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TallKite

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:: If you want, I can post the score on my user page. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 09:47, 1 November 2020 (UTC)
:: If you want, I can post the score on my user page. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 09:47, 1 November 2020 (UTC)
::: Yes, please do!--[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 09:51, 1 November 2020 (UTC)
:::: Alright, the score is up on my user page, and I did in fact respond to your comments on my 11-limit ideas. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 10:32, 1 November 2020 (UTC)
== Harmonize categories of interval pages ==
Hi TallKite, we are interested in your opinion about [[Xenharmonic Wiki:Things to do #Categories of interval pages|Categories of interval pages]], thanks in advance for taking the time. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 21:21, 8 November 2020 (UTC)
:OK--[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 05:19, 9 November 2020 (UTC)
== Fifthspan question ==
Thanks in advance for having a look into [[Talk:Fifthspan #About ringy confusion]]. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 16:55, 20 November 2020 (UTC)
== System for Describing Alpharabian Tuning ==
In evaluating my work on Alpharabian tuning, you asked if one can work backwards from my interval names, and if there a formula or an algorithm for that.  So, I've decided to try and answer the question.  After going through the list of names, and reevaluating the names in my system, yes, there 'is' a set of rules for how the names of the intervals in Alpharabian tuning are derived.  However, there appears to be some modifications to my system that are required, and I will attempt to make some of them here.
There are three fundamental premises of the Alpharabian tuning system:
* Intervals that are in the 2.11 subgroup are all considered "Alpharabian".
* Intervals that result from the modification of a Pythagorean interval by [[1089/1024]] are labeled similarly to those modified in the equivalent fashion by [[2187/2048]], the only difference being that modification by 1089/1024 results in an Alpharabian interval rather than a Pythagorean interval.
* Since 1089/1024 is (33/32)^2, modifying a Pythagorean interval by [[33/32]] always results in an interval that is considered "Alpharabian".
There's also at least one known secondary premise at play:
* As both the [[243/242|rastma]] and [[1331/1296]] are subchromas that form differences between members of the 2.11 subgroup and Pythagorean intervals, both of these subchromas belong to a set of intervals defining different interval sets within Alpharabian tuning, and subchromas within this particular interval set help define the differences between Pythagorean, Alpharabian and Betarabian intervals.
The following rules are directly derived from the above premises:
* Generally, intervals that result from the modification of a Pythagorean interval by 33/32 take either the 'parasuper' or 'parasub' prefixes, however, there are a number of special cases...
:* Augmentation of a Perfect Fourth or Perfect Fifth by 33/32 results in a Paramajor interval
:* Dimunition of a Perfect Fourth or Perfect Fifth by 33/32 results in a Paraminor interval
:* Augmentation of a Pythagorean Minor interval by 33/32 results in a Lesser Neutral interval
:* Dimunition of a Pythagorean Major interval by 33/32 results in a Greater Neutral interval
* Generally, intervals that result that result from the modification of a Pythagorean interval by 1331/1296 take either the 'super' or 'sub' prefixes, with these prefixes generally being stacked where multiple such modifications occur, however, there are some significant caveats...
:* Augmentation of a Pythagorean Minor interval by a single 1331/1296 results in a Supraminor interval, but a second such augmentation results in a Betarabian Major interval due to said interval differing from the nearby Alpharabian Major (covered under modifications by 1089/1024) by a rastma.
:* Dimunition of a Pythagorean Major interval by a single 1331/1296 results in a Submajor interval, but a second such dimunition results in a Betarabian Minor interval due to said interval differing from the nearby Alpharabian Minor (covered under modifications by 1089/1024) by a rastma.
Modifying by combinations of 1331/1296 and 1089/1024 yields interesting results, but I have yet to properly create the part of the system for dealing with these sorts of things.  I think we could afford to work together to develop this and to fix remaining flaws if you have the time. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 17:22, 22 November 2020 (UTC)
: I can name every note and every interval in the 2.3.11 subgroup using only ^ and v. And knowing only that ^1 is slightly less than half a sharp, the size of any interval can easily be estimated.
: Here's a simple formula for converting a 2.3.11 monzo to ups and downs:
: (a, b, c) = c * (-5, 1, 1) + (a + 5c, b - c) = c ups (or -c downs) + pythagorean interval
: The pythagorean intervals are named conventionally as M2, m3, etc. So (0, -2, 1) = ^m3
: Here's simple formulas for converting an upped or downed pythagorean interval to a monzo:
: x ups + (a, b) = (a - 5x, b + x, x)
: x downs + (a, b) = (a + 5x, b - x, -x)
: Here's simple formulas for adding together two upped/downed intervals:
: [x ups + (a, b)] plus [y ups + (c, d)] = (x+y) ups + (a + c, b + d)
: [x ups + (a, b)] plus [y downs + (c, d)] = (x-y) ups + (a + c, b + d)
: You don't even need formulas for this, actually. You just add up the pythagorean intervals as usual, then add in the ups and downs. Adding an interval to a note works the same way, as does finding the interval between two notes.
: Here's the 2.3.11 lattice, with a vertical step equal to 33/32:
<tt>
^^F  ^^C  ^^G  ^^D  ^^A  ^^E  ^^B
  ^F  ^C  ^G  ^D  ^A  ^E  ^B
  F    C    G    D    A    E    B
  vF  vC  vG  vD  vA  vE  vB
vvF  vvC  vvG  vvD  vvA  vvE  vvB
</tt>
: Each row is a chain of 5ths. The top row is the double-up row, next is the up row, next plain, next down, next double-down.
: Another version of the lattice, with vertical steps of 11/8:
<tt>
^^Eb ^^Bb ^^F  ^^C  ^^G  ^^D  ^^A
  ^Bb  ^F  ^C  ^G  ^D  ^A  ^E
  F    C    G    D    A    E    B
  vC  vG  vD  vA  vE  vB  ^F#
vvG  vvD  vvA  vvE  vvB  vvF# vvC#
</tt>
: Another version, with 1/1 - 11/9 - 3/2 and 1/1 - 27/22 - 3/2 triads forming triangles.
<tt>
^^Fb ^^Cb ^^Gb ^^Db ^^Ab ^^Eb ^^Bb
    ^Ab  ^Eb  ^Bb  ^F  ^C  ^G  ^D
  F    C    G    D    A    E    B
    vA  vE  vB  vF#  vC#  vG#  vD#
vvF# vvC# vvG# vvD# vvA# vvE# vvB#
</tt>
: See how simple and clear it all is? Everything follows directly from ^1 = 33/32. So it's quite possible to have a very simple nomenclature for everything.
: You have Alpharabian, Betarabian, Paramajor, Paraminor, Greater Neutral, Lesser Neutral, Supraminor and Submajor. And from your previous comments, Rastmic, Birastmic, and Trirastmic. Your nomenclature is way more complicated than it needs to be.
: I've read what you've written several times and I still have no idea which parts of the lattice are Alpharabian, which are Betarabian, and which are neither. I also have no idea how to add together two intervals, or what note I get from adding an interval to a note, or how to name the interval between two notes. I suspect formulas for those things would be impossible.
: So unfortunately, I don't see much point on working with you to improve your nomenclature. Because my first suggestion would be to drastically simplify it. We seem to have fundamentally different approaches. --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 01:45, 26 November 2020 (UTC)
:: I do agree that we seem to have fundamentally different approaches...  I know I'm taking inspiration from the SHEFKHED interval naming system and Pythagorean tuning, so there's that.  If we cannot work together to define nomenclature, that's fine.  I guess I'll just have to talk with other people about this then. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 02:17, 26 November 2020 (UTC)
== Your current additions to EDO pages ==
Hi Kite, I think it would be better to slow down in these additions. I'm currently evaluating the potential of Lua modules for this wiki, see https://dev.xen.wiki/w/User:Xenwolf/SandBox ... what I already learned is "revolutionary" especially to any ET templates and the prime approximation tables as well. To be more precise, as M2, m2, and A1 can be automatically calculated from P5 and P8 (steps of the given EDO), it's not necessary to do anything by hand any more:
<syntaxhighlight lang="lua">
--- Tonal properties of an EDO and its Fifth (draft)
-- @param P8 mumber of edo steps making an octave
-- @param P5 mumber of edo steps making a fifth
-- @return M2 size of the whole tone
-- @return m2 size of the diatonic semitone
-- @return A1 size of the chromatic semitone
local function tonal_props (P8, P5)
  local M2 = 2*P5 - P8
  local m2 = 3*P8 - 5*P5
  local A1 = 7*P5 - 4*P8
  return M2, m2, A1
end
</syntaxhighlight>
I'll soon add a test case for this in the dev wiki. Hopefully this feature (Scribunto+Lua, see [https://dev.xen.wiki/w/Special:Version Version page there]) will go to production soon. BTW: If you are interested in joining the evaluation effort, you are most welcome. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 11:26, 9 December 2020 (UTC)
: Oh wow, cool! OK, I'll stop working. --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 11:44, 9 December 2020 (UTC)
:: The observation of M2 being sometimes smaller than m2 or A1 makes me wonder if the naming couldn't be somewhat confusing, see [https://dev.xen.wiki/w/User:Xenwolf/SandBox#Test_Module:edo_tools table with M2, m2, A1 of all EDOs between 1 and 100 (inclusively)] using the "patent fifth" <code>round(edo*log2(3/2))</code> in all cases. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 14:21, 9 December 2020 (UTC)
::: I see your point, but I can't see any better option. I think calling them anything else would be even more confusing. I suppose we could omit the data for that handful of edos with a fifth > 3\5 or < 4\7. But to really understand these edos, you have to eventually come to terms with the fact that m2 < 0 or m2 > M2. So I think it's important information that should be included in the template. And for the vast majority of edos, the M2/m2/A1 numbers give an instant "lay of the land". Perhaps the solution is to have the template's phrases "Major 2nd", "Minor 2nd" and "Aug 1sn" link to an explanatory article? I could write something up. I've given supersharp and superflat edos quite a bit of thought over the years.
::: On a side note, I feel that there is a tendency for microtonalists to use too many decimal places. We sometimes forget that it's quite hard to hear a 1 cent difference, and a tenth of a cent is nearly impossible to hear. And yet people routinely write out thousandths of a cent. Of course, if an interval is stacked, those fractions of a cent can add up. Thus precision is good when talking about a rank-2 generator. But in any situation where an interval doesn't get stacked, I'm in favor of fewer decimal places. Because it's extra mental work to read the extra numbers, and filter out the unnecessary information. For example, I see no reason for an edo's table of intervals to have hundredths of a cent. Whole cents are fine. When would you ever need to know that e.g. 7\22 isn't 382¢ but actually 381.818¢? And if you needed the exact cents for some techy reason, you wouldn't get them from a xenwiki page. You would just type 7*1200/22 into a spreadsheet or a calculator. In fact, 22edo has interval tables in both formats. Take a look and ask yourself which is more readable? Now it would be a ton of work to edit all those interval tables, not suggesting that. Instead I bring this up because I saw on the linked page your tables for the edomappings. I see that you have the percentage error with a decimal place. I feel whole numbers is plenty accurate for the percentages. And tenths of a cent are fine for the cents errors.
::: Also, I notice what I call the edomapping you call the degree. But in conventional music theory, degree means something else. https://en.wikipedia.org/wiki/Degree_(music) The degree of 7\12 is not 7, but 5 (for 5th). So I don't think degree is the right term. I see you have both the reduced and unreduced edomappings. That's a good idea, but might it be better to have them on two separate rows of the table?
::: Finally, I see that you omit the prime 2 column. I know the information in that column is pretty redundant, but IMO it logically belongs there, and it would make the table more understandable to newbies. --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 08:38, 10 December 2020 (UTC)
:::: I agree to you in all the points. I'd use ''M2'', ''m2'', and ''A1'' and link the combination of all three to a page we just need a good name for. I'd suggested to name this like "Tonal properties of EDOs", because it's about tonality in general and [[tone]] sizes specifically. FloraC disagreed about the neologism "tonal property". The common use of ''degree'' was unknown to me, so "steps" (sometimes "edomapping") would be good, I even thought of just "#" in interval tables. I also outright ''hate'' these phone numbers. We should have both: 1) easy to understand numbers in tables (sometimes, only in a few cases, higher precision values); 2) easy to understand pages (and lots of links to them) that explain how to calculate all this to deliberate precision. The precision in the interval tables probably needs a broader discussion: I recall that there were users who wished the current precision, I personally would agree with <code>%+.1f</code> for cents and <code>%+.0f</code> for relative cents. The 2-column for the prime interval tables is already built in (by passing an optional third <code>+2</code> argument to the module function, see 3rd table in [[:dev:User:Xenwolf/SandBox#Test Module:primes_in_edo]]). Seems now I answered all your questions; if not, please let me know. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 09:14, 10 December 2020 (UTC)
== Your tonal system on my microtonal platform ==
Hi Kite,
I want to introduce myself and ask you some questions.
This is related to [[User:SAKryukov|my work]] at the [[User:SAKryukov#Microtonal_Music_Study_using_specialized_chromatic_keyboards_and_Web_Audio_API|software microtonal platform]]. With this system, we can quickly develop a playable instrument implementing almost any tonal system and layout. It is not simply playable: one can play with 10 fingers on a touchscreen with unlimited chords and glissando — right in your Web browser. This is a pure in-browser platform — it can play locally, without the Internet and it has a very advanced synthesizer embedded in the code. All the work is totally non-commercial, open-source, and based on permissive licensing.
The platform is already actively used for teaching music in the Brainin method of predictive learning and development of musical intellect, the method developed by the prominent pedagogue [[Valeri_Brainin|V Brainin]].
After the development of a set of instruments implementing some EDOs, I've done some research in rational-number interval systems and regular temperaments, and have been interested in the system and layout I've found presented on [[Color_notation#Interval_Names|your xen.wiki page]] and your site.
So, now I'm developing a couple of new experimental applications and one application is based on your system. It already does basic things, so you can [https://SAKryukov.GitHub.io/microtonal-chromatic-lattice-keyboard/Kite.Giedraitis try the live demo] of this incomplete application — it is already colored :-) and can play. I have some ideas about it and would like to ask you some questions. Also, I would be happy with any ideas of collaboration.
What do you think?
Thank you. &mdash;&nbsp;[[User:SAKryukov|SA]],&nbsp;''Friday&nbsp;2020&nbsp;December&nbsp;11,&nbsp;07:56&nbsp;UTC''
: Sounds great, but when I click on the yellow start button, nothing happens. Even when I select some options. --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 10:50, 11 December 2020 (UTC)
:: I observe the same behavior: nothing. I'm using Firefox 83.0 (64bit) on Windows 8.1. With mostly all of SA I tried I got empty screens or error messages. It seems that the workspace has special browser requirements. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 11:13, 11 December 2020 (UTC)
::: That it disturbing, but I'll fix it. I already have quite a user base. Could you help me? 1) Exact name version of a Web browser and OS? 2) Did you see the diagnostics referring to bad browser/engine? It is oriented to the standard modern level, like Blink+V8 engine. &mdash;&nbsp;[[User:SAKryukov|SA]],&nbsp;''Friday&nbsp;2020&nbsp;December&nbsp;11,&nbsp;16:14&nbsp;UTC''
::: Oh! Of course it cannot be Firefox, unfortunately, it is out of the game for a while now. It's only Blink+V8 based: Chrome, Chromium, Opera, Vivaldi, even the newest Edge, and more. I'll later explain. &mdash;&nbsp;[[User:SAKryukov|SA]],&nbsp;''Friday&nbsp;2020&nbsp;December&nbsp;11,&nbsp;16:20&nbsp;UTC''
:: I was using Firefox, switching to Chrome 65.0 now. Still doesn't work. I'm on OSX 10.9.5. I can try it on a 10.13.6 machine. --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 06:51, 12 December 2020 (UTC)
:: It works on my newer machine. Cool! Initial thoughts: Why do you have two lattices side by side? And how would one play beyond one octave? The note names aren't what I would expect. What are ab, ga and bc? Why is 10/9 labeled Db1? For edos 29, 31, etc., have you seen my [[ups and downs notation]]? --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 07:43, 12 December 2020 (UTC)
::: Thank you, Kite. I tested two recent applications, including the one you are talking about, and found that it was my fault: my usual warning on the browser capabilities is lost. I'll put it right, and then the recommendations/requirements to the browser will be exposed to the user. For the record: the applications are claimed "under development".
::: Now, two lattices: this is how I try to play with different ideas of presenting the lattices with more keys in a window; and this is one of the things I wanted to discuss with you. My initial idea (years ago :-) was to overcome the limitation of the rational-number tonal systems in terms of the ability to transpose and play different tonalities in the same piece. The idea was to have the keyboard re-tuned on the fly, depending on a chosen tonality. Of course, the idea itself is questionable. For example, it is not suitable for atonal music. Now I'm returning to the idea in different forms. First of all, this is research. As you may have guessed, more than playing in different octaves, I'm concerned with the more fundamental problem of the possibility of harmonic modulation with such tonal systems. With two lattices, we have more nicely used room on a page and can experiment with two different tunings at the same time, changing the tunings independently. Or something like that. &mdash;&nbsp;[[User:SAKryukov|SA]],&nbsp;''Saturday&nbsp;2020&nbsp;December&nbsp;12,&nbsp;16:07&nbsp;UTC''
::: The notation with "ab" and 1, 2 is mine, I have some rationale about it. Something symmetrically between A and B is ab, not flat or sharp. Flat or sharp should be the tone closer to the "letter" tone. If you have 5 tones in between, you have two sharps, two flats, and one symmetrically in between. I'll review your ups and downs notation, then we can discuss it later. &mdash;&nbsp;[[User:SAKryukov|SA]],&nbsp;''Saturday&nbsp;2020&nbsp;December&nbsp;12,&nbsp;16:06&nbsp;UTC''
::: On the more general notation topic: I do not accept the entire idea of traditional notation, not only because it is not suitable to variable tonal systems, but only because the idea of notation as the language between music and graphics is totally wrong semiotically: the levels of abstraction are insufficient. There should be at least one graphic-independent layer and different layers of metadata. &mdash;&nbsp;[[User:SAKryukov|SA]],&nbsp;''Saturday&nbsp;2020&nbsp;December&nbsp;12,&nbsp;17:38&nbsp;UTC''
::: By the way, the total number of keys is always a problem. First of all, the technology really pushes the limits and is based on very new possibilities, in particular, of Web API, first of all, the sound synthesis (if you look at my article on Sound Builder). That's why I simply reject all less advanced browsers. In practice, it finally works: I pay a high technological price compared to other approaches but obtain serious benefit: the browser as a platform is highly OS-independent. The combination of arbitrary chords and glissando, even with "only" ten fingers makes it obvious that 100% of keys should be able to sound at the same time. This is a huge memory consumption load, and thus limitation. &mdash;&nbsp;[[User:SAKryukov|SA]],&nbsp;''Saturday&nbsp;2020&nbsp;December&nbsp;12,&nbsp;16:06&nbsp;UTC''
:: More thoughts: For your microtonal chromatic keyboard, I would really like to see [[The Kite Guitar]] layout! It's rectangular not triangular, so a QWERTY keyboard input isn't ideal. Also, I don't have anything with a touchscreen. Wondering if a touchscreen would give some control over the volume? Or is it always a single fixed volume? --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 08:50, 12 December 2020 (UTC)
::: The Kite Guitar? Yes, I know such a thing, but not only that one. Do you really want to be so fast? Please, one step at a time. :-)
::: Now, the QWERTY keyboards in real life don't work at all, because most keyboard manufacturers use one trick to cut the costs, so, electrically, a chord not always can be entered. It should be touchscreen. In principle, I don't have any geometrical limitations. But dynamcs!...
::: I experimented with this a lot. Dynamics, dependency on the "strength" of a touch is a big problem, because it is not signalled in any way. In particular, I tried to explore the fact, that the soft part of the touching finger is deformed by a harder touch, the area of the touch becomes larger with time. It works, but appears totally unrealistic. A performer cannot control this finger flattening properly. Worse, the event of the change is only raised then a centroid of a touch is moved, but in practice it doesn't happen roughly in half of cases.
::: But simulation of a string plucking should work! This is because you slide the finder sidewise to the string, and the speed of this slide motion can be used to indicate the volume of the sound.
::: Overall, I would not hope for very realistic rendering of the dynamics.
::: But if you simply meant the common volume level for the entire keyboard, this is my standard control; I will add everything eventually. It's a lot more: transposition, sustain, other control elements. The most powerful thing is the Recorder. &mdash;&nbsp;[[User:SAKryukov|SA]],&nbsp;''Saturday&nbsp;2020&nbsp;December&nbsp;12,&nbsp;16:41&nbsp;UTC''
::: Then could you also look at [[User:SAKryukov#Live_Play_Applications|other applications]], including "[[User:SAKryukov#Experimental:_Microtonal_Playground|Microtonal Playground]]", another experimental application under development? &mdash;&nbsp;[[User:SAKryukov|SA]],&nbsp;''Saturday&nbsp;2020&nbsp;December&nbsp;12,&nbsp;16:47&nbsp;UTC''
:: All in all, very impressive, thanks so much for sharing all this with me! Good to see that it is all non-commercial and open source! I look forward to collaborating. --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 08:54, 12 December 2020 (UTC)
:::Thank you! Here is what I want to suggest: the present level of the discussion in this section is more than enough for the common reader. I suggest we discuss further detail in a separate section, a sub-page of ''my'' talk page. I suggest we post some final comments to this page (if you think it makes sense), and then move to the page referenced by a link in the last paragraph referenced below. Would you mind? &mdash;&nbsp;[[User:SAKryukov|SA]],&nbsp;''Saturday&nbsp;2020&nbsp;December&nbsp;12,&nbsp;18:48&nbsp;UTC''
::::Sure, let's talk there. --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 21:27, 12 December 2020 (UTC)
::::: All right, I'll add some text and ask you to take a look when I'm ready.
:::::: OK --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 23:02, 13 December 2020 (UTC)
::::::: Kite, will you please look at [[User talk:SAKryukov/Keyboards_based_on_the_designs_by_Kite_Giedraitis|this talk page]] I've just prepared and try to reply? Happy holidays, best wishes in New Year and all... &mdash;&nbsp;[[User:SAKryukov|SA]],&nbsp;''Sunday&nbsp;2020&nbsp;December&nbsp;27,&nbsp;22:31&nbsp;UTC''
:::::::: Thanks, swamped at the moment but I will look at this soon. --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 03:05, 28 December 2020 (UTC)
::::: At this time, the fix I mentioned before is already on the site for the live play for all applications. This is v.&nbsp;4.9.7. With this fix, the problem with the wrong browser will be reported to the user.  &mdash;&nbsp;[[User:SAKryukov|SA]],&nbsp;''Sunday&nbsp;2020&nbsp;December&nbsp;13,&nbsp;16:17&nbsp;UTC''
'''''[[User_talk:SAKryukov/Keyboards_based_on_the_designs_by_Kite_Giedraitis|Further discussion]]'''''
== Siwosu ==
Hi Kite, easier to speak, but probably harder to decode. Seems you are planning to expand color notation to "color language" now? Please don't misunderstand this as criticism: I like ''siwosu'' more than ''sixty-wosu''. It's just that I feel that the chances I will learn color notation on the fly decrease while the chances I'll love it increase. Would it be possible to write a computer program that tells us the color name for a common ratio? I'd rather written that as PM but you didn't configure to be reachable by Wikimail. (Checkbox ''Allow other users to email me'' in: ''Preferences &rarr; User profile'') --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 09:41, 14 December 2020 (UTC)
: Email configured, thanks for the tip. Yes, colorspeak is sort of a miniature language or conlang. It basically turns ratios and monzos into words. As far as learning it on the fly, there's a 1-page glossary at the bottom of the main color notation page that covers everything. We've tried to make it easy to learn and memorize while also making it concise. ("We" these days is mostly Praveen and I, but I'd be happy to run suggested changes past you too.) There's always tension between these two goals, as your "chances I'll learn it / love it" comment shows. Computer code is very possible. I assume you would want to see a website or app that translates monzos to color names and back? Is that possible to do here on the xenwiki?
:: You mean the glossary on [[Color notation #Glossary / Crash Course]]? I have to study this, looks not too easy. Anyway: if the translation can be automated, than it would even be possible within a Lua module and therefore (hopefully soon) in the Xenwiki. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 22:48, 14 December 2020 (UTC)
::: Yes, that's the glossary. It would be *awesome* if translation could be automated! See the "Converting" section of that page for detailed instructions. I picture a template that does the translation like the edo template calculates the stepsize. I also picture a dedicated xenwiki page where the user enters in either a ratio or a monzo or a color name, clicks Go, and the other two fields are filled in. Is that possible? --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 08:42, 15 December 2020 (UTC)
::: With such a translation page, I feel you and others would get the hang of color notation quickly and effortlessly. --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 08:57, 15 December 2020 (UTC)
:::: I have to study this for a while. I'll also contact you via email soon. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 09:02, 15 December 2020 (UTC)
: BTW I can't use the visual editor on various xenwiki pages lately. I get "Error contacting the Parsoid/RESTBase server (HTTP 404)". --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 20:03, 14 December 2020 (UTC)
:: I got another error report about this. I've to admit that I have no idea what this could mean. Would you please report it again to Tyler or Mike? Thanks. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 22:48, 14 December 2020 (UTC)
:: On what page(es) did you observe the error? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 06:48, 15 December 2020 (UTC)
::: Maybe you meanwhile reported the error. Today I saw that Thyler did a configuration change (addressing a VisualEditor bug in the comment), and the error vanished as far as I can see. Can you confirm this? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 08:30, 15 December 2020 (UTC)
:::: I told Tyler about it on the xenwiki workgroup facebook group. He fixed it. The problem was slashes in the title. So it mainly affected the ratio pages. I have confirmed that the bug is fixed. --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]])
::::: Thanks for reporting and the quick reply. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 08:47, 15 December 2020 (UTC)
== I accidentally clicked the rollback button ==
Just browsing using an iPad and accidentally touched on the rollback button, never to expect it's a one-click mechanic. I've re-rollbacked. Sorry about that. It just can happen. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 10:56, 14 December 2020 (UTC)
: No problem. I've made bigger mistakes. :) --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 08:56, 15 December 2020 (UTC)
: Flora, are you sure that it was just one click? I was hoping that I deactivated this feature via [[MediaWiki:Group-sysop.css]]. Maybe we find the time to check this again... --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 15:20, 14 December 2020 (UTC)
:: Confirmed. Plus, if you hover on it it literally reads "Rollback reverts the last contributor's edit(s) to this page in one click". [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 15:42, 14 December 2020 (UTC)
::: I found the answer. In preferences/appearances, click "Show a confirmation prompt when clicking on a rollback link" --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 19:21, 14 December 2020 (UTC)
:::: Cheers. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 02:59, 15 December 2020 (UTC)
:::: Thanks for the preferences hint, @Kite. @Flora, which Skin are you using and where exactly do you see the "rollback" link (Recent changes, Watchlist, History)? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 22:37, 14 December 2020 (UTC)
::::: I use the default skin. Rollback shows in all the pages you mentioned. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 02:59, 15 December 2020 (UTC)
:::::: I see, obviously per-group disabling doesn't work because the organizers group is a custom group that is "below" the built-in sysop group. @both: Can you confirm (maybe only after Browser refresh) that the function is disabled now? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 06:45, 15 December 2020 (UTC)
::::::: Not sure what you want me to do. I don't understand rollbacks so I avoid them. --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 08:56, 15 December 2020 (UTC)
::::::: It's disabled now. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 06:28, 16 December 2020 (UTC)
== Reduce comma tables on EDO pages ==
Please have a look at [[Xenharmonic Wiki: Things to do #Comma tables in EDO_pages]]. Thanks --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 09:09, 11 January 2021 (UTC)
== Help with scale tree ==
Hi Kite,
I'm currently working on [[fifthspan]]s and at the beginning of section [[Fifthspan#Finding the fifthspan of an edo interval]], I found a reference to "scale tree" that I was not able to resolve (in preparation I turned it into internal link syntax). Can you please help me?
--[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 17:27, 14 January 2021 (UTC)
: I replaced "scale tree" with "Stern-Brocot tree", and linked to the wikipedia article on it. That should solve the problem in the short run. no? In the long run, there really should be a xenwiki page about the scale tree. It's nearly identical to the Stern-Brocot tree, but includes improper fractions like 9/15, and most importantly, the fractions are interpreted musically. I have written extensively about the scale tree and would be happy to write such a page. --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 23:59, 14 January 2021 (UTC)
:: Thanks, Kite. Yes, such a page would be good. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 07:03, 15 January 2021 (UTC)
== Request for help on a new microtonal theory ==
Kite, I know that you have much more experience in microtones than I do, so I would like you to take a look at my new microtonal theory, [[User:Userminusone/Intervallic Polarity|Intervallic Polarity]]. This is something that I think has useful implications, but right now, its definition is a bit shaky and also quite subjective. If you are willing, I would really appreciate it if you could give me your thoughts on this theory or maybe even help me refine and expand upon its definition. Best regards, [[User:Userminusone|Userminusone]] ([[User talk:Userminusone|talk]]) 21:56, 1 August 2021 (UTC)
: Yeah, this looks alright. It's probably best as a loose categorization rather than a strict ranking. It's a bit reminiscent of color notation, because IMO two ratios separated by 3/2 or 4/3 tend to have the same quality, as long as the ratios aren't too far away in the lattice. So I have wa, yo, gu, zo, ru etc, which could also be called 3-limit, 5-over, 5-under, 7-over and 7-under. Your cleanly plain ones are the nearby 3-limit intervals. Dirtily plain are further away. For lightly warm I think distinguishing between 5-over and 5-under might be good. They feel like separate categories to me. Likewise dirtily dissonant might distinguish between fourthward and fifthward.
: Darkly warm and overly bright are basically 7-over and 7-under. But 14/9 is in the latter group. It does indeed sound less consonant than 7/4 and 7/6, so it seems reasonable to put it in that group. Maybe what's going on is its proximity to the powerful 3/2 ratio makes it feel like a sharp 3/2 rather than a flat 8/5. I agree that microtonal "strangeness" seems to be based on how far the note is from pythagorean or 12-equal intervals, at least in Western culture.
: 10/7 and 7/5 are tricky. 7/5 is only 8¢ away from 45/32, which to me feels quite 5-over, very similar to 15/8. So 7/5 sort of has that leading-tone quality alongside its septimal nature. And that's the thing. We don't hear ratios, we hear cents and then we deduce the ratios. And unless you've really trained your ears, it's hard to hear that 8¢. And you probably can't count on your listeners hearing it.
: For 11-limit, consider a chain of neutral 3rds centered on the unison: m3-hd5-m7-n2-P4-n6-P1-n3-P5-n7-M2-hA4-M6 where hd = half-dim and hA = half-aug. Consider the 6 intervals hd5-n2-n6-n3-n7-hA4. Coldly suspended seems to mean the central part of this chain. Warmly suspended seems to mean the further away parts. Except hd5 = 16/11 gets its own category. Again, this might be because 3/2 is so powerful, 16/11 sounds more like a very flat 3/2 than an interval in its own right. Note that there's a small comma 243/242 which tends to blur the difference between 11-over and 11-under.
: So your categories seem to correspond to various regions of the lattice, which makes sense to me. Not sure I understand the positive/negative classification. Personally I loosely classify imperfect intervals as supermajor-major-neutral-minor-subminor, 5ths as superperfect-perfect-halfdim-dim-(subdim) and 4ths as (superaug)-aug-halfaug-perfect-subperfect. So basically 5-limit and deviations from there, very 31-edo-like. One could add submajor, superminor, superperfect 4th, etc. to get it down to 3-limit, very 41-edo-like. If you sharpen the 5th, then in the 3-limit chain of 5ths major sounds like supermajor and minor sounds subminor. If you flatten it, you get submajor and superminor, and if you flatten a lot, neutral. Is that the logic behind positive/negative? If so, that might be a better way to describe it, rather than referring to edos. Also note that to get 11/8 and 16/11, you are presumably flattening the 5th by a quartertone. This makes the major 2nd sound minor, and the major 3rd sound diminished! --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 07:23, 2 August 2021 (UTC)
:: Thank you so much for your response! Yes, the logic is that positive polarity refers to intervals generated by sharp fifths while negative polarity refers to intervals generated by flat fifths. I appreciate all of your input and the connection between color notation and intervallic polarity makes a lot of sense. On the other hand, I still wonder if there is something related to the dissonance, harmonic entropy, or complexity of an interval that could be used to derive its intervallic polarity. (This could allow intervallic polarity to possibly be generalized to chords and/or intervals played with different timbres) --[[User:Userminusone|Userminusone]] ([[User talk:Userminusone|talk]]) 21:11, 2 August 2021 (UTC)
== having torsion vs. being enfactored ==
Hi Kite. Per your request I'm continuing discussion with you on your user page where you are more likely to see it sooner. This is a continuation of the discussion started here: [[Talk:Color notation/Temperament names]]
I'm glad you agree about torsion. I like the way you explained it, pointing to the name of RTT itself. As a nit-pick, though, I can't agree with the statement that "you can't hear periodicity blocks". That wasn't what I was trying to say. In fact, I was trying to say something like the opposite. My point was that using e.g. {{vector|-8 8 -2}} instead of {{vector|-4 4 -1}} has an audible effect on periodicity blocks but not on temperaments. For a periodicity block, it causes the size of the scale to double, but half of the notes are a redundant copy of the other half, simply offset. Because this is a real audible effect, and I understand there are maybe even some uses for it or cases where it's desirable, it has a name, "torsion". But for a temperament, though, where the comma is by definition tempered out, there is no audible effect, and thus using {{vector|-8 8 -2}} instead of {{vector|-4 4 -1}} is meaningless. It's just pathological enfactoring that is removed when the comma basis is put into canonical form.
I'm glad you agree about contorsion too. I'm not sure we do, though, because your statement about 12- and 24- ET is not how I would describe it. I would say something more like this: "Calling {{map|24 38 56}} a 'temperament' is misleading because everything it does as a temperament is already done by the simpler {{map|12 19 28}}. In other words, all of its notes are real and audible, but half of them are not used for tempering, or we could say that it is 2-enfactored. Therefore it should not be listed as a strict 'temperament'; perhaps we could call it a 'temperoid' or something like that instead." Does that check out with you?
I found this page of yours this morning which uses the word "torsion" a lot: [[Catalog of rank two temperaments]]. Per my explanation above, would you mind if I renamed uses of "torsion" to "enfactored" there? If you prefer, I could include a footnote on the first one that explains it has historically sometimes been called torsion. Alternatively... why does it matter if they are enfactored? Does anyone need to care? Just defactor them. Maybe it'd be better to just include the canonical form of these temperaments. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 16:56, 30 September 2021 (UTC)
: I stand corrected about periodicity blocks. As for that page, it's actually an attempt to find a canonical comma list. It's complicated, let's discuss it in person when you visit. --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 07:42, 2 October 2021 (UTC)
:: Ah! Yes I seem to recall that someone — Paul, Mike, maybe? — mentioned to me early on that your color notation included some thinking about canonicalization. I am embarrassed to say that I haven't learned color notation yet, besides a few basics. So if you don't mind, if we have time when we meet, maybe you could show me the ropes? I expect we will need a couple sessions! --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 22:31, 3 October 2021 (UTC)
::: I would love to show you! --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 05:57, 5 October 2021 (UTC)
== Chessboard distance ==
I noticed this bit just now: https://en.xen.wiki/w/Commas_by_taxicab_distance#Triangularizing_proposal
FYI, "triangularized taxicab" distance like this has an established name. It's [[Wikipedia:Chebyshev_distance|Chebyshev distance]], AKA "chessboard distance," because if a 2D lattice was like a chessboard, then it's the number of moves the king piece would need to take to reach from point A to point B. I made this chart, in case it helps:
{| class="wikitable"
|+
!L-norm
!eponym
!locale
!agent
|-
|1
|Minkowsky
|Manhattan
|taxicab
|-
|2
|Euclid
|space
|crow
|-
|∞
|Chebyshev
|chessboard
|king
|}
You can see these distances are associated with different L norms. The L₁ norm and L∞ norms are each others' duals and the L₂ norm is self-dual.
These come up in tuning. When you minimize the L∞ norm on the prime error, this causes a minimization of the L1 norm on interval error. That's TIPTOP tuning. The L∞ norm of a vector is simply the max value of any of its entries; I understand it that way because your "king" can move as diagonally as necessary, and so he'll just move diagonally in every dimension until he runs out of dimensions he needs to go except for one, at which point he continues straight along that dimension. And if you minimize the L1 norm on the prime error, this causes a minimization of the L∞ norm on interval error. So if you wanted to use L∞ norm for interval error, you'd set your tuning optimizer to minimize the sum of the absolute values of errors per prime. If you have any questions, let me know -- I'm not rock solid on this stuff yet, but I think it's pretty interesting. Dave and I have attempted to improve our geometric intuition for dual norms' effects on tuning, but it's been a while since I looked at it.
Anyway, just thought you might like to revise that original paragraph to use established nomenclature, or at least reference it! You may not have been aware of it; I only just learned it myself a few months back. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 22:04, 19 January 2022 (UTC)
: Hmm, interesting. But actually, what I'm proposing is different from all of these. In the 2-D case I propose a shearing so that the rectangular lattice becomes triangular.
{| class="wikitable"
|+triangularized
|1
|1
|2
|-
|1
|0
|1
|-
|2
|1
|1
|}
: This applies to all prime subgroups, but let's assume 2.3.5 and see what the ratios are. Note that the ratios that are now two moves away are the ones with the much higher odd-limit of 15. Thus it does seem to reflect the actual musical distance better than any of the 3 ways you listed.
{| class="wikitable"
|+ratios
|5/3
|5/4
|15/8
|-
|4/3
|1/1
|3/2
|-
|16/15
|8/5
|6/5
|}
: In 3-D, 4-D etc., it's better thought of not as shearing but as higher primes cancelling lower primes that are on the opposite side of the ratio.
: I'm not following the L1 stuff. Can you give some actual examples? --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 07:47, 20 January 2022 (UTC)
:: Ah, I see. What you're talking about is completely different. I started making some corrections to my previous statements before I'd noticed you'd replied already. So I'm going to go ahead and make those rather than leave the misinformation up and correct it here, if that's okay (my incorrectness is still preserved in the edit history). I think I probably shouldn't try to say more about the Lp norms yet until I have a better handle on them, so never mind for now, especially since it's irrelevant to your purpose anyway. Sorry for the confusion. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 23:42, 22 January 2022 (UTC)
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