Tour of regular temperaments: Difference between revisions

These are families defined by a 3-limit (color name: wa) comma. If only primes 2 and 3 are part of the [[subgroup]], the comma creates a rank-1 temperament, an [[edo]]. But if another prime such as 5 is present, the comma creates a rank-2 temperament. Since edos are discussed elsewhere, this section assumes the presence of at least one additional prime. The rank-2 temperament created consists of multiple "copies" of an edo. The edo copies can be thought of as being offset from one another by a small comma. This small comma is represented in the [[pergen]] by ^1.  

; [[Whitewood family]] (P8/7, ^1)

: 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.  

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

; [[Ditonmic family]] (P8, c4P4/13)

: This tempers out the [[ditonma]], {{monzo| -27 -2 13 }} (1220703125/1207959552). Thirteen ~{{monzo| -12 -1 6 }} generators of about 407{{c}} equals a quadruple-compound fourth. 5/4 is equated to 1 octave minus 2 generators. An obvious 3-limit interpretation of the generator is 81/64, which implies 53edo, which is a good tuning for this high-accuracy family of temperaments. Its color name is Lala-theyoti.  

; [[Luna family]] (P8, ccP4/15)

: 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.  

; [[Maja family]] (P8, c⁶P4/17)

; [[Gammic family]] (P8, P5/20)

=== Clans defined by a 2.3.7 comma ===

; [[Garischismic clan]] (P8, P5)

; Sasazoti clan (P8, P5)

; [[Buzzardsmic clan]] (P8, P12/4)

: This clan tempers out the [[buzzardsma]], {{monzo| 16 -3 0 -4 }} (65536/64827). Its generator is ~21/16. Four generators makes ~3/1. 7/4 is equated to 2 octaves minus 3 generators. Its color name is Saquadruti. This clan includes as a strong extension the [[Vulture family #Septimal vulture|vulture]] temperament, which is in the vulture family.  

; Quinruti clan (P8, P5/5)

: These temper out the [[avicennma]], {{monzo| -9 1 2 1 }} (525/512), also known as Avicenna's enharmonic diesis. Its color name is Zoyoyoti.  

: Sengic rank-2 temperaments temper out the [[senga]], {{monzo| 1 -3 -2 3 }} (686/675). Its color name is Trizo-aguguti.  

: Cataharry rank-2 temperaments temper out the [[cataharry comma]], {{monzo| -4 9 -2 -2 }} (19683/19600). Its color name is Labiruguti.  

; [[Triwellismic temperaments]]

: The gariboh family of rank-3 temperaments tempers out the gariboh comma, {{monzo| 0 -2 5 -3 }} (3125/3087). Three ~25/21 generators equal the pergen's downmajor sixth of ~5/3. Its color name is Triru-aquinyoti.  

; [[Dimcomp family]] (P8/4, P5, ^1)  

: These temper out the [[4000/3993|wizardharry comma]], {{monzo| 5 -1 3 0 -3 }} (4000/3993), and split the fourth in three. In the pergen, ^1 is either ~33/32 or ~729/704. Its color name is Triluyoti.  

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

== Miscellaneous other temperaments ==

; [[Fractional-octave temperaments]]

: These temperaments all have a fractional-octave period.