No-threes subgroup temperaments: Difference between revisions

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This is a collection of [[subgroup temperament]]s which omit the prime harmonic of 3.

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* For no-fives, see [[#No-threes-or-fives subgroup temperaments]].

* French decimal and trader ~~are with~~ ~2/1 period and ~5/4 generator. There is one-to-one correspondence between 2.5 subgroup and mapped intervals.

* French decimal and trader have a ~2/1 period and ~5/4 generator. There is a one-to-one correspondence between the 2.5 subgroup and mapped intervals.

* Didacus is with a ~28/25 generator, two of which give the ~5/4.

* Ostara, movila and vengeance have variantly expressed generators, three of which give the ~5/2.

* Ostara, movila and vengeance ~~are with variety~~ expressed ~~generator~~, three of which give the ~5/2.

* Insect has a ~55/32 generator, three of which give the ~5/1.

* Insect ~~is with~~ a ~55/32 generator, three of which give the ~5/1.

* Frostburn has a ~28/25 generator, four of which give the ~8/5.

* Frostburn ~~is with~~ a ~28/25 generator, four of which give the ~8/5.

Others have a more complex mapping of 5.

Others ~~are~~ more ~~far~~.

== 2.5.7 temperaments ==

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=== Frostburn ===

[[Subgroup]]: 2.5.7

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=== Mabilic ===

{{See also| Chromatic pairs #Mabilic }}{{Main|Mabilic and trismegistus}}Given below is the no-three version of [[Mavila family#Armodue|armodue]], [[Mabila family#Semabila|semabila]], and [[Magic family#Trismegistus|trismegistus]]. It is the 7 & 9 temperament in the [[2.5.7 subgroup]], and tempers out [[1071875/1048576]], the mabilisma.

Given below is the no-three version of [[Mabila family#Semabila|semabila]], ~~or equivalently the no-threes version of~~ [[Magic family#Trismegistus|trismegistus]]. It is the 7 & 9 temperament in the [[2.5.7 subgroup]], and tempers out [[1071875/1048576]], the mabilisma.

[[Subgroup]]: 2.5.7

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== No-threes-or-fives subgroup temperaments ==

Temperaments discussed elsewhere include

* Orgone → [[Orgonia #Orgone]]

* Orgone → [[Orgonia #Orgone|Orgonia]]

* Berylic → [[4th-octave temperaments #Berylic]]

* Berylic → [[4th-octave temperaments #Berylic|4th-octave temperaments]]

* 21-23-commatic → [[21st-octave temperaments #21-23-commatic]]

* 21-23-commatic → [[21st-octave temperaments #21-23-commatic|21st-octave temperaments]]

* 31-17/13-commatic → [[31st-octave temperaments #31-17/13-commatic]]

* 31-17/13-commatic → [[31st-octave temperaments #31-17/13-commatic|31st-octave temperaments]]

* 37-11-commatic (rank-1) → [[37th-octave temperaments #37-11-commatic (rank-1)]]

* 37-11-commatic (rank-1) → [[37th-octave temperaments #37-11-commatic (rank-1)|37th-octave temperaments]]

* etc.

=== Amaranthine ===

Amaranthine is the high-accuracy 2.7.11 subgroup strong restriction of [[Gamelismic clan#11-limit 3|undecimal mothra]].

[[Subgroup]]: 2.7.11

[[Comma list]]: 5767168/5764801

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~7/4 = 968.913

{{Optimal ET sequence|legend=1| 26, 83, 109, 135, 161, 296, 1641, 1937, 2233, 2529, 2825, 3121, 6538d, 9659d }}

Badness (Sintel): 0.031

=== Score ===

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[[Category:Temperament collections]]

[[Category:Pages with mostly numerical content]]

[[Category:Subgroup temperaments]]

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+{{Technical data page}}
 This is a collection of [[subgroup temperament]]s which omit the prime harmonic of 3.
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 * For no-fives, see [[#No-threes-or-fives subgroup temperaments]].
-* French decimal and trader are with ~2/1 period and ~5/4 generator. There is one-to-one correspondence between 2.5 subgroup and mapped intervals.
+* French decimal and trader have a ~2/1 period and ~5/4 generator. There is a one-to-one correspondence between the 2.5 subgroup and mapped intervals.
-* Didacus is with a ~28/25 generator, two of which give the ~5/4.
+* Ostara, movila and vengeance have variantly expressed generators, three of which give the ~5/2.
-* Ostara, movila and vengeance are with variety expressed generator, three of which give the ~5/2.
+* Insect has a ~55/32 generator, three of which give the ~5/1.
-* Insect is with a ~55/32 generator, three of which give the ~5/1.
+* Frostburn has a ~28/25 generator, four of which give the ~8/5.
-* Frostburn is with a ~28/25 generator, four of which give the ~8/5.
+Others have a more complex mapping of 5.
-Others are more far.
 == 2.5.7 temperaments ==
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 === Frostburn ===
 {{See also| Magic family #Quadrimage }}
+{{See also| Subgroup temperaments #Baldy }}
 [[Subgroup]]: 2.5.7
@@ Line 49: / Line 50: @@
 === Mabilic ===
-{{See also| Chromatic pairs #Mabilic }}
+{{See also| Chromatic pairs #Mabilic }}{{Main|Mabilic and trismegistus}}Given below is the no-three version of [[Mavila family#Armodue|armodue]], [[Mabila family#Semabila|semabila]], and [[Magic family#Trismegistus|trismegistus]]. It is the 7 &amp; 9 temperament in the [[2.5.7 subgroup]], and tempers out [[1071875/1048576]], the mabilisma.
-Given below is the no-three version of [[Mabila family#Semabila|semabila]], or equivalently the no-threes version of [[Magic family#Trismegistus|trismegistus]]. It is the 7 &amp; 9 temperament in the [[2.5.7 subgroup]], and tempers out [[1071875/1048576]], the mabilisma.
 [[Subgroup]]: 2.5.7
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 == No-threes-or-fives subgroup temperaments ==
 Temperaments discussed elsewhere include
-* Orgone → [[Orgonia #Orgone]]
+* Orgone → [[Orgonia #Orgone|Orgonia]]
-* Berylic → [[4th-octave temperaments #Berylic]]
+* Berylic → [[4th-octave temperaments #Berylic|4th-octave temperaments]]
-* 21-23-commatic → [[21st-octave temperaments #21-23-commatic]]
+* 21-23-commatic → [[21st-octave temperaments #21-23-commatic|21st-octave temperaments]]
-* 31-17/13-commatic → [[31st-octave temperaments #31-17/13-commatic]]
+* 31-17/13-commatic → [[31st-octave temperaments #31-17/13-commatic|31st-octave temperaments]]
-* 37-11-commatic (rank-1) → [[37th-octave temperaments #37-11-commatic (rank-1)]]
+* 37-11-commatic (rank-1) → [[37th-octave temperaments #37-11-commatic (rank-1)|37th-octave temperaments]]
 * etc.
+=== Amaranthine ===
+{{See also| No-fives subgroup temperaments #Chrysanthemum }}
+Amaranthine is the high-accuracy 2.7.11 subgroup strong restriction of [[Gamelismic clan#11-limit 3|undecimal mothra]].
+[[Subgroup]]: 2.7.11
+[[Comma list]]: 5767168/5764801
+{{Mapping|legend=2| 1 2 -3 | 0 1 8 }}
+[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~7/4 = 968.913
+{{Optimal ET sequence|legend=1| 26, 83, 109, 135, 161, 296, 1641, 1937, 2233, 2529, 2825, 3121, 6538d, 9659d }}
+Badness (Sintel): 0.031
 === Score ===
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 [[Category:Temperament collections]]
+[[Category:Pages with mostly numerical content]]
 [[Category:Subgroup temperaments]]