Tour of regular temperaments: Difference between revisions

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=== Families defined by a 2.3.5.7 (yaza) comma ===

; [[Marvel family|Marvel or Ruyoyo family]] (P8, P5, ^1)

: The head of the marvel family is marvel, which tempers out {{Monzo|-5 2 2 -1}} = [[225/224]]. It has a number of 11-limit children, including unidecimal marvel, prodigy, minerva and spectacle.

: The head of the marvel family is marvel, which tempers out {{Monzo|-5 2 2 -1}} = [[225/224]]. It divides 8/7 into two 16/15s, or equivalently, two 15/14s. It has a number of 11-limit children, including unidecimal marvel, prodigy, minerva and spectacle.

The marvel comma equates every 7-limit interval to some 5-limit interval, therefore the generators are the same as for 5-limit JI: 2/1, 3/1 and 5/1. These may be reduced to 2/1, 3/2 and 5/4, and 5/4 may be reduced further to 81/80. Hence in the pergen, ^1 = ~81/80.

; [[Starling family|Starling or Zotrigu family]] (P8, P5, ^1)

: Starling tempers out the septimal semicomma or starling comma {{Monzo|1 2 -3 1}} = [[126/125]], the difference between three 6/5s plus one 7/6, and an octave. Like marvel, it has the same generators as 5-limit JI. An excellent tuning for starling is [[77edo|77EDO]], but 31, 46 or 58 also work nicely. In the pergen, ^1 = ~81/80.

: Starling tempers out the septimal semicomma or starling comma {{Monzo|1 2 -3 1}} = [[126/125]], the difference between three 6/5s plus one 7/6, and an octave. It divides 10/7 into two 6/5s. Like marvel, it has the same generators as 5-limit JI. An excellent tuning for starling is [[77edo|77EDO]], but 31, 46 or 58 also work nicely. In the pergen, ^1 = ~81/80.

; [[Sensamagic family|Sensamagic or Zozoyo family]] (P8, P5, ^1)

: These temper out {{Monzo|0 -5 1 2}} = 245/243. In the pergen, ^1 = ~64/63.

: These temper out {{Monzo|0 -5 1 2}} = 245/243, which divides 16/15 into two 28/27s. In the pergen, ^1 = ~64/63.

; Greenwoodmic or Ruruyo family (P8, P5, ^1)

: These temper out the greenwoodma, {{Monzo|-3 4 1 -2}} = 405/392. In the pergen, ^1 = ~64/63.

: These temper out the greenwoodma, {{Monzo|-3 4 1 -2}} = 405/392, which divides 10/9 into two 15/14s. In the pergen, ^1 = ~64/63.

; Avicennmic or ~~Zoyoyo~~ family (P8, P5, ^1)

; Avicennmic or Lazoyoyo family (P8, P5, ^1)

: These temper out the avicennma, {{Monzo|-9 1 2 1}} = 525/512. In the pergen, ^1 = ~81/80.

: These temper out the avicennma, {{Monzo|-9 1 2 1}} = 525/512, which divides 7/6 into two 16/15s. In the pergen, ^1 = ~81/80.

; [[Keemic family|Keemic or Zotriyo family]] (P8, P5, ^1)

: These temper out the keema {{Monzo|-5 -3 3 1}} = 875/864. In the pergen, ^1 = ~81/80.

: These temper out the keema {{Monzo|-5 -3 3 1}} = 875/864, which divides 15/14 into two 25/24s. In the pergen, ^1 = ~81/80.

; [[Orwellismic family|Orwellismic or Triru-agu family]] (P8, P5, ^1)

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; [[Hemifamity family|Hemifamity or Saruyo family]] (P8, P5, ^1)

: The hemifamity family of rank three temperaments tempers out the hemifamity comma, {{Monzo|10 -6 1 -1}} = 5120/5103. In the pergen, ^1 = ~81/80.

: The hemifamity family of rank three temperaments tempers out the hemifamity comma, {{Monzo|10 -6 1 -1}} = 5120/5103, which divides 10/7 into three 9/8s. In the pergen, ^1 = ~81/80.

; [[Horwell family|Horwell or Lazoquinyo family]] (P8, P5, ^1)

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; [[Hemimage family|Hemimage or Satrizo-agu family]] (P8, P5, ^1)

: The hemimage family of rank three temperaments tempers out the hemimage comma, {{Monzo|5 -7 -1 3}} = 10976/10935. In the pergen, ^1 = ~64/63.

: The hemimage family of rank three temperaments tempers out the hemimage comma, {{Monzo|5 -7 -1 3}} = 10976/10935, which divides 10/9 into three 28/27s. In the pergen, ^1 = ~64/63.

; [[Mint family|Mint or Rugu family]] (P8, P5, ^1)

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; Septisemi or Zogu family (P8, P5, ^1)

: These are very low ~~complexity~~ temperaments tempering out the minor septimal semitone, [[21/20]] and hence equating 5/3 with 7/4. In the pergen, ^1 = ~81/80.

: These are very low accuracy temperaments tempering out the minor septimal semitone, [[21/20]] and hence equating 5/3 with 7/4. In the pergen, ^1 = ~81/80.

; [[Jubilismic family|Jubilismic or Biruyo family]] (P8/2, P5, ^1)

@@ Line 463: / Line 463: @@
 === Families defined by a 2.3.5.7 (yaza) comma ===
 ; [[Marvel family|Marvel or Ruyoyo family]] (P8, P5, ^1)
-: The head of the marvel family is marvel, which tempers out {{Monzo|-5 2 2 -1}} = [[225/224]]. It has a number of 11-limit children, including unidecimal marvel, prodigy, minerva and spectacle.
+: The head of the marvel family is marvel, which tempers out {{Monzo|-5 2 2 -1}} = [[225/224]]. It divides 8/7 into two 16/15s, or equivalently, two 15/14s. It has a number of 11-limit children, including unidecimal marvel, prodigy, minerva and spectacle.
 The marvel comma equates every 7-limit interval to some 5-limit interval, therefore the generators are the same as for 5-limit JI: 2/1, 3/1 and 5/1. These may be reduced to 2/1, 3/2 and 5/4, and 5/4 may be reduced further to 81/80. Hence in the pergen, ^1 = ~81/80.
 ; [[Starling family|Starling or Zotrigu family]] (P8, P5, ^1)
-: Starling tempers out the septimal semicomma or starling comma {{Monzo|1 2 -3 1}} = [[126/125]], the difference between three 6/5s plus one 7/6, and an octave. Like marvel, it has the same generators as 5-limit JI. An excellent tuning for starling is [[77edo|77EDO]], but 31, 46 or 58 also work nicely. In the pergen, ^1 = ~81/80.
+: Starling tempers out the septimal semicomma or starling comma {{Monzo|1 2 -3 1}} = [[126/125]], the difference between three 6/5s plus one 7/6, and an octave. It divides 10/7 into two 6/5s. Like marvel, it has the same generators as 5-limit JI. An excellent tuning for starling is [[77edo|77EDO]], but 31, 46 or 58 also work nicely. In the pergen, ^1 = ~81/80.
 ; [[Sensamagic family|Sensamagic or Zozoyo family]] (P8, P5, ^1)
-: These temper out {{Monzo|0 -5 1 2}} = 245/243. In the pergen, ^1 = ~64/63.
+: These temper out {{Monzo|0 -5 1 2}} = 245/243, which divides 16/15 into two 28/27s. In the pergen, ^1 = ~64/63.
 ; Greenwoodmic or Ruruyo family (P8, P5, ^1)
-: These temper out the greenwoodma, {{Monzo|-3 4 1 -2}} = 405/392. In the pergen, ^1 = ~64/63.
+: These temper out the greenwoodma, {{Monzo|-3 4 1 -2}} = 405/392, which divides 10/9 into two 15/14s. In the pergen, ^1 = ~64/63.
-; Avicennmic or Zoyoyo family (P8, P5, ^1)
+; Avicennmic or Lazoyoyo family (P8, P5, ^1)
-: These temper out the avicennma, {{Monzo|-9 1 2 1}} = 525/512. In the pergen, ^1 = ~81/80.
+: These temper out the avicennma, {{Monzo|-9 1 2 1}} = 525/512, which divides 7/6 into two 16/15s. In the pergen, ^1 = ~81/80.
 ; [[Keemic family|Keemic or Zotriyo family]] (P8, P5, ^1)
-: These temper out the keema {{Monzo|-5 -3 3 1}} = 875/864. In the pergen, ^1 = ~81/80.
+: These temper out the keema {{Monzo|-5 -3 3 1}} = 875/864, which divides 15/14 into two 25/24s. In the pergen, ^1 = ~81/80.
 ; [[Orwellismic family|Orwellismic or Triru-agu family]] (P8, P5, ^1)
@@ Line 492: / Line 492: @@
 ; [[Hemifamity family|Hemifamity or Saruyo family]] (P8, P5, ^1)
-: The hemifamity family of rank three temperaments tempers out the hemifamity comma, {{Monzo|10 -6 1 -1}} = 5120/5103. In the pergen, ^1 = ~81/80.
+: The hemifamity family of rank three temperaments tempers out the hemifamity comma, {{Monzo|10 -6 1 -1}} = 5120/5103, which divides 10/7 into three 9/8s. In the pergen, ^1 = ~81/80.
 ; [[Horwell family|Horwell or Lazoquinyo family]] (P8, P5, ^1)
@@ Line 498: / Line 498: @@
 ; [[Hemimage family|Hemimage or Satrizo-agu family]] (P8, P5, ^1)
-: The hemimage family of rank three temperaments tempers out the hemimage comma, {{Monzo|5 -7 -1 3}} = 10976/10935. In the pergen, ^1 = ~64/63.
+: The hemimage family of rank three temperaments tempers out the hemimage comma, {{Monzo|5 -7 -1 3}} = 10976/10935, which divides 10/9 into three 28/27s. In the pergen, ^1 = ~64/63.
 ; [[Mint family|Mint or Rugu family]] (P8, P5, ^1)
@@ Line 504: / Line 504: @@
 ; Septisemi or Zogu family (P8, P5, ^1)
-: These are very low complexity temperaments tempering out the minor septimal semitone, [[21/20]] and hence equating 5/3 with 7/4. In the pergen, ^1 = ~81/80.
+: These are very low accuracy temperaments tempering out the minor septimal semitone, [[21/20]] and hence equating 5/3 with 7/4. In the pergen, ^1 = ~81/80.
 ; [[Jubilismic family|Jubilismic or Biruyo family]] (P8/2, P5, ^1)