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==== Tridecimal meantone ====
==== Tridecimal meantone ====
Subgroup: 2.3.5.7.11.13
{{Temperament data|subgroup=2.3.5.7.11.13|comma_list=66/65, 81/80, 99/98, 105/104|generators=2/1,3/2}}
 
Comma list: 66/65, 81/80, 99/98, 105/104
 
Mapping: {{mapping| 1 0 -4 -13 -25 -20 | 0 1 4 10 18 15 }}
 
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.8552
 
Minimax tuning:
* 13- and 15-odd-limit: ~3/2 = {{monzo| 9/16 -1/8 0 0 1/16 }}
: eigenmonzo (unchanged-interval) basis: 2.11/9
 
{{Optimal ET sequence|legend=1| 12f, 19e, 31 }}
 
Badness: 0.018048


===== 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.  


Subgroup: 2.3.5.7.11.13.17
{{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}}
 
Comma list: 66/65, 81/80, 99/98, 105/104, 121/119
 
Mapping: {{mapping| 1 0 -4 -13 -25 -20 -37 | 0 1 4 10 18 15 26 }}
 
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.6486
 
{{Optimal ET sequence|legend=1| 12fg, 19eg, 31, 50e }}
 
Badness: 0.019037


====== 19-limit ======
====== 19-limit ======
Subgroup: 2.3.5.7.11.13.17.19
{{Temperament data|subgroup=2.3.5.7.11.13.17.19|comma_list=66/65, 77/76, 81/80, 99/98, 105/104, 121/1199|generators=2/1,3/2}}
 
Comma list: 66/65, 77/76, 81/80, 99/98, 105/104, 121/119
 
Mapping: {{mapping| 1 0 -4 -13 -25 -20 -37 -40 | 0 1 4 10 18 15 26 28 }}
 
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.5551
 
{{Optimal ET sequence|legend=1| 12fghh, 19egh, 31, 50e }}
 
Badness: 0.017846


===== Meantoid =====
===== Meantoid =====
Retrieved from "https://en.xen.wiki/w/User:CompactStar/Meantone_family"