Tour of regular temperaments: Difference between revisions

Line 103:

: This tempers out the fifive comma, {{Monzo|-1 -14 10}} = 9765625/9565938. The period is ~4374/3125 = {{Monzo|1 7 -5}}, two of which make an octave. The generator is ~27/25, five of which make ~3/2. 5/4 is equated to 7 generators minus 1 period.

; [[~~Qintosec~~ family|~~Qintosec~~ or Quadsa-quinbigu family]] (P8/5, P5/2)

; [[Quintosec family|Quintosec or Quadsa-quinbigu family]] (P8/5, P5/2)

: This tempers out the ~~qintosec~~ comma, 140737488355328/140126044921875 = {{~~Monzo~~|47 -15 -10}}. The period is ~524288/455625 = {{~~Monzo~~|19 -6 -4}}, five of which equals an octave. The generator is ~16/15. A period plus a generator makes half a fifth. 5/4 is equated to 3 periods minus 3 generators. An obvious 7-limit interpretation of the period is 8/7.

: This tempers out the quintosec comma, 140737488355328/140126044921875 = {{monzo| 47 -15 -10 }}. The period is ~524288/455625 = {{monzo| 19 -6 -4 }}, five of which equals an octave. The generator is ~16/15. A period plus a generator makes half a fifth. 5/4 is equated to 3 periods minus 3 generators. An obvious 7-limit interpretation of the period is 8/7.

; [[Trisedodge family|Trisedodge or Saquintrigu family]] (P8/5, P4/3)

@@ Line 103: / Line 103: @@
 : This tempers out the fifive comma, {{Monzo|-1 -14 10}} = 9765625/9565938. The period is ~4374/3125 = {{Monzo|1 7 -5}}, two of which make an octave. The generator is ~27/25, five of which make ~3/2.  5/4 is equated to 7 generators minus 1 period.
-; [[Qintosec family|Qintosec or Quadsa-quinbigu family]] (P8/5, P5/2)
+; [[Quintosec family|Quintosec or Quadsa-quinbigu family]] (P8/5, P5/2)
-: This tempers out the qintosec comma, 140737488355328/140126044921875 = {{Monzo|47 -15 -10}}. The period is ~524288/455625 = {{Monzo|19 -6 -4}}, five of which equals an octave. The generator is ~16/15. A period plus a generator makes half a fifth. 5/4 is equated to 3 periods minus 3 generators. An obvious 7-limit interpretation of the period is 8/7.
+: This tempers out the quintosec comma, 140737488355328/140126044921875 = {{monzo| 47 -15 -10 }}. The period is ~524288/455625 = {{monzo| 19 -6 -4 }}, five of which equals an octave. The generator is ~16/15. A period plus a generator makes half a fifth. 5/4 is equated to 3 periods minus 3 generators. An obvious 7-limit interpretation of the period is 8/7.
 ; [[Trisedodge family|Trisedodge or Saquintrigu family]] (P8/5, P4/3)