80th-octave temperaments

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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 GPV sequence720, 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 GPV 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 GPV 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

Vals: 320, 1680d, 2000, 2320, 4320