66th-octave temperaments: Difference between revisions
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Comma list: 9801/9800, 10241/10240, 250047/250000, 2955004695936/2954085800435 | Comma list: 9801/9800, 10241/10240, 250047/250000, 2955004695936/2954085800435 | ||
{{Mapping|legend= | {{Mapping|legend=3| 66 3 11 104 208 321 | 0 5 7 4 1 -2 }} | ||
: mapping generators: ~96/95 = 1\66, ~9625/7776 = 369.478 | : mapping generators: ~96/95 = 1\66, ~9625/7776 = 369.478 | ||
Latest revision as of 17:38, 30 September 2026
66edo might not be immediately recognizable for fractional-octave potential, but its step is in direct proximity to 96/95, a comma used in Ben Johnston's notation to distinguish 19-limit intervals from simpler ones.
Dysprosium (add-19)
Dysprosium is named after the 66th chemical element and can be described as the 198 & 1848 temperamet. Conceptualized as an add-19 subgroup temperament to accomodate for the subgroup of 96/95. 1848edo is an exceptional tuning.
Subgroup: 2.3.5.7.11.19
Comma list: 9801/9800, 10241/10240, 250047/250000, 2955004695936/2954085800435
Subgroup-val mapping: [⟨66 3 11 104 208 321], ⟨0 5 7 4 1 -2]]
- mapping generators: ~96/95 = 1\66, ~9625/7776 = 369.478
Optimal tuning (CTE): ~9625/7776 = 369.478
Supporting ETs: 198, 1650, 1848, ...