This is a relatively good explanation for beginners of the mathematical features of 12-tone equal temperament, but it's not at *all* a correct explanation of why we do things the way we do them. There was never some search for the best equal temperament, with 12 winning out over 19 for some practical reason. There were *always* 7 notes (well, 8 if you count both B and Bb separately), and they were tuned fifths apart (when they were tuned) until people started using 5/4 major thirds in the Renaissance, and those 7 notes, with the whole tones and semitones, allow for a note in between them if you move by a semitone instead of a whole tone. For example, if you're at G and move down by a whole tone, you get F, but if you go down a semitone instead, you get F#. These chromatic notes were sung as basically inflections of other notes: you have the natural F, and you have the F#; you have the natural A, and you have the Ab. Sometimes you sing one, sometimes the other. With precise tuning came precise intonations for these inflections, but this led to a problem: G# and Ab were both useful notes, for example, but they have different intonations that are very close to each other. Same thing with D# and Eb. (Db, Gb, and A# didn't get used enough to cause problems with C#, F#, and Bb respectively.) This was only a problem if you were trying to tune a keyboard; of course singers didn't need to care about this. Some English keyboards solved this problem by just having separate keys for G# and Ab and for D# and Eb, for a total of 14 notes per octave. In the rest of Europe, they mostly just opted for 12 and picked one from each set, leading to some out-of-tune-ness on their keyboards. As keyboards became more important culturally, they sought ways to resolve this tuning problem, especially because, with the Baroque period, composers started composing in different keys. In the Renaissance, basically everything was all white notes with some exceptions, but in the Baroque, people would want music in, say, G minor, which had Eb's and F#'s (the F# because you still needed the leading tone for cadences). So people would detune their notes a little bit to spread out the out-of-tune-ness so that more notes were out of tune but by less, and you could play in the more common keys (C, F, G, etc.) without running into any bad sounds. But people wanted to play in more keys, and eventually, *eventually*, people begrudgingly settled on 12-tone equal temperament, where *every* key was out of tune instead of some keys being in tune. There was a lot of resistance to this idea; people liked the purer sounds of well temperament and could just avoid the keys where it was less pure. But in the end, equal temperament won out. The fight was always between well temperament and equal temperament, all with 12 keys per octave, and there was never a search for the best equal temperament. (19-tone and 31-tone keyboards *were* proposed in the 1500's and some prototypes were even built, but they were not actually used generally, and they weren't meant to be equal-tempered either.) NOWADAYS, we can look at the equal temperament possibilities with math and choose the "best" one for our needs, but that is not why the keyboard has 12 keys per octave!

@PocinTheTech

Ай бұрын

thank you for this very detailed comment. While I am 99% with you I feel like I have to chime in. Obviously there is more to the discussion than a simple formula and it took thousands of years till we came to the point where we are now, with many ways to tune before, even many systems that had more than 12 keys per octave. My phrasing may have been a little off in the video but i was mainly trying to proof the point, why any other amount of keys with ET would never have happened (call it proof by refutation). People always were searching for the best way to tune their instrument, but there was never the consideration of a 19 tet piano (or 13 tet piano) because it would have made the main point of our initial "tuning idea" worse, which are 3/2 ratios. If you want to get those ratios as close as possible (and all tuning systems before had one thing in common: They wanted this ratio) you couldn't use any other number of keys than 12. Because everything else had this ratio worse (or it would have been an insanely high amount of keys). Therefor (even tho people didnt discuss it like that) there was never a world, where a different amount of keys was possible (for ET).

@maurobraunstein9497

Ай бұрын

@@PocinTheTech > because it would have made the main point of our initial "tuning idea" worse, which are 3/2 ratios But they *did that*. The standard tuning in the Renaissance was quarter-comma meantone, which narrows each fifth from 3/2 to 5^(1/4) so that the major third is a perfect 5/4. This is actually a kind of equal temperament in that every fifth is the same (as opposed to well temperament), except that, for practical reasons, they only used 12 notes instead of infinity notes, so there was a nasty wolf fifth between the G# and Eb. They could have done something very close and gone to 31-tone equal temperament, but since they weren't really concerned with extending music to remote keys at that point, they just kept their pure 5/4 thirds. 12-tone's strength is its ability to play every key equally badly. This compromise was definitely understood centuries before 12-TET became common, but it was rejected because people wanted their music to sound in tune, and 12-TET doesn't sound in tune. It was only when the need to play in every key began to outweigh the need for in-tune thirds that people acquiesced to 12-TET. Remember, a pure third is 386¢ while a 12-TET third is 400¢, 14¢ sharp. That's a lot! Meantone had a lot going for it. But yeah, my point here is that 12-TET is a great ET because it sounds not *too* bad and it has a manageable number of notes, but historically, people weren't looking for ET's at all, and when they finally did, they had already settled on 12 notes per octave centuries earlier.

@prependedprepended6606

26 күн бұрын

@@maurobraunstein9497 " *people weren't looking for ET's at all, and when they finally did, they had already settled on 12 notes per octave centuries earlier.* " That's correct. The point you both are missing is that the lute was the king of instruments up until the Baroque and it is by default a 12 EDO instrument. The largest body of musical literature before the Baroque was for the lute and music for the lute was prominent even during the first half of the baroque. I'm not really certain why it took keyboards to arrive at the same solution.

@maurobraunstein9497

26 күн бұрын

@@prependedprepended6606 The equal temperament on the lute was solving a rather different problem -- how to make frets that would fit the different open strings. The fact is that musicians didn't *want* 12-TET because the existing alternatives sounded better, until eventually the music evolved such that 12-TET became the better fit to play it. 12-TET is a *bad* compromise for major thirds. The thing it had going for it was that it was only incrementally worse than the compromises of the well temperaments of the 18th century,, so the difference wasn't as jarring as it would have been a century earlier. We treat 12-TET as musical progress, but it was not seen as such at the time.

@cubicinfinity2

22 күн бұрын

There's a lot of reverse logic in the video, but it at least explains how the 12 tone system works for the most part. Personally, I like 15 divisions of the octave a lot and maybe even more than 12, but if all music was in 15 I would probably get tired of it.

Aside from the excellent comments in the subthread about the more complex actual history of eventually choosing 12 equal divisions of the octave (started by @maurobraunstein9497 -- hint: it's a lot more convoluted than presented in this video, and many parts of the world outside Europe DIDN'T make the same choice) . . . . One thing that usually gets overlooked is that 12 equal divisions of the octave actually DOES fall close to just intonations, but not the ones that usually have their names attached to the intervals(*). So for instance, the nominally 6/5 minor third is actually right between 19/16 and 25/21, while the nominally 5/4 major third is actually almost right on top of 63/50 (and just a few cents off from 24/19, useful if you have a well temperament that goes a bit sharp in places). Of course, these complicated just ratios, while mathematically valid, do not resonate very well -- transfer of energy between strings tuned to these ratios is inefficient, so the sound tends to be on the dull side. But if you build more powerful instruments, then you can power through this problem. I haven't seen proof, but I have a strong suspicion that this is the reason that 12 equal divisions of the octave took as long as it did to become widely accepted, but then finally did win out. (*)That is, when trying to be somewhat mathematically accurate and not using the harebrained step counting interval naming scheme -- what connoisseur of obfuscation decided that the third harmonic should be called a fifth, while the fifth harmonic should be called a third? And in modern times, instruments have been built which _will not work_ without 12 equal divisions of the octave -- the unified mutation stops in the generally highly unified theatre organ would not work without the notes being equally tempered in 12 divisions -- anything else short of 53 or at least 41 notes per octave would be inherently impossible to get in tune throughout each octave, and a theatre organ with that many notes simply wouldn't fit where it needed to go, since the reason for unification in the first place was to save on space (as well as cost) to be able to have the instrument at all. And keep in mind that the extra space comes without extra power -- or if it means that you have to have fewer pipes or strings per note, it means LESS power. The same is true on a smaller scale for other keyboard instruments, although the harpsichord design is more forgiving than the of the piano, such that some harpsichords with all the way up to 36 notes per octave were built (although after 31 notes, the ergonomics got terrible) while still fitting within a reasonable amount of space: the Arcicembalo of Nicola Vicentino, who even built an organ similarly (the Arciorgano, again with terrible ergonomics), in the 1500s. Some videos of replicas of these are floating around on KZread. Presumably they didn't catch on due to cost, even in the cases in which they actually had decent ergonomics (cimbalo cromatico, 19 notes per octave, and clavecembalum omnitonum, 31 notes per octave, and a handful of related instruments). Meanwhile, the 24 notes per octave piano that Ivan Wyschnegradsky (quarter-tone pioneer) had built for him appears in the thumbnails for a few videos on KZread, and that thing is a monster, basically 2 pianos stacked vertically, and reportedly he came to the conclusion himself that it wasn't very practical (too bad that he never got together with pioneers of generalized/isomorphic keyboards, other than briefly with Adriaan Fokker who built the 31EDO Fokker organ in 1951; unfortunately, while this came from a good idea, the actual implementation sounds somehow all at once harsh and asthmatic, sounding worse than the aforementioned Arciorgano of the 1500s). I have read that somebody actually managed to build an actual acoustic piano having 41 notes per octave that is now in a museum somewhere, but I have yet to be able to find an image of this. For woodwind instruments, a different ergonomic problem arises: Think about the existing woodwinds for playing 12 notes per octave: You have only 10 fingers, so to play 12 notes per octave (plus you really need a couple of duplicated notes to help get through the transition between octaves), so this is already a problem -- you are guaranteed to have some weird fingerings. On a clarinet, which overblows first at the twelfth (3/1) instead of the octave (2/1), meaning you need 19 notes per twelfth (before you include the couple of extra notes needed to make the transition playable), this is even worse, to the extent that clarinets in different key signatures have persisted into modern times despite attempts to standardize on just one key signature -- the fingerings in remote key signatures just get too hard to play in rapid passages. The Wikipedia article on quarter tones has a photo of a quarter-tone clarinet, and it is one UGLY kludge having two barrels with a valve to select between even and odd multiples of quarter tones. A clarinet of 41 notes per octave would be of 65 notes per twelfth (again before including the requisite couple of extras) . . . and clarinet players still have only 10 fingers each. In very modern times, the onset of availability of (somewhat) affordable isomorphic/generalized keyboards and software synthesizers that actually sound good has led to a great radiation in music using different numbers of notes per octave.

@PocinTheTech

25 күн бұрын

Thank you for your comment! I can agree with it 100%. This is a very western (or even "german") view on tuning, where 3/2 was very dominant. The argument of practicality was a huge consideration in the early times (before computers), since every tone had to be actually physically made (for keyed instruments). Nowadays the implementation of computers allows for more tunings with (almost) no additional cost. While in our niche it seems like there is much experimentation, I have the feeling like the average musician doesn't spend much time on "tuning theory" (at least this is my impression when talking to other musicians). Therefor I sadly feel like the theory needed to get more fancy-tuning-mainstream-records is not spread enough to become "popular" in the shortly foreseeable future.

Wait what? I just watched this video in fullscreen expecting to click off and see 100k views and 200 comments but I found this? Seriously great video and massively underrated. I've always wondered why (especially with digital music) we can't just make songs which don't conform to a specific tuning system, but rather every note's tuning is based on the previously played notes. Then we could keep multiplying by 3/2 and 1/2 along with other ratios to find new melodies, and it would never sound out of tune with the previous note.

@KristallFire

Ай бұрын

Holy moly you are right. People really seem to prefer stupid Videos over real education. This Video was great!

@PocinTheTech

Ай бұрын

with some coding skills this should be possible! I can bet Marc Evanstein did something like this already. Reading all those comments (that I'm incredibly thankful for, I honestly didn't expect so many views and positive feedback) I guess I will make a follow up video with more sound examples and less talking, just to "present" some of those more interesting tunings.

@KristallFire

Ай бұрын

@@PocinTheTech The talking is fine. As far as i consider from the comments, extracting information from your Videos is the Key reason, people watch you. If you wanna Spice it with some examples, that could defenetly help illustrate informational points. Just be careful to not lean to much into Infotainment.

@kumoyuki

Ай бұрын

@@PocinTheTechas a programmer and musician who has been working on this problem for a decade, it's actually not that easy. The biggest problem you encounter is defining what is harmonious in the first place. You can get away with a lot if you are using pure sine tones because they are so simple for the ear to decode, but when you start moving towards complex timbres the interactions between upper harmonics starts to become important. Fundamentally, you have to redefine your theories of harmony and how to construct music: what does tonality even mean if there is no well-defined scale? Or if your harmony leads the melody to resolve at a different frequency (e.g. comma drift) than you started at.

0:30 "We will start with some simple bass-ics." Approved! **slapps like button and subscribes**

@A320step-official

28 күн бұрын

fr!!!

Math and Music. I had that idea as a young teenager and finally found the perfect channel on youtube 20 years later. Keep it up, my sub is in.

now i am become math, destroyer of notes

This is good. Concepts like this - where there is no "precise" derivation, but rather the whole thing is a "good enough compromise," can be the thorniest things to explain, and I think your approach did a great job of it. Well done!

Thank you algorithm for bringing me here, loved it, subbed, keep up!!

With this level of content and quality, your channel is going to lift off really quick.

This was an excellent explanation! Very glad I just found your channel. Looking forward to learning much more from you. Thank you!

There are tools online that will let you listen to various intervals, chords, arpeggios, and so on in equal temperament vs. just intonation. Personally, I can't hear the difference, and in my opinion that's the REAL criterion for "how many notes is enough." Using a 12 note scale gets us "close enough" to the mathematical grace of just intonation that "most people" can't hear the difference. I don't mean that if I do a back and forth comparison of the two I can't detect any difference at all. What I mean is that my ears don't "object" to the equal temperament intervals. They "pass my auditory test," so to speak, as consonant tones. Of course, this is what I hear all the time in the music I'm used to. But the just intonation intervals don't "sound wrong" to me. The 12 note scale is "good enough" for most of us while still being acceptably simple.

awesome stuff...keep this up and you'll achieve what you want out of this channel in no time!

Neat! A bit of additional critique though: (1) Showing frequencies linearly is the least confusing way, but for it is better to transform to a logarithmic axis where there are equal distances between 110, 220, 440 and 880 Hz and the same for other intervals. This makes each interval the same size no matter where it’s going from and to, which makes it clearer to see that there are only two types of intervals in a Pythagoreal diatonic scale: whole tones between C-D-E and F-G-A-B on one hand and semitones between B-C and E-F on another hand. Generally when working with scales, it aids in seeing their intervalic structure better. (2) Pythagorean is not the only just intonation system there are. For one of the neater and well-known examples, take Zarlino’s diatonic scale (aka “Ptolemy’s intense diatonic”; searchable on Wikipedia but I won’t paste a link here because usually this enqueues the comment for moderation or it outright vanishes). It’s not exactly diatonic in the sense of having only 2 equal semitones and 5 equal wholetones, but it’s diatonic in more general musical sense of what you can do with it and how it can sound. The intervals between consecutive notes go L M s L M L s where L = 9/8 a large whole tone, M = 10/9 a small tone and s = 16/15 a semitone. We see in this case what was one kind of interval in a Pythagorean diatonic, bifurcated in this scale. All those intervals now contain powers not only of 2 and 3 but also 5, giving us pretty neat and simple thirds of sizes 5/4 and 6/5 (between _some_ notes). Another feature of this scale is that every second, every third, every fourth, … and so on (except multiples of an octave) comes in three sizes, like it comes in a “normal” diatonic scale-so it’s musically more manageable than an arbitrary scale (though there can be other redeeming qualities which can outweigh this one in other contexts). As far back as the end of antiquity, people already have considered just scales with primes as large as 11 in their intervals, but there are still mostly just tuning explainer videos that mention only Pythagorean scale but not other nice examples. I’d wish for more diversity because it, well, wasn’t that simple after all. And even if it was, it could’ve been a bit different but western music would still have ended up _most surely_ with 12edo (other candidates are 17, 19, 31). But that’s a topic for another video. Starting with Pythagorean to explain stuff is a good way, it would just be much better when a longer video is feasible with more intricacies in it.

@05degrees

28 күн бұрын

Ah also BTW what people could’ve optimized for in tuning, in addition to all other historical ways, if acoustics bloomed several centuries before it actually did, could’ve for example been delta-rational chords: chords that aren’t necessarily composed of rational intervals, but have the same _differences_ of sufficiently many of the intervals their contain. In that case the overal beating of the chord mainly is synchronized beating of those intervals against each other. Like the usual JI effect of single intervals by themselves, this effect is somewhat robust and you can get it for approximately equal differences for chords in many equal-division tunings of moderate sizes (I mean, you don’t need to go as far as like 53 or 311edo: 17 or like 13 have examples already). One can hear this without any acoustics progress, but for systematic approach to finding scales or equal tunings with chords of this type it would be probably a requirement, so these chords got named only recently. (Well and because tuning theory is a niche subject.)

@PocinTheTech

28 күн бұрын

@@05degrees Thank you for this very well versed comment! This video was mainly targeted to people with a bit of maths and a bit of music understanding, not for professionals. So I decided to go for a linear scale, since log may have thrown some people off (even tho it is the better visualisation, as long as you know how to read it). I decided on the (in my mind) simplest ji tuning (didn't want to go full pythagorean, since than I would have need more explaining to do towards white and black keys, here I had a nice middle ground). If I actually wanted a historical wider used tuning I for my part would have picked something well tempered (Werkmeister i guess), but then the explanations would have been to long. I have my next videos already planned (they won't be that tuning related), but after reading through all the comments somehow I want to delve deeper into this. Since you seem very well versed, if you are interested on a collab, hit me up by mail (channel info) and I will send you an idea.

@05degrees

28 күн бұрын

@@PocinTheTech Hehe thanks! I’m quite a disorganized person unfortunately, I hope somebody better suited for a collab will appear. 🙂 I’m bad with big projects.

I'm utterly amazed youtube brought me this high quality af vid, by someone with 95 subscribers. Oh wait, 96. I just subbed. ;)

I was asking myself my whole life why a keyboard has white and black keys and how they associate with frequencies. I woudnt have ever imagined that the concept is that mathematical and that they came up with all this like hundreds of years ago. Well presented and I hope your video quality will attract more viewers that can learn from your videos C:

@familyshare3724

Ай бұрын

The Babylonians came up with this 3000 years ago. The days of the week are the cycle of fifths named after the classical planets: Moon, Mercury, Venus, Sun, ...

@tetrotull3462

Ай бұрын

They didn't just invent it the brain recognizes it intuitively. The maths just puts it into context. 440hz is because the Rockefeller foundation made it the standard

@Chrisamic

Ай бұрын

@@familyshare3724 No, the Babylonians used cyclic tuning, in 1/3s and 1/5s, it looked more like Pocin described at the beginning. There are Babylonian texts describing this. Equal temperament (and the need for sharps and flats) was not really a thing at the beginning of the baroque period but gradually cemented itself during this time, along with modern methods for writing western music during the classical period. A lot of early classical music sounded nothing like it does today... Well maybe a little, but it still used just temperament. While twelve tone equal temperament was first described by Chinese mathematician Zhu Zaiyu in 1584, it wasn't in common use until the early 20th century. Even the concept of A4=440 Hz wasn't actually a thing until 1936. From at least the Boroque period until 1936 it was 432 Hz. Remember that by the time scholars (mostly ecclesiastic scholars in the middle ages) got around to describing musical notation it started with Do. Why would they start with C? The answer is, they didn't. Do Re Mi etc were actually the first words from each line of a common hymn in the middle ages and was devised by a Benedictine monk named Guido d’Arezzo. Do Re Mi is still used in much of Europe but in other places (England) a letter system started to be used. Later when Pianos (actually harpsichords and similar) were invented and a need for a more complex scale arose, the conversion didn't work quite so well so Do became 'C' instead of 'A' as was intended. The reason for the b and # symbols are also tied up in this, specifically the need to add a note below B was marked as b. The stylised '♭' then became the standard notation for a any note a semitone below another. Our current western musical system is the result of smashing just and Pythagorean tunings together with mathematical ideals that gave some kind of universality. We've both lost and gained something in the last 1000 years, mostly in the last 150 years. We've lost some of the beauty of music but at the same time gained a universality that allows percussion instruments like the piano to sound good with stringed instruments and wind instruments. For the greatest part of human history, equal temperament (and sharps and flats) did not exist outside of a mathematicians fevered dreams.

@familyshare3724

Ай бұрын

@@Chrisamic the 12 note chromatic (not equal temperament) and various seven note scales (aka Church modes) was from and before Babylon. Nearly everything attributed to Pythagoras was influenced by or originated from Babylonian.

@prependedprepended6606

26 күн бұрын

@@Chrisamic You must be forgetting that before the Baroque, the lute was the primary instrument and by default, 12 EDO.

No 19 keys sample? Duh

@prependedprepended6606

26 күн бұрын

kzread.info/dash/bejne/i36AytKwXcTXkdI.html

Commenting to help the algorithm! Great video:)

Interesting this showed up on my feed. I've been looking at n-TET recently and if your goals include equal-interval steps, a perfect octave, a perfect fifth within 5 cents of 3/2 and a major third within 15 cents of 5/4, it's gotta be 12. 17 has no major third, 19 has a wonky fifth, and while 41 and 53 are really close to pure they require too much complication to build an instrument. Consider an equal tuning system based on the perfect twelfth. Consider eight steps at 237.744 cents. That is an interesting tuning. You can almost get an octave.

Underrated channel!

Someone has to make a 53-key per-octave piano now for the memes.

@Roxor128

20 күн бұрын

Would be trivial to do in software. At least for the synthesis code. The UI, however, uh, doesn't sound fun.

How does this only have 2k views? This is crazy good quality

Videos to my taste not only teach difficult concepts. They also spark an equally interesting and deepening discussion in the comments. This video definitely fits the bill!

@PocinTheTech

25 күн бұрын

Thank you! I am incredibly happy with the comment section, there are so many smart people around here. When I started this project my friends told me that internet-humans will be mean, but everyone is so nice and helpful!

THANKS FOR USING MY PROFILE PIC IN THE THUMBNAIL ❤ I actually make 15-TET music by the way. For all of you in the comments who are ostensibly curious.

Now I would have loved to hear how a 19-TET would sound like

good video. as a sidenote, the prioritization of the intervals mentioned here is not at all universal. different cultures have prioritized different intervals in their tuning systems; for example indonesian pelog is closest to 9EDO (equal divisions of the octave) and a lot of classical chinese music used something similar to 5EDO. Traditional Georgian music doesn't even subdivide the octave, instead preferring to subdivide the fifth. more modern musicians have been more experimental with tunings, calling their music "xenharmonic" or "microtonal". for example check out (and really do, these people make awesome music) Sevish, benyamind, Xotla Music, E8 Heterotic, Zhea Erose, and others.

@PocinTheTech

Ай бұрын

Thank you for your feedback! I am aware that this is a highly western point of view. I really should have made this more clear. It is even highly debated if whole number ratios are actually liked by people by default, or if we got trained to like them, simply due to the constant exposure. Currently some surveys suggest that people like 12tet more than ji, which would give that argument even more validity.

@angelicamartacahyaningtyas9083

Ай бұрын

Human hearing actually prefers JI due to its simplicity and strong consonance. Any EDO is just practical approach to approximate JI in constructing musical instruments. For western music consist of mostly aerophone and bowed string that have harmonic partials, 12 EDO is the logical choice due to its P4 and P5. For Indonesian gamelan, the backbone of the ensemble is a group of bell-like metallophone with large surface area. They resonate differently compared to wind or string. Gamelan's partials are inharmonic. So, gamelan maker will tune the instrument to any partials present (close to 9EDO for pelog mode and 5EDO for slendro mode). The choice of what EDO chosen is dictated by how the instrument work and resonate.

wow that was really good, u should have more views

really cool video. you should make a follow up making music with the new keyboard layouts

This was an insta-sub.

This is the first explanation of this topic I've seen that makes any sense.

53 is the best we could understand.

Never seen this argument presented in such an interesting way, awesome video.

Thank you for the video. Excuse me if this question isn't relevant, but how and when did people measure the cycles / second of the frequencies? I can't think of a way of deriving the actual numbers in Hz before the early 20th century and the invention of oscilloscope devices.

@PocinTheTech

18 күн бұрын

There are no irrelevant questions ^^ and funnily enough I may know an answer. At least a few hundred years earlier the "Savart wheel" was used to calculate the frequency of a pitch. Simply speaking, they spun a wheel with a more or less well known frequency (by using gears/rims for translation), notched the wheel at constant intervals and held something like a card against it, wich produced a tone. I think this was the first western experiment to show the relation between frequency and pitch.

Yes.

I like middle-C = 256Hz, as then everything is a power of 2! :)

Hmm - why do piano tuners stretch octaves?

@PocinTheTech

28 күн бұрын

That's a very good question! (and a very complicated answer) Pianos are no simple sine waves, but every tone is made of many individual sines, that give the piano its characteristic timbre (they are called harmonics). The problem with (real) pianos is now, that those harmonics start to clash and people tried to find a middle ground between best octaves and best matching of the harmonics. (funnily enough, i am already working on a video on timbre, it may take a bit of time tho ^^)

@mumiemonstret

25 күн бұрын

@@PocinTheTech And they clash because of inharmonicity due to the strings not being ideal. So the "harmonics" aren't the perfect ratios of the base frequency they are supposed to. I guess this is mainly a problem for pianos because they have such a wide range, but there are "sweet tunings" for e.g. guitars too.

@DerekHasted

24 күн бұрын

Because the human ear isn't linear or logarithmic either, and that's something that gets forgotten in the pursuit of "neat mathematics".... The piano tuner stretches octaves so that the octaves sound in tune. Anything else and they don't, despite what analysis tries to tell you... Which is one good reason why analysis will never give the right answer...

Nice! Subscriber #45 o7

Mmmm math you can hear.

12:41 i still dont understand the black key placement, it doesn't look like a piano keyboard here i think. Also a very good video

@PocinTheTech

Ай бұрын

Probably you are thinking about C as the starting point, The red markers are for A tho!

@n45a_

Ай бұрын

@@PocinTheTech oh ok, ye i somehow missed that, i even drew it to compare, probably missed a lone or something

cool video, but quite a letdown. I was really hoping for a demonstration of 12tet.

@AySz88

Ай бұрын

I presume you mean 19? Twelve is what we have now (if you include the black keys).

19TET is good because it's 12TET plus an extra row of white keys. 53TET has 4 rows of white and 5 rows of black keys. Welcome to MOS.

12 is enough

so... how the fk did Bach and Mozart ever have instruments that were in tune in the 1700's?! XD

@8:10 You don't say anything about where the number 1200 came from. Yes, it's based on the division of the octave into 12 notes, but that makes your math circular reasoning - It's 12 notes because it's 12 notes (1200 cents).

@RipleySawzen

18 күн бұрын

The end result is the same either way. Choosing 600 would just make all the numbers half the size, choosing 2400 would double all the numbers. So there's no circular logic here.

@chrisw1462

18 күн бұрын

@@RipleySawzen And choosing 600 would be just as arbitrary as 1200. Where did the number come from?

@PocinTheTech

18 күн бұрын

@@chrisw1462 the number comes, as you rightly said, from the 12 notes. because this way we have 100cents per note. But thats just a matter of convenience. You could use 1 instead of 1200 and consider every step as a percentage of an octave. The 1200 has no impact on the reasoning, it is just used, because it makes it easy to calculate with 12 notes. And since this is the standard definition for cents, which is used for every tuning system nowadays, even if they don't have 12 notes, I didn't want to overcomplicate it by introducing my own "cent-system".

@RipleySawzen

16 күн бұрын

​@@chrisw1462 You have the logic backwards. The number of cents doesn't matter. What matters is how out of tune each note is. 12 makes the most sense. It has nothing to do with the number 1200. Honestly should have left that part out of the video and just used 100%.

omfg why

The main problem is that no factor of two equals any of three, or five. Even God can't change that, if She is logical. Tough oats.

"Don't worry about this formula, its just a simple way to describe...." Simple? Simple? Simple!!!! Argh!!!!!!!!!!!!!! [Bangs head against table!]

Hello! I can tell you know a lot about the technical side of music and youtube sorely needs content like yours but I think you may be doing some things that are harming your new channel. The main thing is that the background music is too loud detracting from your voice which is already a bit harder to understand due to your accent. The visuals from manim and your desk are great, looks very pro! Keep up the good work!

@cemmy410

Ай бұрын

I didn't have any trouble hearing the voiceover over the music, but there are full subtitles for anyone who did. And I don't think the accent is a problem, either. I'd much rather hear an accent than an AI voiceover or something.

@PocinTheTech

Ай бұрын

thank you for your feedback! I can truly understand where you are coming from, I will try to find a better middle ground for the next videos ^^

@sedektime4076

Ай бұрын

No problem with audio and accent... If an Italian like me can understand him perfectly, I think anyone else can 😂. So... Keep it on! Let's goo🔥

Ungezeitlichtnichtsgebar!

hrry partc. just intonation. 51 notes per octave. mmmm.

@PocinTheTech

Ай бұрын

yeah, Partch was a genius. I was not aware of his 51 tone just intonation works, but I could imagine it without a doubt.

@RememberGodHolyBible

Ай бұрын

@@PocinTheTech Parch was very euill and no genius. His muſicke was quite vile as was his philoſophie around muſicke ſummed vp as muſicke being about man, rather than how it ſhould be, which is about God. Partch was a Sataniſt, a ſodomite, and one that was highly eſteemed by the woꝛld. All things that are telltale ſigns to auoid that perſon, oꝛ at leaſt auoid learning their ways and ſeeking counſel from them. A good amount of notes per octaue is 53 and tuning in Pythagoꝛean tuning. 53 is good becauſe there at the end of the chain of fifths Ebbbb is enharmonic to Gxx, it being leſſe than 4 cents off. But hauing 93 notes is good becauſe vnleſſe one intendeth to "circle around" the chain of fifths, one can keep going paſt the 53 point and remain perfectly in tune, But if one would like to leap ouer that tiny comma between Gxx and Ebbbb, one can do that as well with a fairly imperceptible and momentary ſhift in the purity of the interuals. I deueloped a 93 note layout with ergonomics as good if not better than a ſtandard piano layout, it hath all the sextuple ſharps and flats and one ſeptuple ſharp and one ſeptuple flat, Playing in tune is very very impoꝛtant & poſſible. And one ſhould not be as the woꝛld and default to compꝛomiſe, it only hurteth eueryone to do this. There are SO many videos on KZread ſpꝛeading miſinfoꝛmation about pꝛoper intonation, and people eat it vp and giue pꝛaiſes in the comments of theſe videos, becauſe the people know not any better and high pꝛoduction value of a video goeth a long way in conuincing people of a thing. I was taught wꝛong, we all were if we had any kind of muſicke education. True intonation is Pythagoꝛean tuning with the notes and choꝛds coꝛrectly ſpelled. It is poſſible and practical to play muſicke this way, euen with great and farre modulations. Muſicians ſhould be encouraged to ſeek out that which is good, not encouraged into complacency with the compꝛomiſes handed to them by the woꝛld.

Don't give me more notes ! I'm having enough trouble with the original 12 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

123 Subs + Me = 124!

This is really lovely. I've noticed how weird tuning can get when I wrote a song that somehow always seemed horribly out of tune, until I figured out that some note combinations are just more out of whack than others. When I wrote the song, I was playing on a cheap guitar that I tuned by listening to the resonance. It was also not tuned with the a on 440Hz but somewhat lower, almost half a note, which is how I usually start out writing songs, and my voice can then easily find resonance with the guitar, inspiring the songs. Then, when I want to record a song, I want everything nice and tidy for other instruments and I tune to 440hZ, sing a little higher, and that's fine because I'm warmed up instead of lazily singing some nonsense into the ceiling of the bedroom or the shower curtain in front of the toilet, and usually I just get the other instruments to create a nice harmony that I will sing into. But when you start in A minor you already start out with some janky ass shit, and I love it, but it is janky. Then to D minor and via G back to A minor. And no matter how you tune it, 2nd, 3rd, 4th, and 5th notes in those chords, which I use for the melody are just enough off to make it sound bad. We tried to use autotune to correct it, and it made it worse. That's how we found out there are some notes ratios (that I cant name off the top of my head but I know it when I sing them) that I have to deliberately sing higher or lower to make them sound in tune.

I used to think Just Temperament would sound great, but as Mark Chirnside demonstrated with suitably programmed keyboards, JT can sound sickly sweet and gross compared to ET for the same piece. To me, the JT version of the piece he played was the aural equivalent of eating the Wombles orange (pith) flavoured toothpaste mixed with an LD50 of saccharine.

Wonderful presentation. And unfortunately, perfectly in tune is now just a matter of…software. Ugh.

no need for the gesturbating. the hand dramatization is awkwardly artificial and distracting.🔺

The 12 tone system is really QUITE quite sufficient -

That's quite an 18th / 19th century question. Since the 20th century ... all that vibrates is music. Examples: kzread.info/dash/bejne/gHZ6mbOQnba1e9I.html kzread.info/dash/bejne/aWWcsM6Yo866irQ.html kzread.info/dash/bejne/c4uKt9JqYru2oLg.html kzread.info/dash/bejne/ommimauDm86tgKQ.html Behind these sad eyes lives a quite contented brain.

Oh, this is really good. Subscriber #14 reporting for duty 🫡