Gravity family - Revision history

Godtone: /* Abergravity */ brackets

2026-05-26T19:26:25Z

Abergravity: brackets

← Older revision		Revision as of 19:26, 26 May 2026
Line 48:		Line 48:

	== Abergravity ==		== Abergravity ==
	Abergravity is the extension of 2.3.5.11-subgroup gravity with prime 7 by extending the streak [[121/120\|S11]]~[[100/99\|S10]]~[[81/80\|S9]]~[[64/63\|''S8'']], so that the generalized comma 121/120~100/99~81/80 discussed in [[#2.3.5.11 subgroup (larry)]] is equated with a shrunk [[~]][[64/63]], hence a flat-tending [[~]][[8/7]] is characteristic. It is the [[58edo\|58]] & [[65edo\|65d]] temperament, also supported by their [[val]] sum of 58 + 65d = [[123edo\|123df]]. A sharp edo tuning of prime 7 (and hence a flat tuning of 8/7) is also possible with the extreme tuning [[51edo\|51ce-edo]], in which [[1029/1024]] ([[S-expression\|S7/S8]]) vanishes. Note that while [[65edo]] doesn't appear in any of the optimal ET sequences, it is a very viable tuning if you like a sharp 7.		Abergravity is the extension of 2.3.5.11-subgroup gravity with prime 7 by extending the streak [[121/120\|S11]]~[[100/99\|S10]]~[[81/80\|S9]]~[[64/63\|''S8'']], so that the generalized comma 121/120~100/99~81/80 discussed in [[#2.3.5.11 subgroup (larry)]] is equated with a shrunk [[~]][[64/63]], hence a flat-tending [[~]][[8/7]] is characteristic. It is the [[58edo\|58]] & [[65edo\|65d]] temperament, also supported by their [[val]] sum of 58 + 65d = [[123edo\|123df]]. A sharp edo tuning of prime 7 (and hence a flat tuning of 8/7) is also possible with the extreme tuning [[51edo\|51ce-edo]], in which [[1029/1024]] ([[S-expression\|S7/S8]]) vanishes. (Note that while [[65edo]] doesn't appear in any of the optimal ET sequences, it is a very viable tuning if you like a sharp 7.)

	An obvious extension to the 13-limit is by noticing the 'squeeze' of equated commas (S8, S9, S10, S11) as suggesting [[144/143]] ({{S\|12}}) to be tempered out, which fits the 58 & 65d join, and this is intuitively confirmed by also tempering out [[847/845]] ([[S-expression\|S11/S13]]) so that the spacing is made natural, but also because it tempers out [[352/351]] and [[351/350]] in the 13-limit as a natural extension for [[176/175]] ([[S-expression\|S8/S10]]), their product. Arguably the best edo tuning for making sense of this spacing is [[58edo]], a great tuning for [[15-odd-limit]] where the distinction between [[12/11]]~[[13/12]] and [[14/13]]~[[15/14]] helps solidifying each other's identity. Alternatively, [[65edo]] gives a [[marvel]] tuning (16/15~15/14), and any tuning between them, such as [[123edo]], distinguishes 14/13, 15/14 and 16/15.		An obvious extension to the 13-limit is by noticing the 'squeeze' of equated commas (S8, S9, S10, S11) as suggesting [[144/143]] ({{S\|12}}) to be tempered out, which fits the 58 & 65d join, and this is intuitively confirmed by also tempering out [[847/845]] ([[S-expression\|S11/S13]]) so that the spacing is made natural, but also because it tempers out [[352/351]] and [[351/350]] in the 13-limit as a natural extension for [[176/175]] ([[S-expression\|S8/S10]]), their product. Arguably the best edo tuning for making sense of this spacing is [[58edo]], a great tuning for [[15-odd-limit]] where the distinction between [[12/11]]~[[13/12]] and [[14/13]]~[[15/14]] helps solidifying each other's identity. Alternatively, [[65edo]] gives a [[marvel]] tuning (16/15~15/14), and any tuning between them, such as [[123edo]], distinguishes 14/13, 15/14 and 16/15.

Godtone: /* Abergravity */ relink

2026-05-26T19:24:14Z

Abergravity: relink

← Older revision		Revision as of 19:24, 26 May 2026
Line 48:		Line 48:

	== Abergravity ==		== Abergravity ==
	Abergravity is the extension of 2.3.5.11-subgroup gravity with prime 7 by extending the streak [[121/120\|S11]]~[[100/99\|S10]]~[[81/80\|S9]]~[[64/63\|''S8'']], so that the generalized comma 121/120~100/99~81/80 discussed in [[#2.3.5.11 subgroup (larry)]] is equated with a shrunk [[~]][[64/63]], hence a flat-tending [[~]][[8/7]] is characteristic. It is the 58 & 65d temperament, also supported by their [[val]] sum of 58 + 65d = 123df. A sharp edo tuning of prime 7 (and hence a flat tuning of 8/7) is also possible with the extreme tuning [[51edo\|51ce-edo]], in which [[1029/1024]] ([[S-expression\|S7/S8]]) vanishes.		Abergravity is the extension of 2.3.5.11-subgroup gravity with prime 7 by extending the streak [[121/120\|S11]]~[[100/99\|S10]]~[[81/80\|S9]]~[[64/63\|''S8'']], so that the generalized comma 121/120~100/99~81/80 discussed in [[#2.3.5.11 subgroup (larry)]] is equated with a shrunk [[~]][[64/63]], hence a flat-tending [[~]][[8/7]] is characteristic. It is the [[58edo\|58]] & [[65edo\|65d]] temperament, also supported by their [[val]] sum of 58 + 65d = [[123edo\|123df]]. A sharp edo tuning of prime 7 (and hence a flat tuning of 8/7) is also possible with the extreme tuning [[51edo\|51ce-edo]], in which [[1029/1024]] ([[S-expression\|S7/S8]]) vanishes. Note that while [[65edo]] doesn't appear in any of the optimal ET sequences, it is a very viable tuning if you like a sharp 7.

	An obvious extension to the 13-limit is by noticing the 'squeeze' of equated commas (S8, S9, S10, S11) as suggesting [[144/143]] ({{S\|12}}) to be tempered out, which fits the 58 & 65d join, and this is intuitively confirmed by also tempering out [[847/845]] ([[S-expression\|S11/S13]]) so that the spacing is made natural, but also because it tempers out [[352/351]] and [[351/350]] in the 13-limit as a natural extension for [[176/175]] ([[S-expression\|S8/S10]]), their product. Arguably the best edo tuning for making sense of this spacing is [[58edo]], a great tuning for [[15-odd-limit]] where the distinction between [[12/11]]~[[13/12]] and [[14/13]]~[[15/14]] helps solidifying each other's identity. Alternatively, [[65edo]] gives a [[marvel]] tuning (16/15~15/14), and any tuning between them, such as [[123edo]], distinguishes 14/13, 15/14 and 16/15.		An obvious extension to the 13-limit is by noticing the 'squeeze' of equated commas (S8, S9, S10, S11) as suggesting [[144/143]] ({{S\|12}}) to be tempered out, which fits the 58 & 65d join, and this is intuitively confirmed by also tempering out [[847/845]] ([[S-expression\|S11/S13]]) so that the spacing is made natural, but also because it tempers out [[352/351]] and [[351/350]] in the 13-limit as a natural extension for [[176/175]] ([[S-expression\|S8/S10]]), their product. Arguably the best edo tuning for making sense of this spacing is [[58edo]], a great tuning for [[15-odd-limit]] where the distinction between [[12/11]]~[[13/12]] and [[14/13]]~[[15/14]] helps solidifying each other's identity. Alternatively, [[65edo]] gives a [[marvel]] tuning (16/15~15/14), and any tuning between them, such as [[123edo]], distinguishes 14/13, 15/14 and 16/15.

FloraC: /* Abergravity */ complete data & review

2026-05-26T07:32:38Z

Abergravity: complete data & review

← Older revision		Revision as of 07:32, 26 May 2026
Line 48:		Line 48:

	== Abergravity ==		== Abergravity ==
	Abergravity~~, first discovered by [[User:Godtone]] (but left unnamed) and rediscovered and named by [[User:2^67-1]] later,~~ is the extension of 2.3.5.11 gravity to prime 7 by extending the streak [[121/120\|S11]] = [[100/99\|S10]] = [[81/80\|S9]] = [[64/63\|''S8'']], so that the generalized comma 121/120~100/99~81/80 discussed in [[#2.3.5.11 subgroup (larry)]] is equated with a shrunk [[~]][[64/63]], hence a flat-tending [[~]][[8/7]] is characteristic. It is the ~~[[58edo\|~~58]] & ~~[[65edo\|~~65d]] temperament, also supported by their [[val]] sum of 58 + 65d = ~~[[123edo\|~~123df]]. (A sharp edo tuning of prime 7 (and hence a flat tuning of 8/7) is possible ~~if we use~~ the extreme tuning [[51edo\|51ce]] in which ~~we also temper out~~ [[1029/1024~~\|S7/S8~~]]~~.) An obvious extension to the 13-limit is by noticing the 'squeeze' of equated commas~~ (~~S8, S9, S10, S11) as suggesting~~ [[~~144/143~~\|S12]] to be tempered out which fits the 58 & 65d join, and this is intuitively confirmed by also implying tempering out [[847/845\|S11/S13]] so that the spacing is made natural, but also because it implies tempering out [[352/~~351]] and [[351/350]] in the 13-limit as a natural extension for [[176/175\|~~S8~~/S10~~]] = 176/175, their product. Arguably the best edo tuning for making sense of this spacing is [[58edo]], a great tuning for [[15-odd-limit]], as there we use the distinction between 14/13 and 13/12~12/11 to have 15/14~14/13 make sense, though if you want [[marvel]] (16/15~15/14) ~~you will want to use [[65edo]] instead~~.		Abergravity is the extension of 2.3.5.11-subgroup gravity with prime 7 by extending the streak [[121/120\|S11]]~[[100/99\|S10]]~[[81/80\|S9]]~[[64/63\|''S8'']], so that the generalized comma 121/120~100/99~81/80 discussed in [[#2.3.5.11 subgroup (larry)]] is equated with a shrunk [[~]][[64/63]], hence a flat-tending [[~]][[8/7]] is characteristic. It is the 58 & 65d temperament, also supported by their [[val]] sum of 58 + 65d = 123df. A sharp edo tuning of prime 7 (and hence a flat tuning of 8/7) is also possible with the extreme tuning [[51edo\|51ce-edo]], in which [[1029/1024]] ([[S-expression\|S7/S8]]) vanishes.

	Its S-expression-based comma list is {[[5120/5103\|S8/S9]], [[8019/8000\|S9/S10]], [[4000/3993\|S10/S11]], ([[847/845\|S11/S13]],) [[144/143\|S12]], [[256/255\|S16]]}.		An obvious extension to the 13-limit is by noticing the 'squeeze' of equated commas (S8, S9, S10, S11) as suggesting [[144/143]] ({{S\|12}}) to be tempered out, which fits the 58 & 65d join, and this is intuitively confirmed by also tempering out [[847/845]] ([[S-expression\|S11/S13]]) so that the spacing is made natural, but also because it tempers out [[352/351]] and [[351/350]] in the 13-limit as a natural extension for [[176/175]] ([[S-expression\|S8/S10]]), their product. Arguably the best edo tuning for making sense of this spacing is [[58edo]], a great tuning for [[15-odd-limit]] where the distinction between [[12/11]]~[[13/12]] and [[14/13]]~[[15/14]] helps solidifying each other's identity. Alternatively, [[65edo]] gives a [[marvel]] tuning (16/15~15/14), and any tuning between them, such as [[123edo]], distinguishes 14/13, 15/14 and 16/15.

			Abergravity was first discovered by [[User:Godtone\|Godtone]] but left unnamed until being rediscovered and named by [[User:2^67-1\|2^67-1]] in 2026 as a contraction of ''aberschismic'' and ''gravity''. Its S-expression-based comma list is {[[5120/5103\|S8/S9]], [[8019/8000\|S9/S10]], [[4000/3993\|S10/S11]], ([[847/845\|S11/S13]],) [[144/143\|S12]], [[256/255\|S16]]}.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
Line 56:		Line 58:
	[[Comma list]]: 5120/5103, 177147/175000		[[Comma list]]: 5120/5103, 177147/175000

	~~Mapping:~~ {{~~mapping~~\| 1 -1 -5 11 \| 0 6 17 -19 }}		{{Mapping\|legend=1\| 1 -1 -5 11 \| 0 6 17 -19 }}

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[WE]]: ~2 = 1198.~~818~~{{c}}, ~27/20 = 516.~~633~~{{c}}		* [[WE]]: ~2 = 1198.8184{{c}}, ~27/20 = 516.6336{{c}}
	: [[error map]]: {{val\| -1.182 -0.972 +2.366 +2.137 }}		: [[error map]]: {{val\| -1.182 -0.972 +2.366 +2.137 }}
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~27/20 = 517.~~134~~{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~27/20 = 517.1335{{c}}
	: error map: {{val\| 0.000 +0.846 +4.956 +5.637 }}		: error map: {{val\| 0.000 +0.846 +4.956 +5.637 }}

	[[Badness]] (Sintel): 3.~~464~~		{{Optimal ET sequence\|legend=0\| 7, 51c, 58, 123d, 181cd, 239ccdd }}

			[[Badness]] (Sintel): 3.46

	=== 11-limit ===		=== 11-limit ===
	Subgroup: 2.3.5.7.11		Subgroup: 2.3.5.7.11

	Comma list: ~~5120/5103,~~ 176/175, 243/242		Comma list: 176/175, 243/242, 2560/2541

	Mapping: {{mapping\| 1 -1 -5 11 -3 \| 0 6 17 -19 15 }}		Mapping: {{mapping\| 1 -1 -5 11 -3 \| 0 6 17 -19 15 }}

	Optimal tunings:		Optimal tunings:
	* WE: ~2 = 1198.~~737~~{{c}}, ~27/20 = 516.~~587~~{{c}}		* WE: ~2 = 1198.7370{{c}}, ~27/20 = 516.5874{{c}}
	: error map: {{val\| -1.263 -1.168 +1.987 +2.120 +1.282 }}		: error map: {{val\| -1.263 -1.168 +1.987 +2.120 +1.282 }}
	* CWE: ~2 = 1200.000{{c}}, ~27/20 = 517.~~116~~{{c}}		* CWE: ~2 = 1200.000{{c}}, ~27/20 = 517.1165{{c}}
	: error map: {{val\| 0.000 +0.744 +4.666 +5.961 +5.429 }}		: error map: {{val\| 0.000 +0.744 +4.666 +5.961 +5.429 }}

	Badness (Sintel): 1.~~555~~		{{Optimal ET sequence\|legend=0\| 7, 51ce, 58, 123d, 181cde }}

			Badness (Sintel): 1.56

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

	Comma list: ~~5120~~/~~5103~~, 176/175, 243/242, ~~144~~/~~143~~		Comma list: 144/143, 176/175, 243/242, 847/845

	Mapping: {{mapping\| 1 -1 -5 11 -3 5 \| 0 6 17 -19 15 -3 }}		Mapping: {{mapping\| 1 -1 -5 11 -3 5 \| 0 6 17 -19 15 -3 }}

	Optimal tunings:		Optimal tunings:
	* WE: ~2 = 1198.~~562~~{{c}}, ~27/20 = 516.~~528~~{{c}}		* WE: ~2 = 1198.5623{{c}}, ~27/20 = 516.5280{{c}}
	: error map: {{val\| -1.438 -1.349 +1.851 +1.327 +0.916 +2.700 }}		: error map: {{val\| -1.438 -1.349 +1.851 +1.327 +0.916 +2.700 }}
	* CWE: ~2 = 1200.000{{c}}, ~27/20 = 517.~~135~~{{c}}		* CWE: ~2 = 1200.000{{c}}, ~27/20 = 517.1346{{c}}
	: error map: {{val\| 0.000 +0.853 +4.975 +5.617 +5.701 +8.069 }}		: error map: {{val\| 0.000 +0.853 +4.975 +5.617 +5.701 +8.069 }}

	Badness (Sintel): 1.~~144~~		{{Optimal ET sequence\|legend=0\| 7, 51ce, 58, 123df, 181cdeff, 239ccddeefff }}

			Badness (Sintel): 1.14

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

	Comma list: ~~5120~~/~~5103~~, 176/175, 243/242, ~~144/143, 256~~/~~255~~		Comma list: 144/143, 170/169, 176/175, 243/242, 847/845

	Mapping: {{mapping\| 1 -1 -5 11 -3 5 14 \| 0 6 17 -19 15 -3 -23 }}		Mapping: {{mapping\| 1 -1 -5 11 -3 5 14 \| 0 6 17 -19 15 -3 -23 }}
Line 109:		Line 117:
	: error map: {{val\| 0.000 +0.640 +4.373 +6.289 +5.171 +8.175 +1.762 }}		: error map: {{val\| 0.000 +0.640 +4.373 +6.289 +5.171 +8.175 +1.762 }}

	Badness (Sintel): 1.~~248~~		{{Optimal ET sequence\|legend=0\| 7, 58, 123df }}

			Badness (Sintel): 1.25

	== Marvo ==		== Marvo ==

Godtone: /* Abergravity */ add S16 as it was missing from the comma list

2026-05-25T19:58:52Z

Abergravity: add S16 as it was missing from the comma list

← Older revision		Revision as of 19:58, 25 May 2026
Line 50:		Line 50:
	Abergravity, first discovered by [[User:Godtone]] (but left unnamed) and rediscovered and named by [[User:2^67-1]] later, is the extension of 2.3.5.11 gravity to prime 7 by extending the streak [[121/120\|S11]] = [[100/99\|S10]] = [[81/80\|S9]] = [[64/63\|''S8'']], so that the generalized comma 121/120~100/99~81/80 discussed in [[#2.3.5.11 subgroup (larry)]] is equated with a shrunk [[~]][[64/63]], hence a flat-tending [[~]][[8/7]] is characteristic. It is the [[58edo\|58]] & [[65edo\|65d]] temperament, also supported by their [[val]] sum of 58 + 65d = [[123edo\|123df]]. (A sharp edo tuning of prime 7 (and hence a flat tuning of 8/7) is possible if we use the extreme tuning [[51edo\|51ce]] in which we also temper out [[1029/1024\|S7/S8]].) An obvious extension to the 13-limit is by noticing the 'squeeze' of equated commas (S8, S9, S10, S11) as suggesting [[144/143\|S12]] to be tempered out which fits the 58 & 65d join, and this is intuitively confirmed by also implying tempering out [[847/845\|S11/S13]] so that the spacing is made natural, but also because it implies tempering out [[352/351]] and [[351/350]] in the 13-limit as a natural extension for [[176/175\|S8/S10]] = 176/175, their product. Arguably the best edo tuning for making sense of this spacing is [[58edo]], a great tuning for [[15-odd-limit]], as there we use the distinction between 14/13 and 13/12~12/11 to have 15/14~14/13 make sense, though if you want [[marvel]] (16/15~15/14) you will want to use [[65edo]] instead.		Abergravity, first discovered by [[User:Godtone]] (but left unnamed) and rediscovered and named by [[User:2^67-1]] later, is the extension of 2.3.5.11 gravity to prime 7 by extending the streak [[121/120\|S11]] = [[100/99\|S10]] = [[81/80\|S9]] = [[64/63\|''S8'']], so that the generalized comma 121/120~100/99~81/80 discussed in [[#2.3.5.11 subgroup (larry)]] is equated with a shrunk [[~]][[64/63]], hence a flat-tending [[~]][[8/7]] is characteristic. It is the [[58edo\|58]] & [[65edo\|65d]] temperament, also supported by their [[val]] sum of 58 + 65d = [[123edo\|123df]]. (A sharp edo tuning of prime 7 (and hence a flat tuning of 8/7) is possible if we use the extreme tuning [[51edo\|51ce]] in which we also temper out [[1029/1024\|S7/S8]].) An obvious extension to the 13-limit is by noticing the 'squeeze' of equated commas (S8, S9, S10, S11) as suggesting [[144/143\|S12]] to be tempered out which fits the 58 & 65d join, and this is intuitively confirmed by also implying tempering out [[847/845\|S11/S13]] so that the spacing is made natural, but also because it implies tempering out [[352/351]] and [[351/350]] in the 13-limit as a natural extension for [[176/175\|S8/S10]] = 176/175, their product. Arguably the best edo tuning for making sense of this spacing is [[58edo]], a great tuning for [[15-odd-limit]], as there we use the distinction between 14/13 and 13/12~12/11 to have 15/14~14/13 make sense, though if you want [[marvel]] (16/15~15/14) you will want to use [[65edo]] instead.

	Its S-expression-based comma list is {[[5120/5103\|S8/S9]], [[8019/8000\|S9/S10]], [[4000/3993\|S10/S11]], ([[847/845\|S11/S13]],) [[144/143\|S12]]}.		Its S-expression-based comma list is {[[5120/5103\|S8/S9]], [[8019/8000\|S9/S10]], [[4000/3993\|S10/S11]], ([[847/845\|S11/S13]],) [[144/143\|S12]], [[256/255\|S16]]}.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

Godtone: /* Abergravity */ add 17-limit extension as i realised the 13 is high enough damage in 65d that 58 & 65d still makes sense in the 17-limit

2026-05-25T19:54:40Z

Abergravity: add 17-limit extension as i realised the 13 is high enough damage in 65d that 58 & 65d still makes sense in the 17-limit

← Older revision		Revision as of 19:54, 25 May 2026
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	Badness (Sintel): 1.144		Badness (Sintel): 1.144

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

			Comma list: 5120/5103, 176/175, 243/242, 144/143, 256/255

			Mapping: {{mapping\| 1 -1 -5 11 -3 5 14 \| 0 6 17 -19 15 -3 -23 }}

			Optimal tunings:
			* WE: ~2 = 1198.758{{c}}, ~27/20 = 516.566{{c}}
			: error map: {{val\| -1.242 -1.316 +1.521 +2.755 +0.901 +3.564 -3.365 }}
			* CWE: ~2 = 1200.000{{c}}, ~27/20 = 517.099{{c}}
			: error map: {{val\| 0.000 +0.640 +4.373 +6.289 +5.171 +8.175 +1.762 }}

			Badness (Sintel): 1.248

	== Marvo ==		== Marvo ==

Godtone: /* Abergravity */ fix mistakes and add 13-limit extension

2026-05-25T19:44:02Z

Abergravity: fix mistakes and add 13-limit extension

← Older revision		Revision as of 19:44, 25 May 2026
Line 74:		Line 74:

	Optimal tunings:		Optimal tunings:
	* WE: ~2 = ~~1200~~.~~6303~~{{c}}, ~27/20 = 516.~~9658~~{{c}}		* WE: ~2 = 1198.737{{c}}, ~27/20 = 516.587{{c}}
	: error map: {{val\| -1.263 -1.168 +1.987 +2.120 +1.282 }}		: error map: {{val\| -1.263 -1.168 +1.987 +2.120 +1.282 }}
	* CWE: ~2 = 1200.~~0000~~{{c}}, ~27/20 = ~~516~~.~~7131~~{{c}}		* CWE: ~2 = 1200.000{{c}}, ~27/20 = 517.116{{c}}
	: error map: {{val\| 0.000 +0.744 +4.666 +5.961 +5.429 }}		: error map: {{val\| 0.000 +0.744 +4.666 +5.961 +5.429 }}

	Badness (Sintel): 1.555		Badness (Sintel): 1.555

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

			Comma list: 5120/5103, 176/175, 243/242, 144/143

			Mapping: {{mapping\| 1 -1 -5 11 -3 5 \| 0 6 17 -19 15 -3 }}

			Optimal tunings:
			* WE: ~2 = 1198.562{{c}}, ~27/20 = 516.528{{c}}
			: error map: {{val\| -1.438 -1.349 +1.851 +1.327 +0.916 +2.700 }}
			* CWE: ~2 = 1200.000{{c}}, ~27/20 = 517.135{{c}}
			: error map: {{val\| 0.000 +0.853 +4.975 +5.617 +5.701 +8.069 }}

			Badness (Sintel): 1.144

	== Marvo ==		== Marvo ==

Godtone: /* Overview to extensions */ no longer unnamed or undocumented

2026-05-25T19:29:13Z

Overview to extensions: no longer unnamed or undocumented

← Older revision		Revision as of 19:29, 25 May 2026
Line 26:		Line 26:

	=== Overview to extensions ===		=== Overview to extensions ===
	Full 7-limit extensions of gravity include marvo ({{nowrap\| 65d & 72 }}), zarvo ({{nowrap\| 65 & 72 }}), gravid ({{nowrap\| 58 & 65 }}), and harry ({{nowrap\| 58 & 72 }}), all considered below. A notable subgroup extension is larry.		Full 7-limit extensions of gravity include abergravity ({{nowrap\| 58 & 65d }}), marvo ({{nowrap\| 65d & 72 }}), zarvo ({{nowrap\| 65 & 72 }}), gravid ({{nowrap\| 58 & 65 }}), and harry ({{nowrap\| 58 & 72 }}), all considered below. A notable subgroup extension is larry.

	There is also an unnamed {{nowrap\| 58 & 65d }} extension by tempering out [[176/175]] to extend larry to include prime 7 and tempering out [[847/845]] to extend it to the 13-limit, with an [[S-expression]]-based comma list of {[[5120/5103\|S8/S9]], [[8019/8000\|S9/S10]], [[4000/3993\|S10/S11]], ([[847/845\|S11/S13]],) [[144/143\|S12]]}.

	=== 2.3.5.11 subgroup (larry) ===		=== 2.3.5.11 subgroup (larry) ===

Godtone: add 58 & 65d extension as it was named. fumica if you see this i hope you dont mind adding the optimal ET sequence

2026-05-25T19:27:42Z

add 58 & 65d extension as it was named. fumica if you see this i hope you dont mind adding the optimal ET sequence

← Older revision		Revision as of 19:27, 25 May 2026
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	Badness (Sintel): 0.389		Badness (Sintel): 0.389

			== Abergravity ==
			Abergravity, first discovered by [[User:Godtone]] (but left unnamed) and rediscovered and named by [[User:2^67-1]] later, is the extension of 2.3.5.11 gravity to prime 7 by extending the streak [[121/120\|S11]] = [[100/99\|S10]] = [[81/80\|S9]] = [[64/63\|''S8'']], so that the generalized comma 121/120~100/99~81/80 discussed in [[#2.3.5.11 subgroup (larry)]] is equated with a shrunk [[~]][[64/63]], hence a flat-tending [[~]][[8/7]] is characteristic. It is the [[58edo\|58]] & [[65edo\|65d]] temperament, also supported by their [[val]] sum of 58 + 65d = [[123edo\|123df]]. (A sharp edo tuning of prime 7 (and hence a flat tuning of 8/7) is possible if we use the extreme tuning [[51edo\|51ce]] in which we also temper out [[1029/1024\|S7/S8]].) An obvious extension to the 13-limit is by noticing the 'squeeze' of equated commas (S8, S9, S10, S11) as suggesting [[144/143\|S12]] to be tempered out which fits the 58 & 65d join, and this is intuitively confirmed by also implying tempering out [[847/845\|S11/S13]] so that the spacing is made natural, but also because it implies tempering out [[352/351]] and [[351/350]] in the 13-limit as a natural extension for [[176/175\|S8/S10]] = 176/175, their product. Arguably the best edo tuning for making sense of this spacing is [[58edo]], a great tuning for [[15-odd-limit]], as there we use the distinction between 14/13 and 13/12~12/11 to have 15/14~14/13 make sense, though if you want [[marvel]] (16/15~15/14) you will want to use [[65edo]] instead.

			Its S-expression-based comma list is {[[5120/5103\|S8/S9]], [[8019/8000\|S9/S10]], [[4000/3993\|S10/S11]], ([[847/845\|S11/S13]],) [[144/143\|S12]]}.

			[[Subgroup]]: 2.3.5.7

			[[Comma list]]: 5120/5103, 177147/175000

			Mapping: {{mapping\| 1 -1 -5 11 \| 0 6 17 -19 }}

			[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1198.818{{c}}, ~27/20 = 516.633{{c}}
			: [[error map]]: {{val\| -1.182 -0.972 +2.366 +2.137 }}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~27/20 = 517.134{{c}}
			: error map: {{val\| 0.000 +0.846 +4.956 +5.637 }}

			[[Badness]] (Sintel): 3.464

			=== 11-limit ===
			Subgroup: 2.3.5.7.11

			Comma list: 5120/5103, 176/175, 243/242

			Mapping: {{mapping\| 1 -1 -5 11 -3 \| 0 6 17 -19 15 }}

			Optimal tunings:
			* WE: ~2 = 1200.6303{{c}}, ~27/20 = 516.9658{{c}}
			: error map: {{val\| -1.263 -1.168 +1.987 +2.120 +1.282 }}
			* CWE: ~2 = 1200.0000{{c}}, ~27/20 = 516.7131{{c}}
			: error map: {{val\| 0.000 +0.744 +4.666 +5.961 +5.429 }}

			Badness (Sintel): 1.555

	== Marvo ==		== Marvo ==

FloraC: Naming of zarvo (reference thread #101780)

2026-03-27T14:26:07Z

Naming of zarvo (reference thread #101780)

← Older revision		Revision as of 14:26, 27 March 2026
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	== Zarvo ==		== Zarvo ==
			Zarvo was named by [[Petr Pařízek]] in 2011, for it is similar to marvo, but with prime 7 mapped to -26 steps.<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group \| ''Suggested names for the unclasified temperaments'']</ref>

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

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	Badness (Sintel): 0.645		Badness (Sintel): 0.645

			== References ==

	[[Category:Temperament families]]		[[Category:Temperament families]]
	[[Category:Gravity family\| ]] <!-- main article -->		[[Category:Gravity family\| ]] <!-- main article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

FloraC: - redundant category

2026-02-13T15:53:18Z

- redundant category

← Older revision		Revision as of 15:53, 13 February 2026
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	[[Category:Gravity family\| ]] <!-- main article -->		[[Category:Gravity family\| ]] <!-- main article -->
	~~[[Category:Gravity\| ]] <!-- key article -->~~
	[[Category:Rank 2]]		[[Category:Rank 2]]