6th-octave temperaments
- 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