Talk:Small comma

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Calculated 5–limit commas

I was in a calculation of 5–limit commas 4294967296 integer limit below 100 cents. The calculation was blazingly fast but was in a rudimentary format.

List 1:

1600000/1594323 6.153558074133514
81/80 21.5062895967165
131072000/129140163 25.70612688291476
20000/19683 27.65984767084646
128/125 41.05885840550059
6561/6400 43.012579193433 (square of 81/80)
43046721/41943040 44.96629998136541
1638400/1594323 47.21241647963268
250/243 49.166137267562604
648/625 62.565148002217086
531441/512000 64.51886879015092 (cube of 81/80)
3486784401/3355443200 66.4725895780748
20480/19683 68.71870607634492
25/24 70.67242686427875
43046721/40960000 86.025158386866 (fourth power of 81/80)
409600000/387420489 96.37855374719493

6561 3125 84.07143759893216 3 3125 29.613568458779582 129140163 15625 15.352731522582985 59049 15625 98.33227453512521 243 15625 8.107278862061662 1 15625 82.11771681100117 4782969 78125 76.825984938408 19683 78125 13.399010734655548 387420489 390625 55.31969534169292 1594323 390625 34.905300331368494 729 390625 78.77970572634041 3 390625 11.445289946721005 129140163 1953125 56.41158992808357 59049 1953125 57.27341612962533 243 1953125 32.951579543438925 4782969 9765625 35.767126532910254 19683 9765625 54.457869140154 9 9765625 59.227136917559164 387420489 48828125 14.260836936190913 1594323 48828125 75.9641587368705 729 48828125 37.7208473208384 3 48828125 52.504148352227276 129140163 244140625 97.47044833358558 59049 244140625 16.214557724123324 243 244140625 74.01043794894235 1162261467 1220703125 84.93326380046966 4782969 1220703125 5.291731872591754 19683 1220703125 95.51672754565459 9 1220703125 18.168278512052893

List 2: 2197265625 39.674568108773656 263671875 30.997858755506513 4271484375 9.491569158785751 17578125 80.73342651427424 512578125 80.1639960230716 2109375 10.060999649994073 34171875 31.56728924670915 15625 82.11771681100117 553584375 53.073578843429914 253125 60.611427214286095 4100625 39.10513761757102 16875 51.11985805549466 66430125 17.59884802085594 273375 72.62614765220974 125 41.05885840550059 1076168025 3.907441575864823 4428675 94.1324372489305 2025 19.55256880878551 7971615 88.27127488513042 32805 1.9537207879324114 135 92.17871646099525 129140163 66.76498528842103 531441 23.46001038464749 243 90.22499567306284 1 0

List 1 repeats 3 numbers: a power of 3, a power of 5 and a cents value. The fractions have to be manually multiplied with powers of two for octave reduction.

List 2 repeats 2 numbers: a fraction part and a cents value. The fraction part must be counterparted with a power of two.

There may also be redundant squares, cubes, etc. of the fractions. Hope we can get a complete comma list from it!

And someone, please merge Comma with Unnoticeable commas back so that we can have a closer comparison, and complete blank fraction spaces up to like 25 digits.

PiotrGrochowski (talk) 11:54, 18 September 2018 (UTC)

Links in general

I'd like to limit "sophisticated linking" in favor of usability. I'm not very happy with links of type [[A|B]] even if A→B or B→A. If there is a good chance that both are equally (or comparable) common, I suggest to use [[A]] and [[B]]. And sometimes the numbers are easier to remember than names, especially if names are newly invented, so for me 64/63 is easier to remember than septimal comma, and in this special case the ratio is unique which the name isn't. Maybe we should try to discuss this with more people. Here are two cases where the problem is noticeable, and I would like to know more about the ideas others have about their way of linking: 1) FloraC "links on names instead of ratios..." and 2) Xenwolf: "improved apotome link...". Maybe we should start an own project for this? --Xenwolf (talk) 15:37, 27 November 2020 (UTC)

Hmm... that leaves me with questions about commas like the Quartisma, the Nexuma and the Symbiosma... These were all recently named, but the ratios of these commas have too many digits... Also, how unique are the names of these commas? --Aura (talk) 15:43, 27 November 2020 (UTC)
I think names and ratios of these three commas will be obscure to most people, so there will be no best option. This probably applies to commas in general (except 81/80=syntonic or meantone comma and pythagorean comma whose ratio I can remember even worse than my phone number). BTW: in cases like 7/5 and 10/7, who knows (without cheating!) which of them is Euler's and which Huygens' tritone? --Xenwolf (talk) 15:58, 27 November 2020 (UTC)
Yes, it's an issue for commas with non-unique names. Shall we stick to a simple link priciple, where we always link directly to the page in these tables? FloraC (talk) 19:27, 27 November 2020 (UTC)
Would it be too confusing if we link to the existing lemma (in changing columns)? Or should we add a "further reading" column which would help us to place links (like satin comma) that are only loosely coupled with the comma itself? --Xenwolf (talk) 19:41, 27 November 2020 (UTC)
A further-reading column for links sounds rather forced. FloraC (talk) 08:16, 28 November 2020 (UTC)
Okay, then we'll just let it go. Maybe we or someone else will come up with a really good solution for it later. --Xenwolf (talk) 12:56, 28 November 2020 (UTC)

Proposal to change a few comma names

  • Countriton → countertriton or cotriton
"Countriton" sounds like a result of haplology. I, for one, strongly prefer full prefixes. Either countertriton or cotriton would work.
  • Moctdel → motel
"Moctdel" is hard to pronounce. I kinda get that "del" part comes from the grendel temperament (→ Mirkwai clan #Grendel) but I don't see how it's related to moct (millioctave) by any means.

Ideas? FloraC (talk) 14:10, 2 September 2022 (UTC)

Update: Nevermind "countriton". It seems it's formed by co + untriton. FloraC (talk) 09:56, 30 November 2022 (UTC)

A new way to name commas in color notation?

User Gud2228 recently added Yo-28, Gu-31 and Gu-59 to this page. These are generalizations of the Wa-N format for 3-limit commas. The format is obviously Yo-N = [x, 0, N> and Gu-N = [x, 0, -N>. It can be generalized to other primes, with e.g. Tho-10 meaning [-37 0 0 0 0 10> (Laquinbitho 2nd, about 5¢).

I have mixed feelings about this usage. One the one hand, it's great to see people experimenting and improvising with color notation. That's what happens with actual languages after all. And it is a logical extension of existing usage. But still I'd rather not elevate this usage to an official status. IMO it doesn't add enough utility to justify increasing the complexity of the notation.

So if Yo-28 isn't worth doing, why is a 3-limit name like Wa-29 OK? Because the alternative to Wa-29 is Quadsawa, which obscures the number 29. But Yo-28's alternative is Quadla-sepquadyo, in which "sepquad" clearly indicates the number 28.

So I suggest the name Yo-28 be moved to the first column, next to "oquatonic comma", and the 2nd column have the usual color name, Quadla-sepquadyo. Likewise for Gu-31 and Gu-59. -TallKite (talk) 00:46, 11 March 2023 (UTC)

Color names for 3-limit commas

Color names are mostly a straightforward mapping of the numbers in the monzo to syllables, except that it obscures the 2-count and 3-count. You have to deduce those from the degree, the magnitude, etc. Mostly this works quite well. The degree lets you estimate the size in cents, which is usually more useful information than the number of threes in the ratio.

But it doesn't work well with 3-limit commas. The most important fact about such commas is the 3-count! That tells you which edo it implies, which immediately tells you what you get when you temper out the comma. That's why I devised the "wa format", such as Wa-41, or its short form, w-41.

But here and on the other two comma pages, the short forms have been changed from e.g. "w-41" to "s6w5". IMO this isn't a good idea.

One could argue that it's somewhat useful to know that this comma turns out to be a very small 5th. IMO that information belongs on the page dedicated to that comma, where there's room to delve into such details. It doesn't belong in the table of commas.

Also, I don't like seeing the short form removed. It's good to know. It's very useful for equations such as Ly-2 + w-17 = sy2. --TallKite (talk) 05:42, 18 December 2023 (UTC)