Tour of regular temperaments: Difference between revisions

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: The mirkwai family of rank three temperaments tempers out the mirkwai comma, {{Monzo|0 3 4 -5}} = 16875/16807. Four ~7/5 generators equal the pergen's compound upmajor 7th of ~27/7.

== [[~~Rank_four_temperaments~~|~~Rank-4~~ temperaments]] ==

=== Temperaments defined by a comma involving 11 ===

~~Even less explored than rank three temperaments are rank four temperaments. In fact~~, ~~unless one counts 7~~-~~limit JI they don't seem to have been explored at all. However, they could be used; for example [[Hobbits|hobbit scales]] can be constructed for them~~.

; [[Ptolemismic temperaments|Ptolemismic or Luyoyo temperaments]]

: These temper out the ptolemisma, {{monzo| 2 -2 2 0 -1 }} = 100/99.

; [[Valinorismic temperaments|Valinorismic or Lorugugu temperaments]]

: These temper out the valinorsma, {{~~Monzo~~|4 0 -2 -1 1}} = 176/175.

: These temper out the valinorsma, {{monzo| 4 0 -2 -1 1 }} = 176/175.

; [[Rastmic temperaments|Rastmic or Lulu temperaments]]

: These temper out the rastma, {{~~Monzo~~|1 5 0 0 -2}} = 243/242. As an ila (11-limit no-fives no-sevens) rank-2 temperament, ~~it's~~ (P8, P5/2).

: These temper out the rastma, {{monzo| 1 5 0 0 -2 }} = 243/242. As an ila (11-limit no-fives no-sevens) rank-2 temperament, the pergen is (P8, P5/2).

; [[Werckismic temperaments|Werckismic or Luzozogu temperaments]]

: These temper out the werckisma, {{~~Monzo~~|-3 2 -1 2 -1}} = 441/440.

: These temper out the werckisma, {{monzo| -3 2 -1 2 -1 }} = 441/440.

; [[Swetismic temperaments|Swetismic or Lururuyo temperaments]]

: These temper out the swetisma, {{~~Monzo~~|2 3 1 -2 -1}} = 540/539.

: These temper out the swetisma, {{monzo| 2 3 1 -2 -1 }} = 540/539.

; [[Pentacircle temperaments|Pentacircle or Saluzo temperaments]]

: These temper out the pentacircle comma, {{monzo| 7 -4 0 1 -1 }} = 896/891.

; [[Lehmerismic temperaments|Lehmerismic or Loloruyoyo temperaments]]

: These temper out the lehmerisma, {{~~Monzo~~|-4 -3 2 -1 2}} = 3025/3024.

: These temper out the lehmerisma, {{monzo| -4 -3 2 -1 2 }} = 3025/3024.

; [[Kalismic temperaments|Kalismic or Bilorugu temperaments]]

: These temper out the kalisma, {{~~Monzo~~|-3 4 -2 -2 2}} = 9801/9800.

: These temper out the kalisma, {{monzo| -3 4 -2 -2 2 }} = 9801/9800.

== [[Rank-4 temperament]]s ==

Even less explored than rank three temperaments are rank four temperaments. In fact, unless one counts 7-limit JI they don't seem to have been explored at all. However, they could be used; for example [[Hobbits|hobbit scales]] can be constructed for them.

== [[Subgroup temperaments]] ==

@@ Line 545: / Line 545: @@
 : The mirkwai family of rank three temperaments tempers out the mirkwai comma, {{Monzo|0 3 4 -5}} = 16875/16807. Four ~7/5 generators equal the pergen's compound upmajor 7th of  ~27/7.
-== [[Rank_four_temperaments|Rank-4 temperaments]] ==
+=== Temperaments defined by a comma involving 11 ===
-Even less explored than rank three temperaments are rank four temperaments. In fact, unless one counts 7-limit JI they don't seem to have been explored at all. However, they could be used; for example [[Hobbits|hobbit scales]] can be constructed for them.
+; [[Ptolemismic temperaments|Ptolemismic or Luyoyo temperaments]]
+: These temper out the ptolemisma, {{monzo| 2 -2 2 0 -1 }} = 100/99.
 ; [[Valinorismic temperaments|Valinorismic or Lorugugu temperaments]]
-: These temper out the valinorsma, {{Monzo|4 0 -2 -1 1}} = 176/175.
+: These temper out the valinorsma, {{monzo| 4 0 -2 -1 1 }} = 176/175.
 ; [[Rastmic temperaments|Rastmic or Lulu temperaments]]
-: These temper out the rastma, {{Monzo|1 5 0 0 -2}} = 243/242. As an ila (11-limit no-fives no-sevens) rank-2 temperament, it's (P8, P5/2).
+: These temper out the rastma, {{monzo| 1 5 0 0 -2 }} = 243/242. As an ila (11-limit no-fives no-sevens) rank-2 temperament, the pergen is (P8, P5/2).
 ; [[Werckismic temperaments|Werckismic or Luzozogu temperaments]]
-: These temper out the werckisma, {{Monzo|-3 2 -1 2 -1}} = 441/440.
+: These temper out the werckisma, {{monzo| -3 2 -1 2 -1 }} = 441/440.
 ; [[Swetismic temperaments|Swetismic or Lururuyo temperaments]]
-: These temper out the swetisma, {{Monzo|2 3 1 -2 -1}} = 540/539.
+: These temper out the swetisma, {{monzo| 2 3 1 -2 -1 }} = 540/539.
+; [[Pentacircle temperaments|Pentacircle or Saluzo temperaments]]
+: These temper out the pentacircle comma, {{monzo| 7 -4 0 1 -1 }} = 896/891.
 ; [[Lehmerismic temperaments|Lehmerismic or Loloruyoyo temperaments]]
-: These temper out the lehmerisma, {{Monzo|-4 -3 2 -1 2}} = 3025/3024.
+: These temper out the lehmerisma, {{monzo| -4 -3 2 -1 2 }} = 3025/3024.
 ; [[Kalismic temperaments|Kalismic or Bilorugu temperaments]]
-: These temper out the kalisma, {{Monzo|-3 4 -2 -2 2}} = 9801/9800.
+: These temper out the kalisma, {{monzo| -3 4 -2 -2 2 }} = 9801/9800.
+== [[Rank-4 temperament]]s ==
+Even less explored than rank three temperaments are rank four temperaments. In fact, unless one counts 7-limit JI they don't seem to have been explored at all. However, they could be used; for example [[Hobbits|hobbit scales]] can be constructed for them.
 == [[Subgroup temperaments]] ==