34th-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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← 33rd-octave • 34th-octave • 35th-octave →

This page collects rank-2 temperaments with a period that is 1/34 of an octave.

34edo is a good tuning for harmonics 3, 5, 13 and 17, so giving an independent generator with 1/34-octave period makes sense. This approach leads to the hemigoth temperament.

Hemigoth

Hemigoth is identical to 34et in the no-7 subgroups, but has an independent generator for prime 7.

Subgroup: 2.3.5.7

Comma list: 2048/2025, 15625/15552

Mapping: [⟨34 54 79 0], ⟨0 0 0 1]]

Optimal tunings:

• CTE: ~81/80 = 35.294 ¢ (1 ⧵ 34), ~7/4 = 968.826 ¢
• CWE: ~81/80 = 35.294 ¢ (1 ⧵ 34), ~7/4 = 971.146 ¢

Optimal ET sequence: 34d, 68

Badness (Sintel): 3.383