User:BudjarnLambeth/Regular temperament interpretation of lucite23 - Revision history

BudjarnLambeth at 02:48, 21 October 2025

2025-10-21T02:48:15Z

← Older revision		Revision as of 02:48, 21 October 2025
Line 31:		Line 31:
	=== Temperament data (x31eq) ===		=== Temperament data (x31eq) ===

	==== ~~Lower rank temperaments~~ including it ====		==== [[EDO]]s including it ====
	''(not exhaustive)''		''(not exhaustive)''
	* {{EDOs\|34, 68, 102f, 91p, 125p, 57p, 159f, 23p, 136f, 193f}}		* {{EDOs\|34, 68, 102f, 91p, 125p, 57p, 159f, 23p, 136f, 193f}}
Line 126:		Line 126:
	=== Temperament data (x31eq) ===		=== Temperament data (x31eq) ===

	==== ~~Lower rank temperaments~~ including it ====		==== [[EDO]]s including it ====
	''(not exhaustive)''		''(not exhaustive)''
	* {{EDOs\|23de, 34e, 11b, 57ddee, 12bbcde, 45bce, 46bcddee, 68dee, 22bbcf, 80bcdddeee}}		* {{EDOs\|23de, 34e, 11b, 57ddee, 12bbcde, 45bce, 46bcddee, 68dee, 22bbcf, 80bcdddeee}}

BudjarnLambeth: /* Triencata temperament */ added full data

2025-10-21T02:47:35Z

Triencata temperament: added full data

← Older revision		Revision as of 02:47, 21 October 2025
Line 28:		Line 28:

	<big><big>"</big></big>		<big><big>"</big></big>

			=== Temperament data (x31eq) ===

			==== Lower rank temperaments including it ====
			''(not exhaustive)''
			* {{EDOs\|34, 68, 102f, 91p, 125p, 57p, 159f, 23p, 136f, 193f}}

			==== Mappings ====
			Equal Temperament Mappings

			2 3 5 13 17

			[ ⟨ 34 54 79 126 139 ]

			⟨ 91 144 211 337 372 ] ⟩


			Reduced Mapping

			2 3 5 13 17

			[ ⟨ 1 0 1 3 4 ]

			⟨ 0 18 15 8 1 ] ⟩

			==== TE tuning ====
			TE Generator Tunings (cents)

			⟨1199.6283, 105.6795]


			TE Step Tunings (cents)

			⟨19.81091, 5.78085]


			TE Tuning Map (cents)

			⟨1199.628, 1902.232, 2784.821, 4444.321, 4904.193]


			TE Mistunings (cents)

			⟨-0.372, 0.277, -1.492, 3.794, -0.763]

			==== POTE tuning ====
			POTE Generator Tunings (cents)

			⟨1200.0000, 105.7123]


			POTE Step Tunings (cents)

			⟨19.81705, 5.78264]


			POTE Tuning Map (cents)

			⟨1200.000, 1902.821, 2785.684, 4445.698, 4905.712]


			POTE Mistunings (cents)

			⟨-0.000, 0.866, -0.630, 5.171, 0.757]

			==== Complexity and error ====
			Complexity 4.329045

			Adjusted Error 2.360479 cents

			TE Error 0.577493 cents/octave

			==== Commas ====
			Unison Vectors

			[1, 0, 1, -2, 1⟩ ([[170/169]])

			[4, -2, 3, -1, -1⟩ ([[2000/1989]])

			[-3, 2, -2, -1, 2⟩ ([[2601/2600]])

			[-6, -5, 6, 0, 0⟩ ([[15625/15552]])

			[5, -2, 4, -3, 0⟩ ([[20000/19773]])

			[13, 1, -1, 0, -3⟩ ([[24576/24565]])

	== Lucite temperament ==		== Lucite temperament ==

BudjarnLambeth: /* Triencata temperament */

2025-10-21T02:41:22Z

Triencata temperament

← Older revision		Revision as of 02:41, 21 October 2025
Line 3:		Line 3:
	== Triencata temperament ==		== Triencata temperament ==
	Described by [[Osmium]] in October 2025. Relatively high accuracy; tunes the 2.3.5.13.17 [[subgroup]] (so it's a type of no-7s temperament).		Described by [[Osmium]] in October 2025. Relatively high accuracy; tunes the 2.3.5.13.17 [[subgroup]] (so it's a type of no-7s temperament).

			Using Sintel Temperament Finder's [[badness]], it has a badness of: 1.179.

	=== Osmium's post ===		=== Osmium's post ===

BudjarnLambeth: Document Osmium's triencata temperament(will add more data later)

2025-10-21T02:33:57Z

Document Osmium's triencata temperament(will add more data later)

← Older revision		Revision as of 02:33, 21 October 2025
Line 1:		Line 1:
	~~This is a generalisation~~ of [[Gordon Wery]]'s [[343edo#Scales\|lucite23]] scale into a [[regular temperament~~]] in the [[17-limit~~]].		These are generalisations of [[Gordon Wery]]'s [[343edo#Scales\|lucite23]] scale into a [[regular temperament]].

	~~It could be called~~ '''~~lucite~~''' temperament.		== Triencata temperament ==
			Described by [[Osmium]] in October 2025. Relatively high accuracy; tunes the 2.3.5.13.17 [[subgroup]] (so it's a type of no-7s temperament).

			=== Osmium's post ===

			<big><big>"</big></big>

			Looks like the 7 and 11 in [lucite] temperament are suspicious; I recommend removing them to achieve a 2.3.5.13.17-subgroup temperament of considerably more [[accuracy]].
			in order of decreasing sharpness of the fifth, here are the
			* [CE/CEE](<https://sintel.pythonanywhere.com/result?subgroup=17&reduce=on&weights=unweighted&target=&edos=&commas=49%2F48+66%2F65+275%2F273+561%2F560+715%2F714&submit_comma=submit>),
			* [CTE](<https://sintel.pythonanywhere.com/result?subgroup=17&reduce=on&weights=tenney&target=&edos=&commas=49%2F48+66%2F65+275%2F273+561%2F560+715%2F714&submit_comma=submit>)
			* and [CWE](<https://sintel.pythonanywhere.com/result?subgroup=17&reduce=on&weights=weil&target=&edos=&commas=49%2F48+66%2F65+275%2F273+561%2F560+715%2F714&submit_comma=submit>)

			tunings of [lucite] temp where we can see the issue with the 7 and 11 (which becomes more pronounced cuz theyre the only ones with an unambiguous flat tendency) persists in all of these.

			By contrast, for the 2.3.5.13.17 subgroup that I suggest, here are the results in order of ''increasing'' sharpness of the fifth (to keep the order as CE/CEE, CTE, CWE):
			* [CE/CEE](<https://sintel.pythonanywhere.com/result?subgroup=2.3.5.13.17&reduce=on&weights=unweighted&target=&edos=11b+34&submit_edo=submit&commas=>),
			* [CTE](<https://sintel.pythonanywhere.com/result?subgroup=2.3.5.13.17&reduce=on&weights=tenney&target=&edos=11b+34&submit_edo=submit&commas=>) and
			* [CWE](<https://sintel.pythonanywhere.com/result?subgroup=2.3.5.13.17&reduce=on&weights=weil&target=&edos=11b+34&submit_edo=submit&commas=>)

			for which we also notice many much larger viable EDOs of considerable accuracy and interest.

			It also makes clearer that this is related to [[kleismic]], specifically a version of kleismic splitting the ~6/5 gen into three equal parts of 17/16, so I'd suggest a working name of "triencata", as we extend the 2.3.5.13 subgroup of [[cata]] to prime 17 by splitting 6/5 into three 17/16's. Then we know a more accurate tuning range so we can look for extensions.

			<big><big>"</big></big>

			== Lucite temperament ==
			Described by [[Budjarn Lambeth]] in October 2025. Relatively low accuracy but includes the full [[17-limit]].

	Using Sintel Temperament Finder's badness, it has a badness of: 3.052.		Using Sintel Temperament Finder's badness, it has a badness of: 3.052.

	== Links ==		=== Links ===
	* [https://x31eq.com/pyscript/rt.html?ets=23de_11b&limit=17 23de&11b (17-limit) - x31eq.com]		* [https://x31eq.com/pyscript/rt.html?ets=23de_11b&limit=17 23de&11b (17-limit) - x31eq.com]
	* [https://sintel.pythonanywhere.com/result?subgroup=17&reduce=on&weights=weil&target=&edos=&commas=49%2F48%2C+66%2F65%2C+275%2F273%2C+561%2F560%2C+715%2F714&submit_comma=submit 23de&11b (17-limit) - sintel.pythonanywhere.com]		* [https://sintel.pythonanywhere.com/result?subgroup=17&reduce=on&weights=weil&target=&edos=&commas=49%2F48%2C+66%2F65%2C+275%2F273%2C+561%2F560%2C+715%2F714&submit_comma=submit 23de&11b (17-limit) - sintel.pythonanywhere.com]

	== Temperament data (x31eq) ==		=== Temperament data (x31eq) ===

	=== Lower rank temperaments including it ===		==== Lower rank temperaments including it ====
	''(not exhaustive)''		''(not exhaustive)''
	* {{EDOs\|23de, 34e, 11b, 57ddee, 12bbcde, 45bce, 46bcddee, 68dee, 22bbcf, 80bcdddeee}}		* {{EDOs\|23de, 34e, 11b, 57ddee, 12bbcde, 45bce, 46bcddee, 68dee, 22bbcf, 80bcdddeee}}

	=== Mappings ===		==== Mappings ====
	Equal Temperament Mappings		Equal Temperament Mappings

Line 33:		Line 60:
	⟨ 0 18 15 9 5 8 1 ] ⟩		⟨ 0 18 15 9 5 8 1 ] ⟩

	=== TE tuning ===		==== TE tuning ====
	TE Generator Tunings (cents)		TE Generator Tunings (cents)

Line 53:		Line 80:
	⟨2.156, 1.245, 1.842, -12.915, -16.184, 11.806, 9.400]		⟨2.156, 1.245, 1.842, -12.915, -16.184, 11.806, 9.400]

	=== POTE tuning ===		==== POTE tuning ====
	POTE Generator Tunings (cents)		POTE Generator Tunings (cents)

Line 73:		Line 100:
	⟨0.000, -2.167, -3.157, -18.932, -23.599, 3.822, 0.588]		⟨0.000, -2.167, -3.157, -18.932, -23.599, 3.822, 0.588]

	=== Complexity and error ===		==== Complexity and error ====
	Complexity 3.761826		Complexity 3.761826

Line 80:		Line 107:
	TE Error 3.033395 cents/octave		TE Error 3.033395 cents/octave

	=== Commas ===		==== Commas ====
	Unison Vectors		Unison Vectors

BudjarnLambeth at 11:58, 20 October 2025

2025-10-20T11:58:48Z

← Older revision		Revision as of 11:58, 20 October 2025
Line 1:		Line 1:
	This is a generalisation of [[Gordon Wery]]'s [[343edo#Scales\|~~frost23~~]] scale into a [[regular temperament]] in the [[17-limit]].		This is a generalisation of [[Gordon Wery]]'s [[343edo#Scales\|lucite23]] scale into a [[regular temperament]] in the [[17-limit]].

	It could be called '''~~frost~~''' temperament.		It could be called '''lucite''' temperament.

	Using Sintel Temperament Finder's badness, it has a badness of: 3.052.		Using Sintel Temperament Finder's badness, it has a badness of: 3.052.

BudjarnLambeth: BudjarnLambeth moved page User:BudjarnLambeth/Regular temperament interpretation of frost23 to User:BudjarnLambeth/Regular temperament interpretation of lucite23

2025-10-20T11:58:26Z

BudjarnLambeth moved page User:BudjarnLambeth/Regular temperament interpretation of frost23 to User:BudjarnLambeth/Regular temperament interpretation of lucite23

← Older revision	Revision as of 11:58, 20 October 2025
(No difference)

BudjarnLambeth: /* Temperament data (x31eq) */

2025-10-20T08:39:37Z

Temperament data (x31eq)

← Older revision		Revision as of 08:39, 20 October 2025
Line 10:		Line 10:

	== Temperament data (x31eq) ==		== Temperament data (x31eq) ==

			=== Lower rank temperaments including it ===
			''(not exhaustive)''
			* {{EDOs\|23de, 34e, 11b, 57ddee, 12bbcde, 45bce, 46bcddee, 68dee, 22bbcf, 80bcdddeee}}

	=== Mappings ===		=== Mappings ===
Line 88:		Line 92:

	[-1, -1, 1, -1, 1, 1, -1⟩ ([[715/714]])		[-1, -1, 1, -1, 1, 1, -1⟩ ([[715/714]])

	~~=== Lower rank temperaments including it ===~~
	~~''(not exhaustive)''~~
	* {{EDOs\|23de, 34e, 11b, 57ddee, 12bbcde, 45bce, 46bcddee, 68dee, 22bbcf, 80bcdddeee}}

BudjarnLambeth: /* Lower rank temperaments including it */

2025-10-20T08:36:19Z

Lower rank temperaments including it

← Older revision		Revision as of 08:36, 20 October 2025
Line 91:		Line 91:
	=== Lower rank temperaments including it ===		=== Lower rank temperaments including it ===
	''(not exhaustive)''		''(not exhaustive)''
	* 23de, 34e, 11b, 57ddee, 12bbcde, 45bce, 46bcddee, 68dee, 22bbcf, 80bcdddeee		* {{EDOs\|23de, 34e, 11b, 57ddee, 12bbcde, 45bce, 46bcddee, 68dee, 22bbcf, 80bcdddeee}}

BudjarnLambeth: /* Temperament data (x31eq) */

2025-10-20T08:36:07Z

Temperament data (x31eq)

← Older revision		Revision as of 08:36, 20 October 2025
Line 88:		Line 88:

	[-1, -1, 1, -1, 1, 1, -1⟩ ([[715/714]])		[-1, -1, 1, -1, 1, 1, -1⟩ ([[715/714]])

			=== Lower rank temperaments including it ===
			''(not exhaustive)''
			* 23de, 34e, 11b, 57ddee, 12bbcde, 45bce, 46bcddee, 68dee, 22bbcf, 80bcdddeee

BudjarnLambeth at 07:21, 20 October 2025

2025-10-20T07:21:55Z

← Older revision		Revision as of 07:21, 20 October 2025
Line 1:		Line 1:
	This is a generalisation of [[Gordon Wery]]'s [[343edo#Scales\|frost23]] scale into a regular temperament~~. It could be called '''frost''' temperament~~.		This is a generalisation of [[Gordon Wery]]'s [[343edo#Scales\|frost23]] scale into a [[regular temperament]] in the [[17-limit]].

	== ~~x31eq link~~ ==		It could be called '''frost''' temperament.

			Using Sintel Temperament Finder's badness, it has a badness of: 3.052.

			== Links ==
	* [https://x31eq.com/pyscript/rt.html?ets=23de_11b&limit=17 23de&11b (17-limit) - x31eq.com]		* [https://x31eq.com/pyscript/rt.html?ets=23de_11b&limit=17 23de&11b (17-limit) - x31eq.com]
			* [https://sintel.pythonanywhere.com/result?subgroup=17&reduce=on&weights=weil&target=&edos=&commas=49%2F48%2C+66%2F65%2C+275%2F273%2C+561%2F560%2C+715%2F714&submit_comma=submit 23de&11b (17-limit) - sintel.pythonanywhere.com]

	== Temperament data ==		== Temperament data (x31eq) ==

	=== Mappings ===		=== Mappings ===