Sensamagic clan: Difference between revisions

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== BPS ==

The ''BPS'', for ''Bohlen–Pierce–Stearns'', is the 3.5.7 subgroup temperament tempering out 245/243.

The ''BPS'', for ''Bohlen–Pierce–Stearns'', is the 3.5.7 subgroup temperament tempering out 245/243. This subgroup temperament was formerly called as ''lambda temperament'', which was named after [[4L 5s (tritave-equivalent)|lambda scale]].

Subgroup: 3.5.7

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Sval mapping generators: ~3, ~9/7

~~[[Gencom]] [[mapping]]: [{{val| 0 1 1 2 }}, {{val| 0 0 -2 1 }}]~~

[[POTE generator]]: ~9/7 = 440.4881

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[[Bohpier]] is named after its [[Relationship between Bohlen-Pierce and octave-ful temperaments|interesting relationship with the non-octave Bohlen-Pierce equal temperament]].

'''[[Bohpier]]''' is named after its [[Relationship between Bohlen-Pierce and octave-ful temperaments|interesting relationship with the non-octave Bohlen-Pierce equal temperament]].

Subgroup: 2.3.5

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Badness: 0.033949

=== 13-limit ===

==== 13-limit ====

Subgroup: 2.3.5.7.11.13

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* [http://micro.soonlabel.com/bophier/bophier-1.mp3 bophier-1.mp3]

* [http://micro.soonlabel.com/bophier/bophier-12equal-six-octaves.mp3 bophier-12equal-six-octaves.mp3]

=== Triboh ===

'''Triboh''' is named after "[[39edt|Triple Bohlen-Pierce scale]]", which divides each step of the [[13edt|equal-tempered]] [[Bohlen-Pierce]] scale into three equal parts.

Subgroup: 2.3.5.7.11

Comma list: 245/243, 1331/1323, 3125/3087

Mapping: [{{val| 1 0 0 0 0 }}, {{val| 0 39 57 69 85 }}]

POTE generator: ~77/75 = 48.828

Vals: {{Val list| 49, 123ce, 172 }}

Badness: 0.162592

==== 13-limit ====

Subgroup: 2.3.5.7.11.13

Comma list: 245/243, 275/273, 847/845, 1331/1323

Mapping: [{{val| 1 0 0 0 0 0 }}, {{val| 0 39 57 69 85 91 }}]

POTE generator: ~77/75 = 48.822

Vals: {{Val list| 49f, 123ce, 172f, 295ce, 467bccef }}

Badness: 0.082158

== Escaped ==

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This temperament is also called as "sensa" because it tempers out 245/243, 352/351, and 385/384 as a sensamagic temperament. ''Not to be confused with 19e&27 temperament (sensi extension).''

Subgroup: 2.3.5.7

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== Pycnic ==

The fifth of pycnic in size is a meantone fifth, but four of them are not used to reach 5. This has the effect of making the Pythagorean major third, nominally 81/64, very close to 5/4 in tuning, being a cent sharp of it in the POTE tuning for instance. Pycnic has MOS of size 9, 11, 13, 15, 17... which contain these alternative thirds, leading to two kinds of major triads, an official one and a nominally Pythagorean one which is actually in better tune.

Subgroup: 2.3.5.7

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== Magus ==

Magus temperament tempers out 50331648/48828125 (salegu) in the 5-limit. This temperament can be described as 46&49 temperament, which tempers out the sensamagic and 28672/28125 (sazoquingu). Alternative extension [[Starling temperaments #Amigo|amigo]] (43&46) tempers out the same 5-limit comma as the magus, but with the [[126/125|starling comma]] (126/125) rather than the sensamagic tempered out.

Subgroup: 2.3.5

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 == BPS ==
-The ''BPS'', for ''Bohlen–Pierce–Stearns'', is the 3.5.7 subgroup temperament tempering out 245/243.
+The ''BPS'', for ''Bohlen–Pierce–Stearns'', is the 3.5.7 subgroup temperament tempering out 245/243. This subgroup temperament was formerly called as ''lambda temperament'', which was named after [[4L 5s (tritave-equivalent)|lambda scale]].
 Subgroup: 3.5.7
@@ Line 29: / Line 29: @@
 Sval mapping generators: ~3, ~9/7
-[[Gencom]] [[mapping]]: [{{val| 0 1 1 2 }}, {{val| 0 0 -2 1 }}]
 [[POTE generator]]: ~9/7 = 440.4881
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 {{main|Bohpier}}
-[[Bohpier]] is named after its [[Relationship between Bohlen-Pierce and octave-ful temperaments|interesting relationship with the non-octave Bohlen-Pierce equal temperament]].
+'''[[Bohpier]]''' is named after its [[Relationship between Bohlen-Pierce and octave-ful temperaments|interesting relationship with the non-octave Bohlen-Pierce equal temperament]].
 Subgroup: 2.3.5
@@ Line 279: / Line 276: @@
 Badness: 0.033949
-=== 13-limit ===
+==== 13-limit ====
 Subgroup: 2.3.5.7.11.13
@@ Line 307: / Line 304: @@
 * [http://micro.soonlabel.com/bophier/bophier-1.mp3 bophier&#45;1.mp3]
 * [http://micro.soonlabel.com/bophier/bophier-12equal-six-octaves.mp3 bophier&#45;12equal&#45;six&#45;octaves.mp3]
+=== Triboh ===
+'''Triboh''' is named after "[[39edt|Triple Bohlen-Pierce scale]]", which divides each step of the [[13edt|equal-tempered]] [[Bohlen-Pierce]] scale into three equal parts.
+Subgroup: 2.3.5.7.11
+Comma list: 245/243, 1331/1323, 3125/3087
+Mapping: [{{val| 1 0 0 0 0 }}, {{val| 0 39 57 69 85 }}]
+POTE generator: ~77/75 = 48.828
+Vals: {{Val list| 49, 123ce, 172 }}
+Badness: 0.162592
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 245/243, 275/273, 847/845, 1331/1323
+Mapping: [{{val| 1 0 0 0 0 0 }}, {{val| 0 39 57 69 85 91 }}]
+POTE generator: ~77/75 = 48.822
+Vals: {{Val list| 49f, 123ce, 172f, 295ce, 467bccef }}
+Badness: 0.082158
 == Escaped ==
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 This temperament is also called as "sensa" because it tempers out 245/243, 352/351, and 385/384 as a sensamagic temperament. ''Not to be confused with 19e&amp;27 temperament (sensi extension).''
 Subgroup: 2.3.5.7
@@ Line 399: / Line 423: @@
 == Pycnic ==
 The fifth of pycnic in size is a meantone fifth, but four of them are not used to reach 5. This has the effect of making the Pythagorean major third, nominally 81/64, very close to 5/4 in tuning, being a cent sharp of it in the POTE tuning for instance. Pycnic has MOS of size 9, 11, 13, 15, 17... which contain these alternative thirds, leading to two kinds of major triads, an official one and a nominally Pythagorean one which is actually in better tune.
 Subgroup: 2.3.5.7
@@ Line 503: / Line 526: @@
 == Magus ==
 Magus temperament tempers out 50331648/48828125 (salegu) in the 5-limit. This temperament can be described as 46&amp;49 temperament, which tempers out the sensamagic and 28672/28125 (sazoquingu). Alternative extension [[Starling temperaments #Amigo|amigo]] (43&amp;46) tempers out the same 5-limit comma as the magus, but with the [[126/125|starling comma]] (126/125) rather than the sensamagic tempered out.
 Subgroup: 2.3.5