User:CompactStar/Meantone family: Difference between revisions
CompactStar (talk | contribs) Created page with "THIS IS A TESTING PAGE FOR TEMPLATES The 5-limit parent comma of the '''meantone family''' is the syntonic comma, 81/80. This is the one they all temper out. The..." |
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Undecimal meantone maps the [[11/8]] to the double augmented third (C-Ex), and tridecimal meantone maps the [[13/8]] to the double augmented fifth (C-Gx). Note 13/11 is conflated with 6/5, represented by the minor third. Note also 11/10~13/12 is the double augmented unison; 12/11, double diminished third; and 14/13, minor second. | Undecimal meantone maps the [[11/8]] to the double augmented third (C-Ex), and tridecimal meantone maps the [[13/8]] to the double augmented fifth (C-Gx). Note 13/11 is conflated with 6/5, represented by the minor third. Note also 11/10~13/12 is the double augmented unison; 12/11, double diminished third; and 14/13, minor second. | ||
{{Temperament data|subgroup=2.3.5.7.11|comma_list=81/80, 99/98, 126/125|generators=2/1,3/2}} | |||
; Music | ; Music | ||
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==== Tridecimal meantone ==== | ==== Tridecimal meantone ==== | ||
{{Temperament data|subgroup=2.3.5.7.11.13|comma_list=66/65, 81/80, 99/98, 105/104|generators=2/1,3/2}} | |||
===== Meantonic ===== | ===== Meantonic ===== | ||
Dubbed ''meantonic'' here, this extension maps the 17/16 to the triple augmented seventh (C-Bx#) octave reduced, and 19/16 to the quadruple augmented unison (C-Cxx). The major second is now 19/17, and 17/16 is conflated with 19/18, as do all the other extensions discussed below. 31edo also conflates 17/16~19/18 with 16/15 whereas 50edo conflates all of 17/16, 18/17, 19/18, and 20/19, so a good tuning would be somewhere in this range. | Dubbed ''meantonic'' here, this extension maps the 17/16 to the triple augmented seventh (C-Bx#) octave reduced, and 19/16 to the quadruple augmented unison (C-Cxx). The major second is now 19/17, and 17/16 is conflated with 19/18, as do all the other extensions discussed below. 31edo also conflates 17/16~19/18 with 16/15 whereas 50edo conflates all of 17/16, 18/17, 19/18, and 20/19, so a good tuning would be somewhere in this range. | ||
{{Temperament data|subgroup=2.3.5.7.11.13.17|comma_list=66/65, 81/80, 99/98, 105/104, 121/119|generators=2/1,3/2}} | |||
====== 19-limit ====== | ====== 19-limit ====== | ||
{{Temperament data|subgroup=2.3.5.7.11.13.17.19|comma_list=66/65, 77/76, 81/80, 99/98, 105/104, 121/119|generators=2/1,3/2}} | |||
===== Meantoid ===== | ===== Meantoid ===== | ||