44ed5: Difference between revisions
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== Theory == | |||
44ed5 is very similar to [[19edo]], but with the [[5/1]] rather than the 2/1 being just. It is extremely close to the [[The Riemann zeta function and tuning|zeta peak]] near 19; the local zeta peak around 19 is located at 18.948087, which has the octave stretched by 3.2877{{c}}; the octave of 44ed5 is only {{sfrac|1|9}}{{c}} off, thus minimizing relative error as much as possible. Because 19edo itself is a flat-tending system, stretching the octave improves the overall tuning accuracy. | |||
[[Category:Zeta-optimized tunings]] | [[Category:Zeta-optimized tunings]] | ||
Revision as of 13:33, 18 June 2025
| ← 43ed5 | 44ed5 | 45ed5 → |
(semiconvergent)
44 equal divisions of the 5th harmonic (abbreviated 44ed5) is a nonoctave tuning system that divides the interval of 5/1 into 44 equal parts of about 63.3 ¢ each. Each step represents a frequency ratio of 51/44, or the 44th root of 5.
Theory
44ed5 is very similar to 19edo, but with the 5/1 rather than the 2/1 being just. It is extremely close to the zeta peak near 19; the local zeta peak around 19 is located at 18.948087, which has the octave stretched by 3.2877 ¢; the octave of 44ed5 is only 1/9 ¢ off, thus minimizing relative error as much as possible. Because 19edo itself is a flat-tending system, stretching the octave improves the overall tuning accuracy.