When I recorded my Jazz album, I noticed that by using Major 7ths and variations of triads, and minor ninths within the same piece, the playback makes me think of even more derivatives of the arrangements. In other words, I hear tones and subtones within the same piece of music that I did not know were there when I first aid down the tracks. (These often lead to improvements in my choices of melody lines as I lay down solos on top of the rhythmic structure,) I was previously unaware that this had a legacy that was found in a totally different genre that is foundational to the music puzzle. Thank you for the enlightening video and your analysis.
I first experienced the pitch rising effect (possibly the most intuitive name, because it already describes what you're actually hearing) when tuning a bass guitar. Any good modern guitar -- heavy emphasis on good here, and I include basses in this statement -- should be tuned by the frets in order to maintain the **equal tuning.** I had a friend who taught me how to tune to harmonics, and I thought it was the coolest thing ever, because it's much easier to hear that pitch difference as a wobble of fighting vibrations. When you get to the point where you have no oscillating pitch variance, your strings are in tune! (Almost!!) Let's look at an example: say my E string is in tune, and I tune the A string based on harmonic overtones. The 3rd overtone of A is extremely close to the 4th overtone of the E below it, so you may be fooled into thinking it's the same. As you cascade this up through 4 strings (or worse, 5 or 6), that difference gets off, and by the time you get to the G string, that one is slightly out of tune with the E string, but on a bass, it's not super noticeable. If you carried this through 12 strings (circle of fifths), by the time you get back to E, it would be very obvious! I was able to get away with playing that way for years, but at some point, I realized the math meant I was putting the instrument out of tune. The math: octaves are essentially powers of 2, and when you tune to the 3rd overtone, what you do is multiply by 3 and divide by 2 (this video demonstrates that). Using powers of 3 NEVER gets back to a multiple of 2. 3 to the 12th power gets pretty close to 2 to the 19th power, but musically, it will hurt your ears! Side note: I have at least one friend that couldn't stand any time I tuned, because that pitch variance hurt her ears, but more when I used harmonics.
Cool reaction video! I was just messing around with Benedetti's puzzle in 34-tone equal temperament which does not temper out the syntonic comma (81/80) as well. By going through 6 iterations, I was a whole tone higher from where I started (6 steps of 34-TET is a whole tone). I tried lowering the A sustained in the treble clef by 81/80 to keep the pitch from drifting, but I ended up creating a wolf 5th (40/27) with the D in the first beat. Comma drifts can be annoying at times but they can be used for interesting modulations that I plan to exploit :)
If it were possible to tune a piano perfectly (perfect fifths with a ratio of 2:3 and major thirds with a ratio of 4:5 ) then piano tuners would do this. But sadly it's not possible. It's like the leap years. A year does not have exactly 365 days. And an octave does not have exactly 12 fifth (if you play alternating 5th up 4th down 5th up 4th down etc.)
The problem with the "problem" video is that it's not very well presented. What he's trying to demonstrate is the need -- based on pure physics and math -- for *even temperament* tuning which does not strictly follow the laws of physics for perfect intervals. Tuning systems are quite complex. The complexity arises from how the mathematical values of the generated overtone series (harmonics) are managed. In just intonation, the mathematical values and ratios are honored for some notes and intervals, which makes them more "in tune" with each other, but more "out of tune" with other notes and intervals. Because the natural ratios of the overtones are reinforced for those notes and intervals, just intonation tuning sounds more "solid" within a given key, but only in that key, which means it cannot be well-used in other keys. Even (or equal) temperament makes all notes and intervals (except for octaves) approximately equally "out-of-tune". The roughness of even temperament created by inharmonicity is mitigated somewhat by using stretch tuning -- lower notes are stretched slightly lower, and higher notes are stretched slightly higher to reduce inharmonicity. See the wikipedia article on stretch tuning to get some idea of the level of complexity and trade-offs involved with tuning systems.
I’m not a fan of these types of “reaction” videos where you just sit and show us another person’s work for long periods of time without giving us some useful input. It feels like we’re both learning at the same time, when you’re supposed to be teaching us.
How does all of this apply to guitar or any other instrument where the same string is used to generate multiple notes instead of each note having a dedicated string? In the two examples of the Gmajor chord, the second sounded much more pleasant to me. I could hear the beating in the first example which, as a guitarist, tells me something is wrong.
i’m not well versed on guitar, actually started playing it a few weeks after i filmed this video, but i believe this is a very valid question. i hear that the second version is much more accurate to the sound of the chord strummed on a guitar. If i were to guess I would say it’s due to natural timbre of the guitar and the fact that tuning is up to the user themselves meaning every string will never be EXACTLY the right pitch and when we’re dealing with fractions of a tone it’s important to factor in those tiny differences. I think the piano is different because tuning of notes in relation to each other hardly ever changes especially on keyboards. But all of this is pure speculation on my part!
It's actually very interesting. Using the tempered scale, to raise a pitch by a semitone, you would multiply its frequency by the positive twelfth root of two, i.e. the number which when multiplied by itself 12 times becomes two, approx. 1.059. That's an irrational number which means you cannot precisely write out the frequency as a decimal number; there will always be some error involved. I checked this by Wolfram Alpha-ing (like googling but with Wolfram Alpha) "is the 12th root of 2 rational". So if the pitch of A4 is 440 Hz (it's not always), the pitch of A#4 would be 440*2^(1/12) Hz; Wolfram Alpha gives me around 50 digits starting 466.16376 for this number, but that's still not fully precise (but good enough for most purposes of course). Is music that does not use the tempered scale "bad-tempered music?" :D
I actually did this many years ago with a synthesizer, set each key to generate a frequency 12th root 2 above the previous, and as you say, that number being irrational makes it impossible to be precise... you have to choose a number of decimal places, but what happens when the digit immediately after your stopping mark is a 5... do you round up or down? There's no way that you could get all musicians playing all instruments to agree on what the actual pitch of a specific note really is, and in practice if you actually take the trouble to do it to say four or five decimal places using various instruments covering several octaves, the same chord played together in different octaves will sound horrible even though each note is twice the frequency of the one an octave below. There really is no consistent solution. Music be weird.
When I recorded my Jazz album, I noticed that by using Major 7ths and variations of triads, and minor ninths within the same piece, the playback makes me think of even more derivatives of the arrangements. In other words, I hear tones and subtones within the same piece of music that I did not know were there when I first aid down the tracks. (These often lead to improvements in my choices of melody lines as I lay down solos on top of the rhythmic structure,) I was previously unaware that this had a legacy that was found in a totally different genre that is foundational to the music puzzle. Thank you for the enlightening video and your analysis.
I first experienced the pitch rising effect (possibly the most intuitive name, because it already describes what you're actually hearing) when tuning a bass guitar. Any good modern guitar -- heavy emphasis on good here, and I include basses in this statement -- should be tuned by the frets in order to maintain the **equal tuning.** I had a friend who taught me how to tune to harmonics, and I thought it was the coolest thing ever, because it's much easier to hear that pitch difference as a wobble of fighting vibrations. When you get to the point where you have no oscillating pitch variance, your strings are in tune! (Almost!!) Let's look at an example: say my E string is in tune, and I tune the A string based on harmonic overtones. The 3rd overtone of A is extremely close to the 4th overtone of the E below it, so you may be fooled into thinking it's the same. As you cascade this up through 4 strings (or worse, 5 or 6), that difference gets off, and by the time you get to the G string, that one is slightly out of tune with the E string, but on a bass, it's not super noticeable. If you carried this through 12 strings (circle of fifths), by the time you get back to E, it would be very obvious!
I was able to get away with playing that way for years, but at some point, I realized the math meant I was putting the instrument out of tune. The math: octaves are essentially powers of 2, and when you tune to the 3rd overtone, what you do is multiply by 3 and divide by 2 (this video demonstrates that). Using powers of 3 NEVER gets back to a multiple of 2. 3 to the 12th power gets pretty close to 2 to the 19th power, but musically, it will hurt your ears!
Side note: I have at least one friend that couldn't stand any time I tuned, because that pitch variance hurt her ears, but more when I used harmonics.
There is an adage that goes: "Practice always precedes theory".
@@protte225 Wise words!
Cool reaction video! I was just messing around with Benedetti's puzzle in 34-tone equal temperament which does not temper out the syntonic comma (81/80) as well. By going through 6 iterations, I was a whole tone higher from where I started (6 steps of 34-TET is a whole tone). I tried lowering the A sustained in the treble clef by 81/80 to keep the pitch from drifting, but I ended up creating a wolf 5th (40/27) with the D in the first beat. Comma drifts can be annoying at times but they can be used for interesting modulations that I plan to exploit :)
If it were possible to tune a piano perfectly (perfect fifths with a ratio of 2:3 and major thirds with a ratio of 4:5 ) then piano tuners would do this. But sadly it's not possible. It's like the leap years. A year does not have exactly 365 days. And an octave does not have exactly 12 fifth (if you play alternating 5th up 4th down 5th up 4th down etc.)
great analogy!
or maybe a lot of people have unrecognized perfect pitch because it does not match the modern system
A440 hertz and a447 hertz various raise or lower for a brighter sound.chromatic harmonica etc.
it’s crazy to me that a slight difference like that is actually a huge change when it comes the entire tone of an instrument
The problem with the "problem" video is that it's not very well presented. What he's trying to demonstrate is the need -- based on pure physics and math -- for *even temperament* tuning which does not strictly follow the laws of physics for perfect intervals.
Tuning systems are quite complex. The complexity arises from how the mathematical values of the generated overtone series (harmonics) are managed. In just intonation, the mathematical values and ratios are honored for some notes and intervals, which makes them more "in tune" with each other, but more "out of tune" with other notes and intervals. Because the natural ratios of the overtones are reinforced for those notes and intervals, just intonation tuning sounds more "solid" within a given key, but only in that key, which means it cannot be well-used in other keys. Even (or equal) temperament makes all notes and intervals (except for octaves) approximately equally "out-of-tune". The roughness of even temperament created by inharmonicity is mitigated somewhat by using stretch tuning -- lower notes are stretched slightly lower, and higher notes are stretched slightly higher to reduce inharmonicity. See the wikipedia article on stretch tuning to get some idea of the level of complexity and trade-offs involved with tuning systems.
@@aBachwardsfellow Wow! thanks for the insight!
I’m not a fan of these types of “reaction” videos where you just sit and show us another person’s work for long periods of time without giving us some useful input. It feels like we’re both learning at the same time, when you’re supposed to be teaching us.
Thanks for the feedback! Will work on it.
It’s Benedetti not Bendetti
@@rtheben OOPS honest mistake
@@rtheben fixed!
@@musicaljayden thank you bro, it happens to be my last name also
Good job ❤️❤️❤️❤️❤️
To break your "tuning brain" on an even higher level, check out Zhea Erose on one of her hour long discussions on tuning systems. Have mercy!
Thanks for the suggestion!
You know what? Credit to you for realizing you'd left off the 's' at about 5:00 and taking the moment to add it. I appreciate people being self-aware.
How does all of this apply to guitar or any other instrument where the same string is used to generate multiple notes instead of each note having a dedicated string? In the two examples of the Gmajor chord, the second sounded much more pleasant to me. I could hear the beating in the first example which, as a guitarist, tells me something is wrong.
i’m not well versed on guitar, actually started playing it a few weeks after i filmed this video, but i believe this is a very valid question. i hear that the second version is much more accurate to the sound of the chord strummed on a guitar. If i were to guess I would say it’s due to natural timbre of the guitar and the fact that tuning is up to the user themselves meaning every string will never be EXACTLY the right pitch and when we’re dealing with fractions of a tone it’s important to factor in those tiny differences. I think the piano is different because tuning of notes in relation to each other hardly ever changes especially on keyboards. But all of this is pure speculation on my part!
It would only apply on guitar if you changed your tuning system. Not drop tuning, but the actual tuning system.
@@ericchin739 i was thinking similarly
very nice thumbnail. music sure is something
It's actually very interesting. Using the tempered scale, to raise a pitch by a semitone, you would multiply its frequency by the positive twelfth root of two, i.e. the number which when multiplied by itself 12 times becomes two, approx. 1.059. That's an irrational number which means you cannot precisely write out the frequency as a decimal number; there will always be some error involved. I checked this by Wolfram Alpha-ing (like googling but with Wolfram Alpha) "is the 12th root of 2 rational". So if the pitch of A4 is 440 Hz (it's not always), the pitch of A#4 would be 440*2^(1/12) Hz; Wolfram Alpha gives me around 50 digits starting 466.16376 for this number, but that's still not fully precise (but good enough for most purposes of course).
Is music that does not use the tempered scale "bad-tempered music?" :D
Haha, thanks for the insight!
I actually did this many years ago with a synthesizer, set each key to generate a frequency 12th root 2 above the previous, and as you say, that number being irrational makes it impossible to be precise... you have to choose a number of decimal places, but what happens when the digit immediately after your stopping mark is a 5... do you round up or down? There's no way that you could get all musicians playing all instruments to agree on what the actual pitch of a specific note really is, and in practice if you actually take the trouble to do it to say four or five decimal places using various instruments covering several octaves, the same chord played together in different octaves will sound horrible even though each note is twice the frequency of the one an octave below. There really is no consistent solution. Music be weird.
Bach? "Well-tempered clavier"
6:50
It's called "multiplying by the reciprocal"
You do that to divide fractions