User talk:TallKite

From Xenharmonic Wiki
Jump to navigation Jump to search

Infobox Interval

Hi Kite, great to see you in action :)
Just one thing that I found a little awkward: you moved the interval name from the textual into the info box in some cases. I think the synopsis should be kept "intact" so you can just read it out loud, IOW copying is better. Thanks for considering my thought.
--Xenwolf (talk) 07:00, 23 October 2018 (UTC)

I agree. Trying to fix it now. We seem to be bumping into each other. --TallKite
By the way, how do I get my comments here to have the date/time stamp on them?
toolbar in editing mode
It's called signature. You place --~~~~ behind your message.
It's also available in the toolbar in editing mode. The second control from the right places this magic sequence into the wiki text. If you preview the change, the replacement is shown, but it's not replaced in the source code until you save the page. There are other magic sequences ~~~~~ (renders as: 20:58, 23 October 2018 (UTC)) for timestamp only ~~~ (renders as: Xenwolf (talk)) for user name only. You see that the leading -- isn't "magic." ;-)
--Xenwolf (talk) 20:58, 23 October 2018 (UTC)
Thanks!--TallKite (talk) 21:30, 23 October 2018 (UTC)

Changes to Infobox Interval

Thank you for fixing the template. I think it's now better having the parameters in the same order as they (optionally) appear in the page. --Xenwolf (talk) 08:16, 23 October 2018 (UTC)

Delete a page

Members of the Organizer group can delete pages (you are a member). Concerning pages in the article namespace we have currently no convention on when/how to delete them. But there is no need for discussion in case of pages in your own user namespace. Left to the search box there is a [More] with Delete, Move, Protect (these are the function organizers see). BTW: it would be good to have a few words on your user page User:TallKite. Best regards --Xenwolf (talk) 15:41, 31 May 2020 (UTC)

Your user page

the personal wiki toolbox is your faithful companion

Hi TallKite,
This is a great. You know that someone's active in the wiki (as shown in article histories or recent changes) can be confusing to others and as to get into contact a bit of information about the editor helps a lot. Another maybe interesting point for having a users page is that you can collect your favorite links there. This eases the access to them a lot: the wiki web interface (every page, every time) contains a link to it in the upper-right corner (see screenshot: the name next to the user icon is a link).
Best regards --Xenwolf (talk) 10:01, 1 June 2020 (UTC)

Not following you. I created a users page with my real name and a link to my "People" page, which links to my various websites which have my phone # and e-mail. So I'm very easy to contact. And by favorite links, do you mean my contributions? --TallKite (talk) 05:41, 2 June 2020 (UTC)

The purpose of letting others know how to get in touch with you is perfectly served by the current content of your user page. 🙂 I just wanted to point out that this personal page 1) offers you maximum creative freedom and 2) stands out from most other pages because of its easy accessibility to you. For me personally, my user page is an invaluable resource for all the things I don't have in mind when editing the wiki (e.g. copy templates, todo lists, links). I have learned to appreciate it in the course of my work and that's why I wanted to introduce this possibility to you (so I don't want to push you into anything). --Xenwolf (talk) 06:23, 2 June 2020 (UTC)
Oh I see, you can use it like a personal notepad. --TallKite (talk) 22:18, 3 June 2020 (UTC)


Hello there! I see that you've noticed the work that Inthar, Flora and I have done in unearthing an obscure unnoticeable comma from the bowels of this wiki and studying it- specifically from the page on 3125edo- and I do appreciate how you've worked out the color notation for it! Thank you! Oh, and just for the record, I'm the one who dubbed this comma the "quartisma". --Aura (talk) 04:58, 8 September 2020 (UTC)

Glad to help! I hope you don't mind that I changed (33/32)^6 = 77/64 to (33/32)^5 = 7/6. Seemed simpler. --TallKite (talk) 00:31, 9 September 2020 (UTC)
I don't mind, seeing as both options are technically correct. --Aura (talk) 00:46, 9 September 2020 (UTC)

Kite, we have a problem. Ever since I found this site this site things have gotten very complicated very quickly. I find that we now need to go through and redefine terms according to more rigorous standards than we have been, and to that end I've had to even go so far as to delete data on the Quartismic temperaments page in order to make space for this to occur properly. I'm thinking that the data can be re-entered once we've gotten things straightened out. --Aura (talk) 03:18, 11 September 2020 (UTC)

Diatonic Scales

Hey there, Kite! I saw you just posted something on the diatonic scales for the Kite Guitar, so I'm wondering whether or not you've seen my own take on the diatonic scales. Have you? Truth be told I suspect you won't like it, as I prefer 27/16 to 5/3 among other things, but all the same, I can't help but wonder... --Aura (talk) 01:39, 10 September 2020 (UTC)

Haven't seen it until just now, thanks for sharing it with me. I like your "Ionic Dorian" naming system, very logical. Yeah, I prefer 5/3 to 27/16, and I don't like 40/27. My approach, like many others, is to use small pitch shifts to avoid such ratios. Thus certain notes are "fuzzy". This lets me get all 6 triads in tune. But even with fuzziness, I find the dorian and locrian scales to be hard to tune well. (As you can see from my Kite Guitar scales page.)
In your dorian scale, I would use 32/27 in place of 77/64. Smaller odd limit, much smaller prime limit too, and avoids a wolf 5th. In your locrian scale, I would use 7/5. Much more consonant than 64/45.
But hey, to each their own. Can't have microtonalists agreeing on too much! :)
--TallKite (talk) 22:20, 10 September 2020 (UTC)
I have to admit that I prefer my scales to be proper, and the options you propose for Dorian and Locrian don't sit well with me as a result. The 7/5 tritone in particular sounds more like a fourth to me than a fifth. Also, I don't like the idea of fuzzy intervals myself- which is why I decided to be brave and attempt to exploit the grave fifth. If you don't like what I'm doing now, then you really won't like what I have in store for the Neapolitan modes- that will be quite a doozy for me as is... As you said though, to each their own! --Aura (talk) 22:47, 10 September 2020 (UTC)
Did I mention that dissonance has a way of acting as a propulsive force in music? Just something I thought I'd bring up in case you ever find yourself in a position where you're forced to use some kind of grave fifth or other... --Aura (talk) 22:55, 10 September 2020 (UTC)

Help wanted

Hi TallKite,

I saw that you were asked here to help out, but as far as I know the wiki has no such function to notify a user via @username, but maybe I'm wrong about it ... --Xenwolf (talk) 06:46, 11 September 2020 (UTC)

[Technical update] I re-checked the wiki settings. There is really not such a feature available. Wikipedia has an option to get notified if someone links to your user page. --Xenwolf (talk) 06:52, 11 September 2020 (UTC)
Thanks for the notification, Xenwolf. I will try to answer their questions. --TallKite (talk) 05:04, 12 September 2020 (UTC)

Page Split and Reorganization

Hey Kite, so, Xenwolf and I have split the section of the "Quartismic Temperaments" page dealing directly with the quartisma itself into it's own page- Quartisma, while the "Quartismic Temperaments" page itself has been renamed to Quartismic family. In accordance with this, I've decided to add the rank-4 base Quartismic temperament to the page. Now I need help sorting things out and finding good names for the no-fives temperaments. Do you have time to spare for this? --Aura (talk) 21:29, 13 September 2020 (UTC)

Kite, I'm also looking for names for both quartismic temperaments that also temper out the escapade comma, and quartismic temperaments that also temper out the the diaschisma. Do you have any ideas? --Aura (talk) 03:42, 14 September 2020 (UTC)

The page reorganization looks good! I do have a system for naming all temperaments based on a prime subgroup. It's detailed at It's quite complicated. Multi-comma temperaments are tricky, because there's an infinite number of commas tempered out. So identical temperaments arise from different commas, yet the temperament name must be unique.
I call the rank-4 temperament Saquinlu-azo plus Ya. Of course the difference between this and 11-limit JI is inaudible.
Escapade is Sasa-tritriyo, so that plus quartismic makes the Sasa-tritriyo & Saquinlu-azo temperament. Yes, that's a mouthful. That's what happens when the nomenclature is systematic and also has only a small number of terms. Basic information theory says that something has to give. Easy to learn and logical means complex things get long names. And this temperament is *extremely* complex. But this name at 11 syllables is still better than saying "4294967296/4271484375 and 117440512/117406179" out loud! And you can work backwards from the name and derive the prime subgroup, the rank, and the commas. No other name can do that.
Diaschisma is Sagugu, so that makes Sagugu & Saquinlu-azo. Nine syllables, a little better. :)
Not sure what no-fives temperaments you want to name. No-fives quartismic is simply Saquinlu-azo. If for example you also temper out 99/98, that's Loruru & Saquinlu-azo. But there's a rule that's needed to ensure the name is unique: the 1st comma must have only one prime > 3, and it must be the smallest such prime. So you have to eliminale lo/lu by adding 5 of the 1st comma to the 2nd one, to get Satritriru. The final name is Satritriru & Loruru. Notice that the quartisma is no longer part of the name. Often very complex commas tend to get replaced with simpler ones. This is as it should be, because one is far more likely to actually employ a Loruru pump than a Saquinlu-azo pump! And the name should reference the more commonly used commas. Perhaps the most important characteristics of a temperament are the prime subgroup and the pergen. This one's pergen is (P8, P4/9), so it divides the 4th into 9 parts. So you could name it "Zala ninth-fourth". Zala means the prime subgroup. But there will always be other temperaments with the same subgroup and pergen.

Need help for another color name

Hello Kite. I wonder if you've read my post in the FB group. To summarize, I explored a new regular temperament. I've documented it here: Canou family. Could you help me figure out the color name and maybe catalog it in Tour of Regular Temperaments? FloraC (talk) 14:39, 2 October 2020 (UTC)

[4 -14 3 4⟩ is the Saquadzo-atriyo comma. Fun fact, tempering it out divides 81/80 into two Zozoyo commas (245/243). 9801/9800 is the Bilorugu comma. 352/351 is the Thulo comma. 351/350 is Thorugugu.
BTW feel free to tag me on FB if you want color names more promptly. (I check in there more often.)--TallKite (talk) 19:06, 3 October 2020 (UTC)

Upgrades for Ups and Downs notation

Hey Kite, Xenwolf and I are currently trying to come up with a notation system for 159edo, and we're having to use portions of Ups and Downs notation for ease of access. However, as we're also using Helmholtz-Ellis symbols, mainstream quartertone accidentals, and symbols derived from both systems as anchors for reference, so the dart up and dart down- the basic symbols of Ups and Downs notation- need a stylistic upgrade to blend in with the traditional accidentals, and furthermore, the dart up and dart down need to be identical in all respects save for orientation. In addition to this, Ups and Downs notation becomes quite unwieldy for larger EDOs like 159edo, leading us to create new glyphs- like the double dart up and double dart down, as well as the triple dart up and triple dart down- simply to make the representation more compact and reduce the clutter that happens otherwise. I'm hoping you can help us out with this on the relevant discussion page. Thanks. --Aura (talk) 21:19, 5 October 2020 (UTC)

Interesting. I will reply tomorrow. --TallKite (talk) 08:41, 6 October 2020 (UTC)
I'm looking forward to reading your thoughts on this. --Aura (talk) 15:54, 6 October 2020 (UTC)

Laying the Groundwork for New Areas of Music Theory

Hey Kite! I'm trying to lay some groundwork for new areas of music theory... Given your expertise in practical matters, I think you could evaluate what I have so far. Granted there are probably lots of flaws in my work, and that we'll disagree about stuff, but hopefully what I've done so far makes some degree of musical sense... --Aura (talk) 07:30, 17 October 2020 (UTC)

Thanks for asking my opinion. Sorry it's taken so long to get back to you. I'm writing an ear trainer for 41edo, and I've got 1500 lines of computer code in my head. I didn't dare put anything else in there for fear of losing my grasp of it! But now the project is completed enough that I can safely consider other things.
BTW I really like "Folly of a Drunk", very catchy! Do you happen to have a score for it?
I will evaluate your ideas on the discussion tab of your page.
Thanks! Here are some of the key chord progressions in "Folly of a Drunk" in case you missed them... --Aura (talk) 09:26, 1 November 2020 (UTC)
I do in fact have a score for the song, but the copyright listing on the score is outdated... --Aura (talk) 09:30, 1 November 2020 (UTC)
If you want, I can post the score on my user page. --Aura (talk) 09:47, 1 November 2020 (UTC)
Yes, please do!--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. --Aura (talk) 10:32, 1 November 2020 (UTC)

Harmonize categories of interval pages

Hi TallKite, we are interested in your opinion about Categories of interval pages, thanks in advance for taking the time. --Xenwolf (talk) 21:21, 8 November 2020 (UTC)

OK--TallKite (talk) 05:19, 9 November 2020 (UTC)

Fifthspan question

Thanks in advance for having a look into Talk:Fifthspan #About ringy confusion. --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 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. --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:

^^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

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:

^^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#

Another version, with 1/1 - 11/9 - 3/2 and 1/1 - 27/22 - 3/2 triads forming triangles.

^^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#

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. --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. --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 ... 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:

--- 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

I'll soon add a test case for this in the dev wiki. Hopefully this feature (Scribunto+Lua, see Version page there) will go to production soon. BTW: If you are interested in joining the evaluation effort, you are most welcome. --Xenwolf (talk) 11:26, 9 December 2020 (UTC)

Oh wow, cool! OK, I'll stop working. --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 table with M2, m2, A1 of all EDOs between 1 and 100 (inclusively) using the "patent fifth" round(edo*log2(3/2)) in all cases. --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. 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. --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 %+.1f for cents and %+.0f for relative cents. The 2-column for the prime interval tables is already built in (by passing an optional third +2 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. --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 my work at the 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 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 your 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 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. — SAFriday 2020 December 11, 07:56 UTC

Sounds great, but when I click on the yellow start button, nothing happens. Even when I select some options. --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. --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. — SAFriday 2020 December 11, 16:14 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. — SAFriday 2020 December 11, 16:20 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. --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? --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. — SASaturday 2020 December 12, 16:07 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. — SASaturday 2020 December 12, 16:06 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. — SASaturday 2020 December 12, 17:38 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. — SASaturday 2020 December 12, 16:06 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? --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. — SASaturday 2020 December 12, 16:41 UTC
Then could you also look at other applications, including "Microtonal Playground", another experimental application under development? — SASaturday 2020 December 12, 16:47 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. --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? — SASaturday 2020 December 12, 18:48 UTC
Sure, let's talk there. --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 --TallKite (talk) 23:02, 13 December 2020 (UTC)
Kite, will you please look at this talk page I've just prepared and try to reply? Happy holidays, best wishes in New Year and all... — SASunday 2020 December 27, 22:31 UTC
Thanks, swamped at the moment but I will look at this soon. --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. 4.9.7. With this fix, the problem with the wrong browser will be reported to the user. — SASunday 2020 December 13, 16:17 UTC

Further discussion


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 → User profile) --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. --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? --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. --TallKite (talk) 08:57, 15 December 2020 (UTC)
I have to study this for a while. I'll also contact you via email soon. --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)". --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. --Xenwolf (talk) 22:48, 14 December 2020 (UTC)
On what page(es) did you observe the error? --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? --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. --TallKite (talk)
Thanks for reporting and the quick reply. --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. FloraC (talk) 10:56, 14 December 2020 (UTC)

No problem. I've made bigger mistakes. :) --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... --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". 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" --TallKite (talk) 19:21, 14 December 2020 (UTC)
Cheers. 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)? --Xenwolf (talk) 22:37, 14 December 2020 (UTC)
I use the default skin. Rollback shows in all the pages you mentioned. 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? --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. --TallKite (talk) 08:56, 15 December 2020 (UTC)
It's disabled now. 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 --Xenwolf (talk) 09:09, 11 January 2021 (UTC)

Help with scale tree

Hi Kite, I'm currently working on fifthspans 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? --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. --TallKite (talk) 23:59, 14 January 2021 (UTC)
Thanks, Kite. Yes, such a page would be good. --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, 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, 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! --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) --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. [-8 8 -2 instead of [-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 [-8 8 -2 instead of [-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 24 38 56] a 'temperament' is misleading because everything it does as a temperament is already done by the simpler 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. --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. --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! --Cmloegcmluin (talk) 22:31, 3 October 2021 (UTC)
I would love to show you! --TallKite (talk) 05:57, 5 October 2021 (UTC)

Chessboard distance

I noticed this bit just now:

FYI, "triangularized taxicab" distance like this has an established name. It's 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:

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. --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.
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.
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? --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. --Cmloegcmluin (talk) 23:42, 22 January 2022 (UTC)