Talk:Color notation

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Octaves have no color?

I saw that the factor 3 is considered white, so I'd guess that the octaves are completely ignored? --Xenwolf (talk) 20:37, 31 October 2018 (UTC)

Octaves are clear, or ca for short. TallKite (talk) 07:46, 22 November 2018 (UTC)

Suggestions past lavender

13a is neutral, and so purplish (much like 11a's lavender and the purple coming from equating rry1 and zzg3). Now there aren't many colours with a "th" in them, so I had to cheat a bit here. 13o is heather (I know it doesn't begin "th", but it'll have to do), 13u is thistle.

17a is close to ya, but slightly wider than yo and narrower than gu. Therefore, it needs colours that are slightly orange-yellow and slightly blue-green. 17o is sea, 17u is saffron.

19a is similar to 17a, and so needs similar colours. 19o is new leaf (probably should change to avoid clashing with nu, but I can't think of anything else), while 19u is nectarine. -- Jerdle (talk) 17:33, 20 October 2019 (UTC)

These colors would work, except new leaf does clash with nu. And sea sounds too much like the note C. Nectarine-sea is 19u17o, and nectarine C is 19uC. --TallKite (talk) 20:16, 21 October 2019 (UTC)

Haven't found a better 19o, but spring green might work for 17o. --Jerdle (talk) 16:11, 22 October 2019 (UTC)

Subgroups that use non-primes?

How does color notation name subgroups that use non-primes like 2.9.21 if you don't have names like ya, za etc for non-primes? Would saying "wa 2nd plus zo 4th" be okay? IlL (talk) 05:29, 8 July 2020 (UTC)

Good question. I've struggled with this. Your approach seems promising! For 2.9.21 I would say "nowa plus wa 2nd plus zo 4th", to make it explicit that 2 is present and 3 is not. In other words, nowa by itself means 2-limit, and noca by itself means no-twos 3-limit. Then we use your method to add on the non-primes. 3.4 would be noca plus wa 4th. I'm not sure about 4.6, would it be nowaca plus wa 5th plus double wa 8ve? Or maybe nowaca plus wa 5th plus wa 11th?

With 2.9.21, the wa 7th is also a generator, and could replace wa 2nd. The zo 4th could be replaced by the zo 3rd, because 21/(2*9) = 7/6. Or even by the zo 2nd 28/27. There should be a canonical form, so that one subgroup doesn't get two names. Perhaps we could have a convention that the odd limit be as small as possible? And as a tie-breaker, e.g. for w2 vs w7, minimize the degree? Thus 2.9.21 would be nowa plus wa 2nd plus zo 3rd.

2.7.9 would be "za nowa plus wa 2nd". 2.3.7/5 would be "wa plus zogu". No need to say zogu 5th, since any zogu interval could be a generator, as could any ruyo interval. Or perhaps because 2.3.5 is ya not yawa, we can simply call this zogu? --TallKite (talk) 11:55, 22 July 2020 (UTC)

Sev- for 70?

Could sevwo be used for 71, say? I don't think there's any clashes with other names there.

But is it also pronounceable? --Xenwolf (talk) 23:30, 20 December 2020 (UTC)
PS: please sign you comments on talk pages with four tildes (for example like ~~~~) --Xenwolf (talk) 23:30, 20 December 2020 (UTC)
Interesting idea. If seventy-wo is pronounceable, sevwo certainly is. Sevthu, sevna, etc. The only objection I can think of is that we already have sep- for 7-exponent and se- for 17-exponent. For example, the sensei comma [2 9 -7] is the sepgu comma. Sev- is spelled and pronounced distinctly, so in a way there's no problem. But people aren't robots or computers, and you have to account for human fallibility. It already takes a certain mental effort to avoid mixing up sep- and se-. Adding sev- means even more mental effort. Septho = (13^7)-over, setho = (13^17)-over, and sevtho = 73-over. And there's no good mnemonic for which is which. This potential confusion is basically inevitable. Seven, seventeen and seventy-one are all primes that have "seven" prominently in their names.
Another thing is that IMO microtonalists tend to overdesign their notations. As one gets into the details, one tends to add term after term. The expert makes the notation more and more powerful, and loses the perspective of the beginner who just wants something simple and easy to learn. That's why I don't like Sagittal, there's just too many symbols. I'm guilty of this too, colorspeak used to have jade/amber for 11-over and 11-under, and emerald/ochre for 13-over/under. Then I went really overboard and had tan/khaki and fawn/umber for 17 and 19. Which is a ridiculous number of things to have to learn and memorize. I can't even remember now if it was tan/khaki and fawn/umber or if it was tan/umber and fawn/khaki! If even the creator can't remember, how could someone else? Fortunately I came to my senses and simplified everything.
More about the perspective of the beginner vs. that of the expert: there's two experts at the office, but the staff has learned not to ask them both for help at the same time. You have to catch one of them alone to ask your question. Because otherwise the two experts start arguing the finer points between themselves, and you don't get an answer. Sound familiar?
So one option is to say, less power/conciseness, more simplicity/obviousness, and stick with seventy-wo for 71-over. Another option is to go ahead and make sev- an official syllable, since it certainly works. A third option is to have a separate xenwiki page called "possible extensions to color notation" and put sev- in there. Put it out there, but not as something a beginner has to know or even think about. And then see if anyone actually uses it.
Now I'm the creator of colorspeak, but I don't want to be a dictator. So this is just one person's opinion. I like option #1. Because adding sev- only gets us a little ways further down the list of primes. The question then becomes, how do you say 83-over? And 97-over? And what about 101, 103, 107 and 109? Just to cover harmonics 64-128 we would need probably 6 new words. And then there's people using harmonics 128-256, and the temptation is to invent even more words. And then you just *know* someone's going to coma along and start talking about how great prime 257 is! So to recap, we have to deal with primes 7 and 17, then the next dozen are pretty easy, then we hit a roadblock, because 71, 73 and 79 are too similar-sounding to 7 and 17. IMO this is a good place for our inevitable surrender to the vast quantity of prime numbers. At least we get harmonics 32-64 all named. --TallKite (talk) 10:25, 21 December 2020 (UTC)
Well Praveen had a brilliant idea and now I have to eat my words. :) 70 can be fitwe (50 + 20). Fits the logic of colorspeak perfectly. This lets us cover harmonics 64-128 without adding any new words.
5, 7, 11, 13, 17, 19, 23, 29, 31, 37
ya za la tha sa na twetha twena thiwa thisa
41, 43, 47, 53, 59, 61, 67
fowa fotha fosa fitha fina siwa sisa
71, 73, 79, 83, 89, 97
fitwewa fitwetha fitwena fithitha fithina fifosa
101, 103, 107, 109, 113, 127
fifiwa fifitha fifisa fifina fisitha sisisa
BTW the first two lines can be sung to the tune of Supercalifragilisticexpialidocious!
--TallKite (talk) 06:31, 30 November 2021 (UTC)

Incorrect formula for converting a color name?

I wrote some code implementing this page's formula for converting from a color name to a ratio and found that it's apparently wrong in some cases. For example, for "y1" we have S = 0, M = 0, monzo = [a b 1>, X = 16, and so the formula on this page says: b = (2*0 - 2*(16) + 3) mod 7 + 7*0 - 3 = (-29) mod 7 - 3 = 6 - 3 = 3 and a = (0 - 16 - 11*3) / 7 + 0 = -7, but it should be b = -4, a = 4 since "y1" corresponds to 80/81 = [4 -4 1>. The same problem happens with "g1": the formula gives b = 35 mod 7 - 3 = -3 and a = 7, but it should be b = 4, a = -4 since "g1" corresponds to 81/80 = [-4 4 -1>. The only other code implementation of this conversion I could find is in misotanni's jipci, and I confirmed that it does indeed convert "y1" and "g1" incorrectly.

I wasn't able to understand this formula well enough to fix it, but I was able to come up with a new formula that does work in every case. Let Y = the sum of all the known monzo exponents plus 2*(S-X), divided by 7, and rounded off (i.e. the magnitude of [0 2(S-X) c d e ...>). Then, a = -3(S-X) - 11(M-Y) and b = 2(S-X) + 7(M-Y). I found these formulas by directly solving the equations for degree and magnitude for a and b – I wrote up my derivation here. M-yac (talk) 00:24, 28 June 2021 (UTC)

Great to see someone working on that. I have dreamed of a way to get this information. Hopefully, the inventor(s) and your approach find together in a constructive way. --Xenwolf (talk) 13:22, 28 June 2021 (UTC)
I agree, I think it would be great if we could manage to fix that original nice formula. By the way, if you're just looking to automatically convert to/from color notation, the code I mentioned is now a part of xen-calc – e.g. "81/80" on xen-calc or "gu1" on xen-calc. --M-yac (talk) 22:02, 29 June 2021 (UTC)
This is great news, is it the original one with the error or the fixed one? Anyway, I can now start working off my todo list. --Xenwolf (talk) 22:52, 29 June 2021 (UTC)
Just now seeing this. (Feel free to message me on my user talk page about stuff like this.) Thank you Matt for finding this error and fixing it! I will update the page with the correct formulas.
I looked at your xen-calc, very nice! (Xenwolf, can we add this to the "Useful Tools" page?) I REALLY like your use of e.g. vM3\22. I will add that to the page on ups and downs notation.
But I don't consider y1 a valid name. I would call 80/81 a descending g1, not a y1. Same for z1, zg1 and sgg1. Considering all the possible 7-note segments of all the possible colors, half of them have no unisons, because the 8ves are less than 1200¢. Some don't even have 2nds, e.g. the central bizogu segment. An 8ve minus the 50/49 comma is a zzgg9 of 1165¢, and a zzgg2 would be a descending rryy-2. My reasoning is that intervals can be either ascending or descending, and also either positive or negative.
To this paragraph specifically: to me a "y1" ought to be the interval such that "y1 * w2 = y2", i.e. the interval which "makes things yo". In that sense, 80/81 is y1, to me. The fact that the interval is descending doesn't change the fact that it functions like a y1, in the same way that the fact that 64/63 is ascending doesn't change the fact that functions like a ru1 (i.e. "makes things ru", "ru1 * w2 = ru2"). The fact that y1 is descending is an important fact though, e.g. it can help you remember that y2 is smaller than w2. --M-yac (talk) 03:47, 2 August 2021 (UTC)
I just realized this may not work how I thought in color notation. In the FJS (which is what I'm most familiar with) "P1^5" is always the interval which "makes things up-five", e.g. "P1^5 * M2 = M2^5", "P1^5 * M3 = M3^5", "P1^5 * d12 = d12^5", etc. But in color notation "y1 * w3 = sy3", not "y3". So y1 is not the interval which "makes things yo"? Hmm. I think there's still some argument to be made about the "function" of y1 in color notation, but it gets more complicated with the large and small prefixes. (And unfortunately, I still don't have a great intuition for large and small prefixes.) --M-yac (talk) 04:01, 2 August 2021 (UTC)
Ascending positive intervals (includes most ratios with N > D) go up in pitch, and either up the scale (e.g. 9/8 = w2) or stay the same (e.g. g1 or ry1 = 15/14)
Ascending negative intervals go up in pitch but down the scale, e.g. 50/49 = rryy-2
Descending positive intervals go down in pitch and either down the scale (e.g. 8/9 = desc. w2) or stay the same (e.g. 14/15 = desc. ry1)
Descending negative intervals go down in pitch but up the scale, e.g. 49/50 goes from ry4 "up" to the flatter zg5
Your broader use of the term negative to include descending is mathematically sound. 49/50 is a (positive) zzgg2. It also reduces (eliminates?) invalid color names, which is nice. But negative intervals are different than descending ones, and IMO it's nice to distinguish between them. They feel different. Descending intervals are commonplace and straightforward, but negative intervals only apply to certain JI commas. My narrower usage of negative functions as a warning that interval arithmetic works counter-intuitively. And the concept of descending intervals is well understood and doesn't require a new term like negative. So I think the narrower use of negative is better for pedagogical purposes.
I very much agree with your assessment that just including the word "negative" and not mentioning whether or not the interval is descending could be very misleading. (You writing out those four cases was very helpful!) I've since added an extra line to the output of xen-calc when the interval is descending, e.g. I am still going to keep the old output though, both because of my "how the interval functions" argument above and because of the fact that the "descending" qualifier has no canonical place in the syntax of color notation (e.g. the only name I can give 5/7 that satisfies all the descriptions on this page is "ry-5"). Perhaps you could add it, though? e.g. "dzg5" or "dezogu 5th" for 5/7? --M-yac (talk) 03:47, 2 August 2021 (UTC)
Another objection: I see that xen-calc calls 4/5 a gu negative 3rd. Playing a note and adding a note 5/4 below it makes a yo harmony with a distinctly 5-over sound. If we call that interval a gu negative 3rd, that implies a 5-under sound. Sure, you can deduce from the term negative that the color is inverted, but that's extra mental work. I'd rather say the added note is a yo 3rd below the 1st note than a negative gu 3rd above it.
The old notation is still there for the reasons I gave above, but the output now should make it clear that this interval is primarily a descending yo 3rd: --M-yac (talk) 03:47, 2 August 2021 (UTC)
As I've said elsewhere, I'm the inventor of color notation, but I'm not a dictator. I welcome debate on this matter. :) --TallKite (talk) 09:36, 12 July 2021 (UTC)
Looking over the new formulas here, shouldn't "Y = magnitude([0 2(S-X) d e ...>)" be "Y = magnitude([0 2(S-X) c d e ...>)"? And shouldn't the formula for a end with "+ C"? --TallKite (talk) 09:51, 12 July 2021 (UTC)
Oh yes, good catch on both! I've updated the derivation. --M-yac (talk) 03:47, 2 August 2021 (UTC)
Seeing the xen-calc output, Praveen and I decided that large and small should definitely be abbreviated la- and sa- not only in temperament names, but in all interval names. Likewise double and triple should always become bi- and tri-. I updated this page to reflect that. Again, so nice to have an app for this!! :) --TallKite (talk) 00:44, 13 July 2021 (UTC)
The more I think about calling descending intervals negative, the more strongly I feel that they shouldn't be. Because I have said in the past things like "prime 23 is best mapped to a 5th, not a 4th, because that mapping minimizes negative intervals." That sentence doesn't make any sense with the broader definition of negative. --TallKite (talk) 05:06, 26 July 2021 (UTC)
A response to these comments in general: Thank you so much for taking the time to think so deeply about this! It makes me very happy to know my tool has at least one enthusiastic user. Sorry I took so long to reply. I left some specific comments below the paragraphs to which they are most relevant. --M-yac (talk) 03:47, 2 August 2021 (UTC)
I've been mulling over how to have both uses of "negative" coexist without confusing the user. I do like the narrower meaning, and don't like it being altered. I wouldn't have a problem with you personally using the term that way in your writings, which is what I meant by not being dictatorial. But by labeling your usage "color notation", I feel that words are being put in my mouth.
I think the answer is when your usage occurs, the usage is marked somehow as alternate, and a link is provided to an explanatory paragraph on the about page. (Which I of course would help you write, or you could just pull from what I've written here.) For example the color notation output for 4/5 could be
descending yo 3rd,
gu negative 3rd, g-3
(alternate usage of "negative")
with the underlined text being the aforementioned link. Would this work for you?
As for "dzg5" or "dezogu 5th" for 5/7, I think there's quite enough 1-letter and 2-letter abbreviations already, and 5/7 should simply be written "desc zg5". Funny, in all my years, I've never needed anything beyond desc. But I'm curious, can you give me examples of when dezogu would be used?
I'm being a stickler for this because the quality of your webapp is so high, I'm sure in the future far most people will learn color notation directly from xen-calc than from my writings. Especially now that the xenwiki links to it on every interval page. You will have far, far more than one "enthusiastic user"! But of course with freeware, you never get to see how big your user base becomes. Anyway, once we get this matter straightened out, I'd like to link to xen-calc in the first paragraph of the color notation xenwiki page, and also on my various websites. --TallKite (talk) 11:29, 23 August 2021 (UTC)

Possible extension of colorspeak to describe certain subgroups

Using 9 instead of 3 could be "wawa", as in Laquinyo wawa = 2.9.15 & 3125/3072. See Note that 2.9.5 & 3125/3072 is impossible, so once we know the first 2 elements of the subgroup and the comma, the 3rd element is automatically determined (altho it could also be written as 2.9.5/3). The rule is, use 15 only if the comma's 3-count is an odd number, which incidentally necessitates the 5-count also being odd. Thus Gu wawa uses 2.9.5 not 2.9.15.

A 2.27.whatever subgroup would be triwa. Using 4 instead of 2 would have the unfortunate name "caca". Maybe call it bica instead? Not sure how to name subgroups like 2.3.35 or 2.3.7/5 or 2.7/5.9/5. --TallKite (talk) 22:01, 21 March 2022 (UTC)

Yaza means Barbershop is yaza, but they avoid 7-under intervals. Thus it could be described as yazo music. --TallKite (talk) 06:17, 12 July 2023 (UTC)

Possible "de-colorization" of colorspeak

The five colors wa, yo, gu, zo and ru could all be replaced with words derived directly from the words three, five and seven. This requires a new syllable "te" that means ten or teen, used for primes 13, 17, and 19.

prime -o ("oh") for over -u ("oo") for under -a ("ah") for all -e ("eh") for exponent
2 twa bi ("bee") squared
3 tha tri ("tree") cubed
5 fo 5o fu 5u fa 5a fe ^5
7 iso 7o su 7u isa 7a se ^7
11 ilo 1o lu 1u ila 1a le ^11
13 tetho 3o tethu 3u tetha 3a tethe ^13
17 teso 17o tesu 17u tesa 17a tese ^17
19 teno 19o tenu 19u tena 19a tene ^19

Currently, 41, 43 and 47 are fowo, fotho and foso. But fotho looks like 5-over 3-over. So 41, 43 and 47 must become forwo, fortho and forso.


  • More logical, easier to learn.
  • fewer homonyms: no more "wa", "no" or "nu".


  • The names of intervals using primes 13, 17 and 19 become less concise.
  • Widely used 7-limit colors become less concise: yy -> 5oo, zg -> 7o5u, likewise for ry, rg, zy, ryy, etc.
  • The 4:5:6 triad becomes C5o, which looks like a dyad.
  • The 6:7:9 triad becomes C7o, which looks like a 7th chord.
  • The current nomenclature is widely used in the xenwiki and various apps.

This could be taken further and ilo/lu/ila could become tewo/tewu/tewa. Or it could be taken not as far, and wa could be retained for prime 3, allowing tho/thu/tha for prime 13.

Overall I think the disadvantages of decolorization outweigh the advantages. Just noting the possibility here. --TallKite (talk) 06:17, 12 July 2023 (UTC)

Possible "de-heptatonicization" of colorspeak

Color notation uses the conventional heptatonic degrees 2nd, 3rd, 4th, etc. It's possible to avoid this by using "wo" and "wu" to mean 3-over and 3-under. Thus 10/9 would be not "yo 2nd" but "yowuwu". 27/16 would be "triwo". The Ptolomaic scale would be wa, wowo, yo, wu, wo, yowu, yowo, cowa. Presumably this would free up one's thinking, but one would lose the rough estimate of an interval's size that the degree provides, and it would be difficult to tell how big something like zoguwuwu is. I don't personally recommend this notation, just noting the possibility here. --TallKite (talk) 06:17, 12 July 2023 (UTC)