Tour of regular temperaments: Difference between revisions

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== Clans defined by a 2.5.7 (yaza nowa) comma ==

These are defined by a yaza nowa or 7-limit-no-threes comma. See also [[subgroup temperaments]].

These are defined by a yaza nowa or 7-limit-no-threes comma. See also [[subgroup temperaments]]. The pergen's multigen (the 2nd term, omitting any fraction) is always a 5-limit-no-threes ratio such as 5/4, 8/5, 25/8, etc.

=== [[Jubilismic clan|Jubilismic or Biruyo Nowa clan]] (P8/2, M3) ===

This clan tempers out the jubilisma, [[50/49]], which is the difference between 10/7 and 7/5. The M3 generator is ~5/4. The half-octave period is ~7/5 or ~10/7. 7/4 is equated to 1 period plus 1 generator.

This clan tempers out the jubilisma, [[50/49]], which is the difference between 10/7 and 7/5. The generator is the nowa major 3rd = ~5/4. The half-octave period is ~7/5 or ~10/7. 7/4 is equated to 1 period plus 1 generator.

===[[Hemimean clan|Hemimean or Zozoquingu Nowa clan]] (P8, M2)===

===[[Hemimean clan|Hemimean or Zozoquingu Nowa clan]] (P8, M3/2)===

This clan tempers out the hemimean comma, {{Monzo|6 0 -5 2}} = 3136/3125. The M2 generator is ~28/25 = ~194¢. Two generators equals ~5/4 and five of them equals ~7/4.

This clan tempers out the hemimean comma, {{Monzo|6 0 -5 2}} = 3136/3125. The generator is ~28/25 = ~194¢. Two generators equals the nowa major 3rd = ~5/4, three of them equals ~7/5, and five of them equals ~7/4.

===[[~~Quince~~ clan|~~Quince~~ or ~~Lasepzo~~-~~agugu~~ Nowa clan]] (P8, M2/2)===

===[[Rainy clan|Rainy or Quinzo-atriyo Nowa clan]] (P8, M3/5)===

This clan tempers out the ~~quince~~, {{Monzo|-15 0 ~~-2 7~~}} = ~~823543~~/~~819200~~. The generator is ~~~343~~/~~320~~ = ~~~116¢~~. ~~Two~~ generators equals ~8/7 ~~(a M2),~~ and ~~seven generators~~ equals ~~~8/5. An obvious~~ 5~~-limit interpretation of the generator is 16~~/~~15, leading to the [[miracle]] temperament, which is in the gamelismic clan~~.

This clan tempers out the [[rainy comma]], {{Monzo|-21 0 3 5}} = 2100875/2097152. The rurugu generator is ~256/245 = ~77¢. Three generators equals ~8/7 and five of them equals the nowa major 3rd = ~5/4.

===[[~~Rainy~~ clan|~~Rainy~~ or ~~Quinzo~~-~~atriyo~~ Nowa clan]] (P8, M3/5)===

===[[Quince clan|Quince or Lasepzo-agugu Nowa clan]] (P8, m6/7)===

This clan tempers out the ~~[[rainy comma]]~~, {{Monzo|-21 0 ~~3 5~~}} = ~~2100875~~/~~2097152~~. The generator is ~~~256~~/~~245~~ = ~~~77¢~~. ~~Three~~ generators equals ~8/7 and ~~five of them~~ equals ~5/4.

This clan tempers out the quince, {{Monzo|-15 0 -2 7}} = 823543/819200. The trizo-agu generator is ~343/320 = ~116¢. Two generators equals ~8/7, five generators equals ~7/5, and seven generators equals the nowa minor 6th ~8/5. An obvious 5-limit interpretation of the generator is 16/15, leading to the [[miracle]] temperament, which is in the gamelismic clan.

== Clans defined by a 3.5.7 (yaza noca) comma ==

These are defined by a yaza noca or 7-limit-no-twos comma. Any no-twos comma is a ratio of odd numbers. If no other commas are tempered out, It is a non-octave tuning, with a period of a perfect 12th or tritave, 3/1 (or some fraction of that). See also [[subgroup temperaments]].

These are defined by a yaza noca or 7-limit-no-twos comma. Any no-twos comma is a ratio of odd numbers. If no other commas are tempered out, It is a non-octave tuning, with a period of a perfect 12th or tritave, 3/1 (or some fraction of that). See also [[subgroup temperaments]]. The pergen's multigen (the 2nd term, omitting any fraction) is always a 5-limit-no-twos ratio such as 5/3, 9/5, 25/9, etc.

=== [[Arcturus clan|Arcturus or Rutribiyo Noca clan]] (P12, M6) ===

This 3.5.7 clan tempers out the Arcturus comma {{Monzo|0 -7 6 -1}} = 15625/15309. The generator is a noca M6 = ~5/3, and six generators equals ~21/1.

This 3.5.7 clan tempers out the Arcturus comma {{Monzo|0 -7 6 -1}} = 15625/15309. The generator is the noca major 6th = ~5/3, and six generators equals ~21/1.

===[[Sensamagic clan|Sensamagic or Zozoyo Noca clan]] (P12, M6/2)===

This 3.5.7 clan tempers out the sensamagic comma {{Monzo|0 -5 1 2}} = 245/243. The generator is ~9/7, and two generators equals a noca major 6th = ~5/3.

This 3.5.7 clan tempers out the sensamagic comma {{Monzo|0 -5 1 2}} = 245/243. The generator is ~9/7, and two generators equals the noca major 6th = ~5/3.

===[[Gariboh clan|Gariboh or Triru-aquinyo Noca clan]] (P12, M6/3)===

This 3.5.7 clan tempers out the gariboh comma {{Monzo|0 -2 5 -3}} = 3125/3087. The generator is ~25/21, two generators equals ~7/5, and three generators equals a noca major 6th = ~5/3.

This 3.5.7 clan tempers out the gariboh comma {{Monzo|0 -2 5 -3}} = 3125/3087. The generator is ~25/21, two generators equals ~7/5, and three generators equals the noca major 6th = ~5/3.

===[[Mirkwai clan|Mirkwai or Quinru-aquadyo Noca clan]] (P12, cm7/5)===

This 3.5.7 clan tempers out the mirkwai comma, {{Monzo|0 3 4 -5}} = 16875/16807. The generator is ~7/5, four generators equals ~27/7, and five generators equals a noca compound minor 7th = ~27/5. In a noca ~~pergen~~, "compound" means increased by 3/1 not 2/1.

This 3.5.7 clan tempers out the mirkwai comma, {{Monzo|0 3 4 -5}} = 16875/16807. The generator is ~7/5, four generators equals ~27/7, and five generators equals the noca compound minor 7th = ~27/5. In a noca subgroup, "compound" means increased by 3/1 not 2/1.

===[[Procyon clan|Procyon or Sasepzo-atrigu Noca clan]] (P12, m7/7)===

This 3.5.7 clan tempers out the Procyon comma {{Monzo|0 -8 -3 7}} = 823543/820125. The generator is ~49/45, three generators equals ~9/7, four equals ~7/5, and seven equals a noca minor seventh = ~9/5.

This 3.5.7 clan tempers out the Procyon comma {{Monzo|0 -8 -3 7}} = 823543/820125. The generator is ~49/45, three generators equals ~9/7, four equals ~7/5, and seven equals the noca minor seventh = ~9/5.

== Rank-two temperaments defined by a 2.3.5.7 (yaza) comma ==

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===[[Mirwomo family|Mirwomo or Labizoyo family]] (P8, P5/2, ^1)===

The mirwomo family of rank three temperaments tempers out the mirwomo comma, {{Monzo|-15 3 2 2}} = 33075/32768. In the pergen, half a fifth is ~128/105, and ^1 = ~81/80.

~~===[[Landscape family|Landscape or Trizogugu family]] (P8/3, P5, ^1)===~~

The 7-limit rank three microtemperament which tempers out the lanscape comma, {{Monzo|-4 6 -6 3}} = 250047/250000, extends to various higher limit rank three temperaments such as tyr and odin. In the pergen, the third-octave period is ~63/50, and ^1 = ~81/80.

~~===[[Dimcomp family|Dimcomp or Quadruyoyo family]] (P8/4, P5, ^1)===~~

~~The dimcomp family of rank three temperaments tempers out the dimcomp comma, {{Monzo|-1 -4 8 -4}} = 390625/388962. In the pergen, the quarter-octave period is ~25/21, and ^1 = ~81/80.~~

===[[Sengic family|Sengic or Trizo-agugu family]] (P8, P5, vm3/2)===

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===[[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.

=== [[Landscape family|Landscape or Trizogugu family]] (P8/3, P5, ^1) ===

The 7-limit rank three microtemperament which tempers out the lanscape comma, {{Monzo|-4 6 -6 3}} = 250047/250000, extends to various higher limit rank three temperaments such as tyr and odin. In the pergen, the third-octave period is ~63/50, and ^1 = ~81/80.

===[[Canou family|Canou or Saquadzo-atriyo family]] (P8, P5, vm6/3)===

The canou family of rank three temperaments tempers out the canousma, {{Monzo|4 -14 3 4}} = 4802000/4782969. Three ~81/70 generators equal the pergen's downminor 6th of ~14/9.

=== [[Dimcomp family|Dimcomp or Quadruyoyo family]] (P8/4, P5, ^1) ===

The dimcomp family of rank three temperaments tempers out the dimcomp comma, {{Monzo|-1 -4 8 -4}} = 390625/388962. In the pergen, the quarter-octave period is ~25/21, and ^1 = ~81/80.

===[[Mirkwai family|Mirkwai or Quinru-aquadyo family]] (P8, P5, c^M7/4)===

@@ Line 229: / Line 229: @@
 == Clans defined by a 2.5.7 (yaza nowa) comma ==
-These are defined by a yaza nowa or 7-limit-no-threes comma. See also [[subgroup temperaments]].
+These are defined by a yaza nowa or 7-limit-no-threes comma. See also [[subgroup temperaments]]. The pergen's multigen (the 2nd term, omitting any fraction) is always a 5-limit-no-threes ratio such as 5/4, 8/5, 25/8, etc.
 === [[Jubilismic clan|Jubilismic or Biruyo Nowa clan]] (P8/2, M3) ===
-This clan tempers out the jubilisma, [[50/49]], which is the difference between 10/7 and 7/5. The M3 generator is ~5/4. The half-octave period is ~7/5 or ~10/7. 7/4 is equated to 1 period plus 1 generator.
+This clan tempers out the jubilisma, [[50/49]], which is the difference between 10/7 and 7/5. The generator is the nowa major 3rd = ~5/4. The half-octave period is ~7/5 or ~10/7. 7/4 is equated to 1 period plus 1 generator.
-===[[Hemimean clan|Hemimean or Zozoquingu Nowa clan]] (P8, M2)===
+===[[Hemimean clan|Hemimean or Zozoquingu Nowa clan]] (P8, M3/2)===
-This clan tempers out the hemimean comma, {{Monzo|6 0 -5 2}} = 3136/3125. The M2 generator is ~28/25 = ~194¢. Two generators equals ~5/4 and five of them equals ~7/4.
+This clan tempers out the hemimean comma, {{Monzo|6 0 -5 2}} = 3136/3125. The generator is ~28/25 = ~194¢. Two generators equals the nowa major 3rd = ~5/4, three of them equals ~7/5, and five of them equals ~7/4.
-===[[Quince clan|Quince or Lasepzo-agugu Nowa clan]] (P8, M2/2)===
+===[[Rainy clan|Rainy or Quinzo-atriyo Nowa clan]] (P8, M3/5)===
-This clan tempers out the quince, {{Monzo|-15 0 -2 7}} = 823543/819200. The generator is ~343/320 = ~116¢. Two generators equals ~8/7 (a M2), and seven generators equals ~8/5. An obvious 5-limit interpretation of the generator is 16/15, leading to the [[miracle]] temperament, which is in the gamelismic clan.
+This clan tempers out the [[rainy comma]], {{Monzo|-21 0 3 5}} = 2100875/2097152. The rurugu generator is ~256/245 = ~77¢. Three generators equals ~8/7 and five of them equals the nowa major 3rd = ~5/4.
-===[[Rainy clan|Rainy or Quinzo-atriyo Nowa clan]] (P8, M3/5)===
+===[[Quince clan|Quince or Lasepzo-agugu Nowa clan]] (P8, m6/7)===
-This clan tempers out the [[rainy comma]], {{Monzo|-21 0 3 5}} = 2100875/2097152. The generator is ~256/245 = ~77¢. Three generators equals ~8/7 and five of them equals ~5/4.
+This clan tempers out the quince, {{Monzo|-15 0 -2 7}} = 823543/819200. The trizo-agu generator is ~343/320 = ~116¢. Two generators equals ~8/7, five generators equals ~7/5, and seven generators equals the nowa minor 6th ~8/5. An obvious 5-limit interpretation of the generator is 16/15, leading to the [[miracle]] temperament, which is in the gamelismic clan.
 == Clans defined by a 3.5.7 (yaza noca) comma ==
-These are defined by a yaza noca or 7-limit-no-twos comma. Any no-twos comma is a ratio of odd numbers. If no other commas are tempered out, It is a non-octave tuning, with a period of a perfect 12th or tritave, 3/1 (or some fraction of that). See also [[subgroup temperaments]].
+These are defined by a yaza noca or 7-limit-no-twos comma. Any no-twos comma is a ratio of odd numbers. If no other commas are tempered out, It is a non-octave tuning, with a period of a perfect 12th or tritave, 3/1 (or some fraction of that). See also [[subgroup temperaments]]. The pergen's multigen (the 2nd term, omitting any fraction) is always a 5-limit-no-twos ratio such as 5/3, 9/5, 25/9, etc.
 === [[Arcturus clan|Arcturus or Rutribiyo Noca clan]] (P12, M6) ===
-This 3.5.7 clan tempers out the Arcturus comma {{Monzo|0 -7 6 -1}} = 15625/15309. The generator is a noca M6 = ~5/3, and six generators equals ~21/1.
+This 3.5.7 clan tempers out the Arcturus comma {{Monzo|0 -7 6 -1}} = 15625/15309. The generator is the noca major 6th = ~5/3, and six generators equals ~21/1.
 ===[[Sensamagic clan|Sensamagic or Zozoyo Noca clan]] (P12, M6/2)===
-This 3.5.7 clan tempers out the sensamagic comma {{Monzo|0 -5 1 2}} = 245/243. The generator is ~9/7, and two generators equals a noca major 6th = ~5/3.
+This 3.5.7 clan tempers out the sensamagic comma {{Monzo|0 -5 1 2}} = 245/243. The generator is ~9/7, and two generators equals the noca major 6th = ~5/3.
 ===[[Gariboh clan|Gariboh or Triru-aquinyo Noca clan]] (P12, M6/3)===
-This 3.5.7 clan tempers out the gariboh comma {{Monzo|0 -2 5 -3}} = 3125/3087. The generator is ~25/21, two generators equals ~7/5, and three generators equals a noca major 6th = ~5/3.
+This 3.5.7 clan tempers out the gariboh comma {{Monzo|0 -2 5 -3}} = 3125/3087. The generator is ~25/21, two generators equals ~7/5, and three generators equals the noca major 6th = ~5/3.
 ===[[Mirkwai clan|Mirkwai or Quinru-aquadyo Noca clan]] (P12, cm7/5)===
-This 3.5.7 clan tempers out the mirkwai comma, {{Monzo|0 3 4 -5}} = 16875/16807. The generator is ~7/5, four generators equals ~27/7, and five generators equals a noca compound minor 7th = ~27/5. In a noca pergen, "compound" means increased by 3/1 not 2/1.
+This 3.5.7 clan tempers out the mirkwai comma, {{Monzo|0 3 4 -5}} = 16875/16807. The generator is ~7/5, four generators equals ~27/7, and five generators equals the noca compound minor 7th = ~27/5. In a noca subgroup, "compound" means increased by 3/1 not 2/1.
 ===[[Procyon clan|Procyon or Sasepzo-atrigu Noca clan]] (P12, m7/7)===
-This 3.5.7 clan tempers out the Procyon comma {{Monzo|0 -8 -3 7}} = 823543/820125. The generator is ~49/45, three generators equals ~9/7, four equals ~7/5, and seven equals a noca minor seventh = ~9/5.
+This 3.5.7 clan tempers out the Procyon comma {{Monzo|0 -8 -3 7}} = 823543/820125. The generator is ~49/45, three generators equals ~9/7, four equals ~7/5, and seven equals the noca minor seventh = ~9/5.
 == Rank-two temperaments defined by a 2.3.5.7 (yaza) comma ==
@@ Line 443: / Line 443: @@
 ===[[Mirwomo family|Mirwomo or Labizoyo family]] (P8, P5/2, ^1)===
 The mirwomo family of rank three temperaments tempers out the mirwomo comma, {{Monzo|-15 3 2 2}} = 33075/32768. In the pergen, half a fifth is ~128/105, and ^1 = ~81/80.
-===[[Landscape family|Landscape or Trizogugu family]] (P8/3, P5, ^1)===
-The 7-limit rank three microtemperament which tempers out the lanscape comma, {{Monzo|-4 6 -6 3}} = 250047/250000, extends to various higher limit rank three temperaments such as tyr and odin. In the pergen, the third-octave period is ~63/50, and ^1 = ~81/80.
-===[[Dimcomp family|Dimcomp or Quadruyoyo family]] (P8/4, P5, ^1)===
-The dimcomp family of rank three temperaments tempers out the dimcomp comma, {{Monzo|-1 -4 8 -4}} = 390625/388962. In the pergen, the quarter-octave period is ~25/21, and ^1 = ~81/80.
 ===[[Sengic family|Sengic or Trizo-agugu family]] (P8, P5, vm3/2)===
@@ Line 464: / Line 458: @@
 ===[[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.
+=== [[Landscape family|Landscape or Trizogugu family]] (P8/3, P5, ^1) ===
+The 7-limit rank three microtemperament which tempers out the lanscape comma, {{Monzo|-4 6 -6 3}} = 250047/250000, extends to various higher limit rank three temperaments such as tyr and odin. In the pergen, the third-octave period is ~63/50, and ^1 = ~81/80.
 ===[[Canou family|Canou or Saquadzo-atriyo family]] (P8, P5, vm6/3)===
 The canou family of rank three temperaments tempers out the canousma, {{Monzo|4 -14 3 4}} = 4802000/4782969. Three ~81/70 generators equal the pergen's downminor 6th of ~14/9.
+=== [[Dimcomp family|Dimcomp or Quadruyoyo family]] (P8/4, P5, ^1) ===
+The dimcomp family of rank three temperaments tempers out the dimcomp comma, {{Monzo|-1 -4 8 -4}} = 390625/388962. In the pergen, the quarter-octave period is ~25/21, and ^1 = ~81/80.
 ===[[Mirkwai family|Mirkwai or Quinru-aquadyo family]] (P8, P5, c^M7/4)===