Tour of regular temperaments: Difference between revisions

Line 384:

== 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. Other family members include negri, sharp, mavila, wizard, tritonic, septimin, slender, triton, escapade and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august and compton.

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 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]], but 31, 46 or 58 also work nicely~~. Its family includes myna, sensi, valentine, casablanca and nusecond temperaments, not to mention meantone, keemun, muggles and opossum~~. 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. Like marvel, it has the same generators as 5-limit JI. An excellent tuning for starling is [[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.

===[[Greenwoodmic ~~temperaments~~|Greenwoodmic or Ruruyo family]] (P8, P5, ^1)===

===[[Greenwoodmic family|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.

===[[Avicennmic ~~temperaments~~|Avicennmic or Zoyoyo family]] (P8, P5, ^1)===

===[[Avicennmic family|Avicennmic or Zoyoyo family]] (P8, P5, ^1)===

These temper out the avicennma, {{Monzo|-9 1 2 1}} = 525/512~~, also known as Avicenna's enharmonic diesis~~. In the pergen, ^1 = ~81/80.

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

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

Line 410:

===[[Ragisma family|Ragisma or Zoquadyo family]] (P8, P5, ^1)===

The 7-limit rank three microtemperament which tempers out the ragisma, {{Monzo|-1 -7 4 1}} = 4375/4374, extends to various higher limit rank three temperaments such as thor. These are not by any means all microtemperaments, but those which are not highly accurate are probably best discussed under another heading~~. Accurate ones include ennealimmal, supermajor, enneadecal, amity, mitonic, parakleismic, gamera and vishnu. Pontiac belongs on the list but falls under the schismatic family rubric~~. In the pergen, ^1 = ~81/80.

The 7-limit rank three microtemperament which tempers out the ragisma, {{Monzo|-1 -7 4 1}} = 4375/4374, extends to various higher limit rank three temperaments such as thor. These are not by any means all microtemperaments, but those which are not highly accurate are probably best discussed under another heading. In the pergen, ^1 = ~81/80.

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

Line 427:

The mint temperament is a low complexity, high error temperament, tempering out the septimal quarter-tone 36/35, equating 7/6 with 6/5, and 5/4 with 9/7. In the pergen, ^1 = ~81/80 or ~64/63.

===[[Septisemi ~~temperaments~~|Septisemi or Zogu family]] (P8, P5, ^1)===

===[[Septisemi family|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.

Line 433:

Jubilismic temperament tempers out 50/49 and thereby equates the two septimal tritones, 7/5 and 10/7. This is the half-octave period. In the pergen, ^1 = ~81/80.

===[[Cataharry ~~temperaments~~|Cataharry or Labirugu family]] (P8, P4/2, ^1)===

===[[Cataharry family|Cataharry or Labirugu family]] (P8, P4/2, ^1)===

Cataharry temperaments temper out the cataharry comma, {{Monzo|-4 9 -2 -2}} = 19683/19600. In the pergen, half a 4th is ~81/70, and ^1 = ~81/80.

Line 460:

The hemimean family of rank three temperaments tempers out the hemimean comma, {{Monzo|6 0 -5 2}} = 3136/3125. Two ~28/25 generators equal the pergen's downmajor 3rd of ~5/4.

===[[Wizmic ~~microtemperaments~~|Wizmic or Quinzo-ayoyo family]] (P8, P5, vm7/2)===

===[[Wizmic family|Wizmic or Quinzo-ayoyo family]] (P8, P5, vm7/2)===

A wizmic temperament is one which tempers out the wizma, {{Monzo|-6 -8 2 5}} = 420175/419904. Two ~324/245 generators equal the pergen's downminor 7th of ~7/4.

@@ Line 384: / Line 384: @@
 == 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. Other family members include negri, sharp, mavila, wizard, tritonic, septimin, slender, triton, escapade and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august and compton.
+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 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]], but 31, 46 or 58 also work nicely. Its family includes myna, sensi, valentine, casablanca and nusecond temperaments, not to mention meantone, keemun, muggles and opossum. 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. Like marvel, it has the same generators as 5-limit JI. An excellent tuning for starling is [[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.
-===[[Greenwoodmic temperaments|Greenwoodmic or Ruruyo family]] (P8, P5, ^1)===
+===[[Greenwoodmic family|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.
-===[[Avicennmic temperaments|Avicennmic or Zoyoyo family]] (P8, P5, ^1)===
+===[[Avicennmic family|Avicennmic or Zoyoyo family]] (P8, P5, ^1)===
-These temper out the avicennma, {{Monzo|-9 1 2 1}} = 525/512, also known as Avicenna's enharmonic diesis. In the pergen, ^1 = ~81/80.
+These temper out the avicennma, {{Monzo|-9 1 2 1}} = 525/512. In the pergen, ^1 = ~81/80.
 ===[[Keemic family|Keemic or Zotriyo family]] (P8, P5, ^1)===
@@ Line 410: / Line 410: @@
 ===[[Ragisma family|Ragisma or Zoquadyo family]] (P8, P5, ^1)===
-The 7-limit rank three microtemperament which tempers out the ragisma, {{Monzo|-1 -7 4 1}} = 4375/4374, extends to various higher limit rank three temperaments such as thor. These are not by any means all microtemperaments, but those which are not highly accurate are probably best discussed under another heading. Accurate ones include ennealimmal, supermajor, enneadecal, amity, mitonic, parakleismic, gamera and vishnu. Pontiac belongs on the list but falls under the schismatic family rubric. In the pergen, ^1 = ~81/80.
+The 7-limit rank three microtemperament which tempers out the ragisma, {{Monzo|-1 -7 4 1}} = 4375/4374, extends to various higher limit rank three temperaments such as thor. These are not by any means all microtemperaments, but those which are not highly accurate are probably best discussed under another heading. In the pergen, ^1 = ~81/80.
 ===[[Hemifamity family|Hemifamity or Saruyo family]] (P8, P5, ^1)===
@@ Line 427: / Line 427: @@
 The mint temperament is a low complexity, high error temperament, tempering out the septimal quarter-tone 36/35, equating 7/6 with 6/5, and 5/4 with 9/7. In the pergen, ^1 = ~81/80 or ~64/63.
-===[[Septisemi temperaments|Septisemi or Zogu family]] (P8, P5, ^1)===
+===[[Septisemi family|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.
@@ Line 433: / Line 433: @@
 Jubilismic temperament tempers out 50/49 and thereby equates the two septimal tritones, 7/5 and 10/7. This is the half-octave period. In the pergen, ^1 = ~81/80.
-===[[Cataharry temperaments|Cataharry or Labirugu family]] (P8, P4/2, ^1)===
+===[[Cataharry family|Cataharry or Labirugu family]] (P8, P4/2, ^1)===
 Cataharry temperaments temper out the cataharry comma, {{Monzo|-4 9 -2 -2}} = 19683/19600. In the pergen, half a 4th is ~81/70, and ^1 = ~81/80.
@@ Line 460: / Line 460: @@
 The hemimean family of rank three temperaments tempers out the hemimean comma, {{Monzo|6 0 -5 2}} = 3136/3125.  Two ~28/25 generators equal the pergen's downmajor 3rd of ~5/4.
-===[[Wizmic microtemperaments|Wizmic or Quinzo-ayoyo family]] (P8, P5, vm7/2)===
+===[[Wizmic family|Wizmic or Quinzo-ayoyo family]] (P8, P5, vm7/2)===
 A wizmic temperament is one which tempers out the wizma, {{Monzo|-6 -8 2 5}} = 420175/419904. Two ~324/245 generators equal the pergen's downminor 7th of ~7/4.