Xenharmonic Wiki - Recent changes [en]

Instruments

Naren — Wed, 17 Jun 2026 12:00:11 GMT

Add Experimental Musical Instruments and Fletcher and Rossing to Further reading

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	== Further reading ==		== Further reading ==
	* Hugh Davies/Alexander Bonus, [https://archive.org/details/grovedictionaryo0003unse_w4m2/page/459/ Microtonal instruments], The Grove Dictionary of Musical Instruments, Second Edition, 2014		* Hugh Davies/Alexander Bonus, [https://archive.org/details/grovedictionaryo0003unse_w4m2/page/459/ Microtonal instruments], The Grove Dictionary of Musical Instruments, Second Edition, 2014
			* [https://archive.org/details/emi_archive/ Experimental Musical Instruments] journal
			* Fletcher and Rossing, [https://csclub.uwaterloo.ca/~pbarfuss/The_Physics_of_Musical_Instruments.pdf The Physics of Musical Instruments], Springer-Verlag, 1991

	[[Category:Instruments\| ]] <!-- main article -->		[[Category:Instruments\| ]] <!-- main article -->

Talk:Canou family

FloraC — Wed, 17 Jun 2026 11:44:28 GMT

← Older revision		Revision as of 11:44, 17 June 2026
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	== Introduction ==		== Introduction ==

	Fyi I initiated this project with a post in our FB group of mathematical theory a week ago, and I'm happy to discuss it either place. [[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 05:55, 2 October 2020 (UTC)		Fyi I initiated this project with a post in our FB group of mathematical theory a week ago, and I'm happy to discuss it either place. [[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 05:55, 2 October 2020 (UTC)

	== Temperament names ==		== Temperament names ==

	Okay, so you want a the name for a Canou temperament 896/891 & 472392/471625? Well, let me start by saying that since I don't know how "Canou" is pronounced, I can't help but think from the spelling that it's pronounced like "canoe", and a canoe is a type of boat... If my suspicion is correct, then perhaps a number of the temperaments in this family ought to be named after boats... --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 20:01, 3 October 2020 (UTC)		Okay, so you want a the name for a Canou temperament 896/891 & 472392/471625? Well, let me start by saying that since I don't know how "Canou" is pronounced, I can't help but think from the spelling that it's pronounced like "canoe", and a canoe is a type of boat... If my suspicion is correct, then perhaps a number of the temperaments in this family ought to be named after boats... --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 20:01, 3 October 2020 (UTC)

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	== Relation between family and temperament ==		== Relation between family and temperament ==

	I tried to simplify linking in [[1131edo]], only now I see that there ''is'' a “Canou temperament” within this family. I'd find it better to start with an introduction that tells us something about the family; currently it's starting with the temperament, that's a bot confusing, at least or me. --[[User:Xenwolf\|Xenwolf]] ([[User talk:Xenwolf\|talk]]) 16:07, 5 January 2021 (UTC)		I tried to simplify linking in [[1131edo]], only now I see that there ''is'' a “Canou temperament” within this family. I'd find it better to start with an introduction that tells us something about the family; currently it's starting with the temperament, that's a bot confusing, at least or me. --[[User:Xenwolf\|Xenwolf]] ([[User talk:Xenwolf\|talk]]) 16:07, 5 January 2021 (UTC)

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	== From rank 3 to rank 2 Canou temperaments ==		== From rank 3 to rank 2 Canou temperaments ==

	Hey FloraC, are you planning on naming a few rank 2 temperaments based on the rank 3 temperaments you already have? I think these temperaments are quite interesting but I personally prefer rank 2 or rank 1 temperaments as they are easier to work with. --[[User:Userminusone\|Userminusone]] ([[User talk:Userminusone\|talk]]) 22:12, 19 March 2021 (UTC)		Hey FloraC, are you planning on naming a few rank 2 temperaments based on the rank 3 temperaments you already have? I think these temperaments are quite interesting but I personally prefer rank 2 or rank 1 temperaments as they are easier to work with. --[[User:Userminusone\|Userminusone]] ([[User talk:Userminusone\|talk]]) 22:12, 19 March 2021 (UTC)

	: There's a page to collect those: ''Canousmic temperaments''. Make sure you've seen that. And we can talk if you have new temperaments to propose. [[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 06:58, 20 March 2021 (UTC)		: There's a page to collect those: ''Canousmic temperaments''. Make sure you've seen that. And we can talk if you have new temperaments to propose. [[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 06:58, 20 March 2021 (UTC)

			== I wanna move on from this ==
			I no longer feel attached to these temps as my focus shifted, altho 311edo remains one of my favorite tunings around its range. I've thought about a rename for a while but had no idea what to call it otherwise, until just now.

			''Cathartic'', maybe, cuz that's the feeling I always associate with 28/27, and these temps were "designed" to have an abundance of it. The corresponding comma would be ''cathartic comma''. Semicanou would become ''semicathart'' and semicanousma be ''semicathartisma'' with corresponding rank-4 ''semicathartismic''. Deuteromere could be changed to ''semicathartic'' tho I'm not 100% sure about that. As for hemireiwa, first, it's a demi- rather than hemi-, and second, it tempers out the seascape comma, so ''seadeute'' might be an option. It's not very notable however, so I might as well just delete it.

			I'll initiate the changes in a few days if no one has a problem…

			I have another temp I might consider naming after myself, but I won't re-use any of these names.

			—[[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 11:44, 17 June 2026 (UTC)

User:FloraC/Workbench

FloraC — Wed, 17 Jun 2026 10:42:26 GMT

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	* [[Hemimean clan]]		* [[Hemimean clan]]
	* [[Hemimean family]]		* [[Hemimean family]]
	* <s>~~Hemifamity~~ temperaments</s>		* <s>Aberschismic temperaments</s>
	* <s>~~Hemifamity~~ family</s>		* <s>Aberschismic family</s>
	* <s>Porwell temperaments</s>		* <s>Porwell temperaments</s>
	* <s>Porwell family</s>		* <s>Porwell family</s>
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	* <s>Canousmic temperaments</s>		* <s>Canousmic temperaments</s>
	* <s>Canou family</s>		* <s>Canou family</s>
	* [[Semicanousmic clan]]		* <s>Semicanousmic clan</s>
	* [[Semiporwellismic clan]]		* <s>Semiporwellismic clan</s>
	* <s>Olympic clan</s>		* <s>Olympic clan</s>
	* <s>Alphaxenic rank-3 clan</s>		* <s>Alphaxenic rank-3 clan</s>

Semicanousmic clan

FloraC — Wed, 17 Jun 2026 10:40:36 GMT

Re-organize

Show changes

Semiporwellismic clan

FloraC — Wed, 17 Jun 2026 10:17:13 GMT

Re-organize

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	The '''semiporwellismic clan''' of [[rank-3 temperament]]s [[tempering out\|tempers out]] the [[semiporwellisma]] ({{monzo\|legend=1\| 14 -3 -1 0 -2 }}, [[ratio]]: 16384/16335).		The '''semiporwellismic clan''' of [[rank-3 temperament]]s [[tempering out\|tempers out]] the [[semiporwellisma]] ({{monzo\|legend=1\| 14 -3 -1 0 -2 }}, [[ratio]]: 16384/16335).

	~~Temperaments discussed elsewhere are:~~		For the rank-4 temperament, see [[Catalog of rank-4 temperaments #Semiporwellismic (16384/16335)]].
	* [[Sensamagic]] (+385/384 or 896/891) → [[Sensamagic family #Undecimal sensamagic\|Sensamagic family]]
	* ''[[Kapo]]'' (+3025/3024 or 5120/5103) → [[Aberschismic family #Kapo\|Aberschismic family]]
	* ''[[Semiporwell]]'' (+6144/6125 or 9801/9800) → [[Porwell family #Semiporwell\|Porwell family]]

	~~Considered below is semiporwellic, the no-7 subgroup temperament.~~ For the rank-4 temperament, see [[~~Rank~~-4 ~~temperament~~ #Semiporwellismic (16384/16335)]].

	== Semiporwellic ==		== Semiporwellic ==
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	[[Badness]] (Sintel): 0.761		[[Badness]] (Sintel): 0.761

	=== 2.3.5.11.31 ~~subgroup~~ ===		=== Overview to extensions ===
			Temperaments discussed elsewhere are:
			* [[Sensamagic]] (+385/384 or 896/891) → [[Sensamagic family #Undecimal sensamagic\|Sensamagic family]]
			* ''[[Kapo]]'' (+3025/3024 or 5120/5103) → [[Aberschismic family #Kapo\|Aberschismic family]]
			* ''[[Semiporwell]]'' (+6144/6125 or 9801/9800) → [[Porwell family #Semiporwell\|Porwell family]]

			Considered below is the add-31 subgroup temperament of semiporwellic.

			== Subgroup extensions ==
			=== Semiporwellic (2.3.5.11.31) ===
	Subgroup: 2.3.5.11.31		Subgroup: 2.3.5.11.31

935edo

FloraC — Wed, 17 Jun 2026 10:04:56 GMT

Note a subset edo for providing some of its primes

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	== Theory ==		== Theory ==
	935edo is a very strong [[23-limit]] system, and is [[consistent]] through to the [[27-odd-limit]]. It does reasonably well in the higher limits, though the sharply tuned [[11/1\|11]] and [[23/1\|23]] and the flatly tuned [[29/1\|29]] and [[31/1\|31]] create inconsistencies together, those being [[29/22]], [[29/23]], [[31/22]], [[31/23]] and their [[octave complement]]s; it is otherwise consistent to the [[39-odd-limit]]. It is a [[zeta peak edo]].		935edo is a very strong [[23-limit]] system, and is [[consistent]] through to the [[27-odd-limit]]. It does reasonably well in the higher limits, though the sharply tuned [[11/1\|11]] and [[23/1\|23]] and the flatly tuned [[29/1\|29]] and [[31/1\|31]] create inconsistencies together, those being [[29/22]], [[29/23]], [[31/22]], [[31/23]] and their [[octave complement]]s; it is otherwise consistent to the [[39-odd-limit]]. Its tuning of [[7/1\|7]], [[11/1\|11]], [[13/1\|13]], and [[23/1\|23]] comes from [[187edo]]. It is a [[zeta peak edo]].

	As an equal temperament, it [[tempering out\|tempers out]] the {{monzo\| 39 -29 3 }} ([[alphatricot comma]]), {{monzo\| -52 -17 34 }} ([[septendecima]]), and {{monzo\| 91 -12 -31 }} (astro comma) in the 5-limit; [[4375/4374]] and 52734375/52706752 in the 7-limit; [[117649/117612]], [[151263/151250]], [[161280/161051]] in the [[11-limit]]; [[2080/2079]], [[4096/4095]], [[4225/4224]] in the [[13-limit]]; [[2058/2057]], [[2500/2499]], [[4914/4913]] in the [[17-limit]]; [[2432/2431]], [[3136/3135]], [[3250/3249]], [[4200/4199]] in the 19-limit; and [[2025/2024]], [[2300/2299]], [[2646/2645]] among others in the 23-limit.		As an equal temperament, it [[tempering out\|tempers out]] the {{monzo\| 39 -29 3 }} ([[alphatricot comma]]), {{monzo\| -52 -17 34 }} ([[septendecima]]), and {{monzo\| 91 -12 -31 }} ([[astro comma]]) in the [[5-limit]]; [[4375/4374]] and 52734375/52706752 in the [[7-limit]]; [[117649/117612]], [[151263/151250]], [[161280/161051]] in the [[11-limit]]; [[2080/2079]], [[4096/4095]], [[4225/4224]] in the [[13-limit]]; [[2058/2057]], [[2500/2499]], [[4914/4913]] in the [[17-limit]]; [[2432/2431]], [[3136/3135]], [[3250/3249]], [[4200/4199]] in the [[19-limit]]; and [[2025/2024]], [[2300/2299]], [[2646/2645]] among others in the 23-limit.

	=== Prime harmonics ===		=== Prime harmonics ===

187edo

FloraC — Wed, 17 Jun 2026 10:00:24 GMT

Linking & formatting

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	{{ED intro}}		{{ED intro}}

	This edo is a bit of a chimera. It has a [[3/2\|fifth]] which is 2.9{{c}} flat and a [[5/4\|classical major third]] 1.3 cents flat, but the [[7/1\|7]], [[11/1\|11]] and [[13/1\|13]] are more accurate. ~~The~~ equal temperament [[tempering out\|tempers out]] 78732/78125 ([[sensipent comma]]) in the 5-limit and [[225/224]] in the 7-limit, providing the [[optimal patent val]] for [[sensei]] which tempers out both. In the 11-limit it tempers out [[441/440]], 1375/1372 and [[4000/3993]] and in the 13-limit [[351/350]], [[625/624]], [[1188/1183]], [[1716/1715]] and [[2200/2197]].		== Theory ==
			This edo is a bit of a chimera. It has a [[3/2\|fifth]] which is 2.9{{c}} flat and a [[5/4\|classical major third]] 1.3 cents flat, but the [[7/1\|7]], [[11/1\|11]] and [[13/1\|13]] are more accurate.

			Using the [[patent val]], the equal temperament [[tempering out\|tempers out]] 78732/78125 ([[sensipent comma]]) in the [[5-limit]] and [[225/224]] in the [[7-limit]], providing the [[optimal patent val]] for [[sensei]], which tempers out both. In the [[11-limit]] it tempers out [[441/440]], [[1375/1372]] and [[4000/3993]], and in the [[13-limit]] [[351/350]], [[625/624]], [[1188/1183]], [[1716/1715]] and [[2200/2197]].

	=== Odd harmonics ===		=== Odd harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 187 factors into {{~~factorization~~\|~~187~~}}, 187edo contains [[11edo]] and [[17edo]] as its subsets.		Since 187 factors into {{nowrap\| 11 × 17 }}, 187edo contains [[11edo]] and [[17edo]] as its subsets.

	=== Music ===		== Music ==
	* ''[https://www.youtube.com/watch?v=vrFU2J25G1Y Pillow(33) ~~(187edo lullaby)]~~'' ~~by [[JUMBLE]~~] (~~Dec~~ 2024, ~~uses MOS~~ [[22L 11s]])		; [[JUMBLE]]
			* [https://www.youtube.com/watch?v=vrFU2J25G1Y ''Pillow(33)''] (2024) – a 187edo lullaby, using the [[22L 11s]] [[mos]]

Semiporwellismic clan

FloraC — Wed, 17 Jun 2026 09:54:09 GMT

Improve linking

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(One intermediate revision by the same user not shown)
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	{{Technical data page}}		{{Technical data page}}
	The '''semiporwellismic clan''' of [[~~Rank-3 temperament\|~~rank-3~~]] [[~~temperament]]s [[~~Tempering~~ out\|tempers out]] the [[semiporwellisma]] ({{monzo\|legend=1\| 14 -3 -1 0 -2 }}, [[ratio]]: 16384/16335).		The '''semiporwellismic clan''' of [[rank-3 temperament]]s [[tempering out\|tempers out]] the [[semiporwellisma]] ({{monzo\|legend=1\| 14 -3 -1 0 -2 }}, [[ratio]]: 16384/16335).

	Temperaments discussed elsewhere are:		Temperaments discussed elsewhere are:
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	[[Badness]] (Sintel): 0.761		[[Badness]] (Sintel): 0.761

			=== 2.3.5.11.31 subgroup ===
			Subgroup: 2.3.5.11.31

			Comma list: 496/495, 961/960

			Subgroup-val mapping: {{mapping\| 1 0 0 0 7 \| 0 1 1 0 -2 \| 0 0 2 0 -1 }}

			Optimal tunings:
			* WE: ~2 = 1199.7927{{c}}, ~3/2 = 702.4205{{c}}, ~31/24 = 442.1885{{c}}
			* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.5302{{c}}, ~31/24 = 442.2374{{c}}

			{{Optimal ET sequence\|legend=0\| 19, 22, 41, 46, 65, 87, 152, 369, 521e }}

			Badness (Sintel): 0.201

	[[Category:Temperament clans]]		[[Category:Temperament clans]]
	[[Category:Semiporwellismic clan\| ]] <!-- main article -->		[[Category:Semiporwellismic clan\| ]] <!-- main article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

Semiporwellisma

FloraC — Wed, 17 Jun 2026 09:49:15 GMT

Expand

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	The '''semiporwellisma''' ([[ratio]]: 16384/16335, {{monzo\|legend=1\| 14 -3 -1 0 -2 }}) is a [[small comma\|small]] [[11-limit]] [[comma]] measuring about 5.19 [[cent]]s, named for it is one of the commas tempered out in the [[semiporwell]] temperament. It is the difference between two instances of [[33/32]], the undecimal quartertone, and [[16/15]], the classical diatonic semitone. It is also the difference between the [[rastma]] and the [[schisma]].		The '''semiporwellisma''' ([[ratio]]: 16384/16335, {{monzo\|legend=1\| 14 -3 -1 0 -2 }}) is a [[small comma\|small]] [[11-limit]] [[comma]] measuring about 5.19 [[cent]]s, named for it is one of the commas tempered out in the [[semiporwell]] temperament. It is the difference between two instances of [[33/32]], the undecimal quartertone, and [[16/15]], the classical diatonic semitone. It is also the difference between the [[rastma]] and the [[schisma]].

	In the full 11-limit, it is the difference between [[896/891]] and [[385/384]]. In the [[13-limit]] it factors into ([[2080/2079]])⋅([[3584/3575]]).		In the full 11-limit, it is the difference between [[896/891]] and [[385/384]]. In the [[13-limit]] it factors into ([[2080/2079]])⋅([[3584/3575]]). In the [[31-limit]] it factors into ([[496/495]])⋅([[1024/1023]]) or ([[961/960]])⋅(1024/1023)<sup>2</sup> and gives rise to the [[S-expression]] S31⋅S32<sup>2</sup>.

	== Temperaments ==		== Temperaments ==
	[[Tempering out]] this comma in the full 11-limit leads to the rank-4 semiporwellismic temperament (→ [[Rank-4 temperament #Semiporwellismic (16384/16335)]]), or in the 2.3.5.11 subgroup, the rank-3 semiporwellic temperament. See [[Semiporwellismic clan]] for ~~extensions~~ of ~~semiporwellic~~.		[[Tempering out]] this comma in the full 11-limit leads to the rank-4 '''semiporwellismic''' temperament (→ [[Rank-4 temperament #Semiporwellismic (16384/16335)]]), or in the [[2.3.5.11 subgroup]], the rank-3 [[semiporwellic]] temperament.

			See [[Semiporwellismic clan]] for the [[clan]] of rank-3 temperaments where it is tempered out.

	== Etymology ==		== Etymology ==

Semiporwellismic clan

FloraC — Wed, 17 Jun 2026 09:41:13 GMT

Switch to Sintel's badness, WE & CWE tunings. - redundant category

← Older revision		Revision as of 09:41, 17 June 2026
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	{{Technical data page}}		{{Technical data page}}
	The '''semiporwellismic clan''' of [[Rank-3 temperament\|rank-3]] [[temperament]]s [[Tempering out\|tempers out]] the [[semiporwellisma]]~~, 16384/16335 =~~ {{monzo\| 14 -3 -1 0 -2 }}.		The '''semiporwellismic clan''' of [[Rank-3 temperament\|rank-3]] [[temperament]]s [[Tempering out\|tempers out]] the [[semiporwellisma]] ({{monzo\|legend=1\| 14 -3 -1 0 -2 }}, [[ratio]]: 16384/16335).

	Temperaments discussed elsewhere are:		Temperaments discussed elsewhere are:
	* [[Sensamagic]] (+385/384 or 896/891) → [[Sensamagic family #Undecimal sensamagic\|Sensamagic family]]		* [[Sensamagic]] (+385/384 or 896/891) → [[Sensamagic family #Undecimal sensamagic\|Sensamagic family]]
	* ''[[Kapo]]'' (+3025/3024 or 5120/5103) → [[~~Hemifamity~~ family #Kapo\|~~Hemifamity~~ family]]		* ''[[Kapo]]'' (+3025/3024 or 5120/5103) → [[Aberschismic family #Kapo\|Aberschismic family]]
	* ''[[Semiporwell]]'' (+6144/6125 or 9801/9800) → [[Porwell family #Semiporwell\|Porwell family]]		* ''[[Semiporwell]]'' (+6144/6125 or 9801/9800) → [[Porwell family #Semiporwell\|Porwell family]]

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	{{Mapping\|legend=2\| 1 0 0 0 7 \| 0 1 1 0 -2 \| 0 0 2 0 -1 }}		{{Mapping\|legend=2\| 1 0 0 0 7 \| 0 1 1 0 -2 \| 0 0 2 0 -1 }}
			: mapping generators: ~2, ~3, ~128/99

	: ~~sval mapping generators~~: ~2, ~3, ~128/99		[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1199.7329{{c}}, ~3/2 = 702.3657{{c}}, ~128/99 = 442.1589{{c}}
	[[~~Optimal tuning~~]] ([[~~CTE~~]]) ~2 = ~~1\1~~, ~3/2 = 702.~~4701~~, ~128/99 = 442.~~1061~~		: [[error map]]: {{val\| -0.267 +0.144 +0.103 +0.456 }}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.5107{{c}}, ~128/99 = 442.2243{{c}}
			: error map: {{val\| 0.000 +0.556 +0.646 +1.436 }}

	{{Optimal ET sequence\|legend=1\| 19, 22, 41, 46, 65, 87, 152, 369, 521e, 1194bcee, 1305bcee, 1457bceee, 1609bcceee, 1674bcceee, 1826bcceeee }}		{{Optimal ET sequence\|legend=1\| 19, 22, 41, 46, 65, 87, 152, 369, 521e, 1194bcee, 1305bcee, 1457bceee, 1609bcceee, 1674bcceee, 1826bcceeee }}

	[[Badness]]: 0.~~0922 × 10<sup>-3</sup>~~		[[Badness]] (Sintel): 0.761

	[[Category:Temperament clans]]		[[Category:Temperament clans]]
	[[Category:Semiporwellismic clan\| ]] <!-- main article -->		[[Category:Semiporwellismic clan\| ]] <!-- main article -->
	~~[[Category:Semiporwellismic\| ]] <!-- key article -->~~
	[[Category:Rank 3]]		[[Category:Rank 3]]

1-3-7-9-11-13-15 enaeikosany

Yourmusic Productions — Wed, 17 Jun 2026 08:35:59 GMT

Create Page.

New page

[[File:1-3-7-9-11-13-15_Enaeikosany.png|thumb|Circle diagram.]] A [[15-odd-limit]] [[enaeikosany]]. This creates a scale of 1 65/64 33/32 13/12 35/32 9/8 7/6 39/32 5/4 21/16 11/8 45/32 143/96 3/2 77/48 13/8 55/32 7/4 11/6 15/8 91/48 2/1, with steps of 65/64 66/65 104/99 105/104 36/35 28/27 117/112 40/39 21/20 22/21 45/44 143/140 144/143 77/72 78/77 55/52 56/55 22/21 45/44 91/90 96/91. With 10 perfect fifths, but also a fair number of awkwardly small comma steps, this is middle of the road for a scale this size, with more than enough familiar simple ratios to produce consonant sounding music, but also enough awkward ones to be highly dissonant as well if simply mashed randomly.
<pre>
! 1-3-7-9-11-13-15_Enaeikosany.scl
!
1 3 7 9 11 13 15 2-combination Enaeikosany
21
!
26.841
53.272
138.572
155.139
203.910
266.871
342.482
386.313
470.781
551.317
590.223
689.890
701.955
818.188
840.527
937.631
968.825
1049.362
1088.268
1107.398
1200
</pre>

[[Category:Enaeikosanies]]
[[Category:21-tone scales]]
[[Category:Pages with Scala files]]

Middle-Eastern music

Naren — Wed, 17 Jun 2026 08:30:35 GMT

Add Inside Arabic Music to further reading

← Older revision		Revision as of 08:30, 17 June 2026
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	== See also ==		== See also ==
	* [[Overtone singing]] – a technique used in some Kurdish and Iranian (Persian) music		* [[Overtone singing]] – a technique used in some Kurdish and Iranian (Persian) music

			== Further reading ==
			* Johnny Farraj and Sami Abu Shumays, ''[https://global.oup.com/academic/product/inside-arabic-music-9780190658366 Inside Arabic Music]'', Oxford University Press, 2019

	[[Category:Arabic music]]		[[Category:Arabic music]]

File:1-3-7-9-11-13-15 Enaeikosany.png

Yourmusic Productions — Wed, 17 Jun 2026 07:54:42 GMT

Yourmusic Productions uploaded File:1-3-7-9-11-13-15 Enaeikosany.png Made with [https://nickvuci.github.io/ScaleCircle ''ScaleCircle''] by Nick Vuci.

New page

== Summary ==
Made with [https://nickvuci.github.io/ScaleCircle ''ScaleCircle''] by [[Nick Vuci]].
== Licensing ==
{{self|cc-by-sa-4.0}}

Indian music

Naren — Wed, 17 Jun 2026 07:49:50 GMT

Fix chandrakantha links, add Bake/Jairazbhoy digital archive link

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	* [http://www.ocf.berkeley.edu/%7Emrahaim/ Hindustani Music Resources] - downloads and links, compiled by Matt Rahaim		* [http://www.ocf.berkeley.edu/%7Emrahaim/ Hindustani Music Resources] - downloads and links, compiled by Matt Rahaim
	* http://www.musicresearch.in (redirected to [http://musicresearchlibrary.net/omeka/ MusicResearchLibrary]) - an indian music research portal		* http://www.musicresearch.in (redirected to [http://musicresearchlibrary.net/omeka/ MusicResearchLibrary]) - an indian music research portal
	* [~~http~~://chandrakantha.com/~~articles~~/~~indian_music~~/ www.chandrakantha.com - Indian classical music]- portal on indian music, with detailed [~~http~~://chandrakantha.com/~~raga_raag~~/ descriptions of a number of north indian rags]		* [https://chandrakantha.com/music-and-dance/i-class-music/ www.chandrakantha.com - Indian classical music]- portal on indian music, with detailed [https://chandrakantha.com/music-and-dance/i-class-music/index-of-rags/ descriptions of a number of north indian rags]
	* http://22shruti.com 22shruti.com		* http://22shruti.com 22shruti.com
	* [https://autrimncpa.wordpress.com Music in Motion] - Recordings synced with videos showing pitch contours		* [https://autrimncpa.wordpress.com Music in Motion] - Recordings synced with videos showing pitch contours
	* [https://archive.org/details/intonationinnort0000mark Intonation in North Indian Music], Mark Levy - Book summarizing theories and giving measurements from recordings		* [https://archive.org/details/intonationinnort0000mark Intonation in North Indian Music], Mark Levy - Book summarizing theories and giving measurements from recordings
			* [https://digital.library.ucla.edu/catalog/ark:/21198/zz002gcntd Bake/Jairazbhoy Digital Archive of South Asian Traditional Music and Arts]

	{{Todo\|inline=1\|expand\|research\|cultural expertise}}		{{Todo\|inline=1\|expand\|research\|cultural expertise}}
	[[Category:Indian music\| ]] <!-- main article -->		[[Category:Indian music\| ]] <!-- main article -->

Guitar

Naren — Wed, 17 Jun 2026 07:41:59 GMT

typo

← Older revision		Revision as of 07:41, 17 June 2026
Line 59:		Line 59:
	* [[Tolgahan Çoğulu]] - [https://www.microtonalguitar.org/ Adjustable Microtonal Guitar]		* [[Tolgahan Çoğulu]] - [https://www.microtonalguitar.org/ Adjustable Microtonal Guitar]
	* [https://fretlet.com/ Fretlet] - produces fretlets of lengths 1 to 6		* [https://fretlet.com/ Fretlet] - produces fretlets of lengths 1 to 6
	* [https://salamuzik.com/products/fretlet-microtonal-guitar-fret-flf-10 Sala Muzik] - ~~procudes~~ fretlets of length 1		* [https://salamuzik.com/products/fretlet-microtonal-guitar-fret-flf-10 Sala Muzik] - produces fretlets of length 1

	=== Quick n Dirty ===		=== Quick n Dirty ===

Xenharmonic Wiki:Policies and guidelines

Fredg999 — Wed, 17 Jun 2026 02:12:21 GMT

Separate theory-level pages into another category

← Older revision		Revision as of 02:12, 17 June 2026
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	:: * [[Xenharmonic Wiki:Manual of Style/Temperament cataloging]]		:: * [[Xenharmonic Wiki:Manual of Style/Temperament cataloging]]
	:: * [[Xenharmonic Wiki:Manual of Style/Temperament pages]]		:: * [[Xenharmonic Wiki:Manual of Style/Temperament pages]]
			* [[Xenharmonic Wiki:Notability guidelines]]

			== Conventions ==
			The following pages explain conventions that are generally observed in the xenharmonic community (with varying levels of consensus depending on the topic). They should be taken into consideration when applying the guidelines above.
	* [[Temperament naming]]		* [[Temperament naming]]
	* [[Xenharmonic Wiki:Notability guidelines]]

	== See also ==		== See also ==

Deleted temperaments

Hkm — Wed, 17 Jun 2026 00:34:22 GMT

← Older revision		Revision as of 00:34, 17 June 2026
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	\|2.3.19		\|2.3.19
	\|7 & 16		\|7 & 16
	\|No reason to interpret the resultant scales as dog rather than mavila		\|No reason to interpret the resultant scales as dog rather than mavila / unenlightening restriction of armodog
	\|}		\|}
	[[Category:Temperament collections]]		[[Category:Temperament collections]]

66edo

Hkm — Tue, 16 Jun 2026 23:04:27 GMT

Theory

← Older revision		Revision as of 23:04, 16 June 2026
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	The 66b val tempers out [[16875/16384]] in the 5-limit, [[126/125]], [[1728/1715]] and [[2401/2400]] in the 7-limit, [[99/98]] and [[385/384]] in the 11-limit, and [[105/104]], [[144/143]] and [[847/845]] in the 13-limit.		The 66b val tempers out [[16875/16384]] in the 5-limit, [[126/125]], [[1728/1715]] and [[2401/2400]] in the 7-limit, [[99/98]] and [[385/384]] in the 11-limit, and [[105/104]], [[144/143]] and [[847/845]] in the 13-limit.

	~~109 steps of 66edo is extremely close to the [[acoustic pi]] with only +0.023{{c}} of error.~~

	=== Odd harmonics ===		=== Odd harmonics ===

Deleted temperaments

Hkm — Tue, 16 Jun 2026 18:14:34 GMT

Show changes

Quintaleap family

Hkm — Tue, 16 Jun 2026 17:27:47 GMT

Quintupole

← Older revision		Revision as of 17:27, 16 June 2026
(One intermediate revision by the same user not shown)
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	{{Main\| Quintupole }}		{{Main\| Quintupole }}

	The ''quintupole'' temperament tempers out the octagar comma (4000/3969) and the mistisma (458752/455625) in the 7-limit; 896/891 (pentacircle), 1375/1372 (moctdel), and 4375/4356 (fantares, luluzoquadyo) in the 11-limit. The word "quintupole" means ''five poles'', but also a play on the words "quintuple" and "polypyth". It is so named because the generator is 1/5 of the [[Porwell temperaments #Polypyth\|polypyth]] fourth (~4/3, about 495.8 cents). [[User:Xenllium\|Xenllium]] proposes the pronunciation of the word "quintupole" as /'kwɪntʊpəʊl/ or /'kwɪntʊpoʊl/, like as "quin-to-pole". ''Not to be confused with [[#Quintapole\|quint<u>'''a'''</u>pole]] temperament (12&85).''		The ''quintupole'' temperament tempers out the octagar comma (4000/3969) and the mistisma (458752/455625) in the 7-limit; 896/891 (pentacircle), 1375/1372 (moctdel), and 4375/4356 (fantares, luluzoquadyo) in the 11-limit. The word "quintupole" means ''five poles'', but also a play on the words "quintuple" and "polypyth". It is so named because the generator is 1/5 of the [[Porwell temperaments #Polypyth\|polypyth]] fourth (~4/3, about 495.8 cents).

	Subgroup: 2.3.5.7		Subgroup: 2.3.5.7

244/243

MisterShafXen — Tue, 16 Jun 2026 16:51:16 GMT

Created page

New page

{{Infobox interval|Name=61-limit formal comma}}

'''244/243''' is a 61-limit small comma. It is significant in the FJS system as the formal comma to translate a [[Pythagorean]] interval to a nearby 61-limit interval, e.g. [[243/128]] to [[61/32]].

== Temperament ==
Rank: 2

Subgroup: 2.3.61

Mapping: ([1 1 3] [0 1 5])

ET join: 12&29

Generators (CWE): ~2=1200.000, ~3/2=702.961

CWE errors: 0.000, 1.006, -2.081

Badness (Sintel): 0.037

28edo

Francium — Tue, 16 Jun 2026 15:47:40 GMT

Music: +music; +links

← Older revision		Revision as of 15:47, 16 June 2026
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	; [[Francium]]		; [[Francium]]
	* [https://www.youtube.com/watch?v=8dubV7STjJA ''~~According to a Tomato~~''] (~~2025~~)		* "According to a Tomato" from ''TOTMC 2025'' (2025) – [https://open.spotify.com/track/7ulkhYBppJCsBKP3cdMdjZ Spotify] \| [https://francium223.bandcamp.com/track/according-to-a-tomato Bandcamp] \| [https://www.youtube.com/watch?v=8dubV7STjJA YouTube]
			* [https://www.youtube.com/watch?v=4hTXsifzkZU ''Happy Birthday in 28edo''] (2026)

	; [[Kosmorksy]]		; [[Kosmorksy]]

Table of 431edo intervals

MisterShafXen — Tue, 16 Jun 2026 13:39:31 GMT

Continued adding ratios

← Older revision		Revision as of 13:39, 16 June 2026
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	\|		\|
	\| 385/384		\| 385/384
			''1375/1372''
	\|		\|
	\|-		\|-
Line 668:		Line 669:
	\|		\|
	\|		\|
	\|		\| 726/637
	\|-		\|-
	\| 82		\| 82
Line 675:		Line 676:
	\|		\|
	\|		\|
	\|		\| 3520/3087
	\|		\|
	\|-		\|-
Line 691:		Line 692:
	\|		\|
	\|		\|
	\|		\| 63/55
	\|		\|
	\|-		\|-
Line 716:		Line 717:
	\|		\|
	\|		\|
	\|		\| ''7371/6400''
	\|-		\|-
	\| 88		\| 88
Line 724:		Line 725:
	\|		\|
	\|		\|
	\|		\| 2200/1911
	\|-		\|-
	\| 89		\| 89
Line 740:		Line 741:
	\|		\|
	\|		\|
	\|		\| 1323/1144
	\|-		\|-
	\| 91		\| 91
Line 747:		Line 748:
	\|		\|
	\|		\|
	\|		\| 1815/1568
	\|		\|
	\|-		\|-
Line 763:		Line 764:
	\|		\|
	\|		\|
	\|		\| ''1225/1056''
	\|		\|
	\|-		\|-
Line 779:		Line 780:
	\|		\|
	\|		\|
	\|		\| ''220/189''
	\|		\|
	\|-		\|-
Line 795:		Line 796:
	\|		\|
	\|		\|
	\|		\| 1029/880
	\|		\|
	\|-		\|-
Line 803:		Line 804:
	\|		\|
	\|		\|
	\|		\| ''1375/1176''
	\|		\|
	\|-		\|-
Line 820:		Line 821:
	\|		\|
	\|		\|
	\|		\| 168/143
	\|-		\|-
	\| 101		\| 101
Line 827:		Line 828:
	\|		\|
	\|		\|
	\|		\| 1210/1029
	\|		\|
	\|-		\|-
Line 844:		Line 845:
	\|		\|
	\|		\|
	\|		\| ''520/441''
	\|-		\|-
	\| 104		\| 104

Tubulong

FloraC — Tue, 16 Jun 2026 10:58:14 GMT

Formatting (bold lemma & - redundant whitespaces)

Show changes

Harmonic template

FloraC — Tue, 16 Jun 2026 10:53:03 GMT

Formatting. + categories

Show changes

Regular temperament

FloraC — Tue, 16 Jun 2026 10:31:22 GMT

History: improve linking

← Older revision		Revision as of 10:31, 16 June 2026
Line 24:		Line 24:
	* [[Adriaan Fokker]] (1887–1972): [[Fokker block\|periodicity blocks]]		* [[Adriaan Fokker]] (1887–1972): [[Fokker block\|periodicity blocks]]
	* [[Harry Partch]] (1901–1974): [[JI\|extended JI]]		* [[Harry Partch]] (1901–1974): [[JI\|extended JI]]
	* [[Erv Wilson]] (1928–2016): extended tonespace (and projections), [[mos]], scale tree, [[~~Harmonic~~ template~~\|harmonic templates~~]]		* [[Erv Wilson]] (1928–2016): extended tonespace (and projections), [[mos]], [[scale tree]], [[harmonic template]]s
	* [[Easley Blackwood]] (1933–2023): Blackwood[10], syntonic comma vanishing relation as equation		* [[Easley Blackwood]] (1933–2023): Blackwood[10], syntonic comma vanishing relation as equation
	* [[George Secor]] (1943–2020): miracle temperament		* [[George Secor]] (1943–2020): miracle temperament

81/76

FloraC — Tue, 16 Jun 2026 10:24:08 GMT

Rework

← Older revision		Revision as of 10:24, 16 June 2026
Line 1:		Line 1:
	{{Infobox Interval		{{Infobox Interval
	\| Name = ~~81/76~~		\| Name = Boethius' chromatic semitone
	\| Color name = 19u1, inu 1sn, <br>Inu comma		\| Color name = 19u1, inu 1sn, <br>Inu comma
	}}		}}
	'''81/76''' is a [[19-limit]] interval, 110.3 [[cent]]s in size. It is the difference between [[19/16]] (otonal minor third) and [[81/64]] (Pythagorean major third) and thus is [[81/80]] larger than [[20/19~~]]. It differs from [[16/15]] by [[1216/1215]], and from [[2187/2048]] by [[513/512~~]].		'''81/76''', '''Boethius' chromatic semitone''', is a [[19-limit]] interval of about 110.3 [[cent]]s in size. It differs from [[2187/2048]], the Pythagorean apotome, by [[513/512]], the undevicesimal schisma or Boethius' comma, hence the name. It also differs from [[16/15]] by [[1216/1215]], and is the difference between [[19/16]] (otonal minor third) and [[81/64]] (Pythagorean major third) and thus is [[81/80]] larger than [[20/19]].

	== ~~Proposed name~~ ==		== Temperaments ==
	The ~~word~~ ''dog'' ~~for this interval~~ was suggested by [[~~User:Xenllium\|~~Xenllium]] in 2023~~. It was~~ translated from Japanese word ~~<span style="font-family:san-serif" lang="ja">~~犬~~</span>~~ (~~<span style="font-family:san-serif" lang="ja">~~いぬ~~</span>~~, inu), a play of its [[~~Color~~ notation\|color name]], ''inu'' (as the identical pronunciation).		This interval has been proposed to be used as a [[comma]] to be [[tempering out\|tempered out]], though the musical utility of it is unknown yet. The name ''dog comma'' was suggested by [[Xenllium]] in 2023, translated from Japanese word 犬 (いぬ, inu), a play of its [[Kite's color notation\|color name]], ''inu'' (as the identical pronunciation).

	== See also ==		== See also ==
Line 12:		Line 12:

	[[Category:Semitone]]		[[Category:Semitone]]
	~~[[Category:Commas named after their color name]]~~
	~~[[Category:Commas named by translating something into another language]]~~

1-3-5-9-11-13-15 pentatriandekany

Yourmusic Productions — Tue, 16 Jun 2026 10:13:51 GMT

Create Page.

New page

[[File:1-3-5-9-11-13-15_Pentatriandekany.png|thumb|Circle diagram.]] A [[15-odd-limit]] [[pentatriandekany]]. This creates a scale of 1 65/64 33/32 13/12 11/10 143/128 9/8 143/120 39/32 99/80 5/4 13/10 429/320 11/8 45/32 117/80 143/96 3/2 99/64 13/8 33/20 27/16 55/32 143/80 9/5 117/64 11/6 15/8 39/20 2/1, with steps of 65/64 66/65 104/99 66/65 65/64 144/143 143/135 45/44 66/65 100/99 26/25 33/32 40/39 45/44 26/25 55/54 144/143 33/32 104/99 66/65 45/44 55/54 26/25 144/143 65/64 352/351 45/44 26/25 40/39. (6 notes are duplicated, reducing this to a 29 note scale) It has 18 perfect fifths, plus multiple imperfect but still diatonic ones on top of that. Particularly notable is that it has a diatonic fourth which is sharp by [[1287/1280]] above the root note, which is rare in combination product sets, which usually have a diatonic scale in the lydian mode above the root if they have one at all and require rotating to best translate common practise music to them. That makes this scale particularly accessible for its size as long as you know how to correctly use the comma steps to evade or accentuate dissonance.

<pre>
! 1-3-5-9-11-13-15_Pentatriandekany.scl
!
1 3 5 9 11 13 15 3-combination Pentatriandekany
29
!
26.841
53.272
138.572
165.004
191.845
203.910
303.576
342.482
368.914
386.313
454.213
507.486
551.317
590.223
658.123
689.890
701.955
755.227
840.527
866.959
905.865
937.631
1005.531
1017.596
1044.437
1049.437
1088.268
1156.168
1200
</pre>

[[Category:Pentatriandekanies]]
[[Category:29-tone scales]]
[[Category:Pages with Scala files]]

File:1-3-5-9-11-13-15 Pentatriandekany.png

Yourmusic Productions — Tue, 16 Jun 2026 09:54:43 GMT

Yourmusic Productions uploaded File:1-3-5-9-11-13-15 Pentatriandekany.png Made with [https://nickvuci.github.io/ScaleCircle ''ScaleCircle''] by Nick Vuci.

New page

== Summary ==
Made with [https://nickvuci.github.io/ScaleCircle ''ScaleCircle''] by [[Nick Vuci]].
== Licensing ==
{{self|cc-by-sa-4.0}}

Seesaw

FloraC — Tue, 16 Jun 2026 09:51:46 GMT

FloraC deleted page Seesaw See discussion on Discord

Bixby

FloraC — Tue, 16 Jun 2026 09:51:30 GMT

FloraC deleted page Bixby See discussion on Discord

Talk:Archon

FloraC — Tue, 16 Jun 2026 09:50:33 GMT

FloraC deleted page Talk:Archon Deleted together with the associated page with reason: See discussion on Discord

Archon

FloraC — Tue, 16 Jun 2026 09:50:33 GMT

FloraC deleted page Archon See discussion on Discord

Dog

Hkm — Tue, 16 Jun 2026 06:00:23 GMT

Changed redirect target from No-fives subgroup temperaments#Dog to Deleted temperaments#Dog

← Older revision		Revision as of 06:00, 16 June 2026
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	#redirect [[~~No-fives subgroup~~ temperaments#Dog]]		#redirect [[Deleted temperaments#Dog]]

Quintapole

Hkm — Tue, 16 Jun 2026 05:59:20 GMT

Changed redirect target from Quintaleap family#Quintapole to Deleted temperaments#Quintapole

← Older revision		Revision as of 05:59, 16 June 2026
Line 1:		Line 1:
	#REDIRECT [[~~Quintaleap family~~#Quintapole]]		#REDIRECT [[Deleted temperaments#Quintapole]]

	[[Category:Quintapole]]		[[Category:Quintapole]]

Oviminor

Hkm — Tue, 16 Jun 2026 05:58:39 GMT

Changed redirect target from Ragismic microtemperaments#Oviminor to Deleted temperaments#Oviminor

← Older revision		Revision as of 05:58, 16 June 2026
Line 1:		Line 1:
	#REDIRECT [[~~Ragismic microtemperaments~~ #Oviminor]]		#REDIRECT [[Deleted temperaments#Oviminor]]

	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	[[Category:Microtemperaments]]		[[Category:Microtemperaments]]
	[[Category:Ragismic microtemperaments]]		[[Category:Ragismic microtemperaments]]

Deleted temperaments

Hkm — Tue, 16 Jun 2026 04:10:16 GMT

@@ Line 1: / Line 1: @@
 These temperament names are no longer in use, although older material may still reference them. If one must refer to these temperaments, it is recommended to do so with an ET join (e. g. "11-limit 12 & 85") or as a restriction of a different temperament (e. g. "no-7s cassandra")
 == Maqamschismic (2.3.5.11) ==
@@ Line 451: / Line 473: @@
 Badness (Sintel): 1.77
 [[Category:Temperament collections]]

No-fives subgroup temperaments

Hkm — Tue, 16 Jun 2026 04:04:53 GMT

Dog

← Older revision		Revision as of 04:04, 16 June 2026
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	[[Badness]] (Sintel): 0.0294		[[Badness]] (Sintel): 0.0294

	~~=== Dog ===~~
	~~Dog is based by [[2L 5s]] or [[7L 2s]] scale that makes [[81/76]] vanish, so [[19/16]] is a major third. It can be viewed as a 2.3.19-subgroup analogue of [[mavila]].~~

	~~[[Subgroup]]: 2.3.19~~

	~~[[Comma list]]: 81/76~~

	~~{{Mapping\|legend=2\| 1 0 -2 \| 0 1 4 }}~~
	~~: mapping generators: ~2, ~3~~

	~~[[Optimal tuning]]s:~~
	* [[WE]]: ~2 = 1203.3813{{c}}, ~3/2 = 680.5089{{c}}
	~~: [[error map]]: {{val\| +3.381 -18.065 +31.285 }}~~
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 680.5856{{c}}
	~~: error map: {{val\| 0.000 -21.369 +24.8295 }}~~

	~~{{Optimal ET sequence\|legend=1\| 2, 5h, 7, 16, 23 }}~~

	~~[[Badness]] (Sintel): 0.491~~

	=== Lipsett ===		=== Lipsett ===

81/76

Hkm — Tue, 16 Jun 2026 04:04:29 GMT

← Older revision		Revision as of 04:04, 16 June 2026
Line 1:		Line 1:
	{{Infobox Interval		{{Infobox Interval
	\| Name = ~~dog comma~~		\| Name = 81/76
	\| Color name = 19u1, inu 1sn, <br>Inu comma		\| Color name = 19u1, inu 1sn, <br>Inu comma
	}}		}}
	'''81/76~~''', the '''dog comma~~''' is a [[19-limit]] interval, 110.3 [[cent]]s in size. It is the difference between [[19/16]] (otonal minor third) and [[81/64]] (Pythagorean major third) and thus is [[81/80]] larger than [[20/19]]. It differs from [[16/15]] by [[1216/1215]], and from [[2187/2048]] by [[513/512]].		'''81/76''' is a [[19-limit]] interval, 110.3 [[cent]]s in size. It is the difference between [[19/16]] (otonal minor third) and [[81/64]] (Pythagorean major third) and thus is [[81/80]] larger than [[20/19]]. It differs from [[16/15]] by [[1216/1215]], and from [[2187/2048]] by [[513/512]].

	== ~~Etymology~~ ==		== Proposed name ==
	The word ''dog'' for this interval was ~~introduced~~ by [[User:Xenllium\|Xenllium]] in 2023. It was translated from Japanese word <span style="font-family:san-serif" lang="ja">犬</span> (<span style="font-family:san-serif" lang="ja">いぬ</span>, inu), a play of its [[Color notation\|color name]], ''inu'' (as the identical pronunciation).		The word ''dog'' for this interval was suggested by [[User:Xenllium\|Xenllium]] in 2023. It was translated from Japanese word <span style="font-family:san-serif" lang="ja">犬</span> (<span style="font-family:san-serif" lang="ja">いぬ</span>, inu), a play of its [[Color notation\|color name]], ''inu'' (as the identical pronunciation).

	~~== Temperaments ==~~
	~~{{see also\| No-fives subgroup temperaments #Dog }}~~

	Tempering this interval leads to a 2.3.19 version of [[mavila]] where four mavila fifths yields [[19/16]], so is potentially of relevance in [[16edo]] if one wants to interpret its fifth as a 27{{cent}} flat ~3/2.

	== See also ==		== See also ==

Deleted temperaments

Hkm — Tue, 16 Jun 2026 03:59:01 GMT

← Older revision		Revision as of 03:59, 16 June 2026
Line 394:		Line 394:
	Badness (Sintel): 0.627		Badness (Sintel): 0.627

			== Sept ==
			{{See also\|Whitewood family}}Sept preserves the 2.3.7-subgroup of mapping of 7edo, and harmonic 5 is mapped to an independent generator. As harmonic 5 is way more accurately approximated than 7 by 7edo, this temperament provides little improvement to 7edo's 7-limit tuning, so in what way this temperament is useful remains unexplained. It would make much more sense to, for example, preserve the 5-limit structure of 7edo and give prime 7 an independent generator instead, which is exactly what [[jamesbond]] does.

			This temperament used to be known as ''mujannab''.

			[[Subgroup]]: 2.3.5.7

			[[Comma list]]: 54/49, 64/63

			{{Mapping\|7 11 0 20\|0 0 1 0\|legend=1}}

			[[Optimal tuning\|Optimal tunings]]:

			* [[WE]]: ~9/8 = 170.823{{c}}, ~5/4 = 393.792{{c}} (~15/14 = 52.145{{c}})

			: [[error map]]: {{val\|-4.236 -22.898 -0.994 +47.642}}

			* [[CWE]]: ~9/8 = 171.429{{c}}, ~5/4 = 392.719{{c}} (~15/14 = 49.862{{c}})

			: error map: {{val\|0.000 -16.241 +6.406 +59.746}}

			{{Optimal ET sequence\|7, 14d\|legend=1}}

			[[Badness]] (Sintel): 2.68

			=== 11-limit ===
			Subgroup: 2.3.5.7.11

			Comma list: 45/44, 54/49, 64/63

			Mapping: {{mapping\|7 11 0 20 8\|0 0 1 0 1}}

			Optimal tunings:

			* WE: ~11/10 = 170.817{{c}}, ~5/4 = 393.252{{c}} (~33/32 = 51.619{{c}})
			* CWE: ~11/10 = 171.429{{c}}, ~5/4 = 391.840{{c}} (~33/32 = 48.983{{c}})

			{{Optimal ET sequence\|7, 14de\|legend=0}}

			Badness (Sintel): 2.02

			=== 13-limit ===
			Subgroup: 2.3.5.7.11.13

			Comma list: 27/26, 45/44, 52/49, 64/63

			Mapping: {{mapping\|7 11 0 20 8 26\|0 0 1 0 1 0}}

			Optimal tunings:

			* WE: ~11/10 = 170.795{{c}}, ~5/4 = 393.611{{c}} (~33/32 = 52.021{{c}})
			* CWE: ~11/10 = 171.429{{c}}, ~5/4 = 392.725{{c}} (~33/32 = 49.868{{c}})

			{{Optimal ET sequence\|7, 14de\|legend=0}}

			Badness (Sintel): 1.77
	[[Category:Temperament collections]]		[[Category:Temperament collections]]

Very low accuracy temperaments

Hkm — Tue, 16 Jun 2026 03:58:38 GMT

Sept

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	[[Badness]] (Sintel): 1.22		[[Badness]] (Sintel): 1.22

	~~== Sept ==~~
	~~{{See also\| Whitewood family }}~~

	Sept preserves the 2.3.7-subgroup of mapping of 7edo, and harmonic 5 is mapped to an independent generator. As harmonic 5 is way more accurately approximated than 7 by 7edo, this temperament provides little improvement to 7edo's 7-limit tuning, so in what way this temperament is useful remains unexplained. It would make much more sense to, for example, preserve the 5-limit structure of 7edo and give prime 7 an independent generator instead, which is exactly what [[jamesbond]] does.

	~~This temperament used to be known as ''mujannab''.~~

	~~[[Subgroup]]: 2.3.5.7~~

	~~[[Comma list]]: 54/49, 64/63~~

	~~{{Mapping\|legend=1\| 7 11 0 20 \| 0 0 1 0 }}~~

	~~[[Optimal tuning]]s:~~
	* [[WE]]: ~9/8 = 170.823{{c}}, ~5/4 = 393.792{{c}} (~15/14 = 52.145{{c}})
	~~: [[error map]]: {{val\| -4.236 -22.898 -0.994 +47.642 }}~~
	* [[CWE]]: ~9/8 = 171.429{{c}}, ~5/4 = 392.719{{c}} (~15/14 = 49.862{{c}})
	~~: error map: {{val\| 0.000 -16.241 +6.406 +59.746 }}~~

	~~{{Optimal ET sequence\|legend=1\| 7, 14d }}~~

	~~[[Badness]] (Sintel): 2.68~~

	~~=== 11-limit ===~~
	~~Subgroup: 2.3.5.7.11~~

	~~Comma list: 45/44, 54/49, 64/63~~

	~~Mapping: {{mapping\| 7 11 0 20 8 \| 0 0 1 0 1 }}~~

	~~Optimal tunings:~~
	* WE: ~11/10 = 170.817{{c}}, ~5/4 = 393.252{{c}} (~33/32 = 51.619{{c}})
	* CWE: ~11/10 = 171.429{{c}}, ~5/4 = 391.840{{c}} (~33/32 = 48.983{{c}})

	~~{{Optimal ET sequence\|legend=0\| 7, 14de }}~~

	~~Badness (Sintel): 2.02~~

	~~=== 13-limit ===~~
	~~Subgroup: 2.3.5.7.11.13~~

	~~Comma list: 27/26, 45/44, 52/49, 64/63~~

	~~Mapping: {{mapping\| 7 11 0 20 8 26 \| 0 0 1 0 1 0 }}~~

	~~Optimal tunings:~~
	* WE: ~11/10 = 170.795{{c}}, ~5/4 = 393.611{{c}} (~33/32 = 52.021{{c}})
	* CWE: ~11/10 = 171.429{{c}}, ~5/4 = 392.725{{c}} (~33/32 = 49.868{{c}})

	~~{{Optimal ET sequence\|legend=0\| 7, 14de }}~~

	~~Badness (Sintel): 1.77~~

	== Geryon ==		== Geryon ==

Very low accuracy temperaments

Overthink — Tue, 16 Jun 2026 03:13:36 GMT

Oviminor: That's not exactly "very low" accuracy...

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	~~== Oviminor ==~~
	~~: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Oviminor (5-limit)]].''~~

	Oviminor was named by [[Eliora]] in 2022 after the facts that it takes 184 minor thirds of [[6/5]] to reach the interval class of [[4/3]], the Roman consul was Eggius in the year 184 AD, and the Latin word for egg is ovum, and with prefix ovi-. It sets a new record of complexity for a chain of nineteen 6/5's past [[egads]], though it is less accurate.

	~~[[Subgroup]]: 2.3.5.7~~

	~~[[Comma list]]: 4375/4374, {{monzo\| -100 53 48 -34 }}~~

	~~{{Mapping\|legend=1\| 1 -134 -134 -401 \| 0 184 185 548 }}~~
	~~: mapping generators: ~2, ~5/3~~

	~~[[Optimal tuning]]s:~~
	* [[WE]]: ~2 = 1200.0193{{c}}, ~5/3 = 884.2638{{c}}
	~~: [[error map]]: {{val\| +0.019 +0.010 -0.085 +0.032 }}~~
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/3 = 884.2497{{c}}
	~~: error map: {{val\| 0.000 -0.011 -0.120 +0.008 }}~~

	~~{{Optimal ET sequence\|legend=1\| 19, …, 1600, 1619, 4838, 6457c }}~~

	~~[[Badness]] (Sintel): 14.7~~

Very low accuracy temperaments

Hkm — Tue, 16 Jun 2026 02:29:38 GMT

Show changes

Ragismic microtemperaments

Hkm — Tue, 16 Jun 2026 02:29:13 GMT

Oviminor: due to being less accurate than egads at higher complexity, this temperament should be deleted.

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	[[Badness]] (Sintel): 7.92		[[Badness]] (Sintel): 7.92

	~~== Oviminor ==~~
	~~: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Oviminor (5-limit)]].''~~

	Oviminor was named by [[Eliora]] in 2022 after the facts that it takes 184 minor thirds of [[6/5]] to reach the interval class of [[4/3]], the Roman consul was Eggius in the year 184 AD, and the Latin word for egg is ovum, and with prefix ovi-. It sets a new record of complexity for a chain of nineteen 6/5's past [[egads]], though it is less accurate.

	~~[[Subgroup]]: 2.3.5.7~~

	~~[[Comma list]]: 4375/4374, {{monzo\| -100 53 48 -34 }}~~

	~~{{Mapping\|legend=1\| 1 -134 -134 -401 \| 0 184 185 548 }}~~
	~~: mapping generators: ~2, ~5/3~~

	~~[[Optimal tuning]]s:~~
	* [[WE]]: ~2 = 1200.0193{{c}}, ~5/3 = 884.2638{{c}}
	~~: [[error map]]: {{val\| +0.019 +0.010 -0.085 +0.032 }}~~
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/3 = 884.2497{{c}}
	~~: error map: {{val\| 0.000 -0.011 -0.120 +0.008 }}~~

	~~{{Optimal ET sequence\|legend=1\| 19, …, 1600, 1619, 4838, 6457c }}~~

	~~[[Badness]] (Sintel): 14.7~~

	== Octoid ==		== Octoid ==

Deleted temperaments

Hkm — Tue, 16 Jun 2026 02:27:37 GMT

Show changes