80ed6: Difference between revisions
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{{Harmonics in equal|80|6|1|intervals=prime|columns=11}} | {{Harmonics in equal|80|6|1|intervals=prime|columns=11}} | ||
{{Harmonics in equal|80|6|1|intervals=prime|columns=12|start=12|collapsed=true|Approximation of harmonics in 80ed6 (continued)}} | {{Harmonics in equal|80|6|1|intervals=prime|columns=12|start=12|collapsed=true|Approximation of harmonics in 80ed6 (continued)}} | ||
=== Subsets and supersets === | |||
Since 80 factors into primes as {{nowrap| 2<sup>4</sup> × 5 }}, 80ed6 has subset ed6's {{EDs|equave=6| 2, 4, 5, 8, 10, 16, 20, and 40 }}. | |||
== See also == | == See also == | ||
Revision as of 11:58, 24 March 2025
| ← 79ed6 | 80ed6 | 81ed6 → |
80 equal divisions of the 6th harmonic (abbreviated 80ed6) is a nonoctave tuning system that divides the interval of 6/1 into 80 equal parts of about 38.8 ¢ each. Each step represents a frequency ratio of 61/80, or the 80th root of 6.
Theory
80ed6 is related to 31edo, but with the 6/1 rather than the 2/1 being just. This stretches the octave by about 2 cents.
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.0 | -2.0 | +5.4 | +4.6 | -2.5 | +18.5 | -19.4 | -18.1 | +0.1 | -13.4 | -12.5 |
| Relative (%) | +5.2 | -5.2 | +14.0 | +11.7 | -6.3 | +47.8 | -50.0 | -46.6 | +0.4 | -34.6 | -32.4 | |
| Steps (reduced) |
31 (31) |
49 (49) |
72 (72) |
87 (7) |
107 (27) |
115 (35) |
126 (46) |
131 (51) |
140 (60) |
150 (70) |
153 (73) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | 83 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -8.7 | +7.5 | +2.6 | +3.7 | -10.4 | -2.2 | +17.6 | +10.3 | -12.6 | +16.9 | -3.5 | -11.5 |
| Relative (%) | -22.3 | +19.3 | +6.7 | +9.5 | -26.9 | -5.7 | +45.4 | +26.5 | -32.4 | +43.6 | -9.1 | -29.6 | |
| Steps (reduced) |
161 (1) |
166 (6) |
168 (8) |
172 (12) |
177 (17) |
182 (22) |
184 (24) |
188 (28) |
190 (30) |
192 (32) |
195 (35) |
197 (37) | |
Subsets and supersets
Since 80 factors into primes as 24 × 5, 80ed6 has subset ed6's 2, 4, 5, 8, 10, 16, 20, and 40.