User:Dummy index/Semitritave - Revision history

Dummy index: is-a

2023-08-05T05:39:33Z

is-a

← Older revision		Revision as of 05:39, 5 August 2023
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	==False octave==		==False octave==
	~~Semitritave~~ is available for [[Ed5/3 through ed7/3\|false octave]]. Differ from [[acoustic phi]] or [[ed7/4]], two equave makes 3:1, well-known equave.		Assuming the semitritave is available for [[Ed5/3 through ed7/3\|false octave]]. Differ from [[acoustic phi]] or [[ed7/4]], two equave makes 3:1, well-known equave.

	==2*N-edt==		==2*N-edt==
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	\| 24edo		\| 24edo
	\| hypopent		\| hypopent
	\| "Fifth" is 11\19edst ≈ 11/8. Can convert easily from 19edo. "minor tenth" (e.g. (19+3+2)\19edst) ~ 2/1.		\| "Fifth" is 11\19edst ≈ 11/8. Can convert easily from 19edo. "minor tenth" (e.g. (19+3+2)\19edst) ~ 2/1. "Major triad" ≈ 16:19:22.
	\|-		\|-
	\| 23		\| 23
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	==Rank-2 temperaments==		==Rank-2 temperaments==

	===Tribilo as micromeantone===		===Tribilo as a micromeantone===
	{{See also\|Tribilo family}}		{{See also\|Tribilo family}}

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	http://x31eq.com/cgi-bin/rt.cgi?limit=3_2_11_13%2F5_17&ets=b38_b62&tuning=po		http://x31eq.com/cgi-bin/rt.cgi?limit=3_2_11_13%2F5_17&ets=b38_b62&tuning=po
	===b24 & b66 as microaugust===		===b24 & b66 as a microaugust===

	Subgroup: 3.5/2.11/8		Subgroup: 3.5/2.11/8
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	http://x31eq.com/cgi-bin/rt.cgi?limit=3_5%2F2_16%2F7_11%2F8_13%2F2&ets=b24_b66p&tuning=po		http://x31eq.com/cgi-bin/rt.cgi?limit=3_5%2F2_16%2F7_11%2F8_13%2F2&ets=b24_b66p&tuning=po
	===b32 & b56 as microdiminished===		===b32 & b56 as a microdiminished===

	Subgroup: 3.16.5.11		Subgroup: 3.16.5.11
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	http://x31eq.com/cgi-bin/rt.cgi?limit=3_2_7&ets=b8_b84&tuning=po		http://x31eq.com/cgi-bin/rt.cgi?limit=3_2_7&ets=b8_b84&tuning=po
	===b38 & b54 as microsensi===		===b38 & b54 as a microsensi===

	Subgroup: 3.2.7.11/5		Subgroup: 3.2.7.11/5
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	http://x31eq.com/cgi-bin/rt.cgi?limit=3_2_7_11%2F5_13%2F5&ets=b38_b54&tuning=po		http://x31eq.com/cgi-bin/rt.cgi?limit=3_2_7_11%2F5_13%2F5&ets=b38_b54&tuning=po
	===b26 & b88 as microoneirotonic===		===b26 & b88 as a microoneirotonic===

	Subgroup: 3.5.7.26		Subgroup: 3.5.7.26

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

2023-05-07T17:57:40Z

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

← Older revision		Revision as of 17:57, 7 May 2023
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	[[POTE generator]]: ~121/96 = 400.0108 (or ~11/8 = 550.9667)		[[POTE generator]]: ~121/96 = 400.0108 (or ~11/8 = 550.9667)

	Optimal ~~GPV~~ sequence: b14, b24, b38, b138, b176, b214, b252		[[Optimal ET sequence]]: b14, b24, b38, b138, b176, b214, b252

	[[Badness]]: 2.44 × 10<sup>-3</sup>		[[Badness]]: 2.44 × 10<sup>-3</sup>
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	[[Tp tuning\|POL2 generator]]: ~288/275 = 82.9018 (or ~11/8 = 551.083)		[[Tp tuning\|POL2 generator]]: ~288/275 = 82.9018 (or ~11/8 = 551.083)

	Optimal ~~GPV~~ sequence: b24, b66, b90, b114, b138, b252		[[Optimal ET sequence]]: b24, b66, b90, b114, b138, b252

	[[Tp tuning #T2 tuning\|RMS error]]:		[[Tp tuning #T2 tuning\|RMS error]]:
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	[[Tp tuning\|POL2 generator]]: ~896/729 = 351.4241 (or ~99/70 = 599.5534)		[[Tp tuning\|POL2 generator]]: ~896/729 = 351.4241 (or ~99/70 = 599.5534)

	Optimal ~~GPV~~ sequence: b38, b54, b92		[[Optimal ET sequence]]: b38, b54, b92

	[[Tp tuning #T2 tuning\|RMS error]]:		[[Tp tuning #T2 tuning\|RMS error]]:
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	[[POTE generator]]: ~26/21 = 367.0018 (or ~7/5 = 583.9757)		[[POTE generator]]: ~26/21 = 367.0018 (or ~7/5 = 583.9757)

	Optimal ~~GPV~~ sequence: b10, b16, b26, b62, b88, b114		[[Optimal ET sequence]]: b10, b16, b26, b62, b88, b114

	[[Badness]]: 1.43 × 10<sup>-3</sup>		[[Badness]]: 1.43 × 10<sup>-3</sup>

Dummy index: /* Rank-2 temperaments */

2023-05-07T10:26:59Z

Rank-2 temperaments

← Older revision		Revision as of 10:26, 7 May 2023
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	http://x31eq.com/cgi-bin/rt.cgi?limit=3_16_5_11&ets=b32_b56&tuning=po		http://x31eq.com/cgi-bin/rt.cgi?limit=3_16_5_11&ets=b32_b56&tuning=po
	===Vulture (no-~~five~~ Buzzard)===		===subgroup 3.7.11 seems to be a lot===
			===Vulture (no-fives Buzzard)===

	Subgroup: 3.2.7		Subgroup: 3.2.7

Dummy index: /* Rank-2 temperaments */

2023-05-06T05:26:28Z

Rank-2 temperaments

← Older revision		Revision as of 05:26, 6 May 2023
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	http://x31eq.com/cgi-bin/rt.cgi?limit=3_16_5_11&ets=b32_b56&tuning=po		http://x31eq.com/cgi-bin/rt.cgi?limit=3_16_5_11&ets=b32_b56&tuning=po
			===Vulture (no-five Buzzard)===

			Subgroup: 3.2.7

			http://x31eq.com/cgi-bin/rt.cgi?limit=3_2_7&ets=b8_b84&tuning=po
	===b38 & b54 as microsensi===		===b38 & b54 as microsensi===

Dummy index at 13:54, 21 November 2022

2022-11-21T13:54:39Z

← Older revision		Revision as of 13:54, 21 November 2022
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	http://x31eq.com/cgi-bin/rt.cgi?limit=3_5%2F2_16%2F7_11%2F8_13%2F2&ets=b24_b66p&tuning=po		http://x31eq.com/cgi-bin/rt.cgi?limit=3_5%2F2_16%2F7_11%2F8_13%2F2&ets=b24_b66p&tuning=po
	===~~b24~~ & ~~b32~~ as microdiminished===		===b32 & b56 as microdiminished===

	Subgroup: 3.5.11		Subgroup: 3.16.5.11

	http://x31eq.com/cgi-bin/rt.cgi?limit=~~3_5_11~~&ets=~~b32_b24~~&tuning=po		http://x31eq.com/cgi-bin/rt.cgi?limit=3_16_5_11&ets=b32_b56&tuning=po
	===b38 & b54 as microsensi===		===b38 & b54 as microsensi===

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	\|(2/1)		\|(2/1)
	\|-		\|-
	\|~~8ve~~		\|octave
	\|1344.885		\|1344.885
	\|3L + 4s		\|3L + 4s
	\|C		\|C
	\|24/11		\|24/11
			\|-
			\|neutral 9th
			\|1508.047
			\|3L + 5s
			\|vD
			\|12/5,19/8
			\|-
			\|major 9th
			\|1575.631
			\|4L + 4s
			\|D
			\|(5/2)
			\|-
			\|neutral 10th
			\|1738.793
			\|4L + 5s
			\|vE
			\|30/11,19/7
			\|-
			\|perfect 11th
			\|1901.955
			\|4L + 6s
			\|F
			\|3/1
	\|}		\|}
	<references/>		<references/>

Dummy index: /* Rank-2 temperaments */

2022-11-20T07:38:58Z

Rank-2 temperaments

← Older revision		Revision as of 07:38, 20 November 2022
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	[[POTE generator]]: ~121/96 = 400.0108 (or ~11/8 = 550.9667)		[[POTE generator]]: ~121/96 = 400.0108 (or ~11/8 = 550.9667)

	Optimal GPV sequence: b14, b24, b38, b138, b176, b214, ~~b242~~		Optimal GPV sequence: b14, b24, b38, b138, b176, b214, b252

	[[Badness]]: 2.44 × 10<sup>-3</sup>		[[Badness]]: 2.44 × 10<sup>-3</sup>

Dummy index: /* 3L 4s (1345¢ equivalent) */

2022-11-17T14:57:52Z

3L 4s (1345¢ equivalent)

← Older revision		Revision as of 14:57, 17 November 2022
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	\|0L + 1s		\|0L + 1s
	\|vD		\|vD
	\|11/10, 10/9		\|11/10, 10/9, 21/19
	\|-		\|-
	\|major 2nd		\|major 2nd
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	\|3L + 4s		\|3L + 4s
	\|C		\|C
	\|24/11~~, 13/6~~		\|24/11
	\|}		\|}
	<references/>		<references/>

Dummy index: /* 3L 4s (1345¢ equivalent) */

2022-11-17T14:32:59Z

3L 4s (1345¢ equivalent)

← Older revision		Revision as of 14:32, 17 November 2022
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	!In L's and s's		!In L's and s's
	!Notation		!Notation
	!Approximate ratios		!Approximate ratios<ref>based on treating as a 3.8.10.7.11.19 subgroup; other approaches are possible.</ref>
	\|-		\|-
	\|unison		\|unison
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	\|3L + 3s		\|3L + 3s
	\|vB		\|vB
	\|		\|(2/1)
	\|-		\|-
	\|8ve		\|8ve
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	\|24/11, 13/6		\|24/11, 13/6
	\|}		\|}
	2s ≈ 326.324¢ ≈ 6/5		<references/>

			2s ≈ 326.324¢ ≈ (6/5),11/9

	==Memo==		==Memo==

Dummy index: /* Another periods */

2022-11-17T14:16:58Z

Another periods

@@ Line 239: / Line 239: @@
 ¢ is near 8/7, 163¢ is near 11/10.<br />
 http://x31eq.com/cgi-bin/rt.cgi?limit=3_8_10_7_11_19&ets=b10_b34&tuning=po
 ==Memo==

Dummy index at 14:30, 14 November 2022

2022-11-14T14:30:39Z

← Older revision		Revision as of 14:30, 14 November 2022
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	\| 24edo		\| 24edo
	\| hypopent		\| hypopent
	\| "Fifth" is 11\19edst ≈ 11/8. Can convert easily from 19edo.		\| "Fifth" is 11\19edst ≈ 11/8. Can convert easily from 19edo. "minor tenth" (e.g. (19+3+2)\19edst) ~ 2/1.
	\|-		\|-
	\| 23		\| 23
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	http://x31eq.com/cgi-bin/rt.cgi?limit=3_5%2F2_16%2F7_11%2F8_13%2F2&ets=b24_b66p&tuning=po		http://x31eq.com/cgi-bin/rt.cgi?limit=3_5%2F2_16%2F7_11%2F8_13%2F2&ets=b24_b66p&tuning=po
			===b24 & b32 as microdiminished===

			Subgroup: 3.5.11

			http://x31eq.com/cgi-bin/rt.cgi?limit=3_5_11&ets=b32_b24&tuning=po
	===b38 & b54 as microsensi===		===b38 & b54 as microsensi===

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	Related temperament: [[mirkat]]		Related temperament: [[mirkat]]

	==~~Relationship~~==		==Another periods==
	~~On this micromeantone, "minor tenth"~~ (e.g. "(19+3+2)~~\19"~~) ~~~ 2~~/~~1. Re-breaking by real octave~~, ~~results in [[6L 3s]] i~~. e. ~~LsLLLsLLs, tribilo or triforce~~.
			<math>\sqrt{3}^{\sqrt{2}} \approx \varphi^{\varphi}</math> (off by 3 cents). However, this does not mean that acoustic phi and semitritave should be used together.

			Divide or reverse divide by silver [[Metallic MOS]]:<br />
			<math>\sqrt{3}^{\sqrt{2} - 1}</math> ≈ 394¢<br />
			951¢ => 2 * 394¢ + 1 * 163¢ => 5 * 163¢ + 2 * 68¢<br />
			1 * 951¢ + 1 * 394¢ => 3 * 394¢ + 1 * 163¢ => 3 * 231¢ + 4 * 163¢ (3L 4s (1345¢ equivalent))<br />
			2 * 951¢ + 1 * 394¢ => 5 * 394¢ + 2 * 163¢ (5L 2s (2296¢ equivalent))<br />
			231¢ is near 8/7, 163¢ is near 11/10.<br />
			http://x31eq.com/cgi-bin/rt.cgi?limit=3_8_10_7_11_19&ets=b10_b34&tuning=po

	==Memo==		==Memo==
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	[http://x31eq.com/cgi-bin/pregular.cgi?limit=3.2.5.13.17&error=5.0 3.2.5.13.17 => 54edt],		[http://x31eq.com/cgi-bin/pregular.cgi?limit=3.2.5.13.17&error=5.0 3.2.5.13.17 => 54edt],
	[http://x31eq.com/cgi-bin/pregular.cgi?limit=3.10.14.17.11%2F8&error=5.0 3.10.14.17.11/8 => 62edt]		[http://x31eq.com/cgi-bin/pregular.cgi?limit=3.10.14.17.11%2F8&error=5.0 3.10.14.17.11/8 => 62edt]

	~~<math>\sqrt{3}^{\sqrt{2}} \approx \varphi^{\varphi}</math> (off by 3 cents)<br />~~
	~~Hints for silver [[Metallic MOS]]<br />~~
	~~<math>\sqrt{3}^{\sqrt{2} - 1}</math> ≈ 394¢<br />~~
	~~1 * 951¢ + 1 * 394¢ => 3 * 394¢ + 1 * 163¢ => 3 * 231¢ + 4 * 163¢ (3L 4s)<br />~~
	~~2 * 951¢ + 1 * 394¢ => 5 * 394¢ + 2 * 163¢ (5L 2s)<br />~~