6th-octave temperaments: Difference between revisions
No edit summary |
we don't use temperament data on comma pages so putting it here and cleaning temp data from Spoob |
||
| (14 intermediate revisions by 5 users not shown) | |||
| Line 1: | Line 1: | ||
{{Technical data page}} | |||
{{Infobox fractional-octave|6}} | |||
[[6edo]] is called the whole tone scale, therefore 6th-octave temperaments include various temperaments where the period is an interval classified as a "tone". | [[6edo]] is called the whole tone scale, therefore 6th-octave temperaments include various temperaments where the period is an interval classified as a "tone". | ||
Temperaments discussed elsewhere include [[Augmented family #Hexe|hexe]], [[Misty family #Semimist|semimist]], [[Schismatic family #Semiterm|semiterm]], [[Garischismic clan #Sextile|sextile]], and [[Stearnsmic clan #Stearnscape|stearnscape]]. | |||
Considered below is spoob. | |||
== Spoob == | == Spoob == | ||
{{Main|Spoob}} | |||
[[Subgroup]]: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
| Line 7: | Line 14: | ||
[[Comma list]]: 27682574402/27680640625 | [[Comma list]]: 27682574402/27680640625 | ||
{{mapping|legend=1|6 0 0 0 1|0 1 0 0 0|0 0 1 0 -1|0 0 0 1 2}} | {{mapping|legend=1| 6 0 0 0 1 | 0 1 0 0 0 | 0 0 1 0 -1 | 0 0 0 1 2 }} | ||
: mapping generators: ~55/49, ~3, ~5, ~7 | |||
{{Optimal ET sequence|legend=1| 72, 198, 270, 342, 612, 954, 1236, 1506, 1578, 1848, 3426, 4038, 5616, 6390, 6660, 7002, 7626, 7896, 8238, 8850, 9744, 9816, 10086, 10428, 11664, 11934, 12276, 36216, 48492, 60768, 84978, 97254, 98832d }} | |||
[[Badness]] (Sintel): 3.91 | |||
=== Spoob retraction === | |||
[[Subgroup]]: 2.5.7.11 | |||
[[Comma list]]: 27682574402/27680640625 | |||
{{Mapping|legend=2| 6 0 0 1 | 0 1 0 -1 | 0 0 1 2 }} | |||
: mapping generators: ~55/49, ~5, ~7 | |||
{{Optimal ET sequence|legend=1| 72, 150, 186, 192, 198, 264, 270, 342, 348, 612, 618, 960, 1578, 7542, 8160, 9120, 10698, 12276, 13854, 23592, 25170, 26748, 28326, 40602, 42180, 67350, 68928 }} | |||
[[Badness]] (Sintel): 0.165 | |||
{{Navbox fractional-octave}} | |||
[[ | [[Category:6edo]] | ||
Latest revision as of 23:27, 5 September 2026
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
6edo is called the whole tone scale, therefore 6th-octave temperaments include various temperaments where the period is an interval classified as a "tone".
Temperaments discussed elsewhere include hexe, semimist, semiterm, sextile, and stearnscape.
Considered below is spoob.
Spoob
Subgroup: 2.3.5.7.11
Comma list: 27682574402/27680640625
Mapping: [⟨6 0 0 0 1], ⟨0 1 0 0 0], ⟨0 0 1 0 -1], ⟨0 0 0 1 2]]
- mapping generators: ~55/49, ~3, ~5, ~7
Optimal ET sequence: 72, 198, 270, 342, 612, 954, 1236, 1506, 1578, 1848, 3426, 4038, 5616, 6390, 6660, 7002, 7626, 7896, 8238, 8850, 9744, 9816, 10086, 10428, 11664, 11934, 12276, 36216, 48492, 60768, 84978, 97254, 98832d
Badness (Sintel): 3.91
Spoob retraction
Subgroup: 2.5.7.11
Comma list: 27682574402/27680640625
Subgroup-val mapping: [⟨6 0 0 1], ⟨0 1 0 -1], ⟨0 0 1 2]]
- mapping generators: ~55/49, ~5, ~7
Optimal ET sequence: 72, 150, 186, 192, 198, 264, 270, 342, 348, 612, 618, 960, 1578, 7542, 8160, 9120, 10698, 12276, 13854, 23592, 25170, 26748, 28326, 40602, 42180, 67350, 68928
Badness (Sintel): 0.165