes 8 in total.
Why do we call it October when it's the 10th month?
This is where infinity comes from and why 8 is the symbol of infinity because this 7 note modal scales can technically repeat in octaves forever.
@@AFRoSHEENT3ARCMICHAEL69 Ik this is like 3 months late, but October used to be the 8th month. (Sept)ember (Oct)ober (Nov)ember (Dec)ember. Then the romans screwed up the calendar by adding January and February, and now those names lost their meaning
@@Eidolon2003 I thought it was July and August the Romans added (named after Julius Caesar and Augustus Caesar)?
@@danielcohen2657 According to wikipedia July and August were originally named Quintilis and Sextilis before being renamed to honor Julius and Augustus
en.wikipedia.org/wiki/Roman_calendar
Thank you. I'm studying music by myself, as a hobby. Your channel helped me immensely.
I have one question though. Why the C major scale is so ubiquitous? Why we named all the notes and intervals after it? Is this just history and traditions, or there is something fundamentally "good" about it?
Maxim Salnikov history and tradition. I'm not qualified to give the particulars, bit that's the gist. IIRC there are good googleable answers on the net. Glad you liked the videos!
wow, I love this, learned a lot.
Love your channel - new subscriber! I just wanted to give you my 2-cents worth for the tuning of a pure fifth from a 12-TET 5th. 😄🎹
Oooh, don't know if this is too esoteric for your channel, but I'd love to see a similar take (your explanations are so very clear!) on tempered scales, like 1/4-comma meantone, 1/5-comma meantone, Valotti, and Werkmeister temperaments - etc. (Who's afraid of the Big Bad Wolf Chord?) 🐺
When you played that interval at 3:12 I insantly thought of the song "NF - Remember This", I checked it and indeed it is exactly the same :) And I didnt listen to this song for over a month for sure!
I mean the interval at the very beginning that the song starts with.
@@krzysztofq7420 Hah, good ear, yeah!
Provides excellent insight
"If you watch music theory videos to make yourself a better musician". I resent the accusation!
wow, best explanation I have seen on the net
Conclusion: 7 times the simplest interval (the octave) is pretty close to 12 times the next-simplest interval (the perfect fifth), so we just lowball the perfect fifth a little bit and say it’s exact. This system, 12-tone equal temperament, has the nice side effect that the other simple intervals are reasonably close to notes in here.
Hey, bro. You videos (podcasts))) are amasing! Could you make one about infrasound?
I'll put that on the suggestion list!
Thanks for this great video - like others who have commented, I have been searching for an explanation as clear as yours for a long time. Donation made. Are you able to provide an explanation for what seems to me to be the natural next question? Viz: why does the "Tone, Tone, Semitone, Tone, Tone, Tone, Semitone" sequence for selecting 8 from the 12 tones on the scale make sense? Is it that this selection picks out the 8 tones that are most consonant?
Thanks Daniel, and thanks for the donation! This is a great question. Broadly speaking, the questions of "how many tones in an average scale chosen from the 12 tones" and "which scale out of the 12 tones is likely to be most common" are very influenced by cultural history, but I think a case could be made that there would be a tendency towards something in the neighborhood of 5-9 notes in a scale, for many of the same reasons that are described in this video as applying to the overall tonal system: more tones in a played scale means greater precision required of instrument construction, higher demands on the musician and listener to discriminate pitches, more opportunities for dissonance, etc. Too few tones in a scale means less opportunities for expression. 5-9 seems to be a rough middle ground that works for our monkey brains. As to which tones to select, I'd guess that consonance/dissonance plays a big role. You start with the octave; the fourth and fifth kind of demand a seat at the table. Past that, you pick notes that aren't too close together, are roughly evenly spaced, and which work well in combination with each other. I'm not sure if anyone has proven that the major scale is the most consonant possible collection of notes, but if you add a constraint that you want the fifth of each note in the scale to also be in the scale (i.e. construct the scale using a circle of fifths) then the major scale is as close as you can get (all the notes but the seventh have their fifth in the scale). From this analysis, the root mode of the major scale (AKA the major scale) doesn't have any special claim over the other modes. AFAIK the preference of this mode as the "major scale" over, say, the mixolydian mode (or any of the others, at least the ones with a natural fourth and fifth interval off the root present in the scale), is just an accident of history.
Others: "I studied music for years!"
RUclips: *shows recommended videos*
Me: "learned in a few minutes more than in any music lesson"
This video is music to my eyes and brains
Why not ask you from where is comming one second, one millimetre, or one gramm???
Best Explanation of this topic.
because the consonant 3/2 is the most important one and assuming the number of notes in an octave is an even value, the minimum number of notes in an octave can be calculated with this formula:
log(2)/log((3/2)/sqrt(2))=11.76 (approximately 12)
by the way now i think that notes are not required to be at an equal distance from each other and they can be just the following ratios to sound good (not using more than 5 as denominator):
1, 6/5, 5/4, 4/3, 7/5, 3/2, 8/5, 5/3, 7/4 (mising ratio in the video), 9/5.
Darn that Tritone be real sharp in Equal Temperament in comparison to Just Intonation...
7/5 is a very consonant interval
COOL informative video! 😊
amazing video. I wonder if a digital instrument could be designed that automatically retunes itself to mathematically perfect ratios (rather than even temperament) as it is played?
Yes! It has been done, though the specific vendor escapes me now. Jacob Collier demonstrates it in some video somewhere... I wish I could dig it up. It might be an instrument for Kontakt, I'm not sure, but the idea is exactly as you suggest: as you play, the software is analyzing and guessing the key and so forth, and automatically adjusting chord tunings to cleaner intervals as you go. I think it's a really interesting idea and I hope it gains some more traction. It's not always obvious what the correct adjustment would be: even in a given chord you could argue one way or the other depending on how the intervals stack up. And in a dynamic piece of music what the next chord coming up will be will influence how you tune the current chord, etc, but that doesn't mean it's not worth trying!
I wondered about this too. An alien could find the compromises that "are ok" for humans unacceptable. There could be completely different evolutionary pressures for hearing. Not even earthly other animals seem to care much for human music.
A não ser que você vá pedir para uma capivara analisar sua música.
Se eu não importo com a música que estamos produzindo eu vou me importar com a música de quem? do pássaro que está cantando lindamente aqui fora??
Isso se chama aprendizado ou você coloca o lá 440Hz que o autotune te deu hoje e Aceita isso aí.
Pelo seu comentário digo que sua frequência não é a música.
I think it would also be useful to depict the equal spacing on a linear scale to show how the spacing of the frequencies looks in that view.
Yeah. Note that you can at least get a loose feel for this on the graph at 6:45 which uses a linear scale.
Beautiful stuff
@caseyconnor have you tried to space the 12 tones by 2^(i/12)? So that we have a logarithmic spacing between the notes.
By this spacing the difference is much less then the even spacing.
the good with
sounding the
ratios 2^(i/12)
1,000 1,000
1,067 1,059
1,125 1,122
1,200 1,189
1,250 1,260
1,333 1,335
1,400 1,414
1,500 1,498
1,600 1,587
1,667 1,682
1,800 1,782
1,875 1,888
2,000 2,000
Thanks -- what you describe is in fact the "even spacing" -- remember that the notes shown on screen are shown on a logarithmic scale (this is done because pitch perception is itself logarithmic, or at least roughly so. See around 1:45 for the note on that.) 12TET, the "even spacing" as described in this video, is indeed generated via 2^(i/12) just as you describe. So unless I have misunderstood you, you have invented 12TET on your own! :-)
@@CaseyConnor thanks for your answer! :) indeed I searched for frequencies of musical notes and figured that the ratios are exactly 2^(i/12)... so I just misunderstood even spacing for 1 + i/12 :) haha I guess that I invented it for myself from a misunderstanding... actually from this perspective of logarithmic perception, I interpret the ratios 3/2, 8/5 etc. as accidentally close to the evenly spaced logarithmic ratios, which probably mark the real pleasing ratios for our perception.
13:33 made me finally understand
Wow that's so good, donation made.
Why is 3/2 (1.5) slightly past the middle between 1 and 2? Shouldnt it be halfway? I know you have it right, my brain is just running in circles trying to rationalize this
Is it because its logarithmic?
@@bigbirdmusic8199 yes, exactly - that's the implication of 1:46, that linear points on the scale are skewed a little sure to the logarithmic(ish) nature of pitch perception.
@@CaseyConnor ahh yes that was driving me crazy. thanks for responding so fast! Great video as well!
What a high-quality video.
wow that was so good ,thank you so much , i learned a lot
Fascinating
2:37 amogus
Pay attention to 10:35. This is why xenharmonics work so well.
Thanks for answering the most basic question! Was confused why nobody answered this in these music theory tutorials.
Okay, now what's up with these # notes? Why is it called A, A#, B, C, C#, D, D#, E, F, F#, G, G# and not just A, B, C, D, E, F, G, H, I, J, K, L instead?
Have you watched my "music theory distilled" series? Maybe start there... the precise historical reasons I'm not super clear on myself, but basically there is a naming bias towards the C major scale. There are arguments to be made that other naming systems would be more logical or intuitive. As far as I know the one we use is a mixture of logic and historical happenstance.
@@CaseyConnor Yes, I found the playlist. Thanks for it! I now can connect all these parts of music theory much better. Helps a lot to get a more scientific explanation. 👍
Thank u, that was great :)
So sounds in nature are generally not dissonant? That's fascinating. I was under the impression that musical notes were just a specific fine tuning of sound for a purpose. I wasn't aware that natural sounds also have a tendency to avoid dissonance.
Hmmm... what timestamp (if there is one) are you replying to, exactly? I might have phrased something poorly. I would say that "dissonance" is a bit of a loaded term, with ties to human psychoacoustics, but that to exist it requires a certain degree of specificity in the sound. E.g. the sound of wind is not usually considered dissonant even though it has plenty of (uncorrelated) frequencies present in it that 'conflict' with each other, but two unnaturally-pure sine tones at a strange interval to each other would be called dissonant. So I would say that most natural sounds are dissonant, pedantically speaking, just because noise in general doesn't involve particular relationships between frequencies, but it's a bit of a stretch since we don't perceive them that way because they aren't feeding us much specific pitch information. Presumably birds and many other animals making a noise experience evolutionary pressure to create sounds that are unusual or distinct in some fashion, e.g. not just noise like wind, rustling plants, splashing water, simple thuds, etc, and that leads to sounds that have particular pitches or rhythmic components to them. Said another way, sounds with less "acoustic entropy" become markers for intelligence, intention, or just presence of a life form. As far as those sounds being dissonant or not, I'm not sure I would make a claim that they tend not to be dissonant overall, but in at least some cases (e.g. human speech, bird songs) the ratio of overtones tend to fall into consonant patterns. And consonance does show up a lot in physics, e.g. frequencies generating overtones of themselves in vibrating bodies, such as in a plucked string or blown flute, and physics also govern the sound-producing organs in birds and humans, so, perhaps I should have said "animal-produced sounds tend to have some in-built consonance due to the means of production, but not necessarily consonance from moment to moment.)
At 4:25 you say "There are other pitches with simple ratios as well, but these are the most consonant." But what makes them consonant? Cause I thought simple ratios are what made them consonant. What paper did you get it from? Need something to cite lolol
Having a simple ratio does tend to make a combination consonant, but consonance is a matter of degree, so the degree of consonance depends on the particular ratio. Perceptual consonance is a complex topic... there are a few links in the video description to papers and such (under "Nuances of consonance".) The particular ratios I used come from various places, but if you check the links in the description you will find a few mentioned in there.
"Consonant" means it sounds with it. You have one tone with his harmonics. To create a scale, we used the second harmonic, the first one won't work. To create a harmony, we used the harmonics. This is how it started.
So this is why detuning function in synth sounds nice sometimes. Right?
Hmmm, I'm not familiar with what you describe, but it sounds plausible.
@@CaseyConnor When you use more than one oscillator, you can ie. set the 2nd to n octave(s) lower or higher. And/or you can more or less slightly detune them to obtain certain "effects". @Mike Parmer: yes!
Kind of like when a violinist vibrates it's fingers on a string to detune it slightly, or the "chorus effect" on electronic instruments.it makes the note pass through the tempered tuning even if the instrument is stretched tuning.
15 :16 This graph is really great. I tried something interesting in Sonic Pi. I wrote a script to play a minor chord and shift the 3rd tone gradually upward to the major chord, the result changed along with it. With this tech, it allows me to modify the power of the emotion. This might be useful, since when we make music on computer, we don't need to worry about the instrument. It means ,if an octave is separated into more fragments, we might control the music more exquisitely. This might be extremely useful when making piano music on computer.
let ms(minor second) = 2 to 1/12 == 1.059463
ms to 3 == 1.1892
ms to 4 == 1.259921
ms to 4 - ms to 3 == 0.0707139
6 / 5 == 1.2
( 6 / 5 - ms to 3 ) / ( ms to 4 - ms to 3 ) == 0.01079/ 0.0707139 == 0.1526274 == 1/6.55.
What if we separate an octave into 12*7or 12*8 fragments?
Also, electronic instruments could "retune" themselves on the fly to make each chord sound more consonant.
@@Vandalfoe Oh, so in math, this is not a chord any more, this is a new hue?
Awesome 👏🏽👏🏽👏🏽👏🏽
13:31 was very educational
Consistent overtones appear naturally in analog acoustics (especially humans) and desire to land in these positions because the 12-tone scale comes straight from the amazing designer of music, and of everything: ALMIGHTY GOD.
Seek therapy, not 'god'.
Freaking wow 😮😱 yeah your videos definitely help me I was struggling with sharps and flats your video was so effective I don't need to look chord chart 🤔🎹