Sensipent family: Difference between revisions

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[[Regular temperament|Temperaments]] of the '''sensipent family''' [[tempering out|temper out]] the [[sensipent comma]], 78732/78125, also known as medium semicomma.

~~Note that optimal ET sequences here often omit some [[val]] of [[84edo]].~~

== Sensipent ==

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=== Overview to extensions ===

==== Full 7-limit extensions ====

The second comma of the comma list determines which 7-limit family member we are looking at. Sensi adds [[126/125]]. Sensei adds [[225/224]]. Warrior adds [[5120/5103]]. These are all strong extensions that use the same period and generator as sensipent.

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Temperaments discussed elsewhere include:

* ''[[Catafourth]]'' → [[Breedsmic temperaments #Catafourth|Breedsmic temperaments]] (+2401/2400)

* ''[[Browser]]'' → [[~~Mirkwai~~ clan #Browser|~~Mirkwai~~ clan]] (+16875/16807)

* ''[[Browser]]'' → [[Canopic clan #Browser|Canopic clan]] (+16875/16807)

Considered below are sensi, sensei, warrior, bison, subpental, trisensory and heinz.

==== Subgroup extensions ====

The generator of sensipent can be accurately interpreted as [[31/24]][[~]][[40/31]], tempering out [[961/960]] ({{S|31}}), so that the [[31-limit]] quartertones [[32/31]] and [[31/30]] are equated, as sensipent splits [[16/15]] into two equal parts. This gives the 2.3.5.31-subgroup version of sensipent discussed in [[#Other subgroup extensions]]. It is essentially the only simple and accurate extension that preserves sensipent's tempered 5-limit structure.

This extension can be laid onto many other extensions. Note that optimal ET sequences here often omit some [[val]] of [[84edo]], which is a good tuning for interpreting the generator as 31/24~40/31 such that 24:31:40 is a chord of [0, 1, 2] generator steps, by preferring a flatter fifth as in the 2.3.5.31-subgroup extension, as the 5-limit generator is both complex and relatively high in damage for its complexity.

[[#Sensible|Sensible]] is a less sparse subgroup extension present in smaller edo tunings like [[111edo]] at the cost of a little accuracy, considered immediately below.

=== Sensible ===

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=== Bisensi ===

Bisensi has a 1/2-octave period and the generator can be taken as ~9/7 or its semi-octave complement, ~11/10. Its ploidacot is diploid delta-heptacot (pergen (P8/2, ccP5/7)).

Bisensi has a 1/2-octave period and the generator can be taken as ~9/7 or its semi-octave complement, ~11/10. Its ploidacot is diploid delta-heptacot (pergen (P8/2, ccP5/7)). (As 84edo is even, one might be interested to know its [[17-limit]] val is 84def, corresponding to a strong flat tendency.)

Subgroup: 2.3.5.7.11

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== Other subgroup extensions ==

=== Sensipent (2.3.5.31 subgroup) ===

The generator of sensipent can be accurately interpreted as [[31/24]]~[[40/31]], tempering out [[961/960]] ({{s|31}}), so that the [[31-limit]] quarter-tones [[32/31]] and [[31/30]] are equated, as sensipent splits [[16/15]] into two equal parts. This is essentially the only simple and accurate extension that preserves sensipent's tempered [[5-limit]] structure.

~~For a less sparse subgroup present in smaller edo tunings like [[111edo]] at the cost of a little accuracy, see the extension to the 2.3.5.11.17.31 subgroup [[#Sensible]].~~

Subgroup: 2.3.5.31

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 [[Regular temperament|Temperaments]] of the '''sensipent family''' [[tempering out|temper out]] the [[sensipent comma]], 78732/78125, also known as medium semicomma.
-Note that optimal ET sequences here often omit some [[val]] of [[84edo]].
 == Sensipent ==
@@ Line 28: / Line 26: @@
 === Overview to extensions ===
+==== Full 7-limit extensions ====
 The second comma of the comma list determines which 7-limit family member we are looking at. Sensi adds [[126/125]]. Sensei adds [[225/224]]. Warrior adds [[5120/5103]]. These are all strong extensions that use the same period and generator as sensipent.
@@ Line 34: / Line 33: @@
 Temperaments discussed elsewhere include:
 * ''[[Catafourth]]'' → [[Breedsmic temperaments #Catafourth|Breedsmic temperaments]] (+2401/2400)
-* ''[[Browser]]'' → [[Mirkwai clan #Browser|Mirkwai clan]] (+16875/16807)
+* ''[[Browser]]'' → [[Canopic clan #Browser|Canopic clan]] (+16875/16807)
 Considered below are sensi, sensei, warrior, bison, subpental, trisensory and heinz.
+==== Subgroup extensions ====
+The generator of sensipent can be accurately interpreted as [[31/24]][[~]][[40/31]], tempering out [[961/960]] ({{S|31}}), so that the [[31-limit]] quartertones [[32/31]] and [[31/30]] are equated, as sensipent splits [[16/15]] into two equal parts. This gives the 2.3.5.31-subgroup version of sensipent discussed in [[#Other subgroup extensions]]. It is essentially the only simple and accurate extension that preserves sensipent's tempered 5-limit structure.
+This extension can be laid onto many other extensions. Note that optimal ET sequences here often omit some [[val]] of [[84edo]], which is a good tuning for interpreting the generator as 31/24~40/31 such that 24:31:40 is a chord of [0, 1, 2] generator steps, by preferring a flatter fifth as in the 2.3.5.31-subgroup extension, as the 5-limit generator is both complex and relatively high in damage for its complexity.
+[[#Sensible|Sensible]] is a less sparse subgroup extension present in smaller edo tunings like [[111edo]] at the cost of a little accuracy, considered immediately below.
 === Sensible ===
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 === Bisensi ===
-Bisensi has a 1/2-octave period and the generator can be taken as ~9/7 or its semi-octave complement, ~11/10. Its ploidacot is diploid delta-heptacot (pergen (P8/2, ccP5/7)).
+Bisensi has a 1/2-octave period and the generator can be taken as ~9/7 or its semi-octave complement, ~11/10. Its ploidacot is diploid delta-heptacot (pergen (P8/2, ccP5/7)). (As 84edo is even, one might be interested to know its [[17-limit]] val is 84def, corresponding to a strong flat tendency.)
 Subgroup: 2.3.5.7.11
@@ Line 739: / Line 745: @@
 == Other subgroup extensions ==
 === Sensipent (2.3.5.31 subgroup) ===
-The generator of sensipent can be accurately interpreted as [[31/24]]~[[40/31]], tempering out [[961/960]] ({{s|31}}), so that the [[31-limit]] quarter-tones [[32/31]] and [[31/30]] are equated, as sensipent splits [[16/15]] into two equal parts. This is essentially the only simple and accurate extension that preserves sensipent's tempered [[5-limit]] structure.
-For a less sparse subgroup present in smaller edo tunings like [[111edo]] at the cost of a little accuracy, see the extension to the 2.3.5.11.17.31 subgroup [[#Sensible]].
 Subgroup: 2.3.5.31