Landscape microtemperaments - Revision history

FloraC: + trivish

2026-06-20T15:38:20Z

+ trivish

← Older revision		Revision as of 15:38, 20 June 2026
Line 19:		Line 19:
	* ''[[Triquart]]'' (+117649/116640) → [[Quartonic family #Triquart\|Quartonic family]]		* ''[[Triquart]]'' (+117649/116640) → [[Quartonic family #Triquart\|Quartonic family]]
	* ''[[Stearnscape]]'' (+118098/117649) → [[Stearnsmic clan #Stearnscape\|Stearnsmic clan]]		* ''[[Stearnscape]]'' (+118098/117649) → [[Stearnsmic clan #Stearnscape\|Stearnsmic clan]]
	* ''[[Domain (temperament)\|Domain]]'' (+645700815/645657712) → [[~~Minortonic~~ family #Domain\|~~Minortonic~~ family]]		* ''[[Trivish]]'' (+134217728/133984375) → [[Vishnu family #Trivish\|Vishnu family]]
			* ''[[Domain (temperament)\|Domain]]'' (+645700815/645657712) → [[Minortone family #Domain\|Minortone family]]
	* ''[[Aemilic]]'' (+{{monzo\|-84 53}}) → [[159th-octave temperaments #Aemilic\|159th-octave temperaments]]		* ''[[Aemilic]]'' (+{{monzo\|-84 53}}) → [[159th-octave temperaments #Aemilic\|159th-octave temperaments]]

Hkm: /* 17-limit */

2026-06-08T17:41:18Z

17-limit

← Older revision		Revision as of 17:41, 8 June 2026
Line 74:		Line 74:

	==== 17-limit ====		==== 17-limit ====
	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13.17

	Comma list: 936/935, 1701/1700, 1716/1715, 2025/2023, 61965/61952		Comma list: 936/935, 1701/1700, 1716/1715, 2025/2023, 61965/61952

FloraC: - sextile (more properly addressed in the garischismic clan)

2026-05-16T09:45:54Z

- sextile (more properly addressed in the garischismic clan)

@@ Line 6: / Line 6: @@
 * [[Misty]] (+3136/3125 or 5120/5103) → [[Misty family]]
 * ''[[Term (temperament)|Term]]'' (+32805/32768) → [[Schismatic family #Term|Schismatic family]]
 * ''[[Tritricot]]'' (+{{monzo| 35 -23 -3 3 }}) → [[Alphatricot family #Tritricot|Alphatricot family]]
 * [[Compton]] (+225/224) → [[Compton family #Compton|Compton family]]
@@ Line 21: / Line 22: @@
 * ''[[Aemilic]]'' (+{{monzo|-84 53}}) → [[159th-octave temperaments #Aemilic|159th-octave temperaments]]
-Considered below are septichrome, akjayland, pnict, atomic, slendscape, avicenna, sextile, zinc, magnesium, poe, and chromium in the order of increasing [[badness]].
+Considered below are septichrome, akjayland, pnict, atomic, slendscape, avicenna, zinc, magnesium, poe, and chromium in the order of increasing [[badness]].
 == Septichrome ==
@@ Line 510: / Line 511: @@
 Badness (Sintel): 0.928
 == Zinc ==

FloraC: /* Sextile */ - the useless alt 13-limit extension and re-frame the main temp as no-17 19-limit (see talk)

2026-05-16T09:34:12Z

Sextile: - the useless alt 13-limit extension and re-frame the main temp as no-17 19-limit (see talk)

@@ Line 563: / Line 563: @@
 Badness (Sintel): 0.788
-==== 17-limit ====
+=== 2.3.5.7.11.13.19 subgroup ===
 Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 715/714, 1001/1000, 1216/1215, 1701/1700, 1729/1728, 2912/2907
+Comma list: 1216/1215, 1716/1715, 2080/2079, 2376/2375, 9633/9625
-Mapping: {{mapping| 6 0 71 150 230 -149 -4 35 | 0 1 -6 -14 -22 18 3 -1 }}
+Mapping: {{mapping| 6 0 71 150 230 279 35 | 0 1 -6 -14 -22 -27 -1 }}
 Optimal tunings:
-* WE: ~55/49 = 199.9866{{c}}, ~3/2 = 702.1731{{c}}
+* WE: ~55/49 = 199.9826{{c}}, ~3/2 = 702.1359{{c}}
-* CWE: ~55/49 = 200.0000{{c}}, ~3/2 = 702.2208{{c}}
+* CWE: ~55/49 = 200.0000{{c}}, ~3/2 = 702.2003{{c}}
-{{Optimal ET sequence|legend=0| 12, 258e, 270 }}
+{{Optimal ET sequence|legend=0| 12f, 258ef, 270, 552, 822, 1092 }}
-Badness (Sintel): 1.53
+Badness (Sintel): 0.634
 == Zinc ==

FloraC: /* Sextile */ fixes

2026-04-26T12:28:21Z

Sextile: fixes

← Older revision		Revision as of 12:28, 26 April 2026
Line 541:		Line 541:

	Optimal tunings:		Optimal tunings:
	* ~~CTE~~: ~55/49 = 199.9817{{c}}, ~3/2 = 702.1383{{c}}		* WE: ~55/49 = 199.9817{{c}}, ~3/2 = 702.1383{{c}}
	* ~~POTE~~: ~55/49 = 200.0000{{c}}, ~3/2 = 702.2080{{c}}		* CWE: ~55/49 = 200.0000{{c}}, ~3/2 = 702.2080{{c}}

	{{Optimal ET sequence\|legend=0\| 12, …, 258e, 270, 822, 1092, 1362c }}		{{Optimal ET sequence\|legend=0\| 12, …, 258e, 270, 822, 1092, 1362c }}
Line 586:		Line 586:

	Optimal tunings:		Optimal tunings:
	* ~~CTE~~: ~55/49 = 199.9711{{c}}, ~3/2 = 702.0829{{c}}		* WE: ~55/49 = 199.9711{{c}}, ~3/2 = 702.0829{{c}}
	* CWE: ~55/49 = 200.0000{{c}}, ~3/2 = 702.1890{{c}}		* CWE: ~55/49 = 200.0000{{c}}, ~3/2 = 702.1890{{c}}

FloraC: Sorting

2026-04-24T14:20:03Z

Sorting

Show changes

FloraC: - redundant links

2026-04-24T14:08:47Z

- redundant links

← Older revision		Revision as of 14:08, 24 April 2026
Line 266:		Line 266:

	Atomic tempers out the [[atom]], {{monzo\| 161 -84 -12 }}, and in the [[7-limit]] the [[nommisma]], {{monzo\| -55 30 2 1 }}, so that a stack of two [[schisma]]s gives the [[garischisma]], from which intervals of [[7/1\|7]] can be derived. It may be described as the {{nowrap\| 12 & 612 }} temperament, with a [[ploidacot]] signature of dodecaploid monocot.		Atomic tempers out the [[atom]], {{monzo\| 161 -84 -12 }}, and in the [[7-limit]] the [[nommisma]], {{monzo\| -55 30 2 1 }}, so that a stack of two [[schisma]]s gives the [[garischisma]], from which intervals of [[7/1\|7]] can be derived. It may be described as the {{nowrap\| 12 & 612 }} temperament, with a [[ploidacot]] signature of dodecaploid monocot.

	~~Atomic extensions discussed elsewhere include [[72nd-octave temperaments #Hafnium\|hafnium]].~~

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
Line 730:		Line 728:

	== Zinc ==		== Zinc ==
	{{See also\| 10th-octave temperaments #Neon ~~\| 60th-octave temperaments #Neodymium~~ }}		{{See also\| 10th-octave temperaments #Neon }}

	Zinc maybe described as the {{nowrap\| 270 & 2190 }} temperament. It was named by [[Eliora]] in 2023 after the 30th element for having a 30th-octave period.		Zinc maybe described as the {{nowrap\| 270 & 2190 }} temperament. It was named by [[Eliora]] in 2023 after the 30th element for having a 30th-octave period.

FloraC: - terture (addressed in vulture family)

2026-04-24T14:00:03Z

- terture (addressed in vulture family)

@@ Line 16: / Line 16: @@
 * ''[[Triquart]]'' (+117649/116640) → [[Quartonic family #Triquart|Quartonic family]]
 * ''[[Stearnscape]]'' (+118098/117649) → [[Stearnsmic clan #Stearnscape|Stearnsmic clan]]
-* ''[[Domain (temperament)|Domain]]'' (645700815/645657712) → [[Minortonic family #Domain|Minortonic family]]
+* ''[[Terture]]'' (+359661568/358722675) → [[Vulture family #Domain|Vulture family]]
 * ''[[Tritricot]]'' (+{{monzo| 35 -23 -3 3 }}) → [[Alphatricot family #Tritricot|Alphatricot family]]
 * ''[[Aemilic]]'' (+{{monzo|-84 53}}) → [[159th-octave temperaments #Aemilic|159th-octave temperaments]]
-Considered below are sextile, septichrome, pnict, atomic, avicenna, terture, slendscape, akjayland, magnesium, chromium, zinc, and poe.
+Considered below are sextile, septichrome, pnict, atomic, avicenna, slendscape, akjayland, magnesium, chromium, zinc, and poe.
 == Sextile ==
@@ Line 488: / Line 489: @@
 Badness (Sintel): 0.928
 == Slendscape ==

FloraC: Move hafnium here

2026-04-24T13:46:04Z

Move hafnium here

← Older revision		Revision as of 13:46, 24 April 2026
Line 346:		Line 346:

	Badness (Sintel): 1.50		Badness (Sintel): 1.50

			==== Hafnium ====
			Hafnium (1224 & 4320), named after the 72nd element, splits the 1/12-octave period into six 1/72-octave parts. Since 4320edo and 5544edo have good 31st and 37th harmonics, addition of these primes are also prescribed. In the add-37 version, [[37/22]] is mapped to exact 3\4.

			Subgroup: 2.3.5.7.11.13

			Comma list: 9801/9800, 151263/151250, 184549376/184528125, 308915776/308828625

			Mapping: {{mapping\| 72 0 966 2028 3102 2777 \| 0 1 -7 -16 -25 -22 }}
			: mapping generators: ~105/104, ~3

			Optimal tunings:
			* WE: ~105/104 = 16.666629{{c}}, ~3/2 = 701.945668{{c}}
			* CWE: ~105/104 = 16.666667{{c}}, ~3/2 = 701.947388{{c}}

			{{Optimal ET sequence\|legend=0\| 1224, 3096e, 4320, 5544, 9864c }}

			Badness (Sintel): 4.76

			===== 17-limit =====
			Subgroup: 2.3.5.7.11.13.17

			Comma list: 9801/9800, 12376/12375, 151263/151250, 1713660/1713481, 97144749/97140736

			Mapping: {{mapping\| 72 0 966 2028 3102 2777 979 \| 0 1 -7 -16 -25 -22 -6 }}
			: mapping generators: ~105/104, ~3

			Optimal tunings:
			* WE: ~105/104 = 16.666615{{c}}, ~3/2 = 701.944968{{c}}
			* CWE: ~105/104 = 16.666667{{c}}, ~3/2 = 701.947293{{c}}

			{{Optimal ET sequence\|legend=0\| 1224, 3096e, 4320, 5544, 9864c }}

			Badness (Sintel): 2.73

			===== 2.3.5.7.11.13.17.31 subgroup =====
			Subgroup: 2.3.5.7.11.13.17.31

			Comma list: 9801/9800, 10881/10880, 12376/12375, 57629/57624, 179712/179707, 61456384/61448625

			Subgroup-val mapping: {{mapping\| 72 0 966 2028 3102 2777 979 -328 \| 0 1 -7 -16 -25 -22 -6 6 }}

			Optimal tunings:
			* WE: ~105/104 = 16.666643{{c}}, ~3/2 = 701.946542{{c}}
			* CWE: ~105/104 = 16.666667{{c}}, ~3/2 = 701.947581{{c}}

			{{Optimal ET sequence\|legend=0\| 1224, 3096e, 4320, 5544 }}

			Badness (Sintel): 2.36

			===== 2.3.5.7.11.13.17.31.37 subgroup =====
			Subgroup: 2.3.5.7.11.13.17.31.37

			Comma list: 9801/9800, 10881/10880, 12376/12375, 16576/16575, 57629/57624, 93093/93092, 179712/179707

			Subgroup-val mapping: {{mapping\| 72 0 966 2028 3102 2777 979 -328 3228 \| 0 1 -7 -16 -25 -22 -6 6 -25 }}

			Optimal tunings:
			* WE: ~105/104 = 16.666648{{c}}, ~3/2 = 701.946549{{c}}
			* CWE: ~105/104 = 16.666667{{c}}, ~3/2 = 701.947386{{c}}

			{{Optimal ET sequence\|legend=0\| 1224, 3096el, 4320, 5544 }}

			Badness (Sintel): 1.98

	== Avicenna ==		== Avicenna ==

FloraC: Move minutes and neodymium here

2026-04-24T13:15:34Z

Move minutes and neodymium here

@@ Line 266: / Line 266: @@
 Atomic tempers out the [[atom]], {{monzo| 161 -84 -12 }}, and in the [[7-limit]] the [[nommisma]], {{monzo| -55 30 2 1 }}, so that a stack of two [[schisma]]s gives the [[garischisma]], from which intervals of [[7/1|7]] can be derived. It may be described as the {{nowrap| 12 & 612 }} temperament, with a [[ploidacot]] signature of dodecaploid monocot.
-Atomic extensions discussed elsewhere include [[minutes]] and [[72nd-octave temperaments #Hafnium|hafnium]].
+Atomic extensions discussed elsewhere include [[72nd-octave temperaments #Hafnium|hafnium]].
 [[Subgroup]]: 2.3.5.7
@@ Line 298: / Line 298: @@
 Badness (Sintel): 0.530
 == Avicenna ==
@@ Line 765: / Line 813: @@
 Badness (Sintel): 0.640
-=== 2.3.5.7.11.13.19 subgroup (neozinc) ===
+==== 2.3.5.7.11.13.19 subgroup (neozinc) ====
 Subgroup: 2.3.5.7.11.13.19
@@ Line 779: / Line 827: @@
 Badness (Sintel): 0.477
 == Poe ==