User talk:SAKryukov

Introductions

Hello there! I have to wonder what brings a physicist like you to microtonality... --Aura (talk) 07:57, 24 November 2020 (UTC)

Hello Aura! — SA:

I'm not sure I'm answering in a technically correct way, please help me if I don't. To answer your question: will you take a look at my articles referenced on my page? For example, I can explain how tonal systems work and what part of musical perception is poorly natural, and what part is cultural. I invented some microtonal musical instruments with some exceptional properties. You can try to play them right on your browser, and, if you have a touchscreen, with ten fingers...

I'll first take a look at your Wiki page gladly answer if you have any questions...

Hm... I can't seem to find the articles anymore... --Aura (talk) 15:15, 24 November 2020 (UTC)

What articles? — SA

On the my page I referenced, there are three articles, under «Original publications», and historically first one under «See also» (this first one is not microtonal, but theoretical things are mostly there)...

Here:

Musical Study with Isomorphic Computer Keyboard

Microtonal Music Study with Chromatic Lattice Keyboard

Sound Builder, Web Audio Synthesizer

Can you click and see them?

Okay, I see them now... For the record, I'm trying to work with 159edo, and it would be great if we could devise a way to play with that in actual performance- e.g. different preset tunings for individual notes that can be changed on the fly by a push of two buttons that modify the pitch of any given note by one step of 159edo- and yes, I'm actually trying to write a song that uses an approximation of 159edo. --Aura (talk) 15:30, 24 November 2020 (UTC)

The reason I like 159edo so much is that you have near-perfect approximations of both the 3-limit and the 11-limit. --Aura (talk) 15:35, 24 November 2020 (UTC)

Perhaps we can discuss it later. I consider N-limit systems as artificial (no the system with rational frequency ratio themselves — this is the natural fundamental of the harmony —, but the concept of the limit itself and selection of the intervals for the tonal system, I am presently trying some research in this direction. I already noticed 159-EDO on your page, hard to understand how it's possible to deal with such high-order system, compose and play :-)

I'm working with the prominent theorist and pedagogue Valeri Brainin, creator of "Brainin method", predictive method of music teaching, developing musical hearing understood as musical intellect. He is using my platform and some instruments. He just reported his work at the seminar he created, "Mastering of complicated interval structures by ear". The seminar is remote, he is using the capability we devised for remote work. They record sequences and send/receive across social media. The typical task of the method is to predict and continue (not to reproduce). A student receives the sequence, modify it by playing over it and sends back, and so on...

See Brainin page on this wiki, for links to his materials.

Well, all I have to say about dealings with 159edo- or any other large edo for that matter- is to consider all of the pitches as belonging to one of two classes "main" and "variant", and since I have a background in 24edo, I've started working with chains of 3/2 and 11/8. Yes, I'm very classical-minded in terms of my music theory, however, see my page on Diatonic scales for my particular approach to diatonic scales. For the record, I do think of the traditional seventh of Ionian mode as being in some sense the "Natural Seventh", as it occurs in the harmonic series as the 15th harmonic, and furthermore, when you take the 8th through 16th harmonics, you can remove the 14th harmonic and still have a heptatonic scale that demonstrates Rothenberg propriety, whereas removing the 15th harmonic instead doesn't give you such a scale. --Aura (talk) 16:12, 24 November 2020 (UTC)

Nice reference material on diatonic scales! Interestingly how EDO simplify things: for any 7-element diatonic system rendered as any EDO, it would be enough to describe only one mode, and then say: all other modes are derived by starting from the next element and then cycling through the remaining 6 sequential elements, and then shift by one until you get all 7 modern "natural" diatonic modes. It's remarkable that many musicians don't capture this simple idea from a school where they are taught each natural mode separately.

Thanks! I should point out that 159edo doesn't simplify things that much- only joining the Locrian and Lydian diatonic scales into modes of a single diatonic scale. Besides, when you actually look at the harmonic functions of the notes in the different diatonic "modes", you find that it actually does make sense to try and separate them due to their differing tuning proclivities. I still have to do some work on that page though. --Aura (talk) 16:33, 24 November 2020 (UTC)

Oh, yes, I already mentioned that I cannot even imagine dealing with such high number of microtones. I still have to figure out why it makes sense. (Any quick hints? :-) And yes, from the functional point of view, separate natural diatonic modes have distinctly different properties, so it totally makes sense to study those functions separately, absolutely.

As I said, in dealing with 159edo- or any other large edo for that matter- one of the most important things is to consider all of the pitches in the EDO as belonging to one of two classes "main" and "variant". As for why dealing in such large EDOs makes sense, I said on reddit that while some might think that the complexity of having so many intervals might negate the main advantage of an EDO- which is simplicity- tuning all of the intervals exactly is still a pain, and is ultimately unnecessary when you get to differences of 3.5 cents or less, as differences of 3.5 cents or less are virtually imperceptible to even highly trained listeners. Thus, one of the main draws for higher EDOs- at least for me- is a compromise between simplicity and accuracy. I should also mention as long as the EDO's step size is simultaneously above the average peak JND of human pitch perception, and small enough to be well within the margin of error between Just 5-limit intervals and their 12edo counterparts, you effectively end up with a decent balance between allowing the possibility of seamless modulation to keys that are not in the same series of fifths, and not having so many steps as to have individual steps blend completely into one another. --Aura (talk) 17:15, 24 November 2020 (UTC)

Have you even thought about usable N-EDO systems, why N>12 are always prime numbers (I don't want to consider something like 22-EDO (which is very special) or 24-EDO (which has nothing new at all))?! It resembles the problem of remarkable Ulam spiral, as far as I can see, it still doesn't have a theoretical explanation. Before finding any literature, I started from the algorithm for finding EDOs other than 12-EDO using different criteria of balanced approximating harmonic intervals, and immediately obtained those prime-number EDOs. I called the phenomenon "musical Ulam spiral". And I never found any publications trying to explain it.

I must point out that 24edo is one of the first to approximate both the primes 3 and 11 well, which is part of why it continues to be special to me. As for the rest of what you said here, I don't know what I can add to this. --Aura (talk) 17:19, 24 November 2020 (UTC)

I thought 24-EDO in principle cannot approximate anything harmonic what 12-EDO cannot. Do you think I miss something?

Yes. 24edo approximates 11/8 and 16/11 very well, and because of that, it does enable some interesting harmonic motions- for examples of some of these, listen to my piece "Folly of a Drunk" on my main user page and examine the score to see how this works. Also see this article on 24edo intervals. --Aura (talk) 19:02, 24 November 2020 (UTC)

I'm going to remove my reply message from your "talk" page as redundant and replace with the notice that you have a reply on my page...

Please call me "SA", this is my nick well known by many (from Сергей Александрович, Sergey Alexandrovich, given name + patronym, a Russian form of polite addressing, neither mentioning of a title, nor a family name). And, by the way, typographically correct rendering for "--" is "—", coded as "—" "entity"…" :-)

Right SA. Sorry, I didn't have the link to my page on diatonic scales right the first few times. It's finally corrected. --Aura (talk) 16:15, 24 November 2020 (UTC)

I'll keep reading your materials, I can see some interesting points. And if you find it possible to look through my articles, try to play the instruments (which does not require anything but following the links to the application in your browser) and give me some feedback, I'll be enormously grateful.

The first article requires a build on Windows, but 1) this is not so interesting, because it is not microtonal application, 2) this is just to download and build by one click. Not so interesting anyway, in the Web browser-based application (and Web Audio API) I support number of different EDO which can be changed on the fly.

I seem to have problems with these musical keyboards, because some of the keys on the keyboard that I press don't seem to play the notes in question. Also, I think the software should support more EDOs, such as 24edo and 53edo. On another note, some of the stuff dealing with technology seems to go over my head a little. --Aura (talk) 17:15, 24 November 2020 (UTC)

"Some of the keys?" It sounds troublesome. Do you mean pressing on keys on the computer keyboard (in my article, there is a detailed explanation why it cannot work perfectly on all keyboards), or on-screen keyboard? Could you provide exact problem report (at least for one particular case), starting from exact browser and system versions? — thank you very much.

I do mean pressing on keys on the computer keyboard. All I know is that when I press a key on the keyboard that represents something other than a letter or number, the corresponding note won't play. I don't know where to find the system and browser versions- I know that the system is Windows and the Browser is Google Chrome, but that's it. --Aura (talk) 19:02, 24 November 2020 (UTC)

Okay, SA, the operating system is Windows 10 Version 2004 (OS Build 19041.630), and the browser is Google Chrome 86.0.4240.198 (Official Build) (64-bit) (cohort: Stable). --Aura (talk) 21:36, 24 November 2020 (UTC)

Great! Thank you for this effort! All this is perfectly usable, and if you only have problems with a computer keyboard, I would not care too much, there can be different reasons. In particular, in my article, there is a section explaining that in most keyboard people save on circuitry, so if you try a chord, you cannot play many keys at the same time; this is nasty enough, so it would be the right thing not to consider this keyboard as a serious device for this purpose; real functionality is based on the on-screen keyboard and touchscreen or at least touchpad/mouse.

As to the sets of EDOs, I would need a balanced opinion from a number of users. Most of my users only use 29-EDO, due to the influence from Ogolevets and Brainin. However, adding EDOs is quite possible and even ""almost"" automatic. Anyway, I'll be working at something else for a while, next major release is on the plan, and I'm interested to advance my research on the possibilities of purely harmonic (hence, not equal-division) systems. Could you offer some rationale behind your suggestion of these particular EDOs?

The rationale behind adding 24edo is that this EDO is what most non-microtonalists (to my knowledge) think of when they think of microtonal music- I mean, I got my start with 24edo for a reason. The rationale behind adding 53edo is that this EDO approximates the 3 prime very well (the difference between a 53edo fifth and a just perfect fifth is virtually unnoticeable), and Mercator's comma- which is the amount by which 53 fifths exceed 31 octaves- is the smallest comma forming the difference between a chain of fifths and a chain of octaves until you reach higher EDOs with unreasonably small step sizes. --Aura (talk) 19:02, 24 November 2020 (UTC)

I understand. As to "most non-microtonalists", I also noticed the same thing — some naively thought of "quarter-tones" when you mention "microtonal", but don't see it as a valid argument for anything. One apparent reason of 24-EDO I can see is the melismas of Near/Middle East musical culture. I do appreciate this kind of music and enjoy it, but I think that for this culture, historically, 24-EDO is nothing but a very trivial adaptation of Western common-practice 12-EDO (division semitones into quarter-tones), and maybe more advanced tonal systems could better render the traditional intonation. As to your arguments of 11/8 and 16/11, perhaps I need to listen to "Folly of a Drunk", try to understand the function, and do some calculations. You see, when I said "Do you think I miss something?", I really meant I could miss something. When I started to discover and evaluate different microtonal systems, I mostly work by comparison with "just intonation" in a more narrow sense of this word, precisely this one, and later found the examples of interval relationships not found in this particular system. But this goes too deep in the nesting of the present document. Perhaps I'll add another header at the bottom, write a bit on what I think, and mention this on this line, in case you may want to comment...

For the record, I can already tell you that 11/8 has a function akin to a cross between that of 4/3 and that of 45/32, while 16/11 has a function akin to a cross between that of 64/45 and that of 3/2. Furthermore, both 11/8 and 16/11 are pretty important in modulating to keys that are not in the same series of fifths, and pitches related to the original tonic by these intervals are prime destinations for such modulations. You can expect to see more examples of such exploitation of 11/8 and 16/11 from me in my other songs- yes, even in my 159edo-based songs. --Aura (talk) 01:00, 25 November 2020 (UTC)

I must admit, with my wanna-be-rational approach I don't recognize well any concrete rational numbers by just looking at them :-) Well, unless numerator and denominator are very small numbers and the interval itself is well-known. :-) So, to understand something, I really need to calculate things, to draw and to listen to some sample structure — all of it at the same time. I already thought that I came close to the stage where I'll need to get myself another instrument, some toy which would visualize and, importantly, vocalize some sequences and chords. Only this way I can approach the understanding of the functions. Such an instrument could be very useful to many other people...

Ah. I do know that some of the functions of certain rational intervals- namely tritones- are determined where they fall in relation to the irrational half-octave interval. This is how I separate the Antitonic intervals into "sycophants" and "tyrants". The fact that I'm one of the relatively few composers who seems to have worked rather extensively with Locrian mode (to where I now have a half-decent idea as to how to use it) has undoubtedly shaped my perceptions of tritones in particular... From there, I was able to draw on the fact that both 11/8 and 16/11 have relatively small numerators and denominators (as expected of the early members of the harmonic series and subharmonic series), yet, at the same time seem to have high harmonic entropy like most tritones. --Aura (talk) 02:10, 25 November 2020 (UTC)

Aren't you mixing up something? hopefully just terminology? Tritone is strictly 1/2 of octave, that is, √2, apparently irrational number, not rational even in quotation marks. :-) I think tritone is very fundamental in modern and not-so-modern music, but it is much harder to explain, while rational ratio are apparently fundamental, and their role is on the surface. It's interesting how the concept of "correct" music changed with time. Until a certain time, even the seventh chord widely used these days were considered "disharmonious" and were banned, forget about the tritone... What you are righting looks very interesting though...

No. There are multiple rational intervals that are called tritones- see 45/32 and 64/45 for just two examples, or at least that's the case in English (I assume Russian has different names for intervals). That said, the specific √2/1 tritone- the half-octave, as I'm referring to it here- is definitely a special kind of tritione and is indeed very fundamental in both modern and not-so-modern music. --Aura (talk) 04:30, 25 November 2020 (UTC)

Perhaps I should start making more samples to demonstrate more of the kinds of structures where pitches related to the tonic by 11/8 and 16/11 prove to be very important. If you learn the way you say you do, then I suppose it's only fitting for you to have more of these kinds of samples, as I'm discovering that "Folly of a Drunk" only scratches the surface of what 11/8 and 16/11 are capable of. --Aura (talk) 02:21, 25 November 2020 (UTC)

Would be good. As I understand, one problem is the lack of notation. Recently, we worked with Braining exchanging the sequences produced by my keyboard, as in microtonal EDOs it was the only notation. I devised something roughly similar to MIDI for the exchange. Yes, I've read on some attempts to establish some generalized notation, but I don't think there is something good enough to accept it. Or do you address this problem?

So far, I'm assuming that the first task is to create a set of proper interval names- yes, we do need to build on the historical note names for purposes of making our concepts understandable, and for that, I'm taking inspiration from SHEFKHED interval names, and you can see some my work in dealing with quartertones on the Alpharabian tuning page. I would also recommend attempting to build off of conventional notation for the same reasons, and I do have ideas in the works for 159edo notation. Yes, judging from what I hear you saying, there's bound to be problems, but since the diatonic scale is fundamental on account of one version's close ties to the 3 prime, problems related to this are on some level unavoidable. --Aura (talk) 04:30, 25 November 2020 (UTC)

One other musicologist advised me to write a new section in the notation site (I don't have time now, if you are interested will find out a link), but I answered that I'm not much interested. First of all, this is not very productive work, a big waste of time. More importantly, I'm the one who clearly understands that the modern idea of notation itself is totally wrong, and it is related to the fact that musicians never had enough understanding of the concepts of abstraction, standards, and the like. There is only one layer between the graphically represented musical text and the instrument, and it is beyond any reason. Apparently, some nesting levels of abstraction are needed. Modern notation is usually considered to abstract out concrete instruments, but this is not true — in essence, this is still the same kind of tabs, tied to the piano, and not to abstract tonal system. I know that many musicians find it unbearable to hear such things, but I know it's true.

On one level, you are right, but if you trace the origin of the piano system far enough back, you see that the idea for the default group of seven notes goes back to the Romans, who misunderstood the direction of construction and the arrangement of note names when they tried to borrow it from the Ancient Greeks before them. Regardless of whether you are going through the Greeks, the Romans, or a combination of both, one must realize that the Greeks wanted to create a scale based on a chain of 3/2 just perfect fifths, with the resulting scale consisting of the intervals 1/1, 9/8, 81/64, 4/3, 3/2, 27/16, 243/128, and 2/1- today known as the Pythagorean Diatonic Scale. There's a reason that 3-prime-based just intonation is called "Pythagorean tuning" in English after all, and as you can see, there's a reason for the obsession with the diatonic scale. --Aura (talk) 04:30, 25 November 2020 (UTC)

For the record, if you're interested in advancing your research on Just Intonation, you might want to check out what I'm doing for Alpharabian tuning. --Aura (talk) 21:45, 24 November 2020 (UTC)

Most certainly, I'll try to understand this stuff. I already noticed this page, did not yet realize what it is about. If you don't mind, let me ask you if I have questions — thank you!

Indeed. I do know I need to do some work on this front. --Aura (talk) 00:53, 25 November 2020 (UTC)