Tour of regular temperaments: Difference between revisions

Line 128:

: The sensipent family tempers out the [[sensipent comma]], 78732/78125 ({{monzo| 2 9 -7 }}), also known as the medium semicomma. Its generator is {{nowrap| ~162/125 {{=}} ~443{{c}} }}. Seven generators equals a double-compound fifth of ~6/1. 5/4 is equated to 9 generators minus 3 octaves. Tunings include [[8edo]], [[19edo]], [[46edo]], and [[65edo]]. Its color name is Sepguti. An obvious 7-limit interpretation of the generator is 9/7, leading to the Sasepzoti temperament.

; [[~~Vishnuzmic~~ family]] (P8/2, P4/7)

; [[Vishnu family]] (P8/2, P4/7)

: This tempers out the [[~~vishnuzma~~]], {{monzo| 23 6 -14 }}, or the amount by which seven chromatic semitones (25/24) fall short of a perfect fourth (4/3), or (4/3)/(25/24)7. The period is ~{{monzo| -11 -3 7 }} and the generator is ~25/24. 5/4 is equated to 1 period minus 3 generators. Its color name is Sasepbiguti.

: This tempers out the [[vishnu comma]], {{monzo| 23 6 -14 }}, or the amount by which seven chromatic semitones (25/24) fall short of a perfect fourth (4/3), or (4/3)/(25/24)7. The period is ~{{monzo| -11 -3 7 }} and the generator is ~25/24. 5/4 is equated to 1 period minus 3 generators. Its color name is Sasepbiguti.

; [[Unicorn family]] (P8, P4/8)

Line 161:

: This tempers out the [[vavoom comma]], {{monzo| -68 18 17 }}. The generator is {{nowrap| ~16/15 {{=}} ~111.9{{c}} }}. Seventeen generators equals a twelfth (~3/1). 5/4 is equated to two octaves minus 18 generators. Its color name is Quinla-seyoti.

; [[~~Minortonic~~ family]] (P8, ccP5/17)

; [[Minortone family]] (P8, ccP5/17)

: This tempers out the [[minortone comma]], {{monzo| -16 35 -17 }}. The head of the family is ~~minortonic temperament~~, with a generator of a minor tone (~10/9). Seventeen generators equals a double-compound fifth (~6/1). 5/4 is equated to 35 generators minus 5 octaves. Its color name is Trila-seguti.

: This tempers out the [[minortone comma]], {{monzo| -16 35 -17 }}. The head of the family is minortone, with a generator of a minor tone (~10/9). Seventeen generators equals a double-compound fifth (~6/1). 5/4 is equated to 35 generators minus 5 octaves. Its color name is Trila-seguti.

; [[Maja family]] (P8, c6P4/17)

@@ Line 128: / Line 128: @@
 : The sensipent family tempers out the [[sensipent comma]], 78732/78125 ({{monzo| 2 9 -7 }}), also known as the medium semicomma. Its generator is {{nowrap| ~162/125 {{=}} ~443{{c}} }}. Seven generators equals a double-compound fifth of ~6/1. 5/4 is equated to 9 generators minus 3 octaves. Tunings include [[8edo]], [[19edo]], [[46edo]], and [[65edo]]. Its color name is Sepguti. An obvious 7-limit interpretation of the generator is 9/7, leading to the Sasepzoti temperament.
-; [[Vishnuzmic family]] (P8/2, P4/7)
+; [[Vishnu family]] (P8/2, P4/7)
-: This tempers out the [[vishnuzma]], {{monzo| 23 6 -14 }}, or the amount by which seven chromatic semitones (25/24) fall short of a perfect fourth (4/3), or (4/3)/(25/24)<sup>7</sup>. The period is ~{{monzo| -11 -3 7 }} and the generator is ~25/24. 5/4 is equated to 1 period minus 3 generators. Its color name is Sasepbiguti.
+: This tempers out the [[vishnu comma]], {{monzo| 23 6 -14 }}, or the amount by which seven chromatic semitones (25/24) fall short of a perfect fourth (4/3), or (4/3)/(25/24)<sup>7</sup>. The period is ~{{monzo| -11 -3 7 }} and the generator is ~25/24. 5/4 is equated to 1 period minus 3 generators. Its color name is Sasepbiguti.
 ; [[Unicorn family]] (P8, P4/8)
@@ Line 161: / Line 161: @@
 : This tempers out the [[vavoom comma]], {{monzo| -68 18 17 }}. The generator is {{nowrap| ~16/15 {{=}} ~111.9{{c}} }}. Seventeen generators equals a twelfth (~3/1). 5/4 is equated to two octaves minus 18 generators. Its color name is Quinla-seyoti.
-; [[Minortonic family]] (P8, ccP5/17)
+; [[Minortone family]] (P8, ccP5/17)
-: This tempers out the [[minortone comma]], {{monzo| -16 35 -17 }}. The head of the family is minortonic temperament, with a generator of a minor tone (~10/9). Seventeen generators equals a double-compound fifth (~6/1). 5/4 is equated to 35 generators minus 5 octaves. Its color name is Trila-seguti.
+: This tempers out the [[minortone comma]], {{monzo| -16 35 -17 }}. The head of the family is minortone, with a generator of a minor tone (~10/9). Seventeen generators equals a double-compound fifth (~6/1). 5/4 is equated to 35 generators minus 5 octaves. Its color name is Trila-seguti.
 ; [[Maja family]] (P8, c<sup>6</sup>P4/17)