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Tour of regular temperaments: Difference between revisions

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=== Clans defined by a 2.5.7 comma ===
=== Clans defined by a 2.5.7 comma ===
These are defined by a no-3's 7-limit (color name: yaza nowa) comma. See also [[subgroup temperaments]]. The pergen's multigen (the second term, omitting any fraction) is always a no-3's 5-limit ratio such as 5/4, 8/5, 25/8, etc.
These are defined by a no-3's 7-limit (color name: yaza nowa) comma. See also [[No-threes subgroup temperaments]]. The pergen's multigen (the second term, omitting any fraction) is always a no-3's 5-limit ratio such as 5/4, 8/5, 25/8, etc.


; [[Jubilismic clan]] (P8/2, M3)
; [[Jubilismic clan]] (P8/2, M3)
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; Rainy 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). Its color name is Quinzo-atriyoti Nowa.
: 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)
: This clan tempers out the [[llywelynsma]], {{monzo| 22 0 -1 -7 }} (4194304/4117715). The generator is {{nowrap| ~8/7 {{=}} ~227{{c}} }} and seven of them equals ~5/2. Its color name is Sasepru-aguti Nowa.
; [[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)
; Exodia clan (P8, ccM3/8)
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; Slither clan (P8, ccm6/9)
; Slither clan (P8, ccm6/9)
: This clan tempers out the [[slither comma]], {{monzo| 16 0 4 -9 }} (40960000/40353607). The generator is {{nowrap| ~49/40 {{=}} ~357{{c}} }}. Four generators equals ~16/7, five of them equals ~14/5, and nine of them equals a double-compound minor sixth of ~32/5. Its color name is Satritriru-aquadyoti Nowa.  
: This clan tempers out the [[slither comma]], {{monzo| 16 0 4 -9 }} (40960000/40353607). The generator is {{nowrap| ~49/40 {{=}} ~357{{c}} }}. Four generators equals ~16/7, five of them equals ~14/5, and nine of them equals a double-compound minor sixth of ~32/5. Its color name is Satritriru-aquadyoti Nowa.


=== Clans defined by a 3.5.7 comma ===
=== Clans defined by a 3.5.7 comma ===
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