1759edo: Difference between revisions
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {{comma basis begin}} | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{monzo|2788 -1759}} | | {{monzo|2788 -1759}} | ||
| {{mapping|1759 2788}} | | {{mapping|1759 2788}} | ||
| | | −0.0110 | ||
| 0.0110 | | 0.0110 | ||
| 1.61 | | 1.61 | ||
| Line 70: | Line 62: | ||
| 0.0315 | | 0.0315 | ||
| 4.62 | | 4.62 | ||
{{comma basis end}} | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {{rank-2 begin}} | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 86: | Line 72: | ||
| 16/15 | | 16/15 | ||
| [[Vavoom]] | | [[Vavoom]] | ||
{{rank-2 end}} | |||
{{orf}} | |||
Revision as of 02:38, 16 November 2024
| ← 1758edo | 1759edo | 1760edo → |
Theory
1759edo is consistent to the 23-odd-limit, tempering out 3025/3024, 2500/2499, 5985/5984, 4225/4224, 6175/6174, 3520/3519, 14875/14872 and 256000/255879. It supports etampesic. Essentially tempered chords in 1759et include vicetertismic chords.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.035 | -0.185 | -0.094 | -0.096 | -0.050 | +0.104 | -0.071 | +0.037 | -0.129 | -0.294 |
| Relative (%) | +0.0 | +5.1 | -27.2 | -13.7 | -14.0 | -7.3 | +15.3 | -10.4 | +5.5 | -18.9 | -43.1 | |
| Steps (reduced) |
1759 (0) |
2788 (1029) |
4084 (566) |
4938 (1420) |
6085 (808) |
6509 (1232) |
7190 (154) |
7472 (436) |
7957 (921) |
8545 (1509) |
8714 (1678) | |
Subsets and supersets
1759edo is the 274th prime EDO.
Regular temperament properties
Template:Comma basis begin |- | 2.3 | [2788 -1759⟩ | [⟨1759 2788]] | −0.0110 | 0.0110 | 1.61 |- | 2.3.5 | [-68 18 17⟩, [-4 -59 42⟩ | [⟨1759 2788 4084]] | +0.0193 | 0.0437 | 6.41 |- | 2.3.5.7 | 420175/419904, 48828125/48771072, [44 -28 5 -4⟩ | [⟨1759 2788 4084 4938]] | +0.0228 | 0.0383 | 5.61 |- | 2.3.5.7.11 | 3025/3024, 420175/419904, 1953125/1951488, 645922816/645700815 | [⟨1759 2788 4084 4938 6085]] | +0.0238 | 0.0343 | 5.03 |- | 2.3.5.7.11.13 | 3025/3024, 4225/4224, 256000/255879, 4100625/4100096, 420175/419904 | [⟨1759 2788 4084 4938 6085 6509]] | +0.0221 | 0.0316 | 4.63 |- | 2.3.5.7.11.13.17 | 3025/3024, 2500/2499, 4225/4224, 56595/56576, 14875/14872, 256000/255879 | [⟨1759 2788 4084 4938 6085 6509 7190]] | +0.0153 | 0.0336 | 4.93 |- | 2.3.5.7.11.13.17.19 | 3025/3024, 2500/2499, 5985/5984, 4225/4224, 6175/6174, 14875/14872, 256000/255879 | [⟨1759 2788 4084 4938 6085 6509 7190 7472]] | +0.0155 | 0.0315 | 4.62 Template:Comma basis end
Rank-2 temperaments
Template:Rank-2 begin |- | 1 | 164\1759 | 111.882 | 16/15 | Vavoom Template:Rank-2 end Template:Orf