Sensipent family - Revision history

Hkm: Undo revision 232169 by Hkm (talk)

2026-06-12T05:12:38Z

Undo revision 232169 by Hkm (talk)

← Older revision		Revision as of 05:12, 12 June 2026
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	Sensi tempers out [[245/243]], [[686/675]] and [[4375/4374]] in addition to [[126/125]], and can be described as the {{nowrap\| 19 & 27 }} temperament. It has as a generator half the size of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as 2.3.5.7.13 sensi (sensation) tempers out 91/90. 22/17, in the middle, is even closer to the generator. [[46edo]] is an excellent sensi tuning, and [[mos scale]]s of size 8, 11, 19 and 27 are available.		Sensi tempers out [[245/243]], [[686/675]] and [[4375/4374]] in addition to [[126/125]], and can be described as the {{nowrap\| 19 & 27 }} temperament. It has as a generator half the size of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as 2.3.5.7.13 sensi (sensation) tempers out 91/90. 22/17, in the middle, is even closer to the generator. [[46edo]] is an excellent sensi tuning, and [[mos scale]]s of size 8, 11, 19 and 27 are available.

	=== ~~Sensi~~ ===		=== Septimal sensi ===
	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

Hkm: Undo revision 232170 by Hkm (talk)

2026-06-12T05:11:52Z

Undo revision 232170 by Hkm (talk)

← Older revision		Revision as of 05:11, 12 June 2026
Line 113:		Line 113:
	Sensi tempers out [[245/243]], [[686/675]] and [[4375/4374]] in addition to [[126/125]], and can be described as the {{nowrap\| 19 & 27 }} temperament. It has as a generator half the size of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as 2.3.5.7.13 sensi (sensation) tempers out 91/90. 22/17, in the middle, is even closer to the generator. [[46edo]] is an excellent sensi tuning, and [[mos scale]]s of size 8, 11, 19 and 27 are available.		Sensi tempers out [[245/243]], [[686/675]] and [[4375/4374]] in addition to [[126/125]], and can be described as the {{nowrap\| 19 & 27 }} temperament. It has as a generator half the size of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as 2.3.5.7.13 sensi (sensation) tempers out 91/90. 22/17, in the middle, is even closer to the generator. [[46edo]] is an excellent sensi tuning, and [[mos scale]]s of size 8, 11, 19 and 27 are available.

			=== Sensi ===
	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

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	[[Badness]] (Sintel): 0.648		[[Badness]] (Sintel): 0.648

	=== 2.3.5.7.13 subgroup (sensation) ===		==== 2.3.5.7.13 subgroup (sensation) ====
	Subgroup: 2.3.5.7.13		Subgroup: 2.3.5.7.13

Hkm: /* Sensi */

2026-06-12T03:53:56Z

Sensi

← Older revision		Revision as of 03:53, 12 June 2026
Line 113:		Line 113:
	Sensi tempers out [[245/243]], [[686/675]] and [[4375/4374]] in addition to [[126/125]], and can be described as the {{nowrap\| 19 & 27 }} temperament. It has as a generator half the size of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as 2.3.5.7.13 sensi (sensation) tempers out 91/90. 22/17, in the middle, is even closer to the generator. [[46edo]] is an excellent sensi tuning, and [[mos scale]]s of size 8, 11, 19 and 27 are available.		Sensi tempers out [[245/243]], [[686/675]] and [[4375/4374]] in addition to [[126/125]], and can be described as the {{nowrap\| 19 & 27 }} temperament. It has as a generator half the size of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as 2.3.5.7.13 sensi (sensation) tempers out 91/90. 22/17, in the middle, is even closer to the generator. [[46edo]] is an excellent sensi tuning, and [[mos scale]]s of size 8, 11, 19 and 27 are available.

	~~=== Sensi ===~~
	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

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	[[Badness]] (Sintel): 0.648		[[Badness]] (Sintel): 0.648

	==== 2.3.5.7.13 subgroup (sensation) ====		=== 2.3.5.7.13 subgroup (sensation) ===
	Subgroup: 2.3.5.7.13		Subgroup: 2.3.5.7.13

Hkm: /* Septimal sensi */

2026-06-12T03:52:01Z

Septimal sensi

← Older revision		Revision as of 03:52, 12 June 2026
Line 113:		Line 113:
	Sensi tempers out [[245/243]], [[686/675]] and [[4375/4374]] in addition to [[126/125]], and can be described as the {{nowrap\| 19 & 27 }} temperament. It has as a generator half the size of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as 2.3.5.7.13 sensi (sensation) tempers out 91/90. 22/17, in the middle, is even closer to the generator. [[46edo]] is an excellent sensi tuning, and [[mos scale]]s of size 8, 11, 19 and 27 are available.		Sensi tempers out [[245/243]], [[686/675]] and [[4375/4374]] in addition to [[126/125]], and can be described as the {{nowrap\| 19 & 27 }} temperament. It has as a generator half the size of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as 2.3.5.7.13 sensi (sensation) tempers out 91/90. 22/17, in the middle, is even closer to the generator. [[46edo]] is an excellent sensi tuning, and [[mos scale]]s of size 8, 11, 19 and 27 are available.

	=== ~~Septimal sensi~~ ===		=== Sensi ===
	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

Godtone: /* Sensible */ nowrap for visual sanity

2026-05-21T12:59:27Z

Sensible: nowrap for visual sanity

← Older revision		Revision as of 12:59, 21 May 2026
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	The aforementioned extension with prime 17 through tempering out 1089/1088 implies tempering out [[256/255]] ({{s\|16}}), as {{nowrap\| 256/255 {{=}} (22/17)/(165/128) }}.		The aforementioned extension with prime 17 through tempering out 1089/1088 implies tempering out [[256/255]] ({{s\|16}}), as {{nowrap\| 256/255 {{=}} (22/17)/(165/128) }}.

	Sensible uses the accurate mapping of prime 31 in sensipent, so that the sensible generator serves many roles in subgroup harmony, but it is not ~[[9/7]] or ~[[13/10]] which would incur more damage. Its [[S-expression]]-based comma list is {([[8019/8000\|S9/S10]], [[256/255\|S16]],) [[529/528\|S23]], [[576/575\|S24]], [[961/960\|S31]], [[1024/1023\|S32]], [[1089/1088\|S33]]} implying also tempering out [[496/495]] (S31⋅S32) and [[528/527]] (S32⋅S33) as well as [[16337/16335]] (S31/S33) = ([[17/15]])/([[33/31]])<sup>2</sup>. A notable [[patent val]] tuning not appearing in the optimal ET sequence is [[157edo]].		Sensible uses the accurate mapping of prime 31 in sensipent, so that the sensible generator serves many roles in subgroup harmony, but it is not ~[[9/7]] or ~[[13/10]] which would incur more damage. Its [[S-expression]]-based comma list {{nowrap\| is {([[8019/8000\|S9/S10]], [[256/255\|S16]],) [[529/528\|S23]], [[576/575\|S24]], [[961/960\|S31]], [[1024/1023\|S32]], [[1089/1088\|S33]]} }} implying also tempering out [[496/495]] (S31⋅S32) and [[528/527]] (S32⋅S33) as well as [[16337/16335]] (S31/S33) = ([[17/15]])/([[33/31]])<sup>2</sup>. A notable [[patent val]] tuning not appearing in the optimal ET sequence is [[157edo]].

	Subgroup: 2.3.5.11		Subgroup: 2.3.5.11

Godtone: /* Sensible */ weird ordering

2026-05-21T12:57:59Z

Sensible: weird ordering

← Older revision		Revision as of 12:57, 21 May 2026
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	The aforementioned extension with prime 17 through tempering out 1089/1088 implies tempering out [[256/255]] ({{s\|16}}), as {{nowrap\| 256/255 {{=}} (22/17)/(165/128) }}.		The aforementioned extension with prime 17 through tempering out 1089/1088 implies tempering out [[256/255]] ({{s\|16}}), as {{nowrap\| 256/255 {{=}} (22/17)/(165/128) }}.

	Sensible uses the accurate mapping of prime 31 in sensipent, so that the sensible generator serves many roles in subgroup harmony, but it is not ~[[9/7]] or ~[[13/10]] which would incur more damage. Its [[S-expression]]-based comma list is {([[~~256~~/~~255~~\|~~S16~~]], [[~~8019~~/~~8000~~\|~~S9/S10~~]]), [[529/528\|S23]], [[576/575\|S24]], [[961/960\|S31]], [[1024/1023\|S32]], [[1089/1088\|S33]]} implying also tempering out [[496/495]] (S31⋅S32) and [[528/527]] (S32⋅S33) as well as [[16337/16335]] (S31/S33) = ([[17/15]])/([[33/31]])<sup>2</sup>. A notable [[patent val]] tuning not appearing in the optimal ET sequence is [[157edo]].		Sensible uses the accurate mapping of prime 31 in sensipent, so that the sensible generator serves many roles in subgroup harmony, but it is not ~[[9/7]] or ~[[13/10]] which would incur more damage. Its [[S-expression]]-based comma list is {([[8019/8000\|S9/S10]], [[256/255\|S16]],) [[529/528\|S23]], [[576/575\|S24]], [[961/960\|S31]], [[1024/1023\|S32]], [[1089/1088\|S33]]} implying also tempering out [[496/495]] (S31⋅S32) and [[528/527]] (S32⋅S33) as well as [[16337/16335]] (S31/S33) = ([[17/15]])/([[33/31]])<sup>2</sup>. A notable [[patent val]] tuning not appearing in the optimal ET sequence is [[157edo]].

	Subgroup: 2.3.5.11		Subgroup: 2.3.5.11

Overthink: /* 13-limit */ fix this

2026-01-17T05:52:24Z

13-limit: fix this

← Older revision		Revision as of 05:52, 17 January 2026
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	Comma list: 55/54, 66/65, 77/75, 143/140		Comma list: 55/54, 66/65, 77/75, 143/140

	Mapping: {{mapping\| 1 -1 -1 -2 -1 0 \| 0 7 9 13 12 11}}		Mapping: {{mapping\| 1 -1 -1 -2 -1 0 \| 0 7 9 13 12 10}}

	Optimal tunings:		Optimal tunings:

FloraC: Move a large chunk of sporadic-subgroup temps to the bottom so that we see sensi earlier

2025-12-25T10:51:33Z

Move a large chunk of sporadic-subgroup temps to the bottom so that we see sensi earlier

@@ Line 35: / Line 35: @@
 Considered below are sensi, sensei, warrior, bison, subpental, trisensory and heinz.
 === Sensible ===
 {{See also| Sensipent #Sensible interval table }}
-Sensible is an extension of sensipent with prime 11 of dubious canonicity but significantly higher accuracy than [[sensi]]. It interprets the generator as [[165/128]]~[[128/99]] by tempering out [[8019/8000]] so that [[11/8]] is reached as ([[10/9]])<sup>3</sup>. This extension is very strong as supported by the [[optimal ET sequence]] going very far and as supported by another observation that it also tempers out the [[semiporwellisma]], which is equal to [[961/960|S31]] × [[1024/1023|S32]]<sup>2</sup> (thus forming the S-expression-based comma list). The vanish of the semiporwellisma, a [[lopsided comma]], implies that this temperament equates ([[33/32]])<sup>2</sup> with [[16/15]] as well as that a natural extension to prime 31 exists through {S31, S32}, which we will see is very accurate, but this itself suggests that an extension with prime 17 is reasonably accurate through tempering out [[1089/1088|S33]] so that a slightly sharp ~[[22/17]] is equated with the generator.
+Sensible is an extension of sensipent with prime 11 of dubious canonicity but significantly higher accuracy than [[sensi]]. It interprets the generator as [[165/128]]~[[128/99]] by tempering out [[8019/8000]] so that [[11/8]] is reached as ([[10/9]])<sup>3</sup>. This extension is very strong as supported by the [[optimal ET sequence]] going very far and as supported by another observation that it also tempers out the [[semiporwellisma]], which is equal to [[S-expression|S31⋅S32<sup>2</sup>]] (thus forming the S-expression-based comma list). The vanish of the semiporwellisma, a [[lopsided comma]], implies that this temperament equates ([[33/32]])<sup>2</sup> with [[16/15]] as well as that a natural extension to prime 31 exists through {[[961/960]] ({{s|31}}), [[1024/1023]] ({{s|32}})}, which we will see is very accurate, but this itself suggests that an extension with prime 17 is reasonably accurate through tempering out [[1089/1088]] ({{s|33}}) so that a slightly sharp ~[[22/17]] is equated with the generator.
-The aforementioned extension with prime 17 through tempering out [[1089/1088|S33]] implies tempering out [[256/255]] ({{s|16}}), as {{nowrap| 256/255 {{=}} (22/17)/(165/128) }}.
+The aforementioned extension with prime 17 through tempering out 1089/1088 implies tempering out [[256/255]] ({{s|16}}), as {{nowrap| 256/255 {{=}} (22/17)/(165/128) }}.
-Sensible uses the accurate mapping of prime 31 in sensipent, so that the sensible generator serves many roles in subgroup harmony, but it is not ~[[9/7]] or ~[[13/10]] which would incur more damage. Its [[S-expression]]-based comma list is {([[256/255|S16]], [[8019/8000|S9/S10]],) [[529/528|S23]], [[576/575|S24]], [[961/960|S31]], [[1024/1023|S32]], [[1089/1088|S33]]} implying also tempering out [[496/495]] = S31 × S32 and [[528/527]] = S32 × S33 as well as [[16337/16335]] = S31/S33 = ([[17/15|34/30]])/([[33/31]])<sup>2</sup> = ([[17/15]])/([[33/31]])<sup>2</sup>. A notable [[patent val]] tuning not appearing in the optimal ET sequence is [[157edo]].
+Sensible uses the accurate mapping of prime 31 in sensipent, so that the sensible generator serves many roles in subgroup harmony, but it is not ~[[9/7]] or ~[[13/10]] which would incur more damage. Its [[S-expression]]-based comma list is {([[256/255|S16]], [[8019/8000|S9/S10]]), [[529/528|S23]], [[576/575|S24]], [[961/960|S31]], [[1024/1023|S32]], [[1089/1088|S33]]} implying also tempering out [[496/495]] (S31⋅S32) and [[528/527]] (S32⋅S33) as well as [[16337/16335]] (S31/S33) = ([[17/15]])/([[33/31]])<sup>2</sup>. A notable [[patent val]] tuning not appearing in the optimal ET sequence is [[157edo]].
 Subgroup: 2.3.5.11
@@ Line 772: / Line 734: @@
 Badness (Sintel): 1.12
 [[Category:Temperament families]]
 [[Category:Sensipent family| ]] <!-- main article -->
 [[Category:Rank 2]]

FloraC: Text replacement - "Category:Temperament families↵Category:Pages with mostly numerical content" to "Category:Temperament families"

2025-11-27T12:30:42Z

Text replacement - "Category:Temperament families↵Category:Pages with mostly numerical content" to "Category:Temperament families"

← Older revision		Revision as of 12:30, 27 November 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Sensipent family\| ]] <!-- main article -->		[[Category:Sensipent family\| ]] <!-- main article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

FloraC: /* Sensi */ - typo

2025-11-21T15:18:41Z

Sensi: - typo

← Older revision		Revision as of 15:18, 21 November 2025
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	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[WE]]: ~2 = 1199.7081{c}}, ~9/7 = 443.2748{{c}}		* [[WE]]: ~2 = 1199.7081{{c}}, ~9/7 = 443.2748{{c}}
	: [[error map]]: {{val\| -0.292 +1.261 +3.452 -5.669 }}		: [[error map]]: {{val\| -0.292 +1.261 +3.452 -5.669 }}
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~9/7 = 443.3493{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~9/7 = 443.3493{{c}}