Kite's color notation/Temperament names - Revision history

TallKite: extensive update to use -ma and -ti

2026-04-26T07:52:15Z

extensive update to use -ma and -ti

TallKite: add the -ma suffix

2026-04-16T07:59:41Z

add the -ma suffix

← Older revision		Revision as of 07:59, 16 April 2026
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	== Definition==		== Definition==
	[[Color notation]] can name every regular temperament. The name is the same as that of the comma(s) tempered out, but using an alternate format designed for commas. This format ~~omits~~ the degree (unison, 2nd, etc.). For example, [[Semaphore]] tempers out the ~~zozo 2nd~~ and is called the Zozo temperament, written Zozoti or zzT, where "ti" and "T" mean temperament. The name of the comma or the temperament is ~~always~~ capitalized~~, to distinguish it from the color. Thus zozo refers to all zozo ratios, whereas Zozo refers to one specific zozo ratio, 49/48~~.		[[Color notation]] can name every regular temperament. The name is the same as that of the comma(s) tempered out, but using an alternate format designed for commas. This format replaces the degree (unison, 2nd, etc.) with the suffix -ma. For example, [[Semaphore]] tempers out the zozoma 49/48 and is called the Zozo temperament, written Zozoti or zzT, where "ti" and "T" mean temperament. The name of the comma or the temperament is generally capitalized.

	The color defines a lattice row, and the magnitude (large, small, etc.) defines a '''segment''' of that row. A name without a magnitude, like ~~Zozo~~, refers to the central segment. Each segment contains 7 ratios. The comma that is tempered out is usually the smallest in cents of those 7. If not, '''-bi~~''' or '''-tri~~''' is added to the end of the name to indicate that the comma is the 2nd ~~or 3rd~~ largest ratio in that segment, e.g. the [[Mavila]] comma is ~~Layobi~~ or ~~Ly#2~~. The Mavila temperament is Layobiti or ~~Ly#2T~~. Any comma smaller than 256/243 = 90¢ is guaranteed to be the smallest ratio in its segment, thus -bi ~~and -tri are~~ only used for very large commas.		The color defines a lattice row, and the magnitude (large, small, etc.) defines a '''segment''' of that row. A name without a magnitude, like Zozoti, refers to the central segment. Each segment contains 7 ratios. The comma that is tempered out is usually the smallest in cents of those 7. If not, '''-bi''' is added to the end of the name to indicate that the comma is the 2nd largest ratio in that segment, e.g. the [[Mavila]] comma is layobima or LybM. The Mavila temperament is Layobiti or LybT. Any comma smaller than 256/243 = 90¢ is guaranteed to be the smallest ratio in its segment, thus -bi is only used for very large commas.

	Some 5-limit examples, sorted by color depth. Many more examples can be found on the comma pages ([[Small comma]], [[Medium comma]], [[Large comma]] and [[Unnoticeable comma]]).		Some 5-limit examples, sorted by color depth. Many more examples can be found on the comma pages ([[Small comma]], [[Medium comma]], [[Large comma]] and [[Unnoticeable comma]]).
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	Sometimes the smallest ratio in a segment is some other comma raised to some power. For example, the smallest ratio in the central segment of the zozogugu row is 441/400. But since this is (21/20)<sup>2</sup>, tempering it out would simply result in the Zogu temperament. Thus there is no Bizogu temperament, although there is a Bizogubi one.		Sometimes the smallest ratio in a segment is some other comma raised to some power. For example, the smallest ratio in the central segment of the zozogugu row is 441/400. But since this is (21/20)<sup>2</sup>, tempering it out would simply result in the Zogu temperament. Thus there is no Bizogu temperament, although there is a Bizogubi one.

	La means both large and 11-all, and sa means both small and 17-all~~. To avoid confusion, large and small should never be abbreviated unless part of a longer word~~. La is also the La note in solfege, and Sa is the tonic in saregam. The meaning will always be clear from context. Notes are never large or small, only intervals are.		La means both large and 11-all, and sa means both small and 17-all. La is also the La note in solfege, and Sa is the tonic in saregam. The meaning will always be clear from context. Notes are never large or small, only intervals are.

	Multi-comma temperaments are named as a list of commas. For example, 7-limit porcupine is Triyo & Ruti. See below for further discussion.		Multi-comma temperaments are named as a list of commas. For example, 7-limit porcupine is Triyo & Ruti. See below for further discussion.
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	If the comma is wa, an edo is implied. For the most common cases of 5-edo, 7-edo and 12-edo, the temperament is named after the wa comma. Thus [[Blackwood]] is Sawati + ya, [[Whitewood]] is Lawati + ya, and [[Catler]] is Lalawati + za.		If the comma is wa, an edo is implied. For the most common cases of 5-edo, 7-edo and 12-edo, the temperament is named after the wa comma. Thus [[Blackwood]] is Sawati + ya, [[Whitewood]] is Lawati + ya, and [[Catler]] is Lalawati + za.

	Any other wa comma is named using the Wa-N format. Thus [[Countercomp family\|Countercomp]] is Wa-41 + ya, not the difficult-to-decipher Tribisawati + ya. Note that multi-ring edos such as 10-edo can't be implied by a wa comma, and Wa-10 is not a valid comma name. However 10-edo can be created by a non-wa comma, or by a wa comma plus a non-wa comma, e.g. Sawa & Yoyoti.		Any other wa comma is named using the wa-N format. Thus [[Countercomp family\|Countercomp]] is wa-41 + ya, not the difficult-to-decipher Tribisawati + ya. Note that multi-ring edos such as 10-edo can't be implied by a wa comma, and wa-10 is not a valid comma name. However 10-edo can be created by a non-wa comma, or by a wa comma plus a non-wa comma, e.g. Sawa & Yoyoti.

	More examples of temperaments:		More examples of temperaments:
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	== Finding the comma from the name and vice versa ==		== Finding the comma from the name and vice versa ==
	=== Finding the comma ===		=== Finding the comma ===
	Every ratio can be named either as a standard interval or as a comma/temperament, e.g. 128/125 is both the trigu 2nd and the ~~Trigu comma~~. The latter is awkward for low-odd-limit ratios: 5/4 would be the Yobi "comma" and 6/5 would be the Gutri "comma". But the former is awkward for high odd-limit ratios, because there will be many 2nds and 3rds and even 4ths, and many of them will be negative. So the latter name is used for commas, for brevity. Unfortunately, this makes identifying the comma from the name a little more work.		Every ratio can be named either as a standard interval or as a comma/temperament, e.g. 128/125 is both the trigu 2nd and the triguma. The latter is awkward for low-odd-limit ratios: 5/4 would be the Yobi "comma" and 6/5 would be the Gutri "comma". But the former is awkward for high odd-limit ratios, because there will be many 2nds and 3rds and even 4ths, and many of them will be negative. So the latter name is used for commas, for brevity. Unfortunately, this makes identifying the comma from the name a little more work.

	If the monzo is (a b c d...) then all but a and b are obvious from the color name. Next find the ratio of the midpoint of the segment. For this ratio, the sum of all the monzo exponents except the 2-exponent is a multiple of 7. For example, the gu midpoint is 6/5, and the sayoyo midpoint is (10 -9 2).		If the monzo is (a b c d...) then all but a and b are obvious from the color name. Next find the ratio of the midpoint of the segment. For this ratio, the sum of all the monzo exponents except the 2-exponent is a multiple of 7. For example, the gu midpoint is 6/5, and the sayoyo midpoint is (10 -9 2).
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	{\| class="wikitable"		{\| class="wikitable"
	! rowspan="2" \| If the midpoint<br />ratio is		! rowspan="2" \| If the midpoint<br />ratio is
	! colspan="3" \| Do this to the 3-exponent		! colspan="2" \| Do this to the 3-exponent
	\|-		\|-
	! If no suffix		! If no suffix
	! If "-bi" suffix		! If "-bi" suffix
	~~! If "-tri" suffix~~
	\|-		\|-
	\| 0-204¢		\| 0-204¢
	\| nothing		\| nothing
	\| add 2		\| add 2
	~~\| subtract 3~~
	\|-		\|-
	\| 204-294¢		\| 204-294¢
	\| subtract 2		\| subtract 2
	\| nothing		\| nothing
	~~\| add 2~~
	\|-		\|-
	\| 294-498¢		\| 294-498¢
	\| add 3		\| add 3
	\| subtract 2		\| subtract 2
	~~\| nothing~~
	\|-		\|-
	\| 498-702¢		\| 498-702¢
	\| add 1		\| add 1
	\| add 3		\| add 3
	~~\| subtract 2~~
	\|-		\|-
	\| 702-906¢		\| 702-906¢
	\| subtract 1		\| subtract 1
	\| add 1		\| add 1
	~~\| add 3~~
	\|-		\|-
	\| 906-996¢		\| 906-996¢
	\| subtract 3		\| subtract 3
	\| subtract 1		\| subtract 1
	~~\| add 1~~
	\|-		\|-
	\| 996-1200¢		\| 996-1200¢
	\| add 2		\| add 2
	\| subtract 3		\| subtract 3
	~~\| subtract 1~~
	\|}		\|}

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	\| -bi		\| -bi
	\| -bi		\| -bi
	\|-
	~~\| 294-408¢~~
	~~\| -tri~~
	~~\| -bi~~
	~~\| -bi~~
	~~\| -bi~~
	~~\| -tri~~
	~~\| -tri~~
	~~\| -tri~~
	\|-
	~~\| 408-498¢~~
	~~\| -tri~~
	~~\| -tri~~
	~~\| -tri~~
	~~\| -tri~~
	~~\| -tri~~
	~~\| -tri~~
	~~\| -tri~~
	\|}		\|}

FloraC: Fix linking

2025-09-11T05:28:53Z

Fix linking

← Older revision		Revision as of 05:28, 11 September 2025
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	Some 5-limit examples, sorted by color depth. Many more examples can be found on the comma pages ([[Small comma]], [[Medium comma]], [[Large comma]] and [[Unnoticeable comma]]).		Some 5-limit examples, sorted by color depth. Many more examples can be found on the comma pages ([[Small comma]], [[Medium comma]], [[Large comma]] and [[Unnoticeable comma]]).
	# [[Schismatic]] = Layoti, [[Mavila]] = Layobiti, [[Superpyth]] = Sayoti, [[Meantone]] = Guti, [[Father]] = Gubiti.		# [[Schismatic]] = Layoti, [[Mavila]] = Layobiti, [[Superpyth]] = Sayoti, [[Meantone]] = Guti, [[Father]] = Gubiti.
	# [[Dicot]] = Yoyoti, [[~~Immunity family\|~~Immunity]] = Sasa-yoyoti, [[Bug]] = Guguti, [[Diaschismic]] = Saguguti, [[Beatles]] = Sasa-guguti.		# [[Dicot]] = Yoyoti, [[Immunity]] = Sasa-yoyoti, [[Bug]] = Guguti, [[Diaschismic]] = Saguguti, [[Beatles]] = Sasa-guguti.
	# [[Porcupine]] = Triyoti, [[Augmented]] = Triguti, [[~~Laconic family\|~~Laconic]] = Latriguti, [[~~Misty comma\|~~Misty]] = Sasa-triguti.		# [[Porcupine]] = Triyoti, [[Augmented (temperament)\|Augmented]] = Triguti, [[Laconic]] = Latriguti, [[Misty]] = Sasa-triguti.
	# [[Negri]] = Laquadyoti, [[Tetracot]] = Saquadyoti, [[Vulture]] = Sasa-quadyoti, [[Diminished]] = Quadguti.		# [[Negri]] = Laquadyoti, [[Tetracot]] = Saquadyoti, [[Vulture]] = Sasa-quadyoti, [[Diminished (temperament)\|Diminished]] = Quadguti.
	Exponent syllables like bi or tri are always unaccented. The final "-ti" is too. To emphasize the prime limit, the first occurrence of the highest prime is always accented: Bi'''r<u>u</u>'''yoti, Bi'''<u>zo</u>'''zoguti. In longer names, the 1st occurrence of sa/la and/or of lower primes may also be accented: '''Sa'''sa-'''gu'''guti, '''Zo'''zotri'''gu'''ti.		Exponent syllables like bi or tri are always unaccented. The final "-ti" is too. To emphasize the prime limit, the first occurrence of the highest prime is always accented: Bi'''r<u>u</u>'''yoti, Bi'''<u>zo</u>'''zoguti. In longer names, the 1st occurrence of sa/la and/or of lower primes may also be accented: '''Sa'''sa-'''gu'''guti, '''Zo'''zotri'''gu'''ti.

FloraC: Update a link

2025-08-28T12:16:44Z

Update a link

← Older revision		Revision as of 12:16, 28 August 2025
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	{{~~breadcrumb~~}}		{{Breadcrumb}}
	(Note that Kite has developed a completely different way to name temperaments that looks somewhat similar to color notation, but uses [[Pergen\|pergens]] and his [[List of uniform solfeges for pergens\|uniform solfege]] instead. See [[User:TallKite/Catalog of eleven-limit rank two temperaments with Color names]] for examples.)		(Note that Kite has developed a completely different way to name temperaments that looks somewhat similar to color notation, but uses [[Pergen\|pergens]] and his [[List of uniform solfeges for pergens\|uniform solfege]] instead. See [[User:TallKite/Catalog of eleven-limit rank two temperaments with Color names]] for examples.)

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	* [[User:TallKite/Catalog of thirteen-limit rank two temperaments with Color names]]		* [[User:TallKite/Catalog of thirteen-limit rank two temperaments with Color names]]
	* [[User:TallKite/Catalog of eleven-limit rank three temperaments with Color names]]		* [[User:TallKite/Catalog of eleven-limit rank three temperaments with Color names]]
	* [[Catalog of rank ~~two~~ temperaments]] (under construction)		* [[Kite's color notation/Catalog of rank-2 temperaments]] (under construction)

	== Finding the comma from the name and vice versa ==		== Finding the comma from the name and vice versa ==

TallKite: TallKite moved page Color notation/Temperament names to Kite's color notation/Temperament names: Editor VectorGraphics has repeatedly edited pages I've written about my own research and inserted misinformation. On discord he is openly hostile to me. This move is necessary to avoid a toxic work environment for me.

2025-08-20T01:50:49Z

TallKite moved page Color notation/Temperament names to Kite's color notation/Temperament names: Editor VectorGraphics has repeatedly edited pages I've written about my own research and inserted misinformation. On discord he is openly hostile to me. This move is necessary to avoid a toxic work environment for me.

← Older revision	Revision as of 01:50, 20 August 2025
(No difference)

ArrowHead294: Formatting

2024-10-07T17:56:22Z

Formatting

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TallKite: added -ti

2024-09-24T05:12:21Z

added -ti

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FloraC: /* Definition */ update wa-41's name; ditch "here"-links in favor of using page names

2024-03-29T10:06:46Z

Definition: update wa-41's name; ditch "here"-links in favor of using page names

← Older revision		Revision as of 10:06, 29 March 2024
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	The color defines a lattice row, and the magnitude (large, small, etc.) defines a '''segment''' of that row. A name without a magnitude, like Zozo, refers to the central segment. Each segment contains 7 ratios. The comma that is tempered out is usually the smallest in cents of those 7. If not, '''-bi''' or '''-tri''' is added to the end of the name to indicate that the comma is the 2nd or 3rd largest ratio in that segment, e.g. [[Mavila]] = Layobi. Any comma smaller than 256/243 = 90¢ is guaranteed to be the smallest ratio in its segment, thus -bi and -tri are only used for very large commas.		The color defines a lattice row, and the magnitude (large, small, etc.) defines a '''segment''' of that row. A name without a magnitude, like Zozo, refers to the central segment. Each segment contains 7 ratios. The comma that is tempered out is usually the smallest in cents of those 7. If not, '''-bi''' or '''-tri''' is added to the end of the name to indicate that the comma is the 2nd or 3rd largest ratio in that segment, e.g. [[Mavila]] = Layobi. Any comma smaller than 256/243 = 90¢ is guaranteed to be the smallest ratio in its segment, thus -bi and -tri are only used for very large commas.

	Some 5-limit examples, sorted by color depth. Many more examples can be found on the comma pages [[~~Comma\|here~~]], [[Medium ~~commas\|here~~]], [[Large ~~commas\|here~~]] and [[Unnoticeable comma~~\|here~~]].		Some 5-limit examples, sorted by color depth. Many more examples can be found on the comma pages ([[Small comma]], [[Medium comma]], [[Large comma]] and [[Unnoticeable comma]]).
	#[[Schismatic]] = Layo, [[Mavila]] = Layobi, [[Superpyth]] = Sayo, [[Meantone]] = Gu, [[Father]] = Gubi.		#[[Schismatic]] = Layo, [[Mavila]] = Layobi, [[Superpyth]] = Sayo, [[Meantone]] = Gu, [[Father]] = Gubi.
	#[[Dicot]] = Yoyo, [[Immunity family\|Immunity]] = Sasa-yoyo, [[Bug]] = Gugu, [[Diaschismic]] = Sagugu, [[Beatles]] = Sasa-gugu.		#[[Dicot]] = Yoyo, [[Immunity family\|Immunity]] = Sasa-yoyo, [[Bug]] = Gugu, [[Diaschismic]] = Sagugu, [[Beatles]] = Sasa-gugu.
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	If the comma is wa, an edo is implied. For the most common cases of 5-edo, 7-edo and 12-edo, the temperament is named after the wa comma. Thus [[Blackwood]] is Sawa + ya, [[Whitewood]] is Lawa + ya, and [[Catler]] is Lalawa + za.		If the comma is wa, an edo is implied. For the most common cases of 5-edo, 7-edo and 12-edo, the temperament is named after the wa comma. Thus [[Blackwood]] is Sawa + ya, [[Whitewood]] is Lawa + ya, and [[Catler]] is Lalawa + za.

	Any other wa comma is named using the Wa-N format. Thus [[~~Counterpyth~~ family\|~~Counterpyth~~]] is Wa-41 + ya, not the difficult-to-decipher Tribisawa + ya. Note that multi-ring edos such as 10-edo can't be implied by a wa comma, and Wa-10 is not a valid comma name. However 10-edo can be created by a non-wa comma, or by a wa comma plus a non-wa comma, e.g. Sawa & Yoyo.		Any other wa comma is named using the Wa-N format. Thus [[Countercomp family\|Countercomp]] is Wa-41 + ya, not the difficult-to-decipher Tribisawa + ya. Note that multi-ring edos such as 10-edo can't be implied by a wa comma, and Wa-10 is not a valid comma name. However 10-edo can be created by a non-wa comma, or by a wa comma plus a non-wa comma, e.g. Sawa & Yoyo.

	Temperaments are abbreviated with "T": Zozo = zzT, Triyo = y<sup>3</sup>T, Gu & Rugu = g&rgT, Layobi = Ly#2T, Sawa + ya = sw+yT, Wa-41 + ya = w-41+yT, Gu + zala = g+z1aT, and Biruyo Nowa = rryy-wT.		Temperaments are abbreviated with "T": Zozo = zzT, Triyo = y<sup>3</sup>T, Gu & Rugu = g&rgT, Layobi = Ly#2T, Sawa + ya = sw+yT, Wa-41 + ya = w-41+yT, Gu + zala = g+z1aT, and Biruyo Nowa = rryy-wT.
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	*[[User:TallKite/Catalog of eleven-limit rank three temperaments with Color names]]		*[[User:TallKite/Catalog of eleven-limit rank three temperaments with Color names]]
	*[[Catalog of rank two temperaments]] (under construction)		*[[Catalog of rank two temperaments]] (under construction)

	==Finding the comma from the name and vice versa==		==Finding the comma from the name and vice versa==

Fredg999: Fredg999 moved page Color notation/Temperament Names to Color notation/Temperament names: WP:NCCAPS

2023-07-03T01:24:37Z

Fredg999 moved page Color notation/Temperament Names to Color notation/Temperament names: WP:NCCAPS

← Older revision	Revision as of 01:24, 3 July 2023
(No difference)

TallKite: added a note about pergen/solfege names

2023-01-19T07:55:13Z

added a note about pergen/solfege names

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