Tour of regular temperaments: Difference between revisions

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=== Families defined by a 2.3 (wa) comma ===

These are families defined by a comma that uses a wa or 3-limit comma. If prime 5 is assumed to be part of the subgroup, and no other comma is tempered out, the comma creates a rank-2 temperament. The comma can also stand as parent to a 7-limit or higher family when other commas are tempered out as well, or when prime 7 is assumed to be part of the subgroup. Any temperament in these families can be thought of as consisting of mutiple "copies" of an ~~EDO~~ separated by a small comma. This small comma is represented in the [[pergen]] by ^1.

These are families defined by a comma that uses a wa or 3-limit comma. If prime 5 is assumed to be part of the subgroup, and no other comma is tempered out, the comma creates a rank-2 temperament. The comma can also stand as parent to a 7-limit or higher family when other commas are tempered out as well, or when prime 7 is assumed to be part of the subgroup. Any temperament in these families can be thought of as consisting of mutiple "copies" of an edo separated by a small comma. This small comma is represented in the [[pergen]] by ^1.

; [[Limma family|Limma or Sawa family]] (P8/5, ^1)

: This family tempers out the limma, {{Monzo|8 -5 0}} = 256/243, which implies [[5edo~~|5EDO~~]].

: This family tempers out the limma, {{Monzo|8 -5 0}} = 256/243, which implies [[5edo]].

; [[Apotome family|Apotome or Lawa family]] (P8/7, ^1)

: This family tempers out the apotome, {{Monzo|-11 7 0}} = 2187/2048, which implies [[7edo~~|7EDO~~]].

: This family tempers out the apotome, {{Monzo|-11 7 0}} = 2187/2048, which implies [[7edo]].

; [[Compton family|~~Pythagorean~~ or Lalawa family]] (P8/12, ^1)

; [[Compton family|Compton or Lalawa family]] (P8/12, ^1)

: ~~The Pythagorean family~~ tempers out the [[Pythagorean comma]], 531441/524288 = {{Monzo|-19 12 0}}, which implies [[12edo~~|12EDO~~]]. This family includes the compton and catler temperaments. Temperaments in this family tend to have a period of 1/12th octave The 5-limit compton temperament can be thought of as multiple rings of ~~12-edo~~, offset from one another by a justly tuned 5/4, or alternatively by a tempered 81/80. Several ~~12-edo~~ instruments slightly detuned from each other provide an easy way to make music with these temperaments.

: This tempers out the [[Pythagorean comma]], 531441/524288 = {{Monzo|-19 12 0}}, which implies [[12edo]]. This family includes the compton and catler temperaments. Temperaments in this family tend to have a period of 1/12th octave The 5-limit compton temperament can be thought of as multiple rings of 12edo, offset from one another by a justly tuned 5/4, or alternatively by a tempered 81/80. Several 12edo instruments slightly detuned from each other provide an easy way to make music with these temperaments.

; [[~~Counterpyth~~ family|~~Counterpyth~~ or Wa-41 family]] (P8/41, ^1)

; [[Countercomp family|Countercomp or Wa-41 family]] (P8/41, ^1)

: ~~The Counterpyth~~ family tempers out the [[41-comma|~~counterpyth comma~~]], {{Monzo| 65 -41}}, which implies [[41edo~~|41EDO~~]].

: This family tempers out the [[41-comma|Pythagorean countercomma]], {{Monzo| 65 -41 }}, which implies [[41edo]].

; [[Mercator family|Mercator or Wa-53 family]] (P8/53, ^1)

: ~~The Mercator~~ family tempers out the [[Mercator's comma]], {{Monzo| -84 53 }}, which implies [[53edo~~|53EDO~~]].

: This family tempers out the [[Mercator's comma]], {{Monzo| -84 53 }}, which implies [[53edo]].

=== Families defined by a 2.3.5 (ya) comma ===

@@ Line 5: / Line 5: @@
 === Families defined by a 2.3 (wa) comma ===
-These are families defined by a comma that uses a wa or 3-limit comma. If prime 5 is assumed to be part of the subgroup, and no other comma is tempered out, the comma creates a rank-2 temperament. The comma can also stand as parent to a 7-limit or higher family when other commas are tempered out as well, or when prime 7 is assumed to be part of the subgroup. Any temperament in these families can be thought of as consisting of mutiple "copies" of an EDO separated by a small comma. This small comma is represented in the [[pergen]] by ^1.
+These are families defined by a comma that uses a wa or 3-limit comma. If prime 5 is assumed to be part of the subgroup, and no other comma is tempered out, the comma creates a rank-2 temperament. The comma can also stand as parent to a 7-limit or higher family when other commas are tempered out as well, or when prime 7 is assumed to be part of the subgroup. Any temperament in these families can be thought of as consisting of mutiple "copies" of an edo separated by a small comma. This small comma is represented in the [[pergen]] by ^1.
 ; [[Limma family|Limma or Sawa family]] (P8/5, ^1)
-: This family tempers out the limma, {{Monzo|8 -5 0}} = 256/243, which implies [[5edo|5EDO]].
+: This family tempers out the limma, {{Monzo|8 -5 0}} = 256/243, which implies [[5edo]].
 ; [[Apotome family|Apotome or Lawa family]] (P8/7, ^1)
-: This family tempers out the apotome, {{Monzo|-11 7 0}} = 2187/2048, which implies [[7edo|7EDO]].
+: This family tempers out the apotome, {{Monzo|-11 7 0}} = 2187/2048, which implies [[7edo]].
-; [[Compton family|Pythagorean or Lalawa family]] (P8/12, ^1)
+; [[Compton family|Compton or Lalawa family]] (P8/12, ^1)
-: The Pythagorean family tempers out the [[Pythagorean comma]], 531441/524288 = {{Monzo|-19 12 0}}, which implies [[12edo|12EDO]]. This family includes the compton and catler temperaments. Temperaments in this family tend to have a period of 1/12th octave The 5-limit compton temperament can be thought of as multiple rings of 12-edo, offset from one another by a justly tuned 5/4, or alternatively by a tempered 81/80. Several 12-edo instruments slightly detuned from each other provide an easy way to make music with these temperaments.
+: This tempers out the [[Pythagorean comma]], 531441/524288 = {{Monzo|-19 12 0}}, which implies [[12edo]]. This family includes the compton and catler temperaments. Temperaments in this family tend to have a period of 1/12th octave The 5-limit compton temperament can be thought of as multiple rings of 12edo, offset from one another by a justly tuned 5/4, or alternatively by a tempered 81/80. Several 12edo instruments slightly detuned from each other provide an easy way to make music with these temperaments.
-; [[Counterpyth family|Counterpyth or Wa-41 family]] (P8/41, ^1)
+; [[Countercomp family|Countercomp or Wa-41 family]] (P8/41, ^1)
-: The Counterpyth family tempers out the [[41-comma|counterpyth comma]], {{Monzo| 65 -41}}, which implies [[41edo|41EDO]].
+: This family tempers out the [[41-comma|Pythagorean countercomma]], {{Monzo| 65 -41 }}, which implies [[41edo]].
 ; [[Mercator family|Mercator or Wa-53 family]] (P8/53, ^1)
-: The Mercator family tempers out the [[Mercator's comma]], {{Monzo| -84 53 }}, which implies [[53edo|53EDO]].
+: This family tempers out the [[Mercator's comma]], {{Monzo| -84 53 }}, which implies [[53edo]].
 === Families defined by a 2.3.5 (ya) comma ===