Tour of regular temperaments: Difference between revisions

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: This clan tempers out the [[bleu comma]], {{monzo| 3 7 0 -5 }} (17496/16807). The ~54/49 generator is about 139{{c}}. Two of them equal ~7/6, three equal ~9/7, five equal ~3/2, and seven equal ~7/4.

; ~~Saquinzoti~~ clan (P8, P12/5)

; Septimagic clan (P8, P12/5)

: This clan tempers out the ~~Saquinzo~~ comma, {{monzo| 5 -12 0 5 }} (537824/531441). Its generator is {{nowrap| ~243/196 {{=}} ~380{{c}} }}. Five generators makes ~3/1. 7/4 is equated to 12 generators minus 3 octaves. An obvious 5-limit interpretation of the generator is 5/4, leading to the [[magic]] temperament, which is in the magic family.

: This clan tempers out the [[septimagic comma]], {{monzo| 5 -12 0 5 }} (537824/531441). Its generator is {{nowrap| ~243/196 {{=}} ~380{{c}} }}. Five generators makes ~3/1. 7/4 is equated to 12 generators minus 3 octaves. An obvious 5-limit interpretation of the generator is 5/4, leading to the [[magic]] temperament, which is in the magic family. Its color name is Saquinzoti.

; Lasepzoti clan (P8, P11/7)

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; [[Pentacircle clan]] (P8, P5, ^1)

: These temper out the [[pentacircle comma]], {{monzo| 7 -4 0 1 -1 }} (896/891). The interval between 11/8 and 7/4 is equated to 81/64. Since that is a 3-limit interval, every 2.3.11 interval is equated to a 2.3.7 interval and vice versa, and both the pergen and the lattice are identical to that of either 2.3.7 JI or 2.3.11 JI. In the pergen, ^1 is either ~64/63 or ~33/32 or ~729/704. Its color name is Saluzoti.

; [[Moctdel clan]]

: These temper out the [[moctdel comma]], {{monzo| -2 0 3 -3 1 }} (1375/1372). To be a rank-3 temperament, either an additional comma must vanish or the prime subgroup must omit prime 3. Thus no assumptions can be made about the pergen. Its color name is Lotriruyoti.

; [[Semicanousmic clan]] (P8, P5, ^1)

@@ Line 230: / Line 230: @@
 : This clan tempers out the [[bleu comma]], {{monzo| 3 7 0 -5 }} (17496/16807). The ~54/49 generator is about 139{{c}}. Two of them equal ~7/6, three equal ~9/7, five equal ~3/2, and seven equal ~7/4.
-; Saquinzoti clan (P8, P12/5)
+; Septimagic clan (P8, P12/5)
-: This clan tempers out the Saquinzo comma, {{monzo| 5 -12 0 5 }} (537824/531441). Its generator is {{nowrap| ~243/196 {{=}} ~380{{c}} }}. Five generators makes ~3/1. 7/4 is equated to 12 generators minus 3 octaves. An obvious 5-limit interpretation of the generator is 5/4, leading to the [[magic]] temperament, which is in the magic family.
+: This clan tempers out the [[septimagic comma]], {{monzo| 5 -12 0 5 }} (537824/531441). Its generator is {{nowrap| ~243/196 {{=}} ~380{{c}} }}. Five generators makes ~3/1. 7/4 is equated to 12 generators minus 3 octaves. An obvious 5-limit interpretation of the generator is 5/4, leading to the [[magic]] temperament, which is in the magic family. Its color name is Saquinzoti.
 ; Lasepzoti clan (P8, P11/7)
@@ Line 612: / Line 612: @@
 ; [[Pentacircle clan]] (P8, P5, ^1)
 : These temper out the [[pentacircle comma]], {{monzo| 7 -4 0 1 -1 }} (896/891). The interval between 11/8 and 7/4 is equated to 81/64. Since that is a 3-limit interval, every 2.3.11 interval is equated to a 2.3.7 interval and vice versa, and both the pergen and the lattice are identical to that of either 2.3.7 JI or 2.3.11 JI. In the pergen, ^1 is either ~64/63 or ~33/32 or ~729/704. Its color name is Saluzoti.
+; [[Moctdel clan]]
+: These temper out the [[moctdel comma]], {{monzo| -2 0 3 -3 1 }} (1375/1372). To be a rank-3 temperament, either an additional comma must vanish or the prime subgroup must omit prime 3. Thus no assumptions can be made about the pergen. Its color name is Lotriruyoti.
 ; [[Semicanousmic clan]] (P8, P5, ^1)