80th-octave temperaments: Difference between revisions
→Mercury: just calculated that myself since there's only 3 vals and 2320 has worse te error so it doesn't count |
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
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[[Optimal tuning]] ([[CTE]]): ~7381125/5619712 = 471.7339 | [[Optimal tuning]] ([[CTE]]): ~7381125/5619712 = 471.7339 | ||
{{ | {{Optimal ET sequence|legend=1| 720, 1600, 2320, 3920 }} | ||
[[Badness]]: 1.49 | [[Badness]]: 1.49 | ||
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Optimal tuning (CTE): ~2278125/1734656 = 471.7342 | Optimal tuning (CTE): ~2278125/1734656 = 471.7342 | ||
Optimal | {{Optimal ET sequence|legend=1| 720, 1600, 2320, 3920 }} | ||
Badness: 0.178 | Badness: 0.178 | ||
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Optimal tuning (CTE): ~130/99 = 471.7322 | Optimal tuning (CTE): ~130/99 = 471.7322 | ||
Optimal | {{Optimal ET sequence|legend=1| 720, 1600, 2320, 3920 }} | ||
Badness: 0.0741 | Badness: 0.0741 | ||
Revision as of 16:10, 7 May 2023
This page describes 80th-octave temperaments.
80edo is extremely accurate for the 17th harmonic, a relationship which is seen in some of these temperaments.
Octogintic
Main article: Parkleiness temperaments#Octogintic
Tetraicosic
Tetraicosic is described as 720 & 1600, and named after the fact that 4 × 20 = 80.
Subgroup: 2.3.5.7
Comma list: [-52 17 12 -1⟩, [25 42 -8 -26⟩
Mapping: [⟨80 1 343 -27], ⟨0 4 -5 8]]
Mapping generators: ~31637227888/31381059609, ~7381125/5619712
Optimal tuning (CTE): ~7381125/5619712 = 471.7339
Optimal ET sequence: 720, 1600, 2320, 3920
Badness: 1.49
11-limit
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 928760463360/928426965851, [49 -13 -14 -1 2⟩
Mapping: [⟨80 1 343 -27 434], ⟨0 4 -5 8 -5]]
Optimal tuning (CTE): ~2278125/1734656 = 471.7342
Optimal ET sequence: 720, 1600, 2320, 3920
Badness: 0.178
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 9801/9800, 4100625/4100096, 14236560/14235529, 143327232/143286143
Mapping: [⟨80 1 343 -27 434 13], ⟨0 4 -5 8 -5 9]]
Optimal tuning (CTE): ~130/99 = 471.7322
Optimal ET sequence: 720, 1600, 2320, 3920
Badness: 0.0741
Mercury
Named after the 80th element, defined as the 320 & 2000 temperament. 7 periods are mapped to ~17/16, 11 periods are mapped to ~11/10.
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 9801/9800, 12376/12375, 67392/67375, 392445/392392, 401408/401375, 1549184/1549125
Mapping: [⟨80 3 161 -23 252 197 327 117], ⟨0 5 1 10 1 4 0 9]]
Mapping generators: ~459/455, ~2275/1836.
Optimal tuning (CTE): ~2275/1836 = 371.386