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.

Fractional-octave temperaments

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← 5th-octave • 6th-octave • 7th-octave →

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

Main article: 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