User:Francium/Temperament research - Revision history

Francium: +horwell extensions

2026-03-27T13:28:20Z

+horwell extensions

← Older revision		Revision as of 13:28, 27 March 2026
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	Badness: 2.592		Badness: 2.592

			== Horwell extensions ==
			I noticed, that 31 & 53 & 277 is the [[horwell]] temperament, I have found 11- and 13-limit extensions of it, before I even knew that this temperament already was documented in the wiki.

			=== 11-limit ===

			Subgroup: 2.3.5.7.11

			Comma list: 385/384, 3388/3375

			Mapping: <br>
			{\| class="right-all"
			\| [⟨ \|\| 1 \|\| 0 \|\| 1 \|\| 11 \|\| -5 \|\| ],
			\|-
			\| ⟨ \|\| 0 \|\| 1 \|\| 1 \|\| -6 \|\| 6 \|\| ],
			\|-
			\| ⟨ \|\| 0 \|\| 0 \|\| 2 \|\| -10 \|\| 8 \|\| ]
			\|}

			CTE generators: ~2 = 1200.000, ~3/2 = 702.121, ~5/4 = 386.112

			{{Optimal ET sequence\|legend=1\|9, 22, 31, 53, 84e, 87, 118, 258e, 376de, 547dee}}

			Badness: 0.771

			=== 13-limit ===

			Subgroup: 2.3.5.7.11.13

			Comma list: 385/384, 352/351, 1001/1000

			Mapping: <br>
			{\| class="right-all"
			\| [⟨ \|\| 1 \|\| 0 \|\| 1 \|\| 11 \|\| -5 \|\| 0 \|\| ],
			\|-
			\| ⟨ \|\| 0 \|\| 1 \|\| 1 \|\| -6 \|\| 6 \|\| 3 \|\| ],
			\|-
			\| ⟨ \|\| 0 \|\| 0 \|\| 2 \|\| -10 \|\| 8 \|\| 8 \|\| ]
			\|}

			CTE generators: ~2 = 1200.000, ~3/2 = 702.608, ~5/4 = 385.917

			{{Optimal ET sequence\|legend=1\|9f, 22, 31, 53, 84e, 87, 118, 140, 258e}}

			Badness: 0.986

Francium at 13:23, 27 March 2026

2026-03-27T13:23:25Z

← Older revision		Revision as of 13:23, 27 March 2026
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	~~== Introduction ==~~
	Since my site about the miscellaneous rank-2 temperaments gets too messy and some temperaments even are repeated, I decided to create a structured page, in which I explain the temperaments I have worked with. I am very cautious about giving names, since I'm bad at it, plus it might be an emotional subject for some people (not as controversial as naming commas, but I still get haunted by the sayings of some people who called me Xenllium 2.0).		Since my site about the miscellaneous rank-2 temperaments gets too messy and some temperaments even are repeated, I decided to create a structured page, in which I explain the temperaments I have worked with. I am very cautious about giving names, since I'm bad at it, plus it might be an emotional subject for some people (not as controversial as naming commas, but I still get haunted by the sayings of some people who called me Xenllium 2.0).

Francium at 18:35, 25 March 2026

2026-03-25T18:35:32Z

← Older revision		Revision as of 18:35, 25 March 2026
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	== 31 & 251 ==		== 31 & 251 ==
	31 & 251 is a member of the [[porwell temperaments]]. Its generator is a [[~~major third~~]]. For the 5-limit version, see [[User:Francium/Miscellaneous rank-2 temperaments#31 & 313]].		31 & 251 is a member of the [[porwell temperaments]]. Its generator is [[5/4]]. For the 5-limit version, see [[User:Francium/Miscellaneous rank-2 temperaments#31 & 313]].

	Subgroup: 2.3.5.7		Subgroup: 2.3.5.7

Francium: /* 31 & 251 */

2026-03-25T18:28:57Z

31 & 251

← Older revision		Revision as of 18:28, 25 March 2026
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	== 31 & 251 ==		== 31 & 251 ==
	31 & 251 is a member of the [[porwell temperaments]]. Its generator is a [[major third]]. For the 5-limit version, see [[User:Francium/Miscellaneous rank-2 temperaments#31 & 313]].		31 & 251 is a member of the [[porwell temperaments]]. Its generator is a [[major third]]. For the 5-limit version, see [[User:Francium/Miscellaneous rank-2 temperaments#31 & 313]].


	Subgroup: 2.3.5.7		Subgroup: 2.3.5.7

Francium: Created page with "== Introduction == Since my site about the miscellaneous rank-2 temperaments gets too messy and some temperaments even are repeated, I decided to create a structured page, in which I explain the temperaments I have worked with. I am very cautious about giving names, since I'm bad at it, plus it might be an emotional subject for some people (not as controversial as naming commas, but I still get haunted by the sayings of some people who called me Xenllium 2.0). == 31 & 2..."

2026-03-25T18:26:20Z

Created page with "== Introduction == Since my site about the miscellaneous rank-2 temperaments gets too messy and some temperaments even are repeated, I decided to create a structured page, in which I explain the temperaments I have worked with. I am very cautious about giving names, since I'm bad at it, plus it might be an emotional subject for some people (not as controversial as naming commas, but I still get haunted by the sayings of some people who called me Xenllium 2.0). == 31 & 2..."

New page

== Introduction ==
Since my site about the miscellaneous rank-2 temperaments gets too messy and some temperaments even are repeated, I decided to create a structured page, in which I explain the temperaments I have worked with. I am very cautious about giving names, since I'm bad at it, plus it might be an emotional subject for some people (not as controversial as naming commas, but I still get haunted by the sayings of some people who called me Xenllium 2.0).

== 31 & 251 ==
31 & 251 is a member of the [[porwell temperaments]]. Its generator is a [[major third]]. For the 5-limit version, see [[User:Francium/Miscellaneous rank-2 temperaments#31 & 313]].

Subgroup: 2.3.5.7

Comma list: 6144/6125, 52734375/52706752

Mapping: [{{val|1 -11 2 -3}}, {{val|0 39 1 18}}]

POTE generator: ~5/4 = 387.2386

{{Optimal ET sequence|legend=1|31, 158b, 189, 220, 251, 282, 533d, 815cdd}}

Badness: 2.708

=== 11-limit ===

Subgroup: 2.3.5.7.11

Comma list: 540/539, 5632/5625, 166698/166375

Mapping: [{{val|1 -11 2 -3 -23}}, {{val|0 39 1 18 82}}]

POTE generator: ~5/4 = 387.2309

{{Optimal ET sequence|legend=1|31, 158bee, 189ee, 220e, 251e, 282, 877cdee, 1159cddeee}}

Badness: 1.518

=== 13-limit ===

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 540/539, 4096/4095, 166698/166375

Mapping: [{{val|1 -11 2 -3 -23 35}}, {{val|0 39 1 18 82 -97}}]

POTE generator: ~5/4 = 387.2169

{{Optimal ET sequence|legend=1|31, 282f, 313, 657d}}

Badness: 2.592