User:VIxen/Sandbox - Revision history

Cmloegcmluin: "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

2023-05-07T18:42:44Z

"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

VIxen: /* Odin (harmonismic) */

2022-06-24T02:16:07Z

Odin (harmonismic)

← Older revision		Revision as of 02:16, 24 June 2022
Line 212:		Line 212:
	Mapping generators: ~55/49, ~3, ~325/154		Mapping generators: ~55/49, ~3, ~325/154

	{{Val list\|legend=1\| 12f, ~~108xddeeefff~~, 120cdeeff, 126, 132de, 144, 258ef, 270, 552, 684, 954, 1236, 1506, 2190, 3696, 5886, 6156, 8346, 12042 }}		{{Val list\|legend=1\| 12f, 108cddeeefff, 120cdeeff, 126, 132de, 144, 258ef, 270, 552, 684, 954, 1236, 1506, 2190, 3696, 5886, 6156, 8346, 12042 }}

	[[Badness]]: 0.418 × 10<sup>-3</sup>		[[Badness]]: 0.418 × 10<sup>-3</sup>

VIxen at 02:15, 24 June 2022

2022-06-24T02:15:20Z

← Older revision		Revision as of 02:15, 24 June 2022
Line 199:		Line 199:

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

			== Odin (harmonismic) ==

			(Equave 3/2: q63ef & q70p & q95p)

			Subgroup: 2.3.5.7.11.13

			[[Comma list]]: 9801/9800, 10648/10647, 105644/105625

			[[Mapping]]: [{{val\| 6 0 1 10 20 34 }}, {{val\| 0 1 0 -2 -4 -6 }}, {{val\| 0 0 2 4 6 7 }}]

			Mapping generators: ~55/49, ~3, ~325/154

			{{Val list\|legend=1\| 12f, 108xddeeefff, 120cdeeff, 126, 132de, 144, 258ef, 270, 552, 684, 954, 1236, 1506, 2190, 3696, 5886, 6156, 8346, 12042 }}

			[[Badness]]: 0.418 × 10<sup>-3</sup>

VIxen: /* Gersemi */ +intro, +leprechaunish 13-23 limits

2022-06-23T16:58:44Z

Gersemi: +intro, +leprechaunish 13-23 limits

@@ Line 18: / Line 18: @@
 == Gersemi ==
-{{see also| Kalismic temperaments }}
 Subgroup: 2.3.5.7.11
@@ Line 33: / Line 36: @@
 === 13-limit ===
 Subgroup: 2.3.5.7.11.13
@@ Line 46: / Line 105: @@
 [[Badness]]: 0.867 × 10<sup>-3</sup>
-=== 13-limit (schisminic branch) ===
+=== 13-limit (schisminic) ===
 Subgroup: 2.3.5.7.11.13

VIxen: /* Gersemi */ confused the badnesses of the 13-limit extensions

2022-06-22T16:32:33Z

Gersemi: confused the badnesses of the 13-limit extensions

← Older revision		Revision as of 16:32, 22 June 2022
Line 36:		Line 36:
	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

	[[Comma list]]: ~~4096~~/~~4095~~, ~~9801~~/~~9800~~, ~~41503~~/~~41472~~		[[Comma list]]: 1716/1715, 2080/2079, 17303/17280

	[[Mapping]]: [{{val\| 2 0 1 2 6 21 }}, {{val\| 0 1 4 0 2 -6 }}, {{val\| 0 0 -5 2 -3 3 }}]		[[Mapping]]: [{{val\| 2 0 1 2 6 -3 }}, {{val\| 0 1 4 0 2 1 }}, {{val\| 0 0 -5 2 -3 4 }}]

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

	{{Val list\|legend=1\| 22, ~~72f~~, 94, ~~176~~, ~~248~~, 270, ~~612~~, ~~882~~, ~~1152~~, ~~2034~~ }}		{{Val list\|legend=1\| 10c, 22f, 32cf, 54cff, 72, 166, 198, 270, 634, 904, 1174, 1880ef }}

	[[Badness]]: 0.867 × 10<sup>-3</sup>		[[Badness]]: 0.867 × 10<sup>-3</sup>

	=== 13-limit (~~ibnsinmic~~) ===		=== 13-limit (schisminic branch) ===

	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

	[[Comma list]]: ~~1716~~/~~1715~~, ~~2080~~/~~2079~~, ~~17303~~/~~17280~~		[[Comma list]]: 4096/4095, 9801/9800, 41503/41472

	[[Mapping]]: [{{val\| 2 0 1 2 6 -3 }}, {{val\| 0 1 4 0 2 1 }}, {{val\| 0 0 -5 2 -3 4 }}]		[[Mapping]]: [{{val\| 2 0 1 2 6 21 }}, {{val\| 0 1 4 0 2 -6 }}, {{val\| 0 0 -5 2 -3 3 }}]

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

	{{Val list\|legend=1\| ~~10c~~, ~~22f~~, ~~32cf~~, ~~54cff~~, ~~72, 166, 198~~, 270, ~~634~~, ~~904~~, ~~1174~~, ~~1880ef~~ }}		{{Val list\|legend=1\| 22, 72f, 94, 176, 248, 270, 612, 882, 1152, 2034 }}

	[[Badness]]: 1.56 × 10<sup>-3</sup>		[[Badness]]: 1.56 × 10<sup>-3</sup>

VIxen: /* Rishi */

2022-06-21T21:47:23Z

Rishi

← Older revision		Revision as of 21:47, 21 June 2022
Line 111:		Line 111:
	== Rishi ==		== Rishi ==

	The 7-limit comma [65 -84 10 16⟩ ~ 0.13c has the ratio of the exponents of 3 and 2 that is ~~almost~~ the ~~same -4:3 as~~ 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> ~~in 11-limit~~, which is the kalisma.		The 7-limit comma [65 -84 10 16⟩ ~ 0.13c 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, ~~considering that adding~~ the [[chalmersia]] ~~- the ratio of the kalisma to the [[10648/10647\|harmonisma]] - is an option in 13-limit~~. When 3/2 is chosen as the equave, [[Fokker block]]s of 34 pitches per equave can be used that are close to [[34edf]] and [[58edo]].		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 block]]s of 34 pitches per equave can be used that are close to [[34edf]] and [[58edo]].

	Subgroup: 2.3.5.7.11		Subgroup: 2.3.5.7.11

VIxen: /* Rishi */

2022-06-21T21:36:35Z

Rishi

← Older revision		Revision as of 21:36, 21 June 2022
Line 113:		Line 113:
	The 7-limit comma [65 -84 10 16⟩ ~ 0.13c has the ratio of the exponents of 3 and 2 that is almost the same -4:3 as 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> in 11-limit, which is the kalisma.		The 7-limit comma [65 -84 10 16⟩ ~ 0.13c has the ratio of the exponents of 3 and 2 that is almost the same -4:3 as 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> in 11-limit, 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, considering that adding the [[chalmersia]] - the ratio of the kalisma to the [[10648/10647\|harmonisma]] - is an option in 13-limit. When 3/2 is ~~used~~ as the equave, [[Fokker block]]s of 34 pitches per equave can be used that are close to [[34edf]] and [[58edo]].		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, considering that adding the [[chalmersia]] - the ratio of the kalisma to the [[10648/10647\|harmonisma]] - is an option in 13-limit. When 3/2 is chosen as the equave, [[Fokker block]]s of 34 pitches per equave can be used that are close to [[34edf]] and [[58edo]].

	Subgroup: 2.3.5.7.11		Subgroup: 2.3.5.7.11

VIxen: /* Rishi */

2022-06-21T21:35:42Z

Rishi

← Older revision		Revision as of 21:35, 21 June 2022
Line 113:		Line 113:
	The 7-limit comma [65 -84 10 16⟩ ~ 0.13c has the ratio of the exponents of 3 and 2 that is almost the same -4:3 as 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> in 11-limit, which is the kalisma.		The 7-limit comma [65 -84 10 16⟩ ~ 0.13c has the ratio of the exponents of 3 and 2 that is almost the same -4:3 as 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> in 11-limit, which is the kalisma.

	Apart from 35/11, 35/33, and the equivalents of their squares, 81/8 and 9/8, another ~~possible~~ [[equave]] is 3/2, considering that adding the [[chalmersia]] - the ratio of the kalisma to the [[10648/10647\|harmonisma]] - is an option in 13-limit. When 3/2 is used as the equave, [[Fokker block]]s of 34 pitches per equave can be used that are close to [[34edf]] and [[58edo]].		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, considering that adding the [[chalmersia]] - the ratio of the kalisma to the [[10648/10647\|harmonisma]] - is an option in 13-limit. When 3/2 is used as the equave, [[Fokker block]]s of 34 pitches per equave can be used that are close to [[34edf]] and [[58edo]].

	Subgroup: 2.3.5.7.11		Subgroup: 2.3.5.7.11

VIxen: /* Rishi */ preamble rewording

2022-06-21T21:12:25Z

Rishi: preamble rewording

← Older revision		Revision as of 21:12, 21 June 2022
Line 111:		Line 111:
	== Rishi ==		== Rishi ==

	~~In the monzo of the~~ 7-limit comma [65 -84 10 16⟩ ~ 0.13c, the ratio of the exponents of 3 and 2 is almost the same -4:3 as 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> in 11-limit, which is the kalisma.		The 7-limit comma [65 -84 10 16⟩ ~ 0.13c has the ratio of the exponents of 3 and 2 that is almost the same -4:3 as 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> in 11-limit, which is the kalisma.

	Apart from 35/11, 35/33, and the equivalents of their squares, 81/8 and 9/8, another ~~sensible~~ [[equave]] is 3/2, ~~also~~ considering that adding the [[chalmersia]] - the ratio of the kalisma to the [[10648/10647\|harmonisma]] - is an option in 13-limit. When 3/2 is used as the equave, [[Fokker block]]s of 34 pitches per equave can be used that ~~approximate~~ [[34edf]] and [[58edo]].		Apart from 35/11, 35/33, and the equivalents of their squares, 81/8 and 9/8, another possible [[equave]] is 3/2, considering that adding the [[chalmersia]] - the ratio of the kalisma to the [[10648/10647\|harmonisma]] - is an option in 13-limit. When 3/2 is used as the equave, [[Fokker block]]s of 34 pitches per equave can be used that are close to [[34edf]] and [[58edo]].

	Subgroup: 2.3.5.7.11		Subgroup: 2.3.5.7.11

VIxen: /* Rishi */ +preamble

2022-06-21T20:57:33Z

Rishi: +preamble

← Older revision		Revision as of 20:57, 21 June 2022
Line 110:		Line 110:

	== Rishi ==		== Rishi ==

			In the monzo of the 7-limit comma [65 -84 10 16⟩ ~ 0.13c, the ratio of the exponents of 3 and 2 is almost the same -4:3 as 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> in 11-limit, which is the kalisma.

			Apart from 35/11, 35/33, and the equivalents of their squares, 81/8 and 9/8, another sensible [[equave]] is 3/2, also considering that adding the [[chalmersia]] - the ratio of the kalisma to the [[10648/10647\|harmonisma]] - is an option in 13-limit. When 3/2 is used as the equave, [[Fokker block]]s of 34 pitches per equave can be used that approximate [[34edf]] and [[58edo]].

	Subgroup: 2.3.5.7.11		Subgroup: 2.3.5.7.11

← Older revision		Revision as of 18:42, 7 May 2023
Line 13:		Line 13:
	Mapping generators: ~2, ~3, ~648/245		Mapping generators: ~2, ~3, ~648/245

	{{~~Val list~~\|legend=1\| 5, 17, 22, 27, 45, 49, 50, 72, 99, 171, 441, 612, 2812, 3082, 3253, 3424, 3694, 3865, 4306, 4477d, 4918d, 5089d, 5701d }}		{{Optimal ET sequence\|legend=1\| 5, 17, 22, 27, 45, 49, 50, 72, 99, 171, 441, 612, 2812, 3082, 3253, 3424, 3694, 3865, 4306, 4477d, 4918d, 5089d, 5701d }}

	[[Badness]]: 0.0864 × 10<sup>-3</sup>		[[Badness]]: 0.0864 × 10<sup>-3</sup>
Line 31:		Line 31:
	Mapping generators: ~99/70, ~3, ~144/77		Mapping generators: ~99/70, ~3, ~144/77

	{{~~Val list~~\|legend=1\| 10c, 18bcd, 22, 50, 72, 166, 176, 198, 248, 270, 342, 612, 954, 1566, 4086dee, 5652cddeee }}		{{Optimal ET sequence\|legend=1\| 10c, 18bcd, 22, 50, 72, 166, 176, 198, 248, 270, 342, 612, 954, 1566, 4086dee, 5652cddeee }}

	[[Badness]]: 0.368 × 10<sup>-3</sup>		[[Badness]]: 0.368 × 10<sup>-3</sup>
Line 45:		Line 45:
	Mapping generators: ~99/70, ~3, ~154/65		Mapping generators: ~99/70, ~3, ~154/65

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

	[[Badness]]: 1.06 × 10<sup>-3</sup>		[[Badness]]: 1.06 × 10<sup>-3</sup>
Line 59:		Line 59:
	Mapping generators: ~99/70, ~3, ~154/65		Mapping generators: ~99/70, ~3, ~154/65

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

	[[Badness]]: 1.46 × 10<sup>-3</sup>		[[Badness]]: 1.46 × 10<sup>-3</sup>
Line 73:		Line 73:
	Mapping generators: ~99/70, ~3, ~45/19		Mapping generators: ~99/70, ~3, ~45/19

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

	[[Badness]]: 1.11 × 10<sup>-3</sup>		[[Badness]]: 1.11 × 10<sup>-3</sup>
Line 87:		Line 87:
	Mapping generators: ~99/70, ~3, ~45/19		Mapping generators: ~99/70, ~3, ~45/19

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

	[[Badness]]: 1.23 × 10<sup>-3</sup>		[[Badness]]: 1.23 × 10<sup>-3</sup>
Line 101:		Line 101:
	Mapping generators: ~99/70, ~3, ~144/77		Mapping generators: ~99/70, ~3, ~144/77

	{{~~Val list~~\|legend=1\| 10c, 22f, 32cf, 54cff, 72, 166, 198, 270, 634, 904, 1174, 1880ef }}		{{Optimal ET sequence\|legend=1\| 10c, 22f, 32cf, 54cff, 72, 166, 198, 270, 634, 904, 1174, 1880ef }}

	[[Badness]]: 0.867 × 10<sup>-3</sup>		[[Badness]]: 0.867 × 10<sup>-3</sup>
Line 115:		Line 115:
	Mapping generators: ~99/70, ~3, ~144/77		Mapping generators: ~99/70, ~3, ~144/77

	{{~~Val list~~\|legend=1\| 22, 72f, 94, 176, 248, 270, 612, 882, 1152, 2034 }}		{{Optimal ET sequence\|legend=1\| 22, 72f, 94, 176, 248, 270, 612, 882, 1152, 2034 }}

	[[Badness]]: 1.56 × 10<sup>-3</sup>		[[Badness]]: 1.56 × 10<sup>-3</sup>
Line 133:		Line 133:
	Mapping generators: ~2, ~3, ~5		Mapping generators: ~2, ~3, ~5

	{{~~Val list~~\|legend=1\| 5, 7d, 12d, 39ddd, 44cdd, 46d, 48, 53, 111, 118, 171, 742, 795, 913, 966, 1137, 1308, 2050, 2221, 2392, 3358, 3529, 7229b, 10758bbd }}		{{Optimal ET sequence\|legend=1\| 5, 7d, 12d, 39ddd, 44cdd, 46d, 48, 53, 111, 118, 171, 742, 795, 913, 966, 1137, 1308, 2050, 2221, 2392, 3358, 3529, 7229b, 10758bbd }}

	[[Badness]]: 0.333 × 10<sup>-3</sup>		[[Badness]]: 0.333 × 10<sup>-3</sup>
Line 148:		Line 148:
	Mapping generators: ~99/70, ~3, ~5		Mapping generators: ~99/70, ~3, ~5

	{{~~Val list~~\|legend=1\| 10c, 12de, 44cddeee, 46de, 48, 58, 106, 118, 224, 342, 742, 966, 1084, 1308, 1650, 2392, 2734, 5126bdb, 6776bd }}		{{Optimal ET sequence\|legend=1\| 10c, 12de, 44cddeee, 46de, 48, 58, 106, 118, 224, 342, 742, 966, 1084, 1308, 1650, 2392, 2734, 5126bdb, 6776bd }}

	[[Badness]]: 3.20 × 10<sup>-3</sup>		[[Badness]]: 3.20 × 10<sup>-3</sup>
Line 162:		Line 162:
	Mapping generators: ~99/70, ~3, ~220/117		Mapping generators: ~99/70, ~3, ~220/117

	{{~~Val list~~\|legend=1\| 12de, 46def, 58, 166, 224, 460, 684, 1426, 2334, 3076 }}		{{Optimal ET sequence\|legend=1\| 12de, 46def, 58, 166, 224, 460, 684, 1426, 2334, 3076 }}

	[[Badness]]: 1.31 × 10<sup>-3</sup>		[[Badness]]: 1.31 × 10<sup>-3</sup>
Line 182:		Line 182:
	Mapping generators: ~99/70, ~3, ~17364375/14172488		Mapping generators: ~99/70, ~3, ~17364375/14172488

	{{~~Val list~~\|legend=1\| 24, 34d, 58, 150cdee, 208ccddee, 252ccddeee, 262ccdee, 286ccdee, 310cddee, 320ccee, 344cdee, 378ce, 402de, 436, 460, 494, 954, 1448, 1506, 2460, 2954, 7414, 9874, 12828e }}		{{Optimal ET sequence\|legend=1\| 24, 34d, 58, 150cdee, 208ccddee, 252ccddeee, 262ccdee, 286ccdee, 310cddee, 320ccee, 344cdee, 378ce, 402de, 436, 460, 494, 954, 1448, 1506, 2460, 2954, 7414, 9874, 12828e }}

	[[Badness]]: 2.10 × 10<sup>-3</sup>		[[Badness]]: 2.10 × 10<sup>-3</sup>
Line 196:		Line 196:
	Mapping generators: ~99/70, ~3, ~364/297		Mapping generators: ~99/70, ~3, ~364/297

	{{~~Val list~~\|legend=1\| 24, 34d, 58, 150cdeef, 208ccddeeff, 252ccddeeefff, 262ccdeefff, 286ccdeeff, 310cddeeff, 320cceeff, 344cdeef, 378cef, 402def, 436, 460, 494, 954, 1448, 1506, 2460, 2954, 5414, 6920, 7414, 9874, 12828e }}		{{Optimal ET sequence\|legend=1\| 24, 34d, 58, 150cdeef, 208ccddeeff, 252ccddeeefff, 262ccdeefff, 286ccdeeff, 310cddeeff, 320cceeff, 344cdeef, 378cef, 402def, 436, 460, 494, 954, 1448, 1506, 2460, 2954, 5414, 6920, 7414, 9874, 12828e }}

	[[Badness]]: 0.505 × 10<sup>-3</sup>		[[Badness]]: 0.505 × 10<sup>-3</sup>
Line 212:		Line 212:
	Mapping generators: ~55/49, ~3, ~325/154		Mapping generators: ~55/49, ~3, ~325/154

	{{~~Val list~~\|legend=1\| 12f, 108cddeeefff, 120cdeeff, 126, 132de, 144, 258ef, 270, 552, 684, 954, 1236, 1506, 2190, 3696, 5886, 6156, 8346, 12042 }}		{{Optimal ET sequence\|legend=1\| 12f, 108cddeeefff, 120cdeeff, 126, 132de, 144, 258ef, 270, 552, 684, 954, 1236, 1506, 2190, 3696, 5886, 6156, 8346, 12042 }}

	[[Badness]]: 0.418 × 10<sup>-3</sup>		[[Badness]]: 0.418 × 10<sup>-3</sup>