Tour of regular temperaments: Difference between revisions

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; [[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 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.

: 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.

; [[Mabilismic clan|Mabilismic or Latrizo-aquiniyo Nowa clan]] (P8, cM3/3)

: This clan tempers out the mabilisma, {{~~Monzo~~|-20 0 5 3}} = 1071875/1048576. The generator is ~175/128 = ~527¢. Three generators equals ~5/2 and five of them equals ~32/7.

: This clan tempers out the mabilisma, {{monzo| -20 0 5 3 }} = 1071875/1048576. The generator is ~175/128 = ~527¢. Three generators equals ~5/2 and five of them equals ~32/7.

; Vorwell or Sasatriru-aquadbigu Nowa clan (P8, m6/3)

: This clan tempers out the vorwell comma (named for being tempered in [[septimal vulture]] and [[orwell]]), {{~~Monzo~~|27 0 -8 -3}} = 134217728/133984375. The rutrigu generator is ~1024/875 = ~272¢. Three generators equals ~8/5 and eight of them equals ~7/2.

: This clan tempers out the vorwell comma (named for being tempered in [[septimal vulture]] and [[orwell]]), {{monzo| 27 0 -8 -3 }} = 134217728/133984375. The rutrigu generator is ~1024/875 = ~272¢. Three generators equals ~8/5 and eight of them equals ~7/2.

; Rainy or Quinzo-atriyo Nowa clan (P8, M3/5)

: 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.

: 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.

; [[~~Llywelyn~~ clan|~~Llywelyn~~ or Sasepru-agu Nowa clan]] (P8, cM3/7)

; [[Llywelynsmic clan|Llywelynsmic or Sasepru-agu Nowa clan]] (P8, cM3/7)

: This clan tempers out the ~~llywelyn comma~~, {{~~Monzo~~|22 0 -1 -7}} = 4194304/4117715. The generator is ~8/7 = ~227¢ and seven of them equals ~5/2.

: This clan tempers out the [[llywelynsma]], {{monzo| 22 0 -1 -7 }} = 4194304/4117715. The generator is ~8/7 = ~227¢ and seven of them equals ~5/2.

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

: 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.

: 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.

; Slither or Satritriru-aquadyo Nowa clan (P8, ccm6/9)

: This clan tempers out the slither comma, {{~~Monzo~~|16 0 4 -9}} = 40960000/40353607. The generator is ~49/40 = ~357¢. Four generators equals ~16/7, five of them equals ~14/5, and nine of them equals a double-compound minor 6th of ~32/5.

: This clan tempers out the slither comma, {{monzo| 16 0 4 -9 }} = 40960000/40353607. The generator is ~49/40 = ~357¢. Four generators equals ~16/7, five of them equals ~14/5, and nine of them equals a double-compound minor 6th of ~32/5.

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

@@ Line 278: / Line 278: @@
 ; [[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 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.
+: 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.
 ; [[Mabilismic clan|Mabilismic or Latrizo-aquiniyo Nowa clan]] (P8, cM3/3)
-: This clan tempers out the mabilisma, {{Monzo|-20 0 5 3}} = 1071875/1048576. The generator is ~175/128 = ~527¢. Three generators equals ~5/2 and five of them equals ~32/7.
+: This clan tempers out the mabilisma, {{monzo| -20 0 5 3 }} = 1071875/1048576. The generator is ~175/128 = ~527¢. Three generators equals ~5/2 and five of them equals ~32/7.
 ; Vorwell or Sasatriru-aquadbigu Nowa clan (P8, m6/3)
-: This clan tempers out the vorwell comma (named for being tempered in [[septimal vulture]] and [[orwell]]), {{Monzo|27 0 -8 -3}} = 134217728/133984375. The rutrigu generator is ~1024/875 = ~272¢. Three generators equals ~8/5 and eight of them equals ~7/2.
+: This clan tempers out the vorwell comma (named for being tempered in [[septimal vulture]] and [[orwell]]), {{monzo| 27 0 -8 -3 }} = 134217728/133984375. The rutrigu generator is ~1024/875 = ~272¢. Three generators equals ~8/5 and eight of them equals ~7/2.
 ; Rainy or Quinzo-atriyo Nowa clan (P8, M3/5)
-: 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.
+: 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.
-; [[Llywelyn clan|Llywelyn or Sasepru-agu Nowa clan]] (P8, cM3/7)
+; [[Llywelynsmic clan|Llywelynsmic or Sasepru-agu Nowa clan]] (P8, cM3/7)
-: This clan tempers out the llywelyn comma, {{Monzo|22 0 -1 -7}} = 4194304/4117715. The generator is ~8/7 = ~227¢ and seven of them equals ~5/2.
+: This clan tempers out the [[llywelynsma]], {{monzo| 22 0 -1 -7 }} = 4194304/4117715. The generator is ~8/7 = ~227¢ and seven of them equals ~5/2.
 ; [[Quince clan|Quince or Lasepzo-agugu Nowa clan]] (P8, m6/7)
-: 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.
+: 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.
 ; Slither or Satritriru-aquadyo Nowa clan (P8, ccm6/9)
-: This clan tempers out the slither comma, {{Monzo|16 0 4 -9}} = 40960000/40353607. The generator is ~49/40 = ~357¢. Four generators equals ~16/7, five of them equals ~14/5, and nine of them equals a double-compound minor 6th of ~32/5.
+: This clan tempers out the slither comma, {{monzo| 16 0 4 -9 }} = 40960000/40353607. The generator is ~49/40 = ~357¢. Four generators equals ~16/7, five of them equals ~14/5, and nine of them equals a double-compound minor 6th of ~32/5.
 === Clans defined by a 3.5.7 (yaza noca) comma ===