User talk:SAKryukov

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Wiki discussion moved to User talk:SAKryukov/Wiki — SAMonday 2020 November 30, 01:54 UTC


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...

lp if you followed the l (??? — SA)

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)...
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)
Okay, I finally got myself some time to learn the material on your "Aura's Diatonic Scales" page, listen to the sample. Aha, now, I'm really getting into it.
It may sound trivial, but different interval sets for different modes resembles me my own idea on the microtonal instruments, before I started to work with EDOs. I imagined that the prospective instrument should have some control shifting from mode to mode on the fly. By this change, I meant that the keys should change their frequencies, but always get different rational-number (harmonic) intervals. (Of course, the idea is also limiting: for example, it is not suitable for the "atonal" music and similar less "classical" approaches) Now I'm close to final part of the EDO work, plan to make another release and started to dig into purely rational intervals, similar to your work. I'll try to analyze your scales. As I already mentioned, I need a tool to freely and quickly play with various structures ("play" in both senses of the word: quickly modify and visualize and play sounds), only then I can understand things. Anyway, thank you for the interesting information.
As to one of my microtonal instruments, one interesting property is that the change of EDOs is "locally conservative" to the fingering, can you see what I mean? In certain sense, it makes the change-tuning-on-the-fly approach not necessary, but I'm still not giving it up...
Even I think that the change-tuning-on-the-fly approach is still important- for both large EDOs like 159edo and for just systems. --Aura (talk) 07:11, 25 November 2020 (UTC)
Oh yes, it's a valid point. As to the "large EDOs", I was about to point out, even with that "locally conservative" to the fingering feature, too large EDO makes the system not very manageable; here is how it looks: say, diatonic fingering patterns are preserved, but their locations in different octaves on left and right become more and more distant. Apparently, the same physical space can take less and less of the tonal range. That's why I was about to ask: how can you practically deal even with 53-EDO, not only 159-EDO? Maybe you have some electronic method of entering data without actually playing on any instrument?
For the most part, I myself do indeed work with computers to make the sounds I'm after. As to potential real instruments I can think of for actually working with 53edo and 159edo, I'm pretty sure that trombones, violins, electronic synthesizers and similarly designed instruments are all capable of dealing in something approximating 53edo with a few technique adjustments, so perhaps you could look into instruments like those. Yes, you'd need a series of register keys for temporarily adjusting the tuning of individual strings- especially when dealing with 159edo- but still, perhaps there's a solution on this front. --Aura (talk) 16:06, 25 November 2020 (UTC)
Did I mention that there's such a thing as The Kite Guitar, invented by Kite Giedraitis, who goes by TallKite on this Wiki? --Aura (talk) 16:39, 25 November 2020 (UTC)
No, you did not mention, and I did not know this work, but I was familiar with a number of other microtonal guitars, unfortunately, did not have a change to play on it (I tried to play on a number of different exotic instruments, Indian, Brazilian, Chinese, the oud, even the theremin built by Termen (Leon Theremin) himself.)
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)
Than on what basis 45/32 or 64/45 could be called 3-tone anywhere? How widespread these terms could be and what would be the rationale behind the idea to use the same name for different things? I personally don't use something only because it is used in some books or it is taught in some school, I only can agree or disagree to use some terms on some more or less rational considerations...
I know that 45/32 can be considered a tritone- albeit one made up of two different types of whole tones, specifically, two instances of 9/8 and one instance of 10/9. As for 64/45- well, we can say it falls within an unnoticeable comma's distance from 729/512, which is a Pythagorean tritone consisting of three instances of 9/8. --Aura (talk) 05:55, 25 November 2020 (UTC)
Well thank you, you've answered the question the way I can clearly see the sense of it. But hardly much of practical sense — it only confirms by idea that musicians tend to name things in the most perverted (okay, we sometime call it "convoluted") ways :-).
I don't know about you, but it seems the main basis of labeling intervals ranging from 7/5 to 10/7 as "tritones" has everything to do with either being able to build such intervals with stacks of three whole tones (literal meaning), or, being really close to √2/1 (figurative meaning based on how √2/1 can be made from a stack of three whole tones in 12edo). --Aura (talk) 06:21, 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 Ancient Greeks, the Romans, or a combination of both, one must realize that the Ancient Greeks (or rather, some of the Ancient 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)
At the end of the day, it is because of the Pythagorean Diatonic Scale's connections to the 3 prime that I would recommend we use it as one of the things we build our notation system off of. It may be true that we need to extend this chain of Pythagorean fifths out to where we have a chain of twenty-six pitches related by 3/2 fifths on either side of the starting pitch, but still. For the record, I should also point out that the modern notation seems to have strong connections with the steps in the diatonic scale, and, given all the stuff I've already said about the Pythagorean Diatonic Scale in particular, well, I think I've managed to recover some of the real reasoning behind it. --Aura (talk) 05:13, 25 November 2020 (UTC)
Okay, it looks like I pretty much failed to conduct the idea. I have to think before I could try again...
Maybe you did. I'm not saying there aren't flaws in the current system, but we do need to at least recover the logic behind the modern system and work from there. --Aura (talk) 05:55, 25 November 2020 (UTC)
There's one other thing you need to know... I can and will push back at times, especially if I think there's pieces of the puzzle you're missing. --Aura (talk) 06:21, 25 November 2020 (UTC)
Is it supposed to sound negative? What's wrong with pushing back? I think people should assume such things in the very beginning. Thank you anyway. As to me, I have tons of patience and can be very boring, especially if I'm trying to insist on some point. If I feel somebody miss some pieces, I try to give a person more and more chances by pointing out the missing piece again and again. And after all, I learn a lot from people.
Good to know. At any rate, we need to create a new section to continue our conversations...
If we do, I'll create another section soon on one topic I'm interested in. By the way, I just looked at your "Folly of a Drunk" score and found that you are using not the standardized Stockhausen accidentals (which looks very ugly and poorly readable to me) for 24-EDO, but something else, probably those dots, or what? Is it a widely used notation? Of course, some notation for this particular EDO would not be a big problem with the ad hoc approach, but the entire idea of the approach would not pass for the general microtonal purposes.
If you are talking about the dots above or below the noteheads, they indicate staccato. If you mean the dots behind the noteheads (or rests), they serve to increase the duration of the note (or rest) by half of the written value. --Xenwolf (talk) 08:45, 25 November 2020 (UTC)
Then it's like in common-practice notation. But then I don't understand: where are your quarter-tones, if this is 24-EDO? Or are they somehow implied?
Pay attention to HeQu1.svg (+50¢), HeQd1.svg (-50¢), and HeQu3.svg (+150¢), maybe there is also somewhere a hidden HeQd3.svg (-150¢) but I didn't find it yet. --Xenwolf (talk) 09:07, 25 November 2020 (UTC)
Ha! Even though I expected some signs like those, and even after I've read your note, I failed to find them after several attempts :-)
But why are you using SVGs? There are just normal characters, you could just find, copy and paste them.If it confuses you, I'll bring them to you, could be useful.
The symbols may be contained in some fonts, but as far as I found out not all are supported by Unicode. If you have new information about this, please let me know! --Xenwolf (talk) 09:40, 25 November 2020 (UTC)
Xenwolf, Unfortunately, you are right — these symbols are not on the standards. (As to "some fonts", in practice, it doesn't work as you say: for the fonts of wide character repertoire in general, Unicode is maintained as font-independent: the font will render what you need. Nothing prevents you from having an out-of-standard font, but such fonts cannot be used in public interchange. However there are very few well-known fonts of this kind, like Webdings, Wingdings, still not a good choice.)
I know that I can read the PDF files because my computer has Musescore 3, and thus, it supports all of the associated fonts, I mean, Musescore is the program I used to write "Folly of a Drunk" in the first place. --Aura (talk) 16:35, 25 November 2020 (UTC)
Indeed. Safe to say all of us here on the Xenharmonic Wiki need to know about these kinds of problems. --Aura (talk) 16:06, 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)

Folly of a Drunk

Have you had a chance to listen to "Folly of a Drunk" yet? --Aura (talk) 06:50, 25 November 2020 (UTC)

Yes! Very interesting!
I'm glad you think so! --Aura (talk) 16:06, 25 November 2020 (UTC)

Aura's Diatonic Scales

Look, by this time I've read your "Aura's Diatonic Scales" thoroughly enough and almost realized how those scales and modes work.

(Do you know the exact linguistic term for your manner of naming in the section "Definitions of Scale Degree Name"? Macaronic language. :-)

Okay, but, as I say, to feel how everything works functionally, I really need to visualize and play using these scales, and I realized it could be just about a couple of working days to re-work it into the playing instrument, based on my existing platform.

That's good to know. --Aura (talk) 16:06, 25 November 2020 (UTC)

So, let's say your advice to pay attention to your work was convincing enough. For a while, I'll set aside part of my research as your scales could be a better starting point for a real instrument, to say the least.

What do you mean here? --Aura (talk) 16:06, 25 November 2020 (UTC)
It's a long story, my research, but I developed certain things like algebra of rational numbers (not so trivial thing as it may seem) and sets of intervals and started to play with different tone systems and realized I need to visualize it and make it sound, but still thinking about what I want to get. But then I realized that I should better first implement you set of diatonic scales and modes as you describe it on your page. I think I got a very good idea on the keyboard layout and some features and understanding.
Maybe, but if you want more, as you seem to say, we need to cover more of the modes I know. --Aura (talk) 17:02, 25 November 2020 (UTC)
For example, let me ask you: can you, for example, having a simple composition, introduce a harmonic modulation by moving from one scale to another in the same piece? I think it is possible. Anyway, it's easier to implement and show than to explain. :-)
Yes, it is possible. However, don't be surprised if I also throw in modulation by 11/8 or 16/11- seriously, I like these two intervals for modulation to keys that are not in the same series of fifths... --Aura (talk) 17:02, 25 November 2020 (UTC)
I actually want something more than a set of diatonic scales, but it maybe early to discuss it now.
Depends. I can also deal in Melodic Minor modes (think of the base mode as being like Major only with a flat third), Harmonic Minor modes, Harmonic Major modes and Neapolitan Modes to some extent. Furthermore, I do know a few things about Overtonal Acoustic modes (the base mode consists of the intervals 1/1, 9/8, 5/4, 11/8, 3/2, 13/8, 15/8, and 2/1), and Undertonal Acoustic modes (the base mode consists of the intervals 1/1, 16/15, 16/13, 4/3, 16/11, 8/5, 16/9, and 2/1), as well as the Neutral Paradiatonic Modes. I can think of two other sets of proper modes with supermajor and subminor chords, but I currently can't think of a good name for them at the moment... --Aura (talk) 17:02, 25 November 2020 (UTC)
By the way, are you familiar with Harry Partch "tonality diamond" approach ("otonality", "utonality") and his instruments? If you are, do you have your opinion on this matter? I once found it interesting but a closer look made me very skeptical about it.
Harry Partch's work on the idea of Otonality and Utonality has actually been an influence for me, but so too has the work of Hugo Riemann. I don't know what to say about Partch's work on the tonality diamond and his instruments, however, I do disagree with his choices in terms of preferred EDO from the sounds of things. --Aura (talk) 17:02, 25 November 2020 (UTC)
Sure. Thank you for your answer and opinion. And I do have some reasons to be skeptical about the diamond approach, but I also see the difficulties in the approaches to the construction of alternative rational ("harmonic", "just") systems. At the same time, the diatonic scales seem to be limiting to some near-classical structures; and there are many works beyond that.
It's true that the diatonic scales are limiting by themselves, which is why I'm learning to deal with the other types of modes I've mentioned. Yes, I have a very strong preference for tonal music, but that doesn't stop me from pushing the boundaries in other areas- especially the idea of treble-down tonality... --Aura (talk) 17:40, 25 November 2020 (UTC)
I think I perfectly understand. I also have strong preference for tonal music and something very close to classics (and I know microtonal field mostly theoretically and more from the fundamental and formal side of it, very little about music itself) but feel a strong appeal to pushing the boundaries.
I'm curious... What is it about my diatonic scale system that appeals to you? It's true that in addition to the diatonic scales, we need to cover the other scales I've mentioned, but still... --Aura (talk) 19:31, 25 November 2020 (UTC)
First of all, the way you put it reminds me of my old tune-on-the-fly idea and inspired another idea of approaching from a different side. This is related to the problem of the impossibility of transpositions and harmonic modulation (using traditional fixed-tune instrument) with just intonation, that is, the traditional instrument should be re-tuned to play with a different scale. Now, as I already design non-sequential keyboards, instead of re-tune I can simply create a keyboard where all 7 scales are presented at the same time in rows. Another idea would be to assign the individual transposition values to each row (representing one of 7 scales), which also should be shifted on the fly. Now (as I already asked you), here is my question for you: do you agree that it is possible to combine several fragments of musical motion with different scales in one piece of music? If you agree, we could practically overcome the barrier: we could have the instrument playing purely harmonic intervals "locally", and, at the same time, capable of harmonic modulation and other motion beyond the usual just-intonation scope. What do you think?
Judging from the way you worded the question the first time, I'd have to say yes, and that it's relatively easy as long as we keep the same Tonic pitch. I'll see if I can write some examples for you some time today. However, changing the Tonic pitch is another story, and this will require some more advanced thinking. --Aura (talk) 20:55, 25 November 2020 (UTC)
I also wanted to ask you: how original is your design of diatonic scales? Apparently, special-case mixolydian fully matches known just intonation, it has to, but other scales have different sets of ratio. What part of it you personally designed or invented?
I'd wager that it's not all that original- I mean, the elements were all there before I came along... My preference for 27/16 over of the more common 5/3 as the interval between the Tonic and the Major Sixth scale degree is one of the hallmarks of my style, however, I must point out that I've encountered other microtonalists on reddit who have made mention of the usage of 27/16 in place of 5/3, and that this same sort of thing is sometimes seen in Indian music. Perhaps more unexpected is my preference for 77/64 over of the more common 6/5 as the interval between the Tonic and the Minor Third scale degree, and this relates back to my liking of 11/8, 16/11, 7/4, 8/7, 55/32 and 64/55 as accidentals, as well as the additional use of 11/8 and 16/11 as a basis for modulation. Aside from that, the only thing I can think of that sets my style apart is that unlike a number of microtonalists, I work with a fixed set of pitches and pitch intervals for any given key and mode unless I deliberately try to either use an accidental or modulate. --Aura (talk) 20:55, 25 November 2020 (UTC)
Oh, no doubt. I mean the overall design of the entire system. No one would question if you invented the intervals themselves. I only mean the design of the set, if you've chosen a specific interval set for some of the scales to implement certain function of each degree. I do realize that some scales, by the very approach you use, are just bound to be well-known, and some other ones might be well-known in most of the degrees. Would it be safe to say that the overall design and the decision is your original?
In that case, the only things that might possibly be anything close to original about the design of the set is the use of 77/64 as the minor third above the Tonic in place of 6/5 in order to foster better connectivity between the Tonic and the Minor Third scale degree, and, the deliberate usage of the 40/27 interval between the Major Sixth and the Major Third scale degree above it in order to create a subtle bit of tension in the music and bring out the Contramediant function of the Major Sixth scale degree. --Aura (talk) 21:49, 25 November 2020 (UTC)
Okay, this is fine by me. This is why I was asking: when I start to develop another instrument application, would it be more appropriate to call it something like "Aura Microtonal Diatonic Keyboard" (or based on your real name), or it has to be something else? Please advise. Note that this is open-source development, so, for example, the file names appear to all the public at a very early stage of the development. — SA, 22:23, 25 November 2020 (UTC)
To be frank, it would be better for the instrument name to not reference me, as I don't want to accidentally claim credit for something that's not completely original. Given the selection of pitches we want for this keyboard (which I mention below), we probably need to come up with a name for this keyboard based on the properties of those intervals- something like "Connectivity Microtonal Keyboard" would suffice, since we want more than just the diatonic scales. --Aura (talk) 22:53, 25 November 2020 (UTC)
This is also perfectly fine. It won't prevent me from crediting your work in an article and/or the product credits (unless we decide to get in some collaboration to do some joint work). But then, why "Connectivity" and why not "Diatonic"? Here is the thing: "we want" is not a sufficient reason, the work should not claim any more than it actually does. At this stage, it has to be bound to "microtonal diatonic". If it goes beyond that, there are legitimate ways to reflect this fact: 1) re-naming of the product or just some title information, 2) adding new product or a component... SA, 23:01, 25 November 2020 (UTC)
With the name "Connectivity", I'm trying to say something specific about the nature of the pitch selection- namely referencing the fact that each pitch class on the keyboard belongs to either the Overtone Series or the Undertone Series of the Tonic, which is a property I call "connectivity". Also, I'm hoping there would actually be additional components on the keyboard so that we can play more than just the intervals from my diatonic scales which we are using as the starting point. I mean, out of the selection of pitches for the keyboard that I proposed below, 33/32, 35/32, 8/7, 64/55, 39/32, 16/13, 128/99, 11/8, 16/11, 99/64, 13/8, 64/39, 55/32, 7/4, 64/35 and 64/33 are not actually diatonic intervals at all; instead, they are what I call "paradiatonic" intervals- microtonal intervals that are good for playing alongside the diatonic intervals but which have their own distinct functions and properties relative to Tonic. --Aura (talk) 23:24, 25 November 2020 (UTC)
I'm sure that "Connectivity" will be not understood by most users. Paradoxically, using the word "Paradiatonic" is pretty good for the use in a name/title. I can explain it. I assume people playing on such exotic instruments usually know both "para-" and "diatonic", so they will read the entire word. It's not a problem that the entire word is totally unknown, it can only boost curiosity. Some well-known word like "connectivity" implies very many meanings, and this is what can puzzle people and can be perceived as faceless. (Why did you mention 7/4? You don't have it in your scales on this page. This is one of the intervals I really want to have, in some, well, totally non-diatonic systems.) Anyway, thank you for another idea. I would greatly appreciate some more.
I get it now... I'm glad you like the term "Paradiatonic" though. As to why I mentioned 7/4 and the other paradiatonic intervals... well, they are not diatonic intervals- which is why they were not included on the scales page- but they still have potential for use as borrowed intervals (extra intervals that are not native to your key signature) and for modulation purposes. The 7/4 interval in particular does happen to occur in the sets of proper modes with supermajor and subminor chords I mentioned earlier- you know, the ones that I'm having a hard time finding good names for at the moment. --Aura (talk) 23:58, 25 November 2020 (UTC)
Great, "7/4 and the other paradiatonic intervals... not diatonic intervals" — whatever it is, what tonal system did you mean? Or, rather, can you suggest any rational/harmonic (non-equal-division) tonal system which extends or replaces diatonic or set of diatonic systems, is not based on the "tonality diamond", is well-rounded and self-sufficient, interesting, with good potential?..
At a certain point, I don't think you can totally replace the diatonic scales at a certain point- namely because of their connections to the 3 prime- but you can definitely extend it to a paradiatonic system like the one I proposed using the intervals 1/1, 33/32, 256/243, 16/15, 35/32, 9/8, 8/7, 64/55, 32/27, 77/64, 39/32, 16/13, 5/4, 81/64, 128/99, 4/3, 11/8, 45/32, 64/45, 16/11, 3/2, 99/64, 128/81, 8/5, 13/8, 64/39, 128/77, 27/16, 55/32, 7/4, 16/9, 64/35, 15/8, 243/128, 64/33, and 2/1. It can be extended further, but I'm pretty sure that extending it as far as I would want to go with it would make things really hard without eventually having to temper out commas. Truth be told, I don't base my work entirely on the tonality diamond when I do my work within any given key- at least not to my knowledge.
Basically agree, but by "replacing" I rather mean not every thinkable replacement, but rather something like a (possibly modified) superset of each scale. And I do remember that you mentioned that the work of Harry Partch influenced you, so I think I understood you correctly and never implied that any of your work would be based on the tonality diamond; this is not the same thing. SA, 02:45, 26 November 2020 (UTC)
Ah. That makes sense. --Aura (talk) 02:43, 26 November 2020 (UTC)
Don't you think that some musical ideas did not see proper consideration simply because the creation of the musical instrument just for experimental purposes could not be considered as feasible? But I have in my hands the technology which makes it easy to design a brand new instrument rendering any thinkable tonal systems or the set of them, modify any thinkable properties on the fly, even during playing, developed in an exclusively short time frame, so good amount of experimenting can be done quickly without much regret for the process of the instrument crafting, as its design can be easily thrown out or modified?
It may be true that some musical ideas did not see proper consideration for the reasons you're saying. However, I don't seem to understand why you replied to me quite the way you did... --Aura (talk) 02:23, 26 November 2020 (UTC)
What exactly is unclear? Perhaps you don't see how this topic is related to your post I replied to... If so, I can answer: I put this argument to explain why I'm asking you for some suggestions on those rational tonal systems. I'm trying to probe if you could be interested in approaching things using my method, which is instrumental. I can imagine that some musicians are quite able to play or compose complicated pieces right in their head, so they don't even need any instrument, but for the rest of us vocalizing, visualizing and the live touch of a real instrument is important. I know when a new instrument is invented, it often sparks new ideas in the compositions. Does it tell you something? SA, 02:45, 26 November 2020 (UTC)
Yeah, I definitely didn't see the connection at first. It also sounds like English is not your first language, so I can't help but wonder if that is impacting our communication in some ways. I can definitely see the merits in working with instruments, but at the same time, I also have to do work on the other front with my current approach. I would still like to try and find a way to make 159edo playable on an instrument- although this would undoubtedly take a lot of work- as 159edo seems to be the EDO that tempers out all the the commas I'm looking to temper out and then some, all while representing the 2.3.11 subgroup quite well. Don't get me wrong, though I'm still interested in all the work on JI. --Aura (talk) 02:57, 26 November 2020 (UTC)
For the record, if I extended the just intonation subgroup as far as I wanted to, I would end up with pitches that are only like 7-8 cents apart, and since the step size of 159edo is in this area. Trust me, I'm not exactly what you call a "minimalist". --Aura (talk) 03:12, 26 November 2020 (UTC)
No, nothing wrong. What you're doing seems interesting to me. Maybe I'm getting to the idea of having things like 159-EDO playable, but not likely sooner than I have some other pieces in place. Perhaps I wrote to you too much, as in this case, it would be easier to do the job first. In all cases, I would be interested to hear your opinion. By the way, I clearly understand that I have some "writing accent", but am curious which part of my expressions makes things unclear to you? Really curious, because I'm in the US now, and I know that English-speaking people are so insensitive to the imperfection in the language, as opposed to Russians (many say, also French people) who are just crazy about different cultural peculiarities or mistakes in the Russian language. In all the huge territory of Russia, there are some local variations of the language, but they are very minor. Nevertheless, if you visit a rural area, and local people hear that you pronounce a couple of words in a different way, they may make fun of you... if they know you're Russian, of course. And it somehow combines with the extreme complexity of our language...
I can understand waiting on 159edo, I mean, we would have to establish the main pitches first after all- especially through just intonation- and we would definitely need to get a good handle on both 24edo and 53edo, as both of those EDOs- or rather, the just intervals that are approximated by the steps of those EDOs- play a huge role in shaping how 159edo functions as a whole... As to which parts of your writing accent impact our communication, one thing I can be sure of is idioms. There's also the strange usages of certain pronouns like "it" and "he" and "she" at times- I'd have to go over the whole conversation again just to pick out certain examples, but still. Believe it or not, I find some things about the modern generational "slang" in American English to be a bit confusing and even grating at times, but that's another matter for another conversation. --Aura (talk) 03:46, 26 November 2020 (UTC)
For your information, I'm much less of an idea generator and much more of a one who discovers ideas brought by other people. It happened many times when some person could not realize the value of her/his own idea and I was the one to discover it. :-) SA, 23:48, 25 November 2020 (UTC)
But first of all, I am interested to know if you agree with my statement that you can mix fragments with different scales in one music piece? Sorry in this concern looks either too trivial to you, or not clear.
It doesn't look too trivial to me at all, and yes, I have tried to answer this question before. In fact, I'm actually now trying to write a music piece that utilizes different sections with different tonalities (I think that's what you call them)- you, know, I'm talking about a piece with one section in B Dorian and another section in B Locrian. --Aura (talk) 21:49, 25 November 2020 (UTC)
Okay, this is quite enough for me for now, and sorry if I failed to figure the answer before. Here is my idea: I'm thinking about solving the more difficult problem of playing the instrument, yes, of a multi-tonal piece right at the level of the instrument. Instead of tune-on-the-fly, I could implement a light weight version of it more feasible for the performer. Let's say, for simplicity, you are preparing to play a piece with the harmonic modulations using only two tonalities. Then you use two keyboard rows, one implementing one of your scales, another — another one, and you can also transpose one or both of them to your convenience. At the moment of the modulation, the performer simply shifts fingering to another row. Think of it as a multi-manual organ, only with individual tuning on each manual... In this simple case, you don't switch anything during the performance, you adjust something before you play. What would you say about this idea? — SA, 22:14, 25 November 2020 (UTC)
It's a start, but this would only be fitting when you're changing Tonics, after all, B Dorian and B Locrian use the same Tonic, which is B-Natural. Since this is the case, we could have each octave of each keyboard have access to pitches relating to the Tonic by the following intervals: 1/1, 33/32, 256/243, 16/15, 35/32, 9/8, 8/7, 64/55, 32/27, 77/64, 39/32, 16/13, 5/4, 81/64, 128/99, 4/3, 11/8, 45/32, 64/45, 16/11, 3/2, 99/64, 128/81, 8/5, 13/8, 64/39, 128/77, 27/16, 55/32, 7/4, 16/9, 64/35, 15/8, 243/128, 64/33, and finally, 2/1. This is perhaps the best pitch selection I can think of for the kinds of things I would try. --Aura (talk) 22:53, 25 November 2020 (UTC)

Unnoticeable Commas

Hey SA, in all your work on Just intonation, have you ever thought about the small little commas that people virtually can't hear? Since I've been on this wiki, I've been involved in naming three such commas: the nexus comma, the quartisma, and the symbiotic comma. I have to admit these unnoticeable commas are my favorite commas to mess with just because I like to temper these things out. --Aura (talk) 04:40, 27 November 2020 (UTC)

Sorry, not yet. Again, I did not even hear any sounds from my work on "just intonation" (I don't call it "just intonation" to avoid confusion with well-known meaning of this expression, I call it rational or "harmonic" intervals/systems), only developed some calculation. That said, I know about these commas and understand their nature, but not ready to discuss further detail. I'll keep it in mind, though. All my prior work was either with (practically) continuous frequency set or different EDOs. And finally, I started to work with a new instrument. — SA 04:51, 27 November 2020 (UTC)
Well, part of the reason I brought it up is because I'm trying to develop a nomenclature for intervals in the 2.3.11 subgroup. I wonder if at a certain point you could help me with that... --Aura (talk) 04:55, 27 November 2020 (UTC)
It may eventually happen, I'm not sure right now. I'm busy with other things. — SA 04:59, 27 November 2020 (UTC)
I see. --Aura (talk) 09:31, 27 November 2020 (UTC)
I wanted to ask you: can I understand that by "tempering out" you don't mean EDO temperation? In other words, do you plan to stay within a set of rational numbers? — SA 04:59, 27 November 2020 (UTC)
When I say "tempering out", I mean just what the article linked in this sentence says. That said, there's also such a thing as "fudging", and I see no reason to be opposed to fudging as long as the intervals are small enough to be unnoticeable. Do note that the latter article uses the term "Just Intonation" whereas you might prefer the term "Rational Interval Systems". --Aura (talk) 09:31, 27 November 2020 (UTC)
Sorry, I did not understand the answer, could you clarify? And what is "latter article"?No matter, I don't mind the use of "just intonation", only afraid of the situations when a reader understands it in some more concrete sense. I don't insist that my terms are better to coin them.
It would help if you followed the links in my last comment- I was telling you to follow the links to help you get a sense of what I meant, as the articles explained this better than I can. The term "latter" means the second of two, so the phrase "latter article" means "the second of two articles". --Aura (talk) 17:43, 27 November 2020 (UTC)
Please don't get irritated by this, but now I cannot find 1) what are those two articles, 2) what is "my last comment" :-) Here is what I want to advise: I think you greatly overestimate the ability of other people to navigate (I say only "navigate", not "understand", generally I understand you quite well). You overestimate just the vision, observation of what you said before, ability to associate it, and so on. For communication on such things, there is a great tool: links! The same goes about discussions with the numbers: most people don't imagine them well. (I personally have one of the kinds of the mathematical mind. People like me think abstractly but notoriously bad with numbers. Paradoxically, mathematics and dealing with concrete numbers are almost opposite traits :-) — SA 18:15, 27 November 2020 (UTC)
I'm not irritated by this, rather, I can't help but laugh... Anyhow here are the links to the definitions of the terms you wanted to know about:
tempering out
Hope this helps. --Aura (talk) 18:22, 27 November 2020 (UTC)
Perhaps now this is my turn to laugh. I do know exactly these two links, but the issue was the association between those too links and your words referencing those, so your answer is not redundant information, it is used to restore the association. I actually asked about two associations: "1) what are those two articles, 2) what is "my last comment", but now it is not important, everything is already clear enough — thank you. — SA 18:29, 27 November 2020 (UTC)
Lastly, I was thinking about those commas and have some consideration. Roughly, we need to understand that in a rational-number interval i=A/B makes deep physical sense only if A and B are small enough. This is related to the nature of aural perception of any organisms or even devices. If the numbers became 3-digit numbers or more, the accuracy of the rational number doesn't play its role. Let's see: there are two physical traits: 1) the sense of harmonics in the interval with small A and B; it is based that two oscillators in the ear come in resonance, but not necessarily on their fundamental frequencies, but some low-order harmonics, if harmonics are high, the effect is unnoticeable, 2) the perception of logarithmic distances between frequencies as equal. Now, #1 and #2 are in fundamental contradiction: 1) if all intervals are rational numbers, their system is never ever equidistant, so the equivalence of tonalities is impossible, 2) if intervals are equidistant, the ratio values are never rational, so we won't feel the perfect sense of harmony. So, the question is: with this trade-off, where is the reasonable choice? The common-practice system has chosen the compromise and gave more preference to #2 than before. 12-EDO gives amazingly good compromise, but we pretty easily can perceive the deviation from harmony. At the same time, our trait #1 is more accurate than #2. What is my conclusion? It can be a bit complicated in practice, but this is nothing but some intermediate idea. First, everything depends on the composition. Where we value the sense of equidistant notes? I don't think it is absolutely important in most cases. That said, when your calculations lead you to big natural numbers, A/B, you can easily give up having a rational number for a certain degree and use a mixture of rational numbers and real numbers. I do understand how weird it can be, this is just a vague idea. Another vague idea is that you might extend some tonal system but then classify the resulting tones and their functional roles into two classes: "degrees" and "non-degrees". A "non-degree" tone can have a limited role, it cannot be, for example, used as a root of a chord, and so on. I do understand that this is very weird and not elegant, this is just for discussion. The main point is: the contradictions and trade-offs in the tonal systems are unavoidable in principle, by the very nature of thins, sorry for possible truism. — SA 17:05, 27 November 2020 (UTC)
Given the trade off, I'd say that the reasonable choice is to try and approximate the rational values- especially 1-digit and 2-digit values- within a value of less than 3.5 cents wherever possible, as this is the kind of size difference where people won't really notice the deviation from harmony. As it happens, 159edo and a number of other EDOs in that area do a pretty good job with this from what I see. Yes, there are flaws, such as 159edo's inconsistent treatment of the 19 prime, but since 159edo represents the primes 5, 7 and 13 reasonably well, with the primes 3, 11, and 17 being represented by intervals that are less than a cent away from harmony, and since the primes 2, 3, 5, 7, 11, 13 and 17 are the primes that have the most to really offer, I think we have the most important facets covered where it counts the most. I should point out that the reason I value the sense of equidistant notes is that it enables a sense of uniformity and provides some measure of simplicity, but using a set of equidistant notes that is too small causes problems and doesn't respect the unequal distances between 1-digit and 2-digit values within good enough reason. I definitely try to extend the tonal system but then classify the resulting tones and their functional roles into two classes: "main tones" (akin to your idea of "degrees") and "variant tones" (akin to your idea of "non-degrees"). As far as I'm concerned, "variant tones" mainly act as chord roots during modulation- that is, when you're in the middle of trying to change keys- and don't do anything like that under most other circumstances, so yes "variant tones" do indeed have a more limited role compared to "main tones". Does all of this make sense? --Aura (talk) 17:43, 27 November 2020 (UTC)
I understand. Oh, and it is great that you open to the pretty weird idea (because it can complicate things too much) of "non-degrees" under the name of "variant tones" (probably, clearer name). Yes, so far I think it all makes sense, but right now this is shooting off the heap (is that a correct idiom?). — SA 18:22, 27 November 2020 (UTC)
The phrase "shooting from the hip" is an actual idiom, but I don't know if you mean to say I'm "speaking or acting rashly, recklessly, or bluntly, without consideration of potential consequences" (which is what the idiom means) or not. I was trying to say that large EDOs like 159edo are one way of approaching a solution to the dilemma you're talking about, and I was trying to tell you why it might as a solution if done right. --Aura (talk) 18:32, 27 November 2020 (UTC)
I haven't responded to a number of your posts, took a little time to start cleaning up on that matter. No, I did not have any doubt on the meaning of this idiom, which is international, I worried a bit only about the accuracy of its English form. By the way, I do not quite agree with your description of its semantics. However, the semantics of the idiom is the usual source of arguments. From practice and simple logic, I can see that "shooting from the hip" only means fast (intuitive) action, taken for a reason and, on the contrary to what you say, more typically, consciously, with pretty good "consideration of potential consequences". Why? Because by the very fact using of this idiom, the speaker clearly conducts the idea that the judgment was based on taking a risk. Which is exactly what I meant. — SAMonday 2020 November 30, 23:54 UTC
Ah. While I see what you meant, it seems all the sources I have on the semantics of the phrase "shooting from the hip" do indicate that this idiom implies recklessness. I guess I don't know what the corresponding idiom for what you're talking about is in English. --Aura (talk) 00:06, 1 December 2020 (UTC)
No, this is not a "corresponding" idiom, this is an international idiom, in all cultures using it the phrase is a simple near-literal calc, no matter where the original is. And it "depends" on how to thread the term "reckless". If you address to the prototype, the kind of battle technique of this kind of shooting, sometimes called "Macedonian shooting" (I don't know why) imply that people decide to fight using this technique based on their training and pretty consciously, otherwise all those special-purpose squads would be easily exterminated by the enemies. :-) . As I say, the very fact of using this idiom is a kind of excuse that the speaker takes the changes. I a person makes this note, the saying itself is consciously. Maybe one can think this is compatible with the idea of being "reckless", not so sure... — SATuesday 2020 December 1, 00:34 UTC
From what I see, the English phrase literally means "To discharge a firearm while it is held near the hip, without taking time to aim via the gunsights". The "reckless" thread comes from the lack of aim. --Aura (talk) 00:44, 1 December 2020 (UTC)
Well, you described the origin of the idiom very accurately. And that renders both "lack of the aim" or "without consideration" quite illogical, as the main goal of the technique is to have the aim destroy the target, same goes for the user of the idiom (not destruction, of course, just the goal of the action). — SATuesday 2020 December 1, 01:18 UTC

24edo Harmony

Hey SA, do you think we have the chance to talk about the harmonic possibilities of 24edo in regards to 11/8 and 16/11 now that you have listened to "Folly of a Drunk"? I mean, judging from the absolute error amounts, I'd say that 24edo approximates 11/8 and 16/11 better than 22edo does... --Aura (talk) 19:04, 29 November 2020 (UTC)

We can, but I'm going to be somewhat busy, will hardly spend so much time. I'd better need to do some calculations before I'm ready to talk; this is a very fast thing but needs some distraction. First of all, I already admitted that my judgment on this EDO was not based on comprehensive considerations, as I only used the comparisons with "just intonation" in a very narrow sense of this expression, only the well-know system 9/8 5/4 4/3 3/2 5/3 15/8, closely related to the common-practice one. I forgot to notice that my own research aimed to produce some extended sets of intervals renders that judgment obsolete. Based on that criteria, my old method of finding the EDOs produced only 12- 19- 31- 41-... -EDOs and missed some other EDOs. That said, I'm ready to reconsider 22-EDO.
Unfortunately, I must confess that I'm not as experienced with 22edo, so for dealing with 22edo properly, you'll want to talk to others on the Wiki. However, I myself am writing a song called "Space Tour" in an approximation of 159edo, and it mimics 12edo, 14edo, 17edo, 19edo, 22edo, 24edo, 27edo, 31edo, 35edo and 41edo, and these "retunings" (as I call them) rather closely match the real EDOs. Sure, you may notice a few notes are slightly different when you compare this song against the actual EDOs, but rest assured, this piece can still give you an approximation of some of the things these EDOs are capable of, though to be fair, it is a really long song, and after the 41edo-retuning, it goes on to a near-perfect 53edo as well before going on to use the near-perfect 159edo in the same way that the real 159edo is natively structured. I should also point out that I work with Locrian mode a lot, and this mode only really makes sense when you consider the Tyrant Antitonic's properties relative to the Tonic. --Aura (talk) 03:48, 30 November 2020 (UTC)
As to “Folly of a Drunk”, it sound absolutely logical to my ear, and nice to hear. The only problem with it is: can you produce and publish some more? :-) — SAMonday 2020 November 30, 01:53 UTC
I can indeed do that, but do prepare for a lot of dealings in 24edo and near-perfect 159edo. --Aura (talk) 03:48, 30 November 2020 (UTC)
I know, but it would be very interesting to have and listen to that. — SATuesday 2020 December 1, 00:06 UTC
I'm trying to work on a pretty long song called "Space Tour"- the song I alluded to earlier in which a near-perfect approximation of 159edo is used to mimic other edos. I have yet to think of how to write the last few sections however. --Aura (talk) 00:16, 1 December 2020 (UTC)
Speaking of songs in 24edo, have you checked out "Anticipation"? That song showcases some of the other things that 24edo is capable of, and even outright uses 1edo, 2edo, 3edo, 4edo, 6edo and 8edo- though not in that order- before going to quartertone-enhanced traditional tonality in 24edo itself. --Aura (talk) 04:03, 30 November 2020 (UTC)
I think I listened to everything I found in the links on your pages, including "Anticipation". It is interesting, but “Folly of a Drunk” is something special: Having microtonal structure in а clear melodic motion, plus its aesthetic effect, plus recognizable allusion with the classical presentation of possible "analogous" theme, multiplied by specific kind of humor — this is a different story. — SATuesday 2020 December 1, 00:06 UTC
Really? "Folly of a Drunk" is that special? I have no idea as to exactly how I managed to pull off the emotional components since I have difficulty processing emotions... Truth be told, I came up with the catchy melodic line for "Folly of a Drunk" just by messing around... --Aura (talk) 00:32, 1 December 2020 (UTC)
Yes, this is what I think. I can describe it in a different way, but please try not to get offended, or something: your other pieces remind a lot of very usual things: ambient, science fiction, horror soundtracks, something like that, and only “Folly of a Drunk” hardly cannot be confused with something else, it is distinctly recognizable. At the same time, it follows some very traditional melodic structure, only mangled in some totally logical way. Yes, I understand if it is done by messing around, but maybe only because your intuition did not betray you in this case? My first impression was that you've elaborated a stable technique of interpretation of melodic themes in some "microtonal space". Apparently, your words tell me that it was false impression, but it only makes things more interesting :-) (Of course, taking into account that I know next to nothing about the art of musical composition. :-) After I received your very first comment on this page, first thing I did was listening to this piece. — SATuesday 2020 December 1, 01:31 UTC
I'm not actually offended by you thinking highly of this song- in fact, I'm actually pleasantly surprised by this. I have to say that the chord structure of "Folly of a Drunk" required more work- especially trying to make sure that the song changed keys properly around two thirds of the way through- furthermore, I also have to say that the chord structure is a driving element just like the melody is, and, if I recall correctly, I had to write the chords first in a number of cases. --Aura (talk) 02:51, 1 December 2020 (UTC)
For the record: you misread me here. I was afraid of being offensive not because of thinking highly of this piece, but because of feeling not so impressed by all other pieces — sorry. Indeed, I think that I heard enough of thins giving similar impressions, but only “Folly of a Drunk” is so special. — SATuesday 2020 December 1, 07:03 UTC
Ah. I realise that a lot of my work is sci-fi, but I hope there's still interesting things about "Space Tour" in particular once that gets done. --Aura (talk) 07:19, 1 December 2020 (UTC)
You know, you can think of it whatever you want, but I find almost all science fiction music totally boring. :-) I was deeply impressed by science fiction music only by Eduard Artemyev, first of all, in Solaris (1972, or course) and Stalker. Did you listen to it? But Artemyev is generally one оf the genius composers, isn't he? — SATuesday 2020 December 1, 07:31 UTC
Besides, the name... I thought that the name of this piece is a kind of allusion to the original name of one Bruegel's painting, "The Folly of the World", and, weirdly, the motive of this piece reminded me of this painting. What? Is it just my fantasy? — SATuesday 2020 December 1, 01:40 UTC
In all honestly, I don't think I ever heard of the particular painting you referenced. In truth, this song was written to go along with a very specific scene in mind, though I won't share the totality of that scene at this time. On another note, I have to admit that "Space Tour" is another science-fiction-based song, though I hope there's at least something interesting about it once I get done. --Aura (talk) 02:51, 1 December 2020 (UTC)
Ha-ha, I guess, this is a good illustration of how art critics work: their fantasies find so far-reaching cultural references, associations, and enormously deep meanings, something that actual authors never thought of. :-)
Anyway, it would be good for you to know what is the famous painting your soundtracks comes with. :-) The official name is Flemish Proverbs (Netherlandish Proverbs) after Pieter Bruegel the Elder. This piece of art plays a very special role in culture. Just basically, it illustrates approximately 112 identifiable proverbs and idioms and also related to the author's vision of "absurdity, wickedness and foolishness". — SATuesday 2020 December 1, 05:53 UTC


Hey, SA, I think I ended up naming a few commas that I can't find names for on the Huygens-Fokker Foundation's list of intervals- these would be the quartisma, the nexus comma and the symbiotic comma, the Alpharabian comma and the Betarabian comma... What do you think of these names? --Aura (talk) 23:01, 30 November 2020 (UTC)

Sorry, nothing certain. Even though I'm familiar with many well-known comma names, I did not think enough of the the motivation and the correspondence between the nature of each comma and its naming. Besides, to make your considerations comprehensible, you probably need to explain everything in some definitive order: first, the schema of getting to one or another comma, which intervals or chains come to the comma, in what way, then, you need to present some rationale behind the suggested name, relating the nature (its role, significance, historical facts) and the proposed naming. More generally, I can see some specifically musical communication problems. It is not as trivial as the specific terminology not quite understandable by people from the outside word, no, this is some deficit of communication culture, resembling, say, irregularities of classical chemical nomenclature... — SATuesday 2020 December 1, 00:24 UTC
I have to admit I don't know what you mean by "schema" here. That said, I can tell you which intervals or chains come to the comma and in what way. I can also give some degree of rational behind the suggested name, relating the nature of the comma and the proposed meaning... --Aura (talk) 01:09, 1 December 2020 (UTC)
"Schema" has a very abstract meaning in the general case, and yes, you understood me correctly. Yes, I know you can tell that schema in each case, I only say, that before you do it, everything else is meaningless. I personally love (and often can) to play with words and create names, but I need a really good semantic background. — SATuesday 2020 December 1, 01:47 UTC
In that case, since a worldview is an example of a schema, I guess I do in fact deal in some of them. However, I must also point out that I have Asperger's Syndrome, and people with Asperger's often struggle with abstractions. See Dr. Kenneth Roberson's two articles on the subject. --Aura (talk) 03:07, 1 December 2020 (UTC)
Hm... I happened to read about this phenomenon but never faced such people. Anyway, from what I understand about it (and the references you've provided only confirmed my understanding), the "struggle" is not with the abstraction itself (abstraction is a fundamental trait of any cognitive activity), but only with the communication about abstractions, simply put, solving the problem of the choice of one of the possible meaning of the word, more specific vs. more general/abstract. In this particular case, I responded that 1) you recognized my implied meaning of schema correctly, 2) my construct "schema has a very abstract meaning" simply means that it does not have to be understood in any specific way, but only works as a generalization placeholder for the next part of the sentence, 3) its implied meaning is disclosed by the words "which intervals or chains come to the comma", 4) and the abstraction could be reduced the adding to these words "or something like that". I'm not sure if I made it clearer, but if not, this is not so important, because you already grasped the correct meaning anyway. — SATuesday 2020 December 1, 05:35 UTC
Hm... seeing as that's the case, I can tell you about my reasonings for the name of each of the commas I've mentioned if that's alright with you... --Aura (talk) 07:19, 1 December 2020 (UTC)
It can be interesting but perhaps later. — SATuesday 2020 December 1, 07:35 UTC
Well, since I already typed out my reasoning, I might as well post it before I forget it or lose it, though do feel free to read about it later if need be...
The Quartisma, 117440512/117406179, is the difference between a stack of five 33/32 quartertones and one 7/6 subminor third, and since 33/32 is a quartertone, while the comma itself is unnoticeable, I came up with the name "quartisma" based on "quartertone" and "schisma".
The Nexus comma, 1771561/1769472, is the difference between a stack of three 128/121 Alpharabian diatonic semitones and a 32/27 minor third. The 128/121 semitone is an example of pure 11 prime interval, while the 32/27 minor third is an example of pure 3 prime interval, and both the 11 prime and the 3 prime are significant in their own ways. Specifically, while the 3 prime has its connections to the diatonic scale, and the perfect intervals 3/2 and 4/3, the 11 prime can be mathematically calculated to be the virtually the best prime for representing quartertones in terms of ratio simplicity, with three 33/32 quartertones plus a 4096/3993 quartertone being the simplest known combination of two distinct, rational quartertone intervals that can be added together to make a 9/8 whole tone. Since tempering out 1771561/1769472 joins the 3 prime chain and the 11 prime chain together, it makes sense to call it the "nexus comma".
The Symbiotic comma is the difference between 77/72 and 2187/2048, and the sum of the quartisma and the nexus comma. It gets its name both from the fact that it is tempered out in such notable temperaments as vishnu, newt, kwai, supers, guiron and amity, and, from the fact that it also makes a good extension to a number of other temperaments such as canou.
the Alpharabian comma, 131769/131072, is the difference between a stack of two 128/121 diatonic semitones and a 9/8 whole tone. The comma gets its name from the association between al-Farabi with the 33/32 quartertone- which is part of the 2-3-11-based tuning. Specifically, it comes through an analogy between the familiar association between Pythagoras and 3-prime-based tuning on one hand, and the aformementioned association between al-Farabi with the 33/32 quartertone on the other. This analogy is furthered by the fact that 131769/131072 is similar to that of the Pythagorean comma in that it relates diatonic semitones to the 9/8 whole tone.
The Betarabian comma, 264627/262144, is the sum of the schisma and the biyatisma (121/120), as well as the sum of the Alpharabian comma and the rastma (243/242). The term "Betarabian" is a derivative of "Alpharabian", and was coined on account of both the rastma being the comma which separates primary and secondary 2-3-11-based intervals and the term "Alpharabian" itself containing the word "Alpha" within it- all that was needed was for "Beta" to be put in place of the "Alpha".
I hope this all makes sense now... --Aura (talk) 07:51, 1 December 2020 (UTC)
It's fine to have it here now, but you cannot expect that I digest it right away. :-) The only thing I wanted to ask you in first place: is *arabian related to Arabic culture? I did not expect to face such a crazy word play: it is related not to "Arabic", but to the name of our Kazakhstan location "Farabi", with Arabic form "al" with the meaning close to the preposition "from", which makes the name of a person "from Farab", and the resulting name associated with the letter name "Alpha". After replacement of "Alpha" by "Beta" the name "Farabi" is totally dissolved, due to elimination of "F", forget about "al-". To see the real sophistication of it, we also have to remember that the form "al-" is Arabic, but Arabic analogs of Greek "Alpha" and "Beta" are read differently: "Alif" and "Ba". The wordplay is certainly pretty smart. And what kind of a person is supposed to figure out such puzzles? :-)
The term "Alpharabian" comes from "Alpharabius"– another name for Abu Nasr al-Farabi– and was chosen due to the fact that 33/32, also known as the the "al-Farabi Quartertone", is the primary limma of the 11-limit, a fact which lends itself to the idea of 2.3.11 tuning being called "Alpharabian tuning" in the same way that 2.3 tuning is called "Pythagorean tuning". I imagine that the rest of what you've said about the wordplay is quite true, seeing as I didn't know the meaning of the name "al-Farabi" aside from its connection to the aforementioned person. It is specifically the name "Alpharabius" and the related adjective "Alpharabian" that bear the association with the letter name "Alpha". I'm sorry, I should have mentioned the remaining specifics, but I was struggling with the specifics as to how to express this complicated etymology. --Aura (talk) 15:42, 1 December 2020 (UTC)
Got it. Thank you for another piece of information that makes the naming issue even more complicated. :-) — SATuesday 2020 December 1, 16:38 UTC
I hope the complication doesn't turn you off... I guess you really were right about musicians naming intervals in the most complicated and convoluted ways. Oh, and yes, I can think of one example where musicians have actually given a musical interval a perverse name, but I won't go into the specifics of that here. --Aura (talk) 17:40, 1 December 2020 (UTC)
Turning off..? Not at all, just the opposite: I enjoy and never miss a chance for a linguistic exercise. :-) As to the interval naming and other names, it depends on your understanding of "perverse name". To my taste, most of those names are perverse, but this is not directly related to linguistic itself, but more to the overly ad hoc manner of thinking. — SATuesday 2020 December 1, 18:14 UTC
So, SA, I'm curious... do you like the names I've given the commas? Or, is it too ad hoc for your taste? --Aura (talk) 18:59, 1 December 2020 (UTC)
Sorry, not ready; and I don't want to give you an absolutely immature opinion. Rather, I would need some time; and I'm pretty busy. I won't forget, don't worry. — SATuesday 2020 December 1, 19:36 UTC
Oh, great! Huygens-Fokker Foundation's list of intervals you referenced in the first paragraph of this section. It can help me to explain to you what is that very characteristic of communication problems I can see in the musicians. In the list, you can see the set of rational-number intervals and some names. Hopefully, all rational numbers in the list are irreducible fractions. What information does this page carry? Next to nothing. The only possible use is this: when you already got some interval from some other source, say, from your own calculation, you can check up: is it one of the well-known intervals or not, and, if it is, what is its well-known name? Even this information has some uncertainty, because, strictly speaking, "well-known" is something uncertain, so the only definitive information you get is this: is my interval on the Huygens-Fokker Foundation's list? :-). And yes, this is exactly what you've checked in this case. You cannot learn anything about any of the concrete commas from this page. For the contrast example, look at any good Wikipedia page. Sometimes you can start from some reference and end up with the study of an entire field of science... — SATuesday 2020 December 1, 02:06 UTC

Space Tour

Hey SA, I just finished another song- "Space Tour". It's like 20 minutes long, and I know you find much science-fiction-type songs boring, but this song tells a story. I posted on my userpage, and hope you like it! --Aura (talk) 19:26, 3 December 2020 (UTC)

I finally got myself some time to listen to it all paying attention it deserves. Yes, this is a very interesting piece, and a complicated one, by the way, and it does tell some imaginary story. Still, I certainly like "Folly..." more. I know, I once realized that all musical aesthetics is about some combination of the predictable and the surprise. Probably, this is a total truism, because many said something similar. Back to "Space Tour"... first of all, I'm interested to understand, what exactly do you mean by "mimicking" an EDO? One thing about the sound: I miss low timbers and low voice in general. Don't you think this is a present-day trend to work more on higher-pitch sound, higher-frequency noises, everything is higher? Where is that deep voice? Any comments on it? — SASunday 2020 December 6, 18:21 UTC
When I talk about one EDO "mimicking" another, I refer to a larger EDO using a collection of its own steps to approximate the actual steps of a smaller EDO without the larger EDO actually being a superset of the smaller EDO. As for the deep voices and low timbres, they are often used as chord roots in music- especially the more common variety of music that is built from the bass upwards. I personally think that building music from the bass upwards music like this is but one of two ways to construct good music- the other being to build music from the treble downwards. Music built from the treble downwards (treble-down music) is different from music built from the bass upwards mainly in terms of what I call the "direction of construction", as otherwise the two systems are mirror images of one another. --Aura (talk) 18:33, 6 December 2020 (UTC)
I think I understand the idea, not sure that this is the correct understanding. First of all, a larger EDO is almost never a superset of a smaller EDO, because it would be the defeat of the purpose to provide a better approximation to harmonic intervals using more tones. Naturally, you can use a subset of a larger EDO, corresponding to some smaller EDO (corresponding tones can be simply identical, but only approximately) and use this subset. Perhaps it's just the term "mimicking" sounded confusing to me. — SASunday 2020 December 6, 18:55 UTC
Yeah, the way you put it here is more or less another valid definition of how I'm using the term "mimicking" here, as not every possible subset of the larger EDO actually approximates the smaller EDO, and sometimes, more than one subset of the larger EDO can do the job. For the record, 159edo does have 53edo as a subset- and this is not considered "mimicking"- but that's okay, because 53edo is really really good in its own right when it comes to the 3 prime. --Aura (talk) 19:13, 6 December 2020 (UTC)
As to deep voices: I meant something much more basic: to me, more deep voices and generally the amount of lower voices sounds more tolerable for the ears, and overly high, especially high-frequency noises, sounds more irritating. I noticed that historically the present-day trend is to emphasize higher pitches, even bass and baritone singers are somewhat rarer these days. I did not mean something like "building from the bass", however, this is an interesting topic. Notably, the Baroque perception of music was different from the modern. These days, we typically hear the main themes in a higher-pitch part and then pay attention to the other detail, including bass. In Baroque, basses played much more fundamental role. — SASunday 2020 December 6, 18:55 UTC
To me in music that is built from the bass upwards, the lowest bass serves as the driver of how the accompaniment moves- it is the line that all of the chords and stuff are built on top of, and the lowest bass line, along with the melody, both exert influence on one another at different times. The problem I have with too many deep voices is that even thirds in the bass can sound rather grating when the notes in question are too low, more so than with higher pitches. Higher pitches are more irritating when they're played in the wrong timbers and or when played too loud. --Aura (talk) 19:09, 6 December 2020 (UTC)
Right. Needless to say I only explain my personal feeling about it. Yes, the "build from the bass" is an interesting topic, only I'm pretty far from it and the composition in general. — SASunday 2020 December 6, 19:32 UTC
I understand. --Aura (talk) 19:37, 6 December 2020 (UTC)
I'm busy with my platform and keyboard programming. I decided to take a much wider road: develop some more and some replacement visual components corresponding to different keyboards, including a new one suitable for your paradiatonic constructs — my idea is to present 7 scales at the same time on a single keyboard, still thinking of some form of switching modes on the fly, combined with transpositions, or something like that. At the same time, I implemented a prototype for the playable lattice presented by Kite Giedraitis: Color_notation. Even though it is called "notation", the main point here is the choice of the tonal system itself, which can be reduced to the choice of a 4-generator set, and its mapping to the geometry. (Why, why musicians often mess up musical and notation aspects together? Didn't they figure out that tight coupling is a big anti-pattern?) I've chosen to implement the 27-key variant, which I consider as a good variant of an "extended just" scale. Are you familiar with this particular system? What do you think? — SASunday 2020 December 6, 18:39 UTC
Ah. That makes sense. While I am familiar with color notation to an extent, I should point out that Kite and I have a disagreement when it comes to the usage of intervals like the 40/27 grave fifth. For instance, Kite thinks that interval ought to just be avoided whenever possible, while I think that 40/27 is actually useful when in the right position within a scale and in the hands of the right composer. If you are asking whether or not I'm familiar with a 27-key system, I have to say that I'm mostly familiar with the traditional 12-key layout when it comes to actually playing on instruments. That said, I do think I'm willing to experiment with other key layouts- that is, assuming I ever have the funds to get my hands on such things as I really don't have a lot of money. --Aura (talk) 18:54, 6 December 2020 (UTC)
Any references to those arguments? By the 27-key system, I meant the particular layout on the Kite's page, first picture here. It is already playable on my prototype, you can try it out. Do you want to experiment with other playable keyboards? Then I can offer you my platform and my help... — SASunday 2020 December 6, 19:28 UTC
Here is the main example. Of course, this one is very civil, but I have been rude to the man on other occasions- even though I eventually apologized for it. --Aura (talk) 19:34, 6 December 2020 (UTC)
Thank you! Perhaps I can see some (potential?) weak points in your arguments. First, you don't explain your understanding of "proper". You need to understand one fundamental thing, something usually beyond the comprehension of most people, except those with certain backgrounds: the scope of applicability. If you make some statement insisting on the application of any principle, you have to know its scope. In theory, it's very typical when the scope of applicability is unknown at first (is considered more universal than it actually is), so the limitations of the scope comes into play only when a more general theory is accepted and proven. (Let me give you one example: one theorist and microtonalist claimed that 31-EDO I presented to him makes no musical sense, because, say, ♯C is lower than ♭D, which is an "absurd". I argued that this is merely my notation, and his problem is that he is implicitly using the notion of accidentals, but the applicability of the notion itself may be out of the scope in the microtonal scope, or at least it needs to be proven.) Another problem I can see is that you may underestimate the power of small natural number N/D in rational-number intervals. Indeed, as this power is based on the physics and physiology of perception, the quality of the resonator comes into play. Taking it into account, you may face the situation when two intervals like 32/27 and 77/64 are clearly recognized as different melodically, but make no difference to the sense of the harmony, only because 77 and 64 are pretty big, and their small prime factors don't make a big difference.
When I say "proper" in this context, I'm referring to Rothenberg propriety. Furthermore, I'm aware of the power of small rational intervals, and both 7/5 and 6/5 strongly imply a fundamental other than the Tonic by means of the virtual fundamental effect- this won't do at all as far as I'm concerned, as I like tonal stability. At least 8/5 has the Tonic as a shared harmonic. --Aura (talk) 20:07, 6 December 2020 (UTC)
Aha, thank you for the clarification. I'll try to sort it out and take it into consideration later. For now, I'll complete the playable keyboard based on the exact same layout and the tonal system as Kite's; it won't prevent its modification or development some of variants of it in near future. — SASunday 2020 December 6, 20:14 UTC
For the record, 27/16 has the Tonic as a virtual fundamental as well, and seems to be the strongest example of a major sixth above the Tonic in this respect- 5/3, although simpler, implies a different note as the fundamental- again, this weakens tonal stability. --Aura (talk) 20:16, 6 December 2020 (UTC)
Again, among other things, I'll need to hear some examples by my own ears before I can evaluate it. I'm at the beginning of it, but ultimately I hope to have a convenient playground for doing such things. It already works for EDOs, so it should for the rational-number intervals and systems. Also, I have a comparison application based on circular keyboards, it works nicely and compares with just one intonation system, and I started to generalize it. — SASunday 2020 December 6, 20:26 UTC
I'll be happy to provide some examples, at least for the sake of comparing 5/3 and 27/16, though I'll only do practice pieces for this so you can hear the differences in nature between these two intervals. --Aura (talk) 20:34, 6 December 2020 (UTC)
Later, later... It can be done in different ways, but this is how we did it: I developed a recorder for one of the keyboard applications (important for remote lessons and seminar, this is how they really use it), will add it to all other applications. My colleague plays some sequence and sends me via a chat, I copy and play it. It's pretty much like exchange of MIDI sequences: not audio, but event storage. — SASunday 2020 December 6, 20:50 UTC
Okay, I know you're probably busy, but I still figured I'd give you some sound samples for you to listen to when you're ready. This audio sample track contains two chords consisting of C7, E7, G7 and A7. For both chords, the C7 is standard in terms of tuning while the E7 is flattened by 13.69 cents and the G7 is sharpened by 1.96 cents. The only difference between the two chords is the tuning of the A7, as it is tuned 5.87 cents sharp in the first chord, but 15.64 cents flat in the second chord. If you turn the volume up on your computer (don't turn it up too loud though), you should be able to hear a virtual C3 fundamental for the first chord, and a virtual F3 fundamental for the second chord.
This difference in virtual fundamentals illustrates how the difference in tuning between the two versions of the A7 give the otherwise identical chords different harmonic properties- hence the reason for my preference of 27/16 over 5/3 as the interval for the major sixth. --Aura (talk) 00:07, 7 December 2020 (UTC)
Thank you very much, but you see, it may sound surprising, but I cannot hear much in these settings. To grasp it, I'll need to play it by myself. This is fairly simple. Let me give you an example and list some missing points. First, when you say "contains two chords consisting of C7, E7, G7 and A7", it may mean two "complex chords", such as first, C7+ E7 and second, G7+A7, or something else. When you name chords, I don't care about some detail, but need to know: which C7? in what tonal system? Usually, people using this notation assume 12-EDO. When you say "flattened" or "sharpened", I would need to know which degrees are changed. Even better to give not cent notation, but directly rational-number notation. This is one intentionally simplified example: you say "play C6 as 1, 5/4, 3/2, 5/3 followed by C6 as 1, 5/4, 3/2, 27/16, hear the difference" with your comment on what "weakens tone stability" and other function-related comments. With EDO, you could use the terms such as 12-EDO 3rd, 12-EDO 6th, possibly with ♯/♭. With other EDOs, ♯/♭ are ambiguous, so I add the number of microtones relative to the degree, such as: "41-EDO ♯2 6th". Then I'll easily play absolutely anything, no matter what you specify. — SAMonday 2020 December 7, 00:39 UTC
So, you need to play the audio file when you're by yourself? I understand. Still, given your comments, it sounds like I should perhaps clarify things for you. In this sound file, the two CM6 chords are both built on a C7 that has a frequency of roughly 2093.0045224048 Hz. The first CM6 chord has the configuration of roughly 1/1-5/4-3/2-27/16, while the second CM6 chord has the configuration of roughly 1/1-5/4-3/2-5/3. Because a note forming a 5/3 ratio with C occurs very early in the harmonic series of F and 5/3 does not occur as an interval distance from C in C's own harmonic series, or even the C's own subharmonic series, the 1/1-5/4-3/2-5/3 configuration of the CM6 chord has a strong virtual fundamental effect that implies a Tonic of F even when F itself is not a direct component of the chord, thus destabilizing the 1/1-5/4-3/2-5/3 chord on C in relation to the key of C Major. --Aura (talk) 01:11, 7 December 2020 (UTC)
I guess that at the end of the day, the core idea of my approach to rational intervals and music is that while small rational intervals between the right two notes in a scale can establish and or cement a sense of tonality, small rational intervals between the wrong two notes in a scale can easily disrupt and or destabilize a sense of tonality by means of the virtual fundamental effect and or the lowest shared harmonic. --Aura (talk) 02:08, 7 December 2020 (UTC)
Yes, I can understand it. And thank you for the description on the chord example, it is very close to my guess and now is clear. Today, I got another new idea; it happened when I mentioned "playground". I'll postpone this paradiatonic application and first will try to suggest something similar, but closer to the idea of "Playground". This application will accept user's tonal values and put them in a simple yet ready-to use keyboard. This way, you could combine random ideas, try out by playing and listening, and change the repertoires of available tones in seconds. Doesn't it sound interesting? — SAMonday 2020 December 7, 02:22 UTC
The "Playground" idea does sound interesting, though the question remains as to how exactly to program complicated tonal values. On another note, when you say "Yes, I can understand it," what is the "it" you are referring to? Sorry for the massive edit, but I didn't feel like I was being clear. --Aura (talk) 02:47, 7 December 2020 (UTC)
Well, I think I can understand your consideration of the sense of tonality, disruption, concepts you've shared before.
Right. I guess that means my only question on this front concerns whether or not my aforementioned concepts and considerations in this sphere actually make logical sense in light of known phenomena like the virtual fundamental effect and your own observations of the sound sample of two different CM6 chords that I provided. --Aura (talk) 04:56, 7 December 2020 (UTC)
First of all, the phenomenon of <EDIT>missing fundamental<end EDIT> goes outside the problems of tonal systems, and I'm not sure if you understand it or disagree. I suspect you overestimate its importance. We can afford to ignore this phenomenon for almost all practical purposes. By the way, the case when an overtone suggests a missing degree of a chord is more important. This is why so-called "power chord" works. — SAMonday 2020 December 7, 08:30 UTC
If an overtone can suggest missing chord degrees, it stands to reason that an undertone can do the same thing. For example, when high-pitched power chords are put through a more extensive version of the same process used to produce extra bass sounds, they generate minor chords. --Aura (talk) 19:36, 7 December 2020 (UTC)
I do in fact disagree with you when it comes to the idea of the fundamental frequency being entirely outside the problems of tonal systems. The way I see it, the Tonic is at its strongest when it not only has the smallest possible rational intervals relative to all the notes in the scale, but is also the note that can generate all the other notes in the set purely through its own overtone series and undertone series. It's not just one of these facets that provides a sense of tonality but both. If tonality is like an entire building, then fundamental frequencies matching the tonic's pitch class are like the type of material that makes for the strongest type of foundation- does this analogy make any practical sense? --Aura (talk) 19:53, 7 December 2020 (UTC)
I never meant "the idea of the fundamental frequency being entirely outside...", it was a typo, sorry. Please see above: <EDIT>...<end EDIT>. Are you sure you understand the phenomenon correctly? In this Wikipedia article, some important considerations are missing. It needs some time to describe the idea and the questionable parts. It actually comes to theoretical mechanics (not "theoretical mechanics" learned by engineers, but the real thing, mostly the formalism of Lagrange, Hamilton, and then Emmy Noether), where the orthogonal space of modes can be understood, as well as the role of linearity and non-linear effects. (The usual myth of musicians is to call the physical-mathematics basis of music "acoustics", but in fact, there is next to nothing about real acoustics in music theory, but there is a lot of theoretical mechanics, abstract algebra, infinite-dimension functional spaces, theory of numbers, and the like.) Even for linear mechanics, this Wikipedia article considers only the sets of "similar" modes, like string or air vibrations with different number of nodes. Real life is more complicated. On this site, or maybe on some referenced sites, I saw a simple marimba example with some unrelated modes (all real modes do not interact due to linearity, but some modes are also "unrelated"). Now, we can always have a fundamental on an unrelated type of modes, which is lower than the most perceivable fundamental, and, in this case, these frequencies can be also totally unrelated, without any integer-number fractions. ...I understand my text is messy here. If you are interested, I can explain it properly. — SAMonday 2020 December 7, 20:35 UTC
Thanks for the clarification. Still, missing fundamentals, from what I gather, are important to tonality by virtue of their implying the existence of an actual fundamental frequency that generates the note set in question within a reasonable degree of approximation- unnoticeable commas notwithstanding. Yes, actual fundamentals and the missing fundamental effect are two different mechanisms, and indeed there are parts of Wikipedia's explanation that are questionable and it wouldn't be the first such instance. Nevertheless, the end result is that the missing fundamental effect highlights actual musical relationships- without the highlighted note in question actually being physically present. --Aura (talk) 21:34, 7 December 2020 (UTC)
Hm... Fundamentally (pun unintended), there is no difference between "tones" and "overtones", that's the key. When a sound wave reaches our ears, the information on the way of its generation is already lost. And yet, we "perceive" the audible modes as such, and mentally associate them with some instrument/oscillator, but it happens only because we hear pretty much what we expect to hear — we basically know how a certain type of musical instrument should behave. This is not pure, but a conceptual perception. That said, if we produce some totally alien sound, without an attempt to model any known real-life mechanical objects, there won't be any mode perception. Or, perhaps, the frequencies can be sensed as the "modes" of a speaker device, which is pretty much the same — no modes, there is no implied object having the modes. If it sounds unlikely, here is one less idealized example: throat singing. When many people hear this singing for the very first time, they often cannot realize what's going on, and later cannot reproduce it. We find it difficult to reproduce not because of physical difficulties. No, we simply don't have a model of what's going on, don't see any analog in our previous experience. Likewise, I saw many people nearly incapable of pronouncing a very simple sound of a foreign language or a combination... This is all the mental model issue, no more no less. — SAMonday 2020 December 7, 22:53 UTC
If this is the case, then there is no difference between "tones" and "undertones" either. --Aura (talk) 23:14, 7 December 2020 (UTC)
True. Those are the attributes of some model of an instrument/oscillator. Even if the model is mental, it suggests that some *-tones are the properties of the same object. Without this object, the sound is just an abstract set of frequencies and complex amplitudes (or real amplitudes and phases, which is the representation of the same thing) — SAMonday 2020 December 7, 23:46 UTC
By the way, do you know about the nonlinear properties of our aural system? It was even used in historical organs. I mean, the phenomenon has nothing to do with brain processing. The sound is physically generated in the head out of the sound waves. It can generate a sound which does not physically present in the air, say, combination frequencies which cannot appear in any linear systems due to the superposition principle. — SAMonday 2020 December 7, 20:35 UTC
Oh yes, I know all about that. In fact, while some consonances- such as those involving sum tones and difference tones- are based on a linear mathematical relationship (as noted by Sam Pulley in a conversation we had about the matter), there is an equivalent type of consonances that seems to be based on what I call a "contralinear" mathematical relationship- these particular tones being what I call "contrasum" and "contradifference" tones. We seem to need a new set of mathematical symbols in order to shorten the process of solving the mathematical problems involved in finding these contralinear tones. For example, a 10:12:15 minor triad is identical to a pitch relationship in which the frequencies are related the the following mathematical relationship 1/4:1/5:1/6. In order to solve for the contrasum and contradifference tones with the current set of mathematical relationships, we would currently need to take the multiplicative inverse of each of the fractions in the 1/4:1/5:1/6 ratio, solve for sum and difference tones among the resulting whole number ratios, and then take the multiplicative inverse of the answers we get- or something like that. --Aura (talk) 21:34, 7 December 2020 (UTC)
I would not be so sure. :-) What are you talking about? sum/difference frequencies need at least some mode interaction. But such interaction is by definition a non-linearity. The concept of "mode" fundamentally means that they are orthogonal, the subject of the superposition principle. Roughly speaking, modes don't see each other. When you project two laser lights on two different points and the beams pass across each other, none of the beams affect another one. Non-linearity can happen when the media is linear. For example, when the dielectric permittivity somehow depends on the value of the electric field of the wave, the change created by one beam warps the wave distribution of another beam, so it deflects. Normally, non-linearity happens with very high intensities (of anything). And yes, more sophisticated emission on sum/difference frequencies also takes place. Only all of it is non-linearity, again, by the definition. — SAMonday 2020 December 7, 22:17 UTC
I'm talking about talking about Combination tones, and also about additional pairs of tones that have a relationship to the logarithmic curve of sound perception akin to that of linear tones, only these other tones are along a decidedly non-linear curve. It would help more to go into an example, I think. Say you have a dyad (two note chord) consisting of frequencies of 440 Hz and 528 Hz. I imagine you know more about the combination tones that can result from this set of frequencies that I do, as well as how the frequencies of the combination tones are related to the actual tones by addition and subtraction, right? Well, Sam says that the linear relationship between the frequencies the actual tones and the combination tones leads to a sort of consonance, but, I'm saying that there are another set of tones related to that set of actual frequencies in a manner that is decidedly non-linear, yet is percieved to be just as consonant. In this case, we see the sum and difference tones resulting from 440 Hz and 528 Hz are 968 Hz and 88 Hz respectively, however, when we check the frequency relationships between all the pitches involved, we see a distinct set of intervals. The frequencies of 528 and 440 Hz form a 6/5 ratio, the frequencies of 528 Hz and 968 Hz form an 11/6 ratio, and the frequencies of 88 Hz and 440 Hz form a 5/1 ratio. If we take these ratios and line them up in such a way as to reflect the pitches involved from lowest to highest, we get a chord, that consists of the following steps 1/1-5/1-6/1-11/1, am I right? Now, if we take the multiplicative inverses of the ratios in the sequence, we get 1/1-1/5-1/6-1/11. Now, since we know that the interval between the 5/1 and 6/1 in the chord 1/1-5/1-6/1-11/1, is identical to the interval between the 1/55 and 1/6 in the chord 1/1-1/5-1/6-1/11- both being 6/5- and since we now want to find what I'm calling the "contrasum" and "contradifference" tones of 440 Hz and 528 Hz, we can assume that 440 Hz doubles as the 1/6 interval and that 528 Hz doubles as the 1/5 interval. Since multplying 440 by 6 gives you 2640, and since multiplying 528 by 5 also gives you 2640, that means that 2640 Hz is the "contradifference" tone to 440 Hz and 528 Hz. Since 2640 Hz corresponds to the 1/1 in the 1/1-1/5-1/6-1/11 chord, we now can solve for the "contrasum" tone in one of several ways- for the sake of simplicity, we'll just divide 2640 by 11 in order to find the frequency of the "contrasum" tone represented in the chord by the ratio of 1/11, and this tone turns out to be 240 Hz. Once you arrange the 2640 Hz frequency and the 240 Hz frequency in a chord together with the original 440 Hz and 528 Hz, you find that the resulting chord is just as consonant as the chord consisting of 88 Hz, 440 Hz, 528 Hz, and 968 Hz- once one takes the direction of chord construction into account. If you keep repeating this proceedure with different frequencies with different intervals, you'll eventually have a better idea as to the nature of the pitch relationships that I'm calling "contralinear". --Aura (talk) 23:12, 7 December 2020 (UTC)
Then please read this Wikipedia article and see that this is a non-linear phenomenon. This is exactly what I explained before and in contradiction with your "on a linear mathematical relationship". I understand that you might mean something different, but then it would mean that you did not respond to my considerations about linearity and diverted the discussion to something else. Either way, you are avoiding the essence of things. In your last message, you again ignore my explanations related to non-linearity and address the mass of the facts. Please understand, nothing is resolved by the mass. In mathematics you refer to, there is only the common notion of linearity, roughly speaking, A * x + B, without higher-power members (other functions can be represented by Lorenz). This simple property leads to the fact that waves don't interact unless they penetrate the non-linear head or other non-linear media. :-) — SATuesday 2020 December 8, 01:20 UTC
At first, I thought you were talking about something different- you know, the non-linear logarithmic curve of sound perception. I wasn't talking about the physical non-linearity of the system and the particular set of mathematical relationships associated with that, as indeed I'm not a physicist. I have to admit I don't know enough about physics to know some of those specifics, and I'm sorry for not addressing that properly. Indeed I was working with the common notion of "linearity", and, now that I think of it, I suspect Sam was too. --Aura (talk) 01:42, 8 December 2020 (UTC)
First of all, it tells me that we always will be able to solve those communication problems. I also have something for this purpose: tons of patience; and also I'm not afraid of looking too stupid. Okay, will you now look at new Playground section? — SATuesday 2020 December 8, 01:47 UTC
Come to think of it, I think we actually need to speak to Sam about his ideas of consonance, as well as about how to flesh out the idea of "contralinear tones" based on our discussion. --Aura (talk) 21:57, 7 December 2020 (UTC)
I just looked it through. I'm not quite sure. Don't you think he might confuse "consonance" with some other quality like "resolution", "stability", or something more complicated? On the other hand, perhaps the term "consonance" has other meanings I don't quite understand... Also, historically the attitudes and even "rules" related to "consonance" have changed. But I don't think it changed the understanding of consonance. In my understanding, not the notion itself was changing, but some kind of attitude, understanding of "acceptable degree of dissonance". Closer to modern times, "dissonant" structures became more and more acceptable and more wanted, pleasing in some ways. And I think this is good. — SAMonday 2020 December 7, 22:31 UTC
Well, we won't know for sure if we don't talk to him, that much is a given. However, it is definitely the case that there's more than one type of "consonance"- harmonic entropy minima being a notable example. --Aura (talk) 23:19, 7 December 2020 (UTC)
I don't know, really. How about two examples? I'm absolutely new to "harmonic entropy" though. — SATuesday 2020 December 8, 00:02 UTC
Well, "concordance" (as mentioned in the harmonic entropy article) is one example. Another example can be derived from the fact that 7/5 is a concordant interval, yet, 10/7- 7/5's more discordant octave complement- is also considered "consonant", but this consonance is clearly of a different variety from "concordance"- I'd term 10/7's type of consonance "inverse concordance", at least until we can think up a better name. --Aura (talk) 00:13, 8 December 2020 (UTC)
Oh, and remember what I was talking about when I mentioned "connectivity" before? Basically, "connectivity"- for lack of a better term at the moment- is the type of "consonance" that only exists between a given pitch class and other pitch classes that are generated by the first pitch class's overtone series and undertone series- it's the kind of consonance that seems to do the lion's share of the work when it comes to establishing tonality. --Aura (talk) 00:24, 8 December 2020 (UTC)
Yes, I'm having to invent terminology here, but I'm alluding to stuff that I suspect is very much real in some form or fashion. --Aura (talk)
I do have some more detailed prelimiary ideas on "connectivity" in particular on my page concerning my ideas of consonance. What's perhaps more noteworthy is that I think I have an idea for how to isolate connectivity mathematically- albiet expressed in some rather unsophisticated terms. --Aura (talk) 01:59, 8 December 2020 (UTC)
I think I know one of the problems we're having- the fact is that differing fields of study use the same words in different ways and with different meanings. That might be contributing to our communication issues just between the two of us. --Aura (talk) 23:46, 7 December 2020 (UTC)
I don't think it's a significant problem. Indeed, some people are very much confined to the "profession", then it's difficult, and in practice often an unsolvable problem. It's important to see that the world is only one, and all those "here in chemistry is not like there in physics" reflects more the cognitive limitations of people. As to us, I see that we can resolve such problems. The lack of some parts of education or weak understanding of certain things — this can be a serious problem, not terminology. — SAMonday 2020 December 7, 23:55 UTC
Now, about the problem, how "exactly to program complicated tonal values". First, the problems are solved using the "divide and conquer" method and "separation of concerns". In particular, tone values can be abstracted from the technical means of sound production. Another thing is: it's good to "think by hands". (In our case, "hands" is the generalization of several things: hands, fingers, hearing, etc.) When you don't understand how to solve the problem, of, course, think about understanding but also start working with incomplete understanding and uncertainties. As you try, you can get a better feeling of the problem, will be able to get rid of some illusionary ideas and get new ones... Moreover, in some analogous ways, I many times recommended people to... avoid reading literature. Here is what I mean: it's good to try to solve a problem from scratch by yourself. Why? First, you won't miss a pretty rare chance of inventing something really new. More realistically, when you read, you don't quite understand reading at first, because the illusionary understanding is quite common, besides, you can be affected by some well-established ideas and reduce your chances for a fresh look. And when you tried hard and broke some of your teeth at the problem, you can use what you learned, and then you will ready with much better understanding. — SAMonday 2020 December 7, 04:01 UTC
There are definitely a lot of merits to that approach, but in my experience, incomplete data can lead to wrong conclusions. This is especially true in cases where the data is wrongly interpreted- or worse, outright ignored- though it would be ill-advised for me to talk about specific examples of these sorts of things here and now for a variety of reasons- not the least of which is the potential for pointless arguments. --Aura (talk) 04:56, 7 December 2020 (UTC)
I should have said that it also depends on individual traits, but I thought this is too obvious. Incomplete data? This is what is our brain is sharpened for. I have some arguments in favor of dealing with incomplete data and looking at this incompleteness as a normal thing. First of all, data is always incomplete, when it comes to science. Not all people can interpret an incomplete set of facts objectively, but being misled by other people is worse. Come to think about, this is because we actually tend to be convinced too easily. This is the result of our social skills, social adaptation mechanism. The observation of so many heated discussions should not fool us, this is not the dominant trend. — SAMonday 2020 December 7, 08:45 UTC
By the way, do you really still use MP3?! It is not just obsolete, it is stone age, with ridiculous quality and compression. Top Web standard is .opus, is supported by everything. Probably, MP3 is alive only due to the existence of the devices like car audio — nothing is so conservative as those weird people designing such devices. :-)
Unfortunately, Musescore 3- the program I used to make music- does not support .opus files. --Aura (talk) 01:11, 7 December 2020 (UTC)
This is not important. Okay, Musescore is obsolete in this aspect, but it doesn't matter. It's very usual that you use some standards (sometime proprietary) for everyday work, but something different for publications. This is not a problem; you can convert anything to anything. Most universal FFMpeg does it all on all platforms. Latest news in containers and codecs are amazing, by the way. First of all, this is availability of open-source no-royalty AV1 codec (now even with reasonably fast encoder) for absolutely standard WebM/Matroska containers. It compresses my already compressed phone video 10 times without any noticeable loss of quality. Modern raster graphics standard is WebP, it totally renders obsolete JPEG, PNG, and GIF (because animation is also supported) and even TIFF and all lossless standards, because even lossless compression is better than nearly anything else. And for 2D vector, SVG remains the only standard; you use it. I can show my presentation, it's very interesting (in turn, I rendered obsolete all those offices presentation packages, provide open-source and very lean browser-based alternative; if interested, I'll give you a link) — SAMonday 2020 December 7, 02:14 UTC
Perhaps you can convince Musescore 3's developers to enable the support of things like .opus files. I know that Musescore has many of the kinds of options I actually need for composition, so there's that. --Aura (talk) 03:00, 7 December 2020 (UTC)
Well, I learned to brainwash people less and do more by myself, even though I sometimes managed to influence people by insisting on some right ideas persistently. But in this particular case it doesn't worth it. Simply work on what the product offers you, and convert to what you need for output. — SAMonday 2020 December 7, 03:44 UTC
As to whether or not I want to play with other keyboards, the answer is yes. That said, money is still an issue, and I'm not exactly willing to borrow money to pay for stuff if I can help it. If I need to pay for stuff, I'd rather have the funds to pay for it myself. --Aura (talk) 19:57, 6 December 2020 (UTC)
Very good. First of all, "paying" for anything is totally unrelated to all my activity on this topic now and in foreseeable future. Not only my platform is open-source and based on permissive licenses, but all my help I provide now is based on mutual interests, promotion of collaboration, and so on. Just ask if you have any questions, or I'll present to you my last results when I come to next suitable point. But you don't have to wait for this moment... — SASunday 2020 December 6, 20:08 UTC
Ah. That makes sense. --Aura (talk) 20:12, 6 December 2020 (UTC)

Microtonal Playground (Part 1)

Okay, the application already works, and I already filled in your paradiatonic scales for the demo.

I will publish it as an experimental product under development really soon, then I plan the completion and fully-fledged publication.

So, here is some questions. First, I happen to know your real name (given + family name), so asking just in case: can I mention it publicly in some document (credits/contributors, help, demo file, article)? Of course, you will know the precise context where it can be mentioned.

Can you take the labor of playing with it and some testing? First of all, it would be good if you check up your own scales, both sound and labels on the keys.

Everything works, I only want a bit more testing and fixes, and expose a bunch of small common things which are already there for other applications: controls of volume, sustain, transposition (unfortunately, only by octave in this case, as there is no a well-defined tone or microtone, as this is not necessarily a EDO — any better idea?), and also the presentation of metadata and help. And then, there must be a recorder. We will be able to play exact same things by sending around a record and a tonal system data file. If you want it now, I'll send you a link, but my plan is to prepare a bit more and put a link on my main page as "Experimental"...

What do you think?

You do indeed have permission to mention me by name- though we must work out the exact context for these mentionings, as there may be other info that needs to be either suppressed for privacy concerns or included for clarification. As for the testing, I need a link. --Aura (talk) 01:49, 8 December 2020 (UTC)
Please take a look: Experimental: Microtonal Playground on my main page. This section provides some minimal introduction, and the application comes with incomplete but quite sufficient Help.html.
Note the link under your name, and the "scale" link before. It it fine? There is no any references to you in the application, but my plan is: enter the name/links in the "" metadata properties, provide viewer for current tonal system metadata, add "Credits" sections to the help. Makes sense? Please, if I make any inappropriate or incorrect reference to your material, let me know as soon as possible. — SATuesday 2020 December 8, 20:31 UTC
I actually like most of what I'm seeing in the microtonal playground. The only thing I presently don't like is the current layout of the bottom scale, as 3/2 doesn't appear in that scale where as 4/3 does. Other than that, it is a very interesting thing to play around with, especially since you can create other scales through pressing keys in a diagonal fashion. So far, the information you have presented on your page is accurate. When the page you linked is updated, then we'll discuss how to modify your links, and for that, we need Xenwolf's help, as I forget how to link older versions of pages. --Aura (talk) 22:23, 8 December 2020 (UTC)
Well, thank you. Now, which bottom line? The real bottom row is "Demo", its only purpose to show how to a insert fixed-frequency key, a key with a custom label, a disabled key, and repeat. Don't you say that your "bottom row" named "Locrian" (actually, second last) is wrong? Sorry that I only roughly tested your scales, done them very quickly. (Did you noticed the titles on the keys which read "Ionian", "Dorian", ..., "Locrian", "Demo"?) I meant that the rows show have the same scale as your correspondent scales. Did you double-check that they match? And did you look at the file "" which you could edit (in the same directory)? There is a short explanation on my main page. — SATuesday 2020 December 8, 23:28 UTC
I'm talking about the second-to-bottom row, the lowest row with nothing but notes. Sorry for forgetting about all the technical buttons on the bottom. --Aura (talk) 23:32, 8 December 2020 (UTC)
Yes, thank you! It's Locrian. Fixed. Please re-load the page (usually Ctrl+R) and see. It is the only 5th degree with 4/3 instead of 2/3, right? The usual paste bug. Is it all good now? — SATuesday 2020 December 8, 23:38 UTC
Almost fixed- the fourth degree of the scale is actually 4/3, while the fifth degree of Locrian is actually 64/45- the buttons are in the wrong order. --Aura (talk) 23:42, 8 December 2020 (UTC)
Ah... few sec... — SATuesday 2020 December 8, 23:45 UTC
Yes, fixed, looks correct, but... push did not reach the auto-published product site on GitHub, they have a mysterious delay, may appear later today or tomorrow. I reported this problem to them, they did not reproduce it. No matter, I can notify you. Also, you can download the entire product (there are all links on my main page); first, it will be up-to-date, secondly, you can try editing the tonal system and try. However, this is a very simple thing, but I would like you to take a look, maybe provide some critique... — SATuesday 2020 December 8, 23:58 UTC
Aha, now the fix is propagated to the site, you can take a look. Thank you for the correction! — SAWednesday 2020 December 9, 00:12 UTC
What do you think of my idea of auto-repeated tones? On the example of your scale, you write only the degrees, in your case, 7 of them. Instead of second 1st, you write the special object repeat, for example:
[interval(1), interval(9,8), interval(5,4), interval(4,3), interval(3,2), interval(27,16), interval(15,8), repeat], and then the system automatically fills in missing key data to the end of the key row, moving to next octave on each next 1/1...
What is interval? Even though for this particular application numbers would suffice, what it returns is not a number! This is a more complicated object; the set of them implements the same very systems of regular intervals, a free Abelian group used in this part of musical theory. I developed this formalism for wider purposes, such as generator systems and other group theory approaches. This object is semantically similar to Monzo, it is maintained in the factorized form, the group operations are done on the maps of prime factors, and so on, complete operation set. Are you familiar with all that? I would assume you are, and a lot of material on this site assumes the readers can work with such notions. Right? — SAWednesday 2020 December 9, 00:27 UTC
I have to admit I don't really know how to program all that well, and I'm only partially familiar with some of the terminology on here- some of the other microtonal music theory is not an area I've gotten to yet as I've only been on this wiki since the end of August myself. --Aura (talk) 01:09, 9 December 2020 (UTC)
Surely, you don't need to know how to program it, if you are not into it already, but the mathematical aspects, this group theory things are important for your activity, as many aspects are based on it. Right now, I'm into it very much, can clarify many things. This matter is easy to learn, provided the source of knowledge is reasonably good. By the way, I noticed a lot of really bad mistakes in Mike Battaglia's lectures (plain false statements or simply confusions), commented on them, did not get any reply from the author, only Xenwolf expressed agreement with me. Unfortunately, this entire material has to be replaced. It is referenced from the site's main page and is bad for the site's reputation. — SAWednesday 2020 December 9, 01:47 UTC
@SA: If you'd take the time to write a introduction about group theory in respect to music, at least I would highly appreciate this. Thanks....and sorry for disturbing --Xenwolf (talk) 09:41, 9 December 2020 (UTC)
Wait, did you mean "Monzo" or "Gonzo"? I don't know about "Gonzo" but I do know about "Monzo", and yes, I do work with that bit of math by means of my decade-old graphing calculator. --Aura (talk) 02:12, 9 December 2020 (UTC)
Monzo! Thank you. This is my "favorite" kind of typo, you know. Fixed above.
That makes more sense. --Aura (talk) 03:14, 9 December 2020 (UTC)
Unfortunately, you cannot do any kind of mathematics on a calculator :-). Okay, about those typos, some funny story. I always get into some funny situations. For my very first international conference, I've sent a paper named "Shall we Replace...?" And I made a typo in the very title. It was "Shell we...?". People praised me for the quality of the article text itself, and they fixed the typo in the Proceedings... years after the conference. Someone explained to me, that the editors thought that my title was made with the intent to make some funny wordplay. Probably, someone imagined that by saying "Shell we Replace...?" I implied some kind of software "shell" I proposed to replace with my technology.
Also, for years I thought that "weather" and "whether" is the same word, one word, and thought it was perfectly reasonable. I thought that the weather is so uncertain that nobody can know whether it can be good or not tomorrow, hence the same word in the language. — SAWednesday 2020 December 9, 03:07 UTC
For the record, my calculator is a TI-89 Titanium, so it's not just your common desktop calculator. I agree that there's some calculators that your really can't do good math on, but this one you actually can- at least you can get the Monzos of rational intervals with the "factor" function. --Aura (talk) 03:14, 9 December 2020 (UTC)
I did not mean that, about the calculator. Ah, you probably call calculations "math". This calculator still works with numbers, right? But, in a way, mathematics is something opposite to the numbers, even though there is a big theory of numbers in mathematics, and a lot more. Sometimes I say that going in for mathematics is one of the ways to avoid doing any calculations whatsoever. :-) Software and computing science too, by the way... — SAWednesday 2020 December 9, 03:22 UTC 03:22, 9 December 2020 (UTC)
So "mathematics" isn't the same as "number crunching". Interesting idea, but I suppose there's merit to that idea after all- especially if it turns out that the formula for deductive logic can be stated as something like A + AN → C with "A" being the additional argument, "AN" being the sum of any and all additional arguments, and "C" being the conclusion (an idea I've had floating around for a while now). --Aura (talk) 03:34, 9 December 2020 (UTC)
Well, it's not just this. I meant that in practice if you do some mathematics, on a personal level you can distance yourself from any kinds of practical calculations. One of the driving forces is the elimination of all kinds of repetitive work and too concrete notions. Even the merit of mathematics is not just the calculation, even though the absolutely concrete solutions of practical problems is the major part of it. First of all, it gives a common language to the sciences. This way, it helps to unite the sciences. Remember, I mentioned "real" theoretical mechanics, as opposed to what engineers usually learn? Here, the popular physical paradigm "same equations => same solutions" works. Say, in Hamiltonian/Lagrangian formalism the objects are not necessarily mechanical objects. Simply put, you can assemble a thingy made of weights, springs, solenoids, resistors and capacitors and analyze it with a single common system of equations, which is totally agnostic to which part of it is "mechanical" and which one is "electrical". And this is exactly the same notion of "theoretical mechanics" relevant to the theory of music. You don't need to classify vibrations into mechanical, acoustical, electrical, or, say, hydrodynamical — they all can be composed in a single instrument, working together and not separated theoretically. I noticed some usual fallacy in some musical theorist I knew: they often consider the human ear as something separate from the musical instruments, a pure receptor device. But the correct approach is to consider the ear as the same kind of system as any musical instrument — working together. Well, I also know people who do understand that. — SAWednesday 2020 December 9, 05:08 UTC
Excuse me, I still don't know: do you confirm that after my last fix your 7 scales are put correctly in the Microtonal Playground? — SAWednesday 2020 December 9, 05:18 UTC
Yes. The 64/45 interval is a diminished fifth, and Locrian actually does have this kind of fifth. A 64/45 diminished fifth doesn't operate in the exact same way as a 3/2 perfect fifth when it comes to music- even though there are operational similarities- and this is one reason why many musicians don't seem to know how to handle Locrian mode. --Aura (talk) 05:26, 9 December 2020 (UTC)
So, all seems to be right? — thank you! I knew that Locrian was considered tricky. :-) — SAWednesday 2020 December 9, 05:29 UTC
And may I ask you to avoid separating my paragraphs separated by the indent into separate fragments by your newer comments? I'm trying to support this: if I use two indented paragraphs without separating them by an empty line, I mean to keep them together, so your added comment can come after them, but not in between. Two funny stories about my typos became separated due to this problem, I just moved them back together. Ok? — SAWednesday 2020 December 9, 05:34 UTC
Right then. Some paragraphs seem to be suitable for splitting apart from one another, while others are not. It doesn't help that not every user has the same style in regards to this. --Aura (talk) 06:47, 9 December 2020 (UTC)
Thank you for understanding. "Not the same style" could be a problem, but the priority should be given to the author of the original post, as this person knows the original intent better than the author of a secondary comment; I hope you'll agree. — SAWednesday 2020 December 9, 06:53 UTC
I do agree when it comes to the original content rule. However, we should perhaps talk to Xenwolf about how to more reliably distinguish the two types of multiparagraph posts. --Aura (talk) 06:56, 9 December 2020 (UTC)
Ah, when we both post in parallel on the same page, I noticed that my comment sometimes get lost. Maybe I'm just not careful enough... — SAWednesday 2020 December 9, 05:34 UTC
We both make that same mistake to be honest, and I do think Xenwolf will have to teach you the exact procedure for what to do when your text is what gets deleted due to an edit conflict. I may have basically summarized the general essence of that procedure on his page, and it may be true that whether it's my comment that gets lost or your comment that gets lost is kind of up to timing, but truth be told, I imagine that there are other details and nuances that he's better able to fill in- because he's an admin. --Aura (talk) 06:46, 9 December 2020 (UTC)
I'm not sure. If you think we both done some mistakes, can you explain how to avoid it? Maybe your first comment on the topic was correct: this is the simple behavior of the system: earlier post knocks out the uncommitted post when another user is still in an editing state? This is not good enough, but is simple and kind of natural. :-)
The systems I worked with were on top of the revision control, where the resolutions are fundamental. By the way, do you use any revision control in your work? Believe me, this is heaven. When I started to use them in all cases, all my life went much easier. Even if I have the smallest project, even if the entire project is a pretty short post or a document in a single text file, I create a local revision control repository and work on it. All steps are reversible, you cannot possibly lose anything, you can find traces of your earlier efforts in no time, and so on... It takes absolute minimum of resources, installs and configures in a minute, just brilliant help from a tiny piece of software. — SAWednesday 2020 December 9, 07:06 UTC
Yes, the earlier post does in fact seem to knock out the uncommitted post while the other person is still editing, so there's that. If revision control involves a program I don't have I might not be able to use it- then again, revision control in talk pages doesn't seem to make as much sense as revision control in the actual articles, and you and I both seem to be spectacularly prone to typos, even though you use revision control all the time. Revision control on my end is more likely when I'm attempting to edit another type of document. That said, I do think Xenwolf should walk you through the procedure of preventing the complete loss of those uncommitted posts for good measure, and I asked him about it. --Aura (talk) 07:14, 9 December 2020 (UTC)
Okay, probably we understand how such posts conflict. Now, "revision control in talk pages doesn't seem to make as much sense as revision control in the actual articles"? No, I think you are not right. 1) In the present situation, there is no difference between articles and talks, so revision control would be equally useful. 2) In better situation, say, on GitHub where wiki is fundamentally integrated, the talk looks "more talkative", much closer to the chat software, which is much more usable: people are not working at the same document. Instead, each post goes in a separate section, everything is automatic, you don't have to do these very annoying indents, and yet it's quite apparent which comment you are commenting. And when people work at the same document, this is just a work at a file, no matter if this is a wiki or any other file, same revision-controlled behavior. Also, there are no special "Talk" pages, which is also very good. Instead, a discussion can be opened on every event, first of all, a commit pushed to the central repository. A commit, release, tag, some action, but not a file. This is very logical: what we discuss? Not a file itself, but rather a decision: adding a bunch of tiles, changing them, a request, and so on. It absolutely cannot prevent any free discussions. Say, you request some approval from members for the decision affecting others? Okay, we discuss it first, then decide together. It is not related to actual permissions, we can use different permission policies, from a very free one to a very strict. Mediawiki is great, simple but just overly generalized, maybe oversimplified: the concept of Talk is no different from an article, so we don't have chat-specific features, so this is not so convenient in first place. Maybe you simply need to look at such systems where wiki is integrated with revision control, then you would have a better feel of it. — SAWednesday 2020 December 9, 08:03 UTC
And, as you often say, for a record: I do not use any revision control for my talks on this site (more exactly, I do have some repository, but this is more of a TODO collection). If revision control is not well integrated, the trade-off between efforts and the usefulness is not so good. With real articles, the story is totally different: I developed a pretty big publishing system, worked as a contributor for the Microsoft Visual Studio Code (in contrast to bulky Visual Studio, brilliant editor and IDE: open-source, multi-platform, very light weight). I easily adopt any article project to any reasonable requirements, always work on revision control, and almost never use any online editors. But then this approach helps me to push an article to the publication pretty much in a single shot. For a talk with its small posts, it would be way to much bothering... — SAWednesday 2020 December 9, 08:36 UTC
It sounds like we actually have a somewhat similar stance regarding revision control for talks on this site- the only thing is that talk pages on this Wiki are those pages that are specifically designated for host such talks, where as other pages (especially the ones I'm referring to as actual articles) are not. There may not be any difference from a technical standpoint, but I'm more concerned about the designated function of the page when it comes to this. On my end, I have to admit I don't have even a proper repository in most cases, so that's on me. Also, I don't exactly keep track of Mediawiki's technical aspects as I'm not an admin. --Aura (talk) 17:23, 9 December 2020 (UTC)
On another note, the statement I use is "for the record", not "for a record". I've done enough studies on Russian (informal studies of course) to know that the function of words like "a" and "the" in English is accounted for in Russian by the definite and indefinite forms on verbs, with "the" corresponding to the marker on Russian's definite forms while "a" and "an" correspond to the marker on Russian's indefinite forms whenever they actually appear. Yes there's functional differences between words like "a", "an" and "the" and the markers on Russian's definite and indefinite forms- namely that in some cases, such as with Proper nouns, the word "the" isn't always needed, while "a" and "an" are only use for single objects- other functional aspects are quite similar. Just thought you might want to know. --Aura (talk) 17:23, 9 December 2020 (UTC)
Ha! Thank you for the note. What you say is perfectly true. You know, I sometimes participate in discussions over one great Russian Youtube channel devoted to English, have some involvement in linguistics, and understand such issues related to different patterns and lines of thinking in different cultures. You probably know that Russian is very complicated, highly synthetic-inflectional, and lacks articles, but article functions do exist in some strange ways. We discussed a lot of interesting and often very funny things. I'm not sure you correctly understand the expression of "article functions" in Russian. First of all, I don't know what is "indefinite form of nouns", I only understand "indefinite verb", and I think the notion "indefinite" is not even used in Russian. Article function is more typically expressed with an adjective. However, nouns also can play some role. I'll give you only some funny examples. For example, in modern jargon, people often use the moderately rude word "pepper" (or "horseradish", with the jargon use of complicated euphemism origin) meaning simply "male person". In certain contexts, one of this jargon meanings is "a man" as opposed to "the man", that is, some man, no matter who, or unknown one. There are many similar cases. Now, one funny adjective example. One day, my friend and former roommate make my guest laugh by saying in the discussion on some legal matter: "Suppose, you have some abstract wife...". I knew him better, so for me, his manner of expression was natural. Indeed, in some "cultured" communities the adjective "abstract" is used to carry just the function of the indefinite article. :-) — SAWednesday 2020 December 9, 19:04 UTC
Sorry, I forgot that Russian does the definite-indefinite distinction with verbs rather than nouns, but funny enough, some languages- if I recall correctly- express the definite-indefinite function on nouns rather than verbs. My mistake. Fixed in my above comment. --Aura (talk) 19:16, 9 December 2020 (UTC)
Please, no need to apologize, and thank you! This is just a very interesting topic. — SAWednesday 2020 December 9, 19:56 UTC
I must also point out that for one of my other projects, I'm actually trying to create a language that is descended from English in the same way that Spanish, Italian and French are all descended from Latin. This language is weird in some ways because the parts that decline verbs in this language of mine are prefixes rather than suffixes- oh, and there's a realist future tense for things that are bound to happen as opposed to irrealis future tenses that have distinct deontic, conditional, or epistemic modality. --Aura (talk) 19:27, 9 December 2020 (UTC)
Oh! It sounds so interesting! You know, it was my guess based on some of your comments, that you also take special interest in linguistics. Any more information? Links? — SAWednesday 2020 December 9, 19:54 UTC
The majority of the fruits of my labors in this particular arena are not to be found online, and that is for a reason- they are connected to what should eventually be a serialized novel roughly the size of "War and Peace" that I have yet to finish. That said, we can exchange emails about some of the present details of this language- especially since talking in depth about this matter is not a topic that is suitable for this Wiki. --Aura (talk) 20:02, 9 December 2020 (UTC)
"War and Piece" size? Great, please don't forget to include your chapters on historical philosophy. :-)
Now, about e-mail exchange — this is the right idea. I don't mind at all. Let's do the following: really, let's set aside all further discussions here (except musical/mathematical/software topics potentially interesting to the Xenharmonic readers) and move them in private. More exactly: to start, will you look at my contact section on my main page. I reference two means of indirect mailing: via my site or You can try both and decide what is more convenient for you. Then we'll have a further choice: to continue in any of these ways, or go further away from any of these sites, which would be even simpler. To do so, you may choose to share some real e-mail address, and then we will have more choices. First, I can send my real e-mail in response. I will ask you to keep it secret and address other people to my page. Also, I can invite you for a chat, which is more convenient than e-mail, but it would be better to use both chat and e-mail, depending on the purpose. Finally, I have a choice of chats I actively use: 1) I can create a channel on my Slack site, it is more convenient and mostly used for my discussions with musicians, 2) Skype, which is much less convenient, 3) I have some settings for an ad-hoc chat. Now, all chat channels I have are non-commercial, but they allow voice and video over IP (but only one facility has screen sharing). I have the applications, but on your side, you don't have to install anything, pure Web browser would suffice. I don't really like using video, but would not mind talking in voice. I really prefer char for small talks. Also, we can only try different channels and then decide. So, what do you think? Will you do it? If you will, the next step is yours. — SAWednesday 2020 December 9, 20:53 UTC
Truth be told, there are a lot of elements concerning the historical philosophy that I'm keeping secret at this time, though perhaps we can talk about some of them during our discussion. I did go to your contact section on your main page, and I decided to send an email via, and chances are we will likely continue our conversations among personal email exchanges. I do intend to keep things secret as much as possible, but given the nature of technology, and the fact that I'm only now starting to get help on the actual novel from other people, some elements of our conversation may end up on Discord, though we will have to discuss which things we can allow to make their way to Discord and which things we need to keep under wraps. --Aura (talk) 21:03, 9 December 2020 (UTC)
For the record, I have no intention of sharing your real email with other people, so no need to worry about that. It's other things that I'm concerned about keeping secret on my end. --Aura (talk) 21:08, 9 December 2020 (UTC)
I do understand it, no worries at all; I mentioned it just for keeping things proper. So, will you write to me? If you share your real e-mail in any of your communications, I'll surely keep it secret, naturally. — SAWednesday 2020 December 9, 21:16 UTC
Frankly, as you could have noticed, I mentioned historical philosophy only to make a humorous reference to L. Tolstoy. (At school, many children make fun of Tolstoy, because these chapters are enormously big, so many consider them as inappropriate, but I've read them very carefully even at that time.) At the same time, somehow I'm not too surprised that you have something real on this topic. — SAWednesday 2020 December 9, 21:23 UTC
I attempted to write to you by means of soon after I mentioned us emailing one another. However, I'm now wondering if that email went through. You may need to check your email's files for junk, as the email I sent could have ended up there for some weird reason. --Aura (talk) 21:28, 9 December 2020 (UTC)
Not to worry, your message arrived just as expected, thank you. Now, do you want to go further and share your e-mail, or I can send a message in the same way first, share my e-mail, so we can communicate independently from this site, more conveniently? — SAWednesday 2020 December 9, 21:50 UTC
Finally! I was wondering when it would. I think it would be better for you to respond to my message. Given my experience exchanging emails with Xenwolf, I think it best that you actually respond to the message I sent. Hopefully from there, I can respond and give you my actual email. If not, we'll try another means of exchanging emails. --Aura (talk) 21:59, 9 December 2020 (UTC)
Done. Please give me the confirmation here, just for this first time. — SAWednesday 2020 December 9, 22:25 UTC
I got your message, and I've sent a reply. We should be good from there. --Aura (talk) 22:33, 9 December 2020 (UTC)
Yes, everything looks fine. Thank you. You got my reply; no need to send confirmations anymore.
I got a pleasant surprise: I tried to explain the pretty nasty Wiki styling bug with external links (at least for Vector I use), and Xenwolf kept saying that everything is fine, there was nothing to fix. But recently I found that the bug is fixed by someone. It feels nice! — SAWednesday 2020 December 9, 23:46 UTC
I do however think I should mention that "Folly of a Drunk" sprang out of an early draft of one particular scene in my serialized novel, as do a number of my non-microtonal songs. --Aura (talk) 20:08, 9 December 2020 (UTC)
Yes, interesting. — SAWednesday 2020 December 9, 20:27 UTC
Also, only today I faced the problem with sound degraded with time, don't know how to reproduce; this problem was never exposed with the rest of the applications based on the same synthesis engine. That problem may take time... — SAWednesday 2020 December 9, 00:01 UTC
I've noticed it too honestly. --Aura (talk) 01:09, 9 December 2020 (UTC)
Thank you for telling me. Okay, it's better to have the problem exposed than having wanna-be fine operation with a time bomb inside. This is troublesome, but I should fix it. For the pre-production, it is acceptable to expose the problem to the public. — SAWednesday 2020 December 9, 01:38 UTC
I should also mention that the current link to my user page may eventually need to be changed to link to another page on this wiki- namely a page with my real name detailing what I'm known for in the future. However, that day has not come yet- this is just something we may need to keep on the radar for the future. --Aura (talk) 22:27, 8 December 2020 (UTC)
I remember that. But this is the ideology of Wiki: as everyone can edit everything, if you change your URL and know someone references it, you can go to this person's page and fix it. I would invite you to do so when you change your URL. If you don't want to change it by yourself, just notify me. — SATuesday 2020 December 8, 23:28 UTC
If you link to or cite my pages here on this wiki, we also need to take stock of the fact that the content of these pages is liable to change in the future. Sorry I didn't say this right the first time. --Aura (talk) 01:56, 8 December 2020 (UTC)


V. 4.9.5: Added mechanism of customization of user's tonal system in a separate file, refined user's error reporting.

The customization is shown on the sample playground/custom-demo.

This is how customization works:

The user creates a new copy of the file in some separate location. The application can start with this file if it is specified in the Web browser address line as a query parameter, for example:


The path should be relative to “...playground/index.html”.

For simplification, this address line could be placed in another custom file, an HTML file, such as the demo file “index.html” in playground/custom-demo. In this case, the application can be started with the custom tonal system data in one click.

Customization cannot work in live demo. Instead, the entire project should be downloaded. See the green button entitled “Code”. In the downloaded code, we only need its sub-directory “docs”, everything else can be deleted. (The weird directory name “docs” is related to the GitHub naming requirements for the content served by a product's Web site used for live demo. In fact, all the production code is in this directory).

Keyboards based on the designs by Kite Giedraitis

The discussion on this topic shall be moved to a separate sub-page

Reduce comma tables on EDO pages

Please have a look at Xenharmonic Wiki: Things to do #Comma tables in EDO_pages. Thanks --Xenwolf (talk) 09:09, 11 January 2021 (UTC)

Looking... — thank you. — SATuesday 2021 January 12, 21:23 UTC

Microtonal Playground (Part 2)

Hey, SA, it seems that the Microtonal playground has one problem, at least in the 12-edo version. The "B" in the Mixolydian row should be renamed "B-Flat" to match the other instances of that same note in other rows. Sorry about this. --Aura (talk) 22:02, 19 February 2021 (UTC)

Thank you, that's correct. Fixed. — SASaturday 2021 February 20, 17:05 UTC