7th-octave temperaments - Revision history

FloraC at 16:07, 3 July 2026

2026-07-03T16:07:02Z

← Older revision		Revision as of 16:07, 3 July 2026
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	A comma that frequently appears in 7th-octave temps is [[akjaysma]], which sets [[105/64]] to be equal to 5\7.		A comma that frequently appears in 7th-octave temps is [[akjaysma]], which sets [[105/64]] to be equal to 5\7.

	Temperaments discussed elsewhere include:		Temperaments discussed elsewhere include:
			* ''[[Sevond]]'' → [[Keemic temperaments #Sevond\|Keemic temperaments]]
	* ''[[Septant]]'' → [[Schismatic family #Septant\|Schismatic family]]		* ''[[Septant]]'' → [[Schismatic family #Septant\|Schismatic family]]
	* ''[[Brahmagupta]]'' → [[Ragismic microtemperaments #Brahmagupta\|Ragismic microtemperaments]]		* ''[[Brahmagupta]]'' → [[Ragismic microtemperaments #Brahmagupta\|Ragismic microtemperaments]]
	* ''[[Absurdity]]'' → [[Porwell temperaments #Absurdity\|Porwell temperaments]]		* ''[[Absurdity]]'' → [[Porwell temperaments #Absurdity\|Porwell temperaments]]
			* ''[[Neutron]]'' → [[Mistismic temperaments #Neutron\|Mistismic temperaments]]

	== Nitrogen ==		== Nitrogen ==

2026-06-08T11:47:18Z

- jamesbond (more properly addressed in whitewood family)

@@ Line 6: / Line 6: @@
 Temperaments discussed elsewhere include:
-* ''Septant →'' [[Schismatic family#Septant|Schismatic family]]
+* ''[[Septant]]'' → [[Schismatic family #Septant|Schismatic family]]
-* ''Brahmagupta →'' [[Ragismic microtemperaments#Brahmagupta|Ragismic microtemperaments]]
+* ''[[Brahmagupta]]'' → [[Ragismic microtemperaments #Brahmagupta|Ragismic microtemperaments]]
-* ''Absurdity'' ''→'' [[Syntonic&ndash;chromatic equivalence continuum#Absurdity|Syntonic&ndash;chromatic equivalence continuum]]
+* ''[[Absurdity]]'' → [[Porwell temperaments #Absurdity|Porwell temperaments]]
 == Nitrogen ==

2026-05-30T08:59:52Z

- akjaysmic (addressed in very high accuracy temps)

← Older revision		Revision as of 08:59, 30 May 2026
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	Badness (Sintel): 0.933		Badness (Sintel): 0.933

	~~== Akjaysmic (rank-3) ==~~
	~~{{See also\| Akjaysma }}~~

	~~[[Subgroup]]: 2.3.5.7~~

	~~[[Comma list]]: {{monzo\| 47 -7 -7 -7 }}~~

	~~{{Mapping\|legend=1\| 7 0 0 47 \| 0 1 0 -1 \| 0 0 1 -1 }}~~
	~~: mapping generators: ~1157625/1048576, ~3, ~5~~

	~~[[Optimal tuning]]s:~~
	* [[WE]]: ~1157625/1048576 = 171.427811{{c}}, ~3/2 = 701.962313{{c}}, ~5/4 = 386.328628{{c}}
	~~: [[error map]]: {{val\| -0.0053 +0.0020 +0.0043 +0.0062 }}~~
	* [[CWE]]: ~1157625/1048576 = 171.428571{{c}}, ~3/2 = 701.964859{{c}}, ~5/4 = 386.330310{{c}}
	~~: error map: {{val\| 0.0000 +0.0099 +0.0166 +0.0218 }}~~

	~~{{Optimal ET sequence\|legend=1\| 56, 63, 77, 84, 140, 217, 224, 301, 441, 966, 1106, 1407, 1547, 1848, 2513, 2954, 6349, 9303, 11151, 14105, 17500, 20454 }}~~

	~~[[Badness]] (Sintel): 2.22~~

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

	~~Comma list: 184549376/184528125, 199297406/199290375~~

	~~Mapping: {{mapping\| 7 0 0 47 -168 \| 0 1 0 -1 10 \| 0 0 1 -1 5 }}~~
	~~: mapping generators: ~29160/26411, ~3, ~5~~

	~~Optimal tunings:~~
	* WE: ~29160/26411 = 171.427802{{c}}, ~3/2 = 701.964561{{c}}, ~5/4 = 386.329837{{c}}
	* CWE: ~29160/26411 = 171.428571{{c}}, ~3/2 = 701.967291{{c}}, ~5/4 = 386.331624{{c}}

	~~{{Optimal ET sequence\|legend=0\| 301, 441, 665e, 742, 1106, 1547, 1848, 3395, 4501, 5243, 6349, 17941, 24290, 30639, 45185cde, 63126bcde, 69475bccdde, 75824bccddee }}~~

	~~Badness (Sintel): 1.32~~

	== Nitrogen ==		== Nitrogen ==

2026-05-30T08:56:37Z

Switch to Sintel's badness, WE & CWE tunings

2026-05-29T11:42:43Z

- profanity (addressed in no-5)

2026-05-29T11:37:46Z

There's no 3 in the jackpot comma

2025-07-10T09:04:17Z

Profanity: Added mapping generators

2025-07-10T08:52:01Z

Jackpot: Added profanity temperament

2025-06-12T05:36:21Z

← Older revision		Revision as of 05:36, 12 June 2025
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	== Jamesbond ==		== Jamesbond ==
	This temperament uses exactly the same 5-limit as 7et, but the harmonic 7 is mapped to an independent generator. It is so named because its [[wedgie]] starts with {{multival\| 0 0 7 … }} (in fact, it is {{Multival\|legend=\| 0 0 7 0 11 16 }})		This temperament uses exactly the same 5-limit as 7et, but the harmonic 7 is mapped to an independent generator. It is so named because its "[[wedgie]]" (a kind of mathematical object representing the temperament) starts with {{multival\| 0 0 7 … }} (in fact, it is {{Multival\|legend=\| 0 0 7 0 11 16 }})

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

2025-06-12T04:10:04Z

kept the wedgie cuz its relevant, but moved it out of the temperament info section

← Older revision		Revision as of 04:10, 12 June 2025
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	== Jamesbond ==		== Jamesbond ==
	This temperament uses exactly the same 5-limit as 7et, but the harmonic 7 is mapped to an independent generator. It is so named because its [[wedgie]] starts with {{multival\| 0 0 7 … }}.		This temperament uses exactly the same 5-limit as 7et, but the harmonic 7 is mapped to an independent generator. It is so named because its [[wedgie]] starts with {{multival\| 0 0 7 … }} (in fact, it is {{Multival\|legend=\| 0 0 7 0 11 16 }})

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	{{Mapping\|legend=1\| 7 11 16 0 \| 0 0 0 1 }}		{{Mapping\|legend=1\| 7 11 16 0 \| 0 0 0 1 }}

	~~{{Multival\|legend=1\| 0 0 7 0 11 16 }}~~

	[[Optimal tuning]] ([[POTE]]): ~10/9 = 1\7, ~7/4 = 941.861		[[Optimal tuning]] ([[POTE]]): ~10/9 = 1\7, ~7/4 = 941.861