Fractional-octave temperaments: Difference between revisions
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typed in the data, i'll finish the vals once I can |
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* [[Tritrizo clan #Schisennealimmal|Schisennealimmal]] (1\171 period) | * [[Tritrizo clan #Schisennealimmal|Schisennealimmal]] (1\171 period) | ||
* [[Tritrizo clan #Lunennealimmal|Lunennealimmal]] (1\441 period) | * [[Tritrizo clan #Lunennealimmal|Lunennealimmal]] (1\441 period) | ||
== 14th-octave temperaments == | |||
While 14edo is poor in LCJI harmonics, some of its multiples (such as [[224edo]] and [[742edo]]) are members of zeta edo list. | |||
=== Silicon === | |||
The name of silicon temperament comes from the 14th element. Defined upwards to the 13-limit. In 742edo, what's also unique is that it is generated by a [[53edo]] fifth intermingled with [[14edo]] periods. | |||
==== 5-limit ==== | |||
Subgroup: 2.3.5 | |||
Comma list: {{Monzo|-145 112 -14}} | |||
Mapping generators: ~282429536481/268435456000, ~3/2 | |||
Mapping: [{{val|14 14 -33}}, {{val|0 1 8}}] | |||
Optimal tuning (CTE): ~3/2 = 701.864 | |||
==== 7-limit ==== | |||
Subgroup: 2.3.5.7 | |||
Comma list: 14348907/14336000, 56358560858112/56296884765625 | |||
Mapping generators: ~6125/5832, ~3/2 | |||
Mapping: [{{val|14 14 -33 113}}, {{val|0 1 8 -9}}] | |||
Optimal tuning (CTE): ~3/2 = 701.870 | |||
==== 11-limit ==== | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 9801/9800, 1240029/1239040, 2359296/2358125 | |||
Mapping generators: ~605/576, ~3/2 | |||
Mapping: [{{val|14 14 -33 113 73}}, {{val|0 1 8 -9 -3}}] | |||
Optimal tuning (CTE): ~3/2 = 701.872 | |||
==== 13-limit ==== | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 4096/4095, 9801/9800, 67392/67375, 59535/59488 | |||
Mapping generators: ~104/99, ~3/2 | |||
Mapping: [{{val|14 14 -33 113 73 60}}, {{val|0 1 8 -9 -3 -1}}] | |||
Optimal tuning (CTE): ~3/2 = 701.873 | |||
Vals: {{EDOs|70d, 224, 294, 448, 518, 672, 742, 966, 1190, 1260}} | |||
== 37th-octave temperaments == | == 37th-octave temperaments == | ||