Sensipent - Revision history

Lériendil: unnecessary number of links

2025-10-09T14:06:55Z

unnecessary number of links

← Older revision		Revision as of 14:06, 9 October 2025
Line 1:		Line 1:
	If we take a look at the 5-limit version of [[sensi]] called [[sensipent]], we find a high-accuracy extension that specifically only requires prime 31, interpreting the generator accurately as [[~]][[40/31]][[~]][[31/24]] (by splitting [[16/15]] into [[~]][[32/31]][[~]][[31/30]]). This can be left as is, or one can extend to other slightly less accurate primes; the main two strategies for doing so are called [[sendai]], focusing on accuracy and adding primes 23 and 29, and [[sensible]], which adds primes 11, 17 and 23 and focuses on adding more primes, in both cases doing so while avoiding the less accurate [[~]][[9/7]] and [[~]][[13/10]] interpretations of the sensi generator. They merge meaningfully (though ''not'' uniquely) in [[65edo]], which can be seen by that 65edo is an amazing no-7's no-13's [[31-limit]] temperament, where we've gained prime 19 through a possible extension of either sendai or sensible. Furthermore, 65edo can also be used as a tuning of 7-limit sensi, though the mapping of 13 that identifies the sensi generator as ~13/10 is the 65f val (with a flat 13, which makes better sense than the patent val).		If we take a look at the 5-limit version of [[sensi]] called [[sensipent]], we find a high-accuracy extension that specifically only requires prime 31, interpreting the generator accurately as [[~]][[40/31]]~[[31/24]] (by splitting [[16/15]] into ~[[32/31]]~[[31/30]]). This can be left as is, or one can extend to other slightly less accurate primes; the main two strategies for doing so are called [[sendai]], focusing on accuracy and adding primes 23 and 29, and [[sensible]], which adds primes 11, 17 and 23 and focuses on adding more primes, in both cases doing so while avoiding the less accurate ~[[9/7]] and ~[[13/10]] interpretations of the sensi generator. They merge meaningfully (though ''not'' uniquely) in [[65edo]], which can be seen by that 65edo is an amazing no-7's no-13's [[31-limit]] temperament, where we've gained prime 19 through a possible extension of either sendai or sensible. Furthermore, 65edo can also be used as a tuning of 7-limit sensi, though the mapping of 13 that identifies the sensi generator as ~13/10 is the 65f val (with a flat 13, which makes better sense than the patent val).

	For technical data, see:		For technical data, see:
Line 7:		Line 7:

	=== Sensipent interval table ===		=== Sensipent interval table ===
	Amazingly, in the 2.3.5.31-subgroup-limited 155-odd-limit, every interval of every number of generators up to 23 is given at least one interpretation, so that the 27-note MOS ([[19L 8s]]) is surprisingly well-supplied with harmony. The main "holes" are at 24 and 26 gens (as 25 is [[~]][[75/64]]) and that these interpretations tend to be rather complex, requiring a good tuning and a context to justify them. For these reasons, the extensions [[sensible]] and [[sendai]] are likely to be preferred in practice, whose interval tables are thus also documented here, being alternative but higher-accuracy extensions to 2.3.5.31 sensipent.		Amazingly, in the 2.3.5.31-subgroup-limited 155-odd-limit, every interval of every number of generators up to 23 is given at least one interpretation, so that the 27-note [[MOS]] ([[19L 8s]]) is surprisingly well-supplied with harmony. The main "holes" are at 24 and 26 gens (as 25 is ~[[75/64]]) and that these interpretations tend to be rather complex, requiring a good tuning and a context to justify them. For these reasons, the extensions sensible and sendai are likely to be preferred in practice, whose interval tables are thus also documented here, being alternative but higher-accuracy extensions to 2.3.5.31 sensipent.
	{\| class="wikitable"		{\| class="wikitable"
	! Gens		! Gens

Lériendil: sensi is 65p, not 65d

2025-10-09T14:05:33Z

sensi is 65p, not 65d

← Older revision		Revision as of 14:05, 9 October 2025
Line 1:		Line 1:
	If we take a look at the 5-limit version of sensi called [[sensipent]], we find a high-accuracy extension that specifically only requires prime 31, interpreting the generator accurately as [[~]][[40/31]][[~]][[31/24]] (by splitting [[16/15]] into [[~]][[32/31]][[~]][[31/30]]). This can be left as is, or one can extend to other slightly less accurate primes; the main two strategies for doing so are called [[sendai]], focusing on accuracy and adding primes 23 and 29, and [[sensible]], which adds primes 11, 17 and 23 and focuses on adding more primes, in both cases doing so while avoiding the less accurate [[~]][[9/7]] and [[~]][[13/10]] interpretations of the sensi generator. They merge meaningfully (though ''not'' uniquely) in [[65edo]], which can be seen by that [[65edo]] is an amazing no-7's no-13's [[31-limit]] temperament, where we've gained prime 19 through a possible extension of either sendai or sensible. Furthermore, [[65edo]] can also be used as a tuning of 7-limit sensi ~~through the 65d [[val]] (which corresponds to 65edo roughly supporting [[garibaldi]])~~, though ~~note~~ that ~~if one tries to use its patent but very sharp [[~~~~~]][[~~13/8\|13~~]] (~~which makes ~~the most~~ sense ~~if one accepts~~ the ~~65d~~ val) ~~then [[13/10]] is mapped distinctly and sharp of the [[~]][[9/7]] sensi generator~~.		If we take a look at the 5-limit version of [[sensi]] called [[sensipent]], we find a high-accuracy extension that specifically only requires prime 31, interpreting the generator accurately as [[~]][[40/31]][[~]][[31/24]] (by splitting [[16/15]] into [[~]][[32/31]][[~]][[31/30]]). This can be left as is, or one can extend to other slightly less accurate primes; the main two strategies for doing so are called [[sendai]], focusing on accuracy and adding primes 23 and 29, and [[sensible]], which adds primes 11, 17 and 23 and focuses on adding more primes, in both cases doing so while avoiding the less accurate [[~]][[9/7]] and [[~]][[13/10]] interpretations of the sensi generator. They merge meaningfully (though ''not'' uniquely) in [[65edo]], which can be seen by that 65edo is an amazing no-7's no-13's [[31-limit]] temperament, where we've gained prime 19 through a possible extension of either sendai or sensible. Furthermore, 65edo can also be used as a tuning of 7-limit sensi, though the mapping of 13 that identifies the sensi generator as ~13/10 is the 65f val (with a flat 13, which makes better sense than the patent val).

	For technical data, see:		For technical data, see:

Lériendil: standardized decimal places

2025-10-09T14:03:08Z

standardized decimal places

← Older revision		Revision as of 14:03, 9 October 2025
Line 114:		Line 114:
	\|-		\|-
	\|1		\|1
	\|442.~~989338~~		\|442.989
	\|[[31/24]], [[40/31]]		\|[[31/24]], [[40/31]]
	\|-		\|-
	\|2		\|2
	\|885.~~978677~~		\|885.979
	\|[[5/3]]		\|[[5/3]]
	\|-		\|-
	\|3		\|3
	\|128.~~968015~~		\|128.968
	\|[[27/25]], [[29/27]]		\|[[27/25]], [[29/27]]
	\|-		\|-
	\|4		\|4
	\|571.~~957354~~		\|571.957
	\|[[32/23]], [[25/18]]		\|[[32/23]], [[25/18]]
	\|-		\|-
	\|5		\|5
	\|1014.~~946692~~		\|1014.947
	\|[[9/5]]		\|[[9/5]]
	\|-		\|-
	\|6		\|6
	\|257.~~936031~~		\|257.936
	\|[[36/31]], [[29/25]]		\|[[36/31]], [[29/25]]
	\|-		\|-
	\|7		\|7
	\|700.~~925369~~		\|700.925
	\|[[3/2]]		\|[[3/2]]
	\|-		\|-
	\|8		\|8
	\|1143.~~914707~~		\|1143.915
	\|[[31/16]], [[29/15]], [[60/31]]		\|[[31/16]], [[29/15]], [[60/31]]
	\|-		\|-
	\|9		\|9
	\|386.~~904046~~		\|386.904
	\|[[5/4]]		\|[[5/4]]
	\|-		\|-
	\|10		\|10
	\|829.~~893384~~		\|829.893
	\|[[29/18]], [[50/31]]		\|[[29/18]], [[50/31]]
	\|-		\|-
	\|11		\|11
	\|72.~~882723~~		\|72.883
	\|[[24/23]], [[25/24]]		\|[[24/23]], [[25/24]]
	\|-		\|-
	\|12		\|12
	\|515.~~872061~~		\|515.872
	\|[[27/20]], [[31/23]]		\|[[27/20]], [[31/23]]
	\|-		\|-
	\|13		\|13
	\|958.~~8614~~		\|958.861
	\|[[40/23]], [[54/31]]		\|[[40/23]], [[54/31]]
	\|-		\|-
	\|14		\|14
	\|201.~~850738~~		\|201.851
	\|[[9/8]]		\|[[9/8]]
	\|-		\|-
	\|15		\|15
	\|644.~~840076~~		\|644.840
	\|[[29/20]]		\|[[29/20]]
	\|-		\|-
	\|16		\|16
	\|1087.~~829415~~		\|1087.829
	\|[[15/8]], [[58/31]]		\|[[15/8]], [[58/31]]
	\|-		\|-
	\|17		\|17
	\|330.~~818753~~		\|330.819
	\|[[29/24]]		\|[[29/24]]
	\|-		\|-
	\|18		\|18
	\|773.~~808092~~		\|773.808
	\|[[25/16]], [[36/23]]		\|[[25/16]], [[36/23]]
	\|}		\|}
Line 210:		Line 210:
	\|-		\|-
	\| 5		\| 5
	\| 1016.27		\| 1016.270
	\| '''[[115/64]]''', [[124/69]], [[9/5]], [[92/51]]		\| '''[[115/64]]''', [[124/69]], [[9/5]], [[92/51]]
	\|-		\|-
Line 230:		Line 230:
	\|-		\|-
	\| 10		\| 10
	\| 832.54		\| 832.540
	\| [[50/31]], [[160/99]], [[186/115]], [[55/34]], [[81/50]], [[138/85]]		\| [[50/31]], [[160/99]], [[186/115]], [[55/34]], [[81/50]], [[138/85]]
	\|-		\|-
Line 250:		Line 250:
	\|-		\|-
	\| 15		\| 15
	\| 648.81		\| 648.810
	\| [[100/69]], [[45/31]], '''[[93/64]]''', '''[[16/11]]''', [[99/68]], [[124/85]]		\| [[100/69]], [[45/31]], '''[[93/64]]''', '''[[16/11]]''', [[99/68]], [[124/85]]
	\|-		\|-
Line 270:		Line 270:
	\|-		\|-
	\| 20		\| 20
	\| 465.08		\| 465.080
	\| [[30/23]], [[81/62]], [[115/88]], [[72/55]]		\| [[30/23]], [[81/62]], [[115/88]], [[72/55]]
	\|-		\|-
Line 290:		Line 290:
	\|-		\|-
	\| 25		\| 25
	\| 281.35		\| 281.350
	\| '''[[75/64]]''', [[27/23]], [[20/17]]		\| '''[[75/64]]''', [[27/23]], [[20/17]]
	\|-		\|-

Lériendil: standardized decimal places (use CWE 2.3.5.31)

2025-10-09T14:02:15Z

standardized decimal places (use CWE 2.3.5.31)

← Older revision		Revision as of 14:02, 9 October 2025
Line 14:		Line 14:
	\|-		\|-
	\| 1		\| 1
	\| 443.05		\| 443.047
	\| [[40/31]], [[31/24]], [[162/125]]		\| [[40/31]], [[31/24]], [[162/125]]
	\|-		\|-
	\| 2		\| 2
	\| 886.1		\| 886.095
	\| [[5/3]]		\| [[5/3]]
	\|-		\|-
	\| 3		\| 3
	\| 129.15		\| 129.142
	\| [[100/93]], [[155/144]], [[27/25]]		\| [[100/93]], [[155/144]], [[27/25]]
	\|-		\|-
	\| 4		\| 4
	\| 572.2		\| 572.190
	\| [[25/18]], [[216/155]]		\| [[25/18]], [[216/155]]
	\|-		\|-
	\| 5		\| 5
	\| 1015.25		\| 1015.237
	\| [[9/5]]		\| [[9/5]]
	\|-		\|-
	\| 6		\| 6
	\| 258.3		\| 258.284
	\| [[125/108]], [[36/31]], [[93/80]]		\| [[125/108]], [[36/31]], [[93/80]]
	\|-		\|-
	\| 7		\| 7
	\| 701.35		\| 701.332
	\| '''[[3/2]]'''		\| '''[[3/2]]'''
	\|-		\|-
	\| 8		\| 8
	\| 1144.4		\| 1144.379
	\| [[60/31]], '''[[31/16]]'''		\| [[60/31]], '''[[31/16]]'''
	\|-		\|-
	\| 9		\| 9
	\| 387.45		\| 387.427
	\| '''[[5/4]]'''		\| '''[[5/4]]'''
	\|-		\|-
	\| 10		\| 10
	\| 830.5		\| 830.474
	\| [[50/31]], [[155/96]], [[81/50]]		\| [[50/31]], [[155/96]], [[81/50]]
	\|-		\|-
	\| 11		\| 11
	\| 73.55		\| 73.521
	\| [[25/24]], [[162/155]]		\| [[25/24]], [[162/155]]
	\|-		\|-
	\| 12		\| 12
	\| 516.6		\| 516.569
	\| [[125/93]], [[27/20]]		\| [[125/93]], [[27/20]]
	\|-		\|-
	\| 13		\| 13
	\| 959.65		\| 959.616
	\| [[125/72]], [[54/31]]		\| [[125/72]], [[54/31]]
	\|-		\|-
	\| 14		\| 14
	\| 202.7		\| 202.664
	\| '''[[9/8]]'''		\| '''[[9/8]]'''
	\|-		\|-
	\| 15		\| 15
	\| 645.75		\| 645.711
	\| [[45/31]], '''[[93/64]]'''		\| [[45/31]], '''[[93/64]]'''
	\|-		\|-
	\| 16		\| 16
	\| 1088.8		\| 1088.758
	\| '''[[15/8]]'''		\| '''[[15/8]]'''
	\|-		\|-
	\| 17		\| 17
	\| 331.85		\| 331.806
	\| [[75/62]], '''[[155/128]]'''		\| [[75/62]], '''[[155/128]]'''
	\|-		\|-
	\| 18		\| 18
	\| 774.9		\| 774.853
	\| '''[[25/16]]'''		\| '''[[25/16]]'''
	\|-		\|-
	\| 19		\| 19
	\| 17.95		\| 17.901
	\| [[125/124]], [[81/80]]		\| [[125/124]], [[81/80]]
	\|-		\|-
	\| 20		\| 20
	\| ~~461~~.0		\| 460.948
	\| [[125/96]], [[81/62]]		\| [[125/96]], [[81/62]]
	\|-		\|-
	\| 21		\| 21
	\| ~~904~~.05		\| 903.995
	\| '''[[27/16]]'''		\| '''[[27/16]]'''
	\|-		\|-
	\| 22		\| 22
	\| 147.1		\| 147.043
	\| [[135/124]]		\| [[135/124]]
	\|-		\|-
	\| 23		\| 23
	\| 590.15		\| 590.090
	\| '''[[45/32]]'''		\| '''[[45/32]]'''
	\|}		\|}

FloraC: - parent category

2025-04-28T14:39:51Z

- parent category

← Older revision		Revision as of 14:39, 28 April 2025
Line 300:		Line 300:

	{{todo\|inline=1\|expand}}		{{todo\|inline=1\|expand}}
	~~[[Category:Temperaments]]~~
	[[Category:Sensipent\| ]] <!-- main article -->		[[Category:Sensipent\| ]] <!-- main article -->
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	[[Category:Sensipent family]]		[[Category:Sensipent family]]

Lériendil at 23:45, 19 April 2025

2025-04-19T23:45:42Z

← Older revision		Revision as of 23:45, 19 April 2025
Line 302:		Line 302:
	[[Category:Temperaments]]		[[Category:Temperaments]]
	[[Category:Sensipent\| ]] <!-- main article -->		[[Category:Sensipent\| ]] <!-- main article -->
			[[Category:Rank-2 temperaments]]
	[[Category:Sensipent family]]		[[Category:Sensipent family]]

BudjarnLambeth: Todo

2024-12-15T01:50:24Z

Todo

← Older revision		Revision as of 01:50, 15 December 2024
Line 298:		Line 298:
	\|}		\|}

	{{~~Stub~~}}
			{{todo\|inline=1\|expand}}
	[[Category:Temperaments]]		[[Category:Temperaments]]
	[[Category:Sensipent\| ]] <!-- main article -->		[[Category:Sensipent\| ]] <!-- main article -->
	[[Category:Sensipent family]]		[[Category:Sensipent family]]

Godtone: add sensipent table

2024-10-27T21:52:11Z

add sensipent table

@@ Line 5: / Line 5: @@
 * [[Sensipent family#Sendai]] for the 2.3.5.23.29.31-subgroup version, and
 * [[Sensipent family#Sensible]] for the 2.3.5.11.17.23.31-subgroup version.
 === Sendai interval table ===

Godtone: /* Sensible interval table */ improve table

2024-10-27T21:44:35Z

Sensible interval table: improve table

Show changes

Godtone: /* Sensible interval table */ add interval table of Sensible

2024-10-27T21:01:28Z

Sensible interval table: add interval table of Sensible

@@ Line 7: / Line 7: @@
 === Sendai interval table ===
-The following is the table of the 31-odd-limited 2.3.5.23.29.31 equivalents of the intervals of the 19-note MOS ([[8L 11s]]) in the [[CTE]] tuning of [[Sensipent_family#Sendai|sendai]], the sensipent extension 19 & 65 = {[[465/464]] [[576/575]] [[621/620]] [[900/899]]}, made by [[User:VIxen|VIxen]].
+The following is the table of the 31-odd-limited 2.3.5.23.29.31 equivalents of the intervals of the 19-note MOS ([[8L 11s]]) in the [[CTE]] tuning of [[sendai]], the sensipent extension 19 & 65 = {[[465/464]] [[576/575]] [[621/620]] [[900/899]]}, made by [[User:VIxen|VIxen]].
 {| class="wikitable"
 ! Gens
@@ Line 85: / Line 85: @@
 |[[25/16]], [[36/23]]
 |}
-{{todo | Sensible interval table}}
 {{Stub}}