Sensipent family: Difference between revisions

==== Subgroup extensions ====

[[#Sensible|Sensible]] is a less sparse subgroup extension present in smaller edo tunings like [[111edo]] at the cost of a little accuracy. [[#Sendai|Sendai]] is perhaps more accurate but the subgroup is very sparse, only having one prime that sensible doesn't (29). In general, one should consider combining multiple interpretations of the sensi genchain structure, but the mappings may conflict/be too high in damage, but generally, up to warts, [[65edo]] and [[111edo]] are good general tunings, while [[46edo]] is good for lower-accuracy interpretations. All support sensible by patent val, and in that regard {{nowrap| 65 + 111 = 176g }} is almost patent val.

 

=== Full 7-limit extensions ===

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

==== 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 [[#Subgroup extensions]]. It is essentially the only simple and accurate extension that preserves sensipent's tempered 5-limit structure.  

This extension can be applied to 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.  

{{Mapping|legend=0| 1 -1 -1 -2 0| 0 7 9 13 10 }}

{{Mapping|legend=0| 1 -1 -1 -2 9 | 0 7 9 13 -15 }}

{{Mapping|legend=0| 1 -1 -1 -2 9 0 | 0 7 9 13 -15 10 }}

{{Mapping|legend=0| 1 -1 -1 -2 9 0 10 | 0 7 9 13 -15 10 -16 }}

{{Mapping|legend=0| 1 -1 -1 -2 -8| 0 7 9 13 31 }}

{{Mapping|legend=0| 1 -1 -1 -2 -8 0 | 0 7 9 13 31 10 }}

{{Mapping|legend=0| 1 -1 -1 -2 -8 0 -7 | 0 7 9 13 31 10 30 }}

{{Mapping|legend=0| 1 -1 -1 -2 2| 0 7 9 13 4 }}

{{Mapping|legend=0| 1 -1 -1 -2 2 0 | 0 7 9 13 4 10 }}

{{Mapping|legend=0| 1 -1 -1 -2 -1| 0 7 9 13 12 }}

{{Mapping|legend=0| 1 -1 -1 -2 -1 0 | 0 7 9 13 12 10}}

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.)

{{Mapping|legend=0| 2 -2 -2 -4 1 | 0 7 9 13 8 }}

{{Mapping|legend=0| 2 -2 -2 -4 1 0 | 0 7 9 13 8 10 }}

{{Mapping|legend=0| 2 -2 -2 -4 1 0 3 | 0 7 9 13 8 10 7 }}

{{Mapping|legend=0| 1 -1 -1 -2 -3 | 0 14 18 26 35 }}

{{Mapping|legend=0| 1 -1 -1 -2 -3 0 | 0 14 18 26 35 20 }}

{{Mapping|legend=0| 1 -1 -1 15 9 | 0 7 9 -33 -15 }}

{{Mapping|legend=0| 1 -1 -1 15 9 17 | 0 7 9 -33 -15 -36 }}

{{Mapping|legend=0| 1 -1 -1 15 9 17 10 | 0 7 9 -33 -15 -36 -16 }}

Bison has a 1/2-octave period and the generator can be taken as [[~]][[162/125]] or its semi-octave complement, ~[[35/32]]. Its [[ploidacot]] is diploid delta-heptacot ([[pergen]] (P8/2, ccP5/7)).  

{{Mapping|legend=0| 2 -2 -2 13 18 | 0 7 9 -10 -15 }}

{{Mapping|legend=0| 2 -2 -2 13 18 17 | 0 7 9 -10 -15 -13 }}

{{Mapping|legend=0| 1 -8 -10 -28 24 | 0 14 18 45 -30 }}

{{Mapping|legend=0| 1 -8 -10 -28 24 -23 | 0 14 18 45 -30 39 }}

{{Mapping|legend=0| 1 -8 -10 6 3 | 0 21 27 -7 1}}

{{Mapping|legend=0| 1 -8 -10 6 3 11 | 0 21 27 -7 1 -16}}

{{Mapping|legend=0| 1 -8 -10 6 3 11 5 | 0 21 27 -7 1 -16 -2}}

{{Mapping|legend=0| 1 -8 -10 6 3 11 5 12 | 0 21 27 -7 1 -16 -2 -17 }}

{{Mapping|legend=0| 3 4 6 8 8 | 0 7 9 4 22 }}

{{Mapping|legend=0| 3 4 6 8 8 11 | 0 7 9 4 22 1 }}

{{Mapping|legend=0| 3 4 6 8 8 11 10 | 0 7 9 4 22 1 21 }}

{{Mapping|legend=0| 3 4 6 8 8 11 10 12 | 0 7 9 4 22 1 21 7 }}

== Subgroup extensions ==

=== Sensipent (2.3.5.31) ===

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

=== Sendai (2.3.5.23) ===

Sendai is an accurate extension of sensipent with primes [[23/16|23]] and [[29/16|29]] found by [[User:VIxen|VIxen]]. It is named after the body of acquis designed to prevent disaster risk and improve civil protection through international cooperation and after the city in Japan of the same name where it was signed (and where an international music competition is held). Note that [[84edo]] is an alternative possible [[patent val]] tuning not appearing in the optimal ET sequence. It is ideal in tuning for ambiguating the generator's 2.3.5.31 interpretation as 40/31~31/24, being between these (and hence also a good tuning of 2.3.5.31 sensipent at the cost of some 5-limit accuracy).

 

[[Category:Catalogs of rank-2 temperaments]]