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.

; Septimagic clan (P8, P12/5)

; [[Septimagic clan]] (P8, P12/5)

: 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.

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: This 2.3.11 clan tempers out the [[nexus comma]] {{monzo| -16 -3 0 0 6 }}. Its 1/3-octave period is ~121/96 and its least-cents generator is ~12/11. A period plus a generator equals ~11/8. Six of these generators equals ~27/16. A period minus a generator equals ~1331/1152 or ~1536/1331. Two of these alternative generators equals ~4/3. Its color name is Tribiloti.

; Alphaxenic ~~or Laquadloti~~ clan (P8/2, M2/4)

; Alphaxenic clan (P8/2, M2/4)

: This 2.3.11 clan tempers out the [[Alpharabian comma]] {{monzo| -17 2 0 0 4 }}. Its half-octave period is ~363/256, and its generator is ~33/32. Four generators equals ~9/8. 3/2 is equated to a period plus 2 generators, and 11/8 is equated to a period minus a generator. This clan includes a strong extension to the comic or Saquadyobiti temperament, which is in the jubilismic clan. Its color name is Laquadloti.

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

; ~~Quinzo-atriyoti Nowa~~ clan (P8, M3/5)

; Rainy clan (P8, M3/5)

: This clan tempers out the [[rainy comma]], {{monzo| -21 0 3 5 }} (2100875/2097152). The generator is {{nowrap| ~256/245 {{=}} ~77{{c}} }}. Three generators equals ~8/7 and five of them equals the classic major third (~5/4).

: This clan tempers out the [[rainy comma]], {{monzo| -21 0 3 5 }} (2100875/2097152). The generator is {{nowrap| ~256/245 {{=}} ~77{{c}} }}. Three generators equals ~8/7 and five of them equals the classic major third (~5/4). Its color name is Quinzo-atriyoti Nowa.

; [[Llywelynsmic clan]] (P8, cM3/7)

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; [[Quince clan]] (P8, m6/7)

: This clan tempers out the [[quince comma]], {{monzo| -15 0 -2 7 }} (823543/819200). The generator is {{nowrap| ~343/320 {{=}} ~116{{c}} }}. Two generators equals ~8/7, five generators equals ~7/5, and seven generators equals the classical minor sixth ~8/5. An obvious 5-limit interpretation of the generator is ~16/15, leading to the [[miracle]] temperament, which is in the gamelismic clan. Its color name is Lasepzo-aguguti Nowa.

; Exodia clan (P8, ccM3/8)

: This clan tempers out the [[exodia comma]], {{monzo| -48 0 11 8 }}. The generator is {{nowrap| ~262144/214375 {{=}} ~348{{c}} }}. Eight generators equals ~5/1, 11 of them equals ~64/7, and 19 of them equals ~320/7 (five octaves above ~10/7). Its color name is Trila-quadbizo-aleyoti Nowa.

; Slither clan (P8, ccm6/9)

@@ 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.
-; Septimagic clan (P8, P12/5)
+; [[Septimagic clan]] (P8, P12/5)
 : 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.
@@ Line 257: / Line 257: @@
 : This 2.3.11 clan tempers out the [[nexus comma]] {{monzo| -16 -3 0 0 6 }}. Its 1/3-octave period is ~121/96 and its least-cents generator is ~12/11. A period plus a generator equals ~11/8. Six of these generators equals ~27/16. A period minus a generator equals ~1331/1152 or ~1536/1331. Two of these alternative generators equals ~4/3. Its color name is Tribiloti.
-; Alphaxenic or Laquadloti clan (P8/2, M2/4)
+; Alphaxenic clan (P8/2, M2/4)
 : This 2.3.11 clan tempers out the [[Alpharabian comma]] {{monzo| -17 2 0 0 4 }}. Its half-octave period is ~363/256, and its generator is ~33/32. Four generators equals ~9/8. 3/2 is equated to a period plus 2 generators, and 11/8 is equated to a period minus a generator. This clan includes a strong extension to the comic or Saquadyobiti temperament, which is in the jubilismic clan. Its color name is Laquadloti.
@@ Line 287: / Line 287: @@
 : This clan tempers out the [[vorwell comma]] (named for being tempered in [[septimal vulture]] and [[orwell]]), {{monzo| 27 0 -8 -3 }} (134217728/133984375). The generator is {{nowrap| ~1024/875 {{=}} ~272{{c}} }}. Three generators equals ~8/5 and eight of them equals ~7/2. Its color name is Sasatriru-aquadbiguti Nowa.
-; Quinzo-atriyoti Nowa clan (P8, M3/5)
+; Rainy clan (P8, M3/5)
-: This clan tempers out the [[rainy comma]], {{monzo| -21 0 3 5 }} (2100875/2097152). The generator is {{nowrap| ~256/245 {{=}} ~77{{c}} }}. Three generators equals ~8/7 and five of them equals the classic major third (~5/4).
+: This clan tempers out the [[rainy comma]], {{monzo| -21 0 3 5 }} (2100875/2097152). The generator is {{nowrap| ~256/245 {{=}} ~77{{c}} }}. Three generators equals ~8/7 and five of them equals the classic major third (~5/4). Its color name is Quinzo-atriyoti Nowa.
 ; [[Llywelynsmic clan]] (P8, cM3/7)
@@ Line 295: / Line 295: @@
 ; [[Quince clan]] (P8, m6/7)
 : This clan tempers out the [[quince comma]], {{monzo| -15 0 -2 7 }} (823543/819200). The generator is {{nowrap| ~343/320 {{=}} ~116{{c}} }}. Two generators equals ~8/7, five generators equals ~7/5, and seven generators equals the classical minor sixth ~8/5. An obvious 5-limit interpretation of the generator is ~16/15, leading to the [[miracle]] temperament, which is in the gamelismic clan. Its color name is Lasepzo-aguguti Nowa.
+; Exodia clan (P8, ccM3/8)
+: This clan tempers out the [[exodia comma]], {{monzo| -48 0 11 8 }}. The generator is {{nowrap| ~262144/214375 {{=}} ~348{{c}} }}. Eight generators equals ~5/1, 11 of them equals ~64/7, and 19 of them equals ~320/7 (five octaves above ~10/7). Its color name is Trila-quadbizo-aleyoti Nowa.
 ; Slither clan (P8, ccm6/9)