User:VIxen/Cemetery - Revision history

VIxen at 19:13, 18 May 2025

2025-05-18T19:13:36Z

← Older revision		Revision as of 19:13, 18 May 2025
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			=== Shaka ===
			{{See also\|Kalismic temperaments}}

			Two commas that split 2/1 in half, corresponding to convergents to sqrt(2), are the [[1682/1681\|''sha''ftesburisma]] [[Square superparticular\|S29]]/S41 and the [[9801/9800\|''ka''lisma S99]], prompting to temper out {S29, S41, S99}, approximating /29 and /41 [[Primodality\|primodal]] chords well.

			Subgroup: 2.3.35.11.29.41

			Comma list: 841/840, 1189/1188, 1681/1680

			{{Mapping\|legend=2\|2 2 6 5 7 8\|0 1 1 -1 1 1\|0 0 2 2 1 1}}

			Optimal tuning (CTE): ~41/29 = 1\2, ~3/2 = 702.031, ~41/24 = 926.693

			[[Support]]ing [[ET]]s: {{EDOs\|22, 26, 36, 48, 70, 96, 106, 118, 140, 154, 176, 188, 224, 272, 294, 342}}

			Scale: [[Shaka10]]

	=== Spog ===		=== Spog ===

VIxen at 19:06, 18 May 2025

2025-05-18T19:06:56Z

← Older revision		Revision as of 19:06, 18 May 2025
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	[[Support]]ing [[ET]]s: 8[+9, +7, +13], 11, 14[-13], 19[+9, +7, ++13], 25[-13], 36, 47, 58, 61[-13], 69[+13], 80[+13], 83, 91[+9, +7, +13], 105		[[Support]]ing [[ET]]s: 8[+9, +7, +13], 11, 14[-13], 19[+9, +7, ++13], 25[-13], 36, 47, 58, 61[-13], 69[+13], 80[+13], 83, 91[+9, +7, +13], 105

			== Hnoss ==
			To the [[wizma]] {{monzo\| -6 -8 2 5 }} = 420175/419904, the kalisma is a natural complement, as their product is the [[argyria]], {{monzo\| -9 -4 0 3 2 }} = 41503/41472. [[User:VIxen\|VIxen]] named it and [[#Gersemi\|gersemi]] after Odr's and Freya's daughters since in 11-limit, they both temper out one comma of [[odin]] (9801/9800) and one of [[freya]] (41503/41472). There is also a word play on "semi-" that hints at the split of the octave in half.

			[[Subgroup]]: 2.3.5.7.11

			[[Comma list]]: 9801/9800, 41503/41472

			{{Mapping\|legend=1\| 2 0 1 2 6 \| 0 1 4 0 2 \| 0 0 -5 2 -3 }}

			: mapping generators: ~99/70, ~3, ~144/77

			{{Optimal ET sequence\|legend=1\| 22, 50, 72, 166, 176, 198, 248, 270, 342, 612, 954, 1566, 4086dee, 5652cddeee }}

			[[Badness]]: 0.368 × 10<sup>-3</sup>

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

			Comma list: 1716/1715, 2080/2079, 17303/17280

			Mapping: {{mapping\| 2 0 1 2 6 -3 \| 0 1 4 0 2 1 \| 0 0 -5 2 -3 4 }}

			{{Optimal ET sequence\|legend=1\| 22f, 32cf, 54cff, 72, 166, 198, 270, 634, 904, 1174, 1880ef }}

			Badness: 0.867 × 10<sup>-3</sup>

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

			Comma list: 715/714, 1089/1088, 1225/1224, 2025/2023

			Mapping: {{mapping\| 2 0 1 2 6 -3 0 \| 0 1 4 0 2 1 6 \| 0 0 -5 2 -3 4 -6 }}

			{{Optimal ET sequence\|legend=1\| 22f, 54cffgg, 72, 166g, 198g, 270, 364, 436, 634g, 706f }}

			Badness: 0.862 × 10<sup>-3</sup>

			==== 19-limit ====
			Subgroup: 2.3.5.7.11.13.17.19

			Comma list: 715/714, 1225/1224, 1540/1539, 2080/2079, 4200/4199

			Mapping: {{mapping\| 2 0 1 2 6 -3 0 13 \| 0 1 4 0 2 1 6 2 \| 0 0 -5 2 -3 4 -6 -6 }}

			{{Optimal ET sequence\|legend=1\| 72, 94, 166g, 198g, 270, 436, 634g, 706f }}

			Badness: 0.901 × 10<sup>-3</sup>

			==== 23-limit ====
			Subgroup: 2.3.5.7.11.13.17.19.23

			Comma list: 715/714, 1225/1224, 1540/1539, 2080/2079, 2530/2527, 2737/2736

			Mapping: {{mapping\| 2 0 1 2 6 -3 0 13 19 \| 0 1 4 0 2 1 6 2 -2 \| 0 0 -5 2 -3 4 -6 -6 -2 }}

			{{Optimal ET sequence\|legend=1\| 72, 94, 166g, 270, 342f, 436, 706fi }}

			Badness: 1.14 × 10<sup>-3</sup>

			=== Gersemi ===
			The extension to 13-limit with [[4225/4224]] is weak but facilitates the use of 18/7 as the equave. [[Fokker block]]s of 128 notes are available for the latter, corresponding to 94edo. 18/7 is split into 4 parts that become ~19/15 in 19-limit. Also, (18/7)<sup>3</sup> ~ 17/1 via the [[5832/5831\|chlorisma]]. However, the tones 9/8 and (19/15)/(9/8) = 152/135 have distinct mappings.

			Subgroup: 2.3.5.7.11.13

			Comma list: 4225/4224, 9801/9800, 41503/41472

			Mapping: {{mapping\| 2 0 1 2 6 9 \| 0 1 9 -2 5 -6 \| 0 0 -10 4 -6 7 }}

			: mapping generators: ~99/70, ~3, ~154/65

			{{Optimal ET sequence\|legend=1\| 44, 50, 94, 144, 176, 220, 270, 590, 684, 954 }}

			Badness: 1.06 × 10<sup>-3</sup>

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

			Comma list: 1089/1088, 1225/1224, 2025/2023, 4225/4224

			Mapping: {{mapping\| 2 0 1 2 6 9 0 \| 0 1 9 -2 5 -6 12 \| 0 0 -10 4 -6 7 -12 }}

			{{Optimal ET sequence\|legend=1\| 44, 50, 94, 144g, 176g, 220g, 270, 364, 414, 634g, 684 }}

			Badness: 1.46 × 10<sup>-3</sup>

			==== 19-limit ====
			Subgroup: 2.3.5.7.11.13.17.19

			Comma list: 1089/1088, 1225/1224, 1729/1728, 2926/2925, 3762/3757

			Mapping: {{mapping\| 2 0 1 2 6 9 0 1 \| 0 1 9 -2 5 -6 12 11 \| 0 0 -10 4 -6 7 -12 -11 }}

			{{Optimal ET sequence\|legend=1\| 44, 50, 94, 144gh, 176g, 220g, 270, 414h, 590, 634g, 684h }}

			Badness: 1.11 × 10<sup>-3</sup>

			==== 23-limit ====
			Subgroup: 2.3.5.7.11.13.17.19.23

			Comma list: 897/896, 1089/1088, 1225/1224, 1729/1728, 2737/2736, 2926/2925

			Mapping: {{mapping\| 2 0 1 2 6 9 0 1 7 \| 0 1 9 -2 5 -6 12 11 3 \| 0 0 -10 4 -6 7 -12 -11 -3 }}

			{{Optimal ET sequence\|legend=1\| 44, 50, 94, 144gh, 176g, 220g, 226, 270, 320i, 364i, 414hi }}

			Badness: 1.23 × 10<sup>-3</sup>

			== Rishi ==
			The 7-limit comma {{monzo\| 65 -84 10 16 }} ~ 0.13¢ has the ratio of the exponents of 3 and 2 that is close to the one in 81/8. The square root of the latter is close to 35/11. This suggests tempering out (81/8)(35/11)<sup>-2</sup>, which is the kalisma.

			Apart from 35/11, 35/33, and the equivalents of their squares, 81/8 and 9/8, another equave that comes to mind is 3/2, especially after tempering out the [[chalmersia]]. When 3/2 is chosen as the equave, Fokker blocks of 34 notes can be used that are close to [[34edf]] and 58edo.

			When [[User:VIxen\|VIxen]] was naming this temperament, [[sruti]] was its only named rank-2 subtemperament. Rishis (sages) are believed to have created shruti texts.

			[[Subgroup]]: 2.3.5.7.11

			[[Comma list]]: 9801/9800, 572145834917888/571919811374025

			{{Mapping\|legend=1\| 2 0 3 -10 -4 \| 0 1 2 4 4 \| 0 0 8 -5 3 }}

			: mapping generators: ~99/70, ~3, ~17364375/14172488

			{{Optimal ET sequence\|legend=1\| 24, 34d, 58, …, 436, 460, 494, 954, 1448, 1506, 2460, 2954, 7414, 9874, 12828e }}

			[[Badness]]: 2.10 × 10<sup>-3</sup>

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

			Comma list: 9801/9800, 10648/10647, 371293/371250

			Mapping: {{mapping\| 2 0 3 -10 -4 2 \| 0 1 2 4 4 3 \| 0 0 8 -5 3 7 }}

			{{Optimal ET sequence\|legend=1\| 24, 34d, 58, …, 436, 460, 494, 954, 1448, 1506, 2460, 2954, 5414, 6920, 7414, 9874, 12828e }}

			[[Badness]]: 0.505 × 10<sup>-3</sup>

VIxen at 18:55, 18 May 2025

2025-05-18T18:55:52Z

← Older revision		Revision as of 18:55, 18 May 2025
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	[[Support]]ing [[ET]]s: 9[-725], 14[+725], 23, 32, 41[-725], 55, 73[-725], 87, 105[-725], 119, 151, 183, 206[+725], 311		[[Support]]ing [[ET]]s: 9[-725], 14[+725], 23, 32, 41[-725], 55, 73[-725], 87, 105[-725], 119, 151, 183, 206[+725], 311

			=== Poggers ===
			Related temperaments: [[Stearnsmic_clan#Pogo\|pogo]], [[Stearnsmic_clan#Supers\|supers]]

			[[Subgroup]]: 2.9.7.15/11.13

			[[Comma list]]: [[540/539]], [[1716/1715]], [[2080/2079]]

			{{Mapping\|legend=2\| 1 1 1 -1 -1 \| 0 6 5 4 13 }}

			[[Optimal tuning]] (subgroup [[CTE]]): ~9/7 = 433.888

			[[Support]]ing [[ET]]s: 8[+9, +7, +13], 11, 14[-13], 19[+9, +7, ++13], 25[-13], 36, 47, 58, 61[-13], 69[+13], 80[+13], 83, 91[+9, +7, +13], 105

VIxen: Created page with "=== Spog === This temperament produces superpelog-like semiquartal scales while being more accurate (see rational approximations to their intervals). Subgroup: 2.15.55 Comma list: 100663296/100656875 {{Mapping|legend=2| 1 0 5 | 0 5 1 }} Optimal tuning (subgroup CTE): ~55/32 = 937.655 {{Optimal ET sequence|legend=1|5, 9, 23, 32, 151, 183, 215, 247, 956, 1203,..."

2025-05-18T18:49:04Z

Created page with "=== Spog === This temperament produces superpelog-like semiquartal scales while being more accurate (see rational approximations to their intervals). Subgroup: 2.15.55 Comma list: 100663296/100656875 {{Mapping|legend=2| 1 0 5 | 0 5 1 }} Optimal tuning (subgroup CTE): ~55/32 = 937.655 {{Optimal ET sequence|legend=1|5, 9, 23, 32, 151, 183, 215, 247, 956, 1203,..."

New page

=== Spog ===

This temperament produces [[Slendro_clan#Superpelog|superpelog]]-like [[5L 4s|semiquartal]] scales while being more accurate ([[Subgroup temperaments#2.15.189.55.325.725.279|see]] rational approximations to their intervals).

[[Subgroup]]: 2.15.55

[[Comma list]]: [[100663296/100656875]]

{{Mapping|legend=2| 1 0 5 | 0 5 1 }}

[[Optimal tuning]] (subgroup [[CTE]]): ~55/32 = 937.655

{{Optimal ET sequence|legend=1|5, 9, 23, 32, 151, 183, 215, 247, 956, 1203, 1450, 3147, 4597 }}

==== 2.15.55.325 ====
[[Subgroup]]: 2.15.55.325

[[Comma list]]: [[4225/4224]], [[6656/6655]]

{{Mapping|legend=2| 1 0 5 6 | 0 5 1 3 }}

[[Optimal tuning]] (subgroup [[CTE]]): ~55/32 = 937.647

[[Support]]ing [[ET]]s: 5, 9, 13[-15], 14, 23, 32, 37, 41, 50, 55, 64, 73, 78, 87, 96, 101, 105, 119, 128, 151, 183, 206, 311

==== 2.15.189.55.325 ====
Related temperament: [[Lehmerismic_temperaments#Lux|lux]]

[[Subgroup]]: 2.15.189.55.325

[[Comma list]]: [[2080/2079]], [[3025/3024]], [[4096/4095]]

{{Mapping|legend=2| 1 0 6 5 6 | 0 5 2 1 3 }}

[[Optimal tuning]] (subgroup [[CTE]]): ~55/32 = 937.677

[[Support]]ing [[ET]]s: 5, 9, 14, 23, 32, 37, 41, 50, 55, 64, 73, 78, 87, 96, 101, 105, 119, 128, 151, 183, 206, 311

==== 2.15.189.55.325.725 ====

[[Subgroup]]: 2.15.189.55.325.725

[[Comma list]]: [[1625/1624]], [[2080/2079]], [[3025/3024]], [[4096/4095]]

{{Mapping|legend=2| 1 0 6 5 6 -3 | 0 5 2 1 3 16 }}

[[Optimal tuning]] (subgroup [[CTE]]): ~55/32 = 937.649

[[Support]]ing [[ET]]s: 9[-725], 14[+725], 23, 32, 41[-725], 55, 73[-725], 87, 105[-725], 119, 142[+725], 151, 183, 206[+725], 311

==== 2.15.189.55.325.725.279 ====

Here are rational approximations to the intervals of the semiquartal scale.

Sharp: 12/11, 25/21, 33/26, 18/13, 31/21 ~ 65/44 ~ 96/65, 50/31 ~ 29/18, 55/32, 15/8.

Flat: 16/15, 64/55, 31/25 ~ 36/29, 42/31 ~ 65/48 ~ 88/65, 13/9, 52/33, 42/25, 11/6.

[[Subgroup]]: 2.15.189.55.325.725.279

[[Comma list]]: [[1625/1624]], [[2016/2015]], [[2080/2079]], [[3025/3024]], [[4096/4095]]

{{Mapping|legend=2| 1 0 6 5 6 -3 5 | 0 5 2 1 3 16 4 }}

[[Optimal tuning]] (subgroup [[CTE]]): ~55/32 = 937.638

[[Support]]ing [[ET]]s: 9[-725], 14[+725], 23, 32, 41[-725], 55, 73[-725], 87, 105[-725], 119, 151, 183, 206[+725], 311