116ed5: Difference between revisions
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m == Harmonics == {{Harmonics in equal|116|5|1}} {{stub}} |
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It is almost exactly identical to [[50edo]], having the same [[val]]s for all of the first 43 [[prime harmonic]]s. The [[relative error]] of its approximations is almost identical to 50edo too. It supports all the same [[rank-2 temperament]]s as 50edo, most notably [[meantone]]. Compared to 50edo, the octave is [[octave stretch|stretched]] by about 1 cent. | |||
All of that could make 116ed5 useful as a [[:Category:Piano|piano]] tuning to be used alongside other instruments in 50edo. Because pianos usually use stretched octaves, 116ed5 accommodates this, while also being so close to 50edo that it still preserves all 50edo’s properties. | |||
== Harmonics == | == Harmonics == | ||
{{Harmonics in equal|116|5|1}} | {{Harmonics in equal|116|5|1}} | ||
[[Category:50edo]] | |||
[[Category:Meantone]] | |||
[[Category:Piano]] | |||
Revision as of 08:25, 8 January 2025
| ← 115ed5 | 116ed5 | 117ed5 → |
It is almost exactly identical to 50edo, having the same vals for all of the first 43 prime harmonics. The relative error of its approximations is almost identical to 50edo too. It supports all the same rank-2 temperaments as 50edo, most notably meantone. Compared to 50edo, the octave is stretched by about 1 cent.
All of that could make 116ed5 useful as a piano tuning to be used alongside other instruments in 50edo. Because pianos usually use stretched octaves, 116ed5 accommodates this, while also being so close to 50edo that it still preserves all 50edo’s properties.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.0 | -4.4 | +2.0 | +0.0 | -3.4 | -6.0 | +3.0 | -8.8 | +1.0 | +4.1 | -2.4 |
| Relative (%) | +4.2 | -18.2 | +8.3 | +0.0 | -14.1 | -25.1 | +12.5 | -36.5 | +4.2 | +17.2 | -9.9 | |
| Steps (reduced) |
50 (50) |
79 (79) |
100 (100) |
116 (0) |
129 (13) |
140 (24) |
150 (34) |
158 (42) |
166 (50) |
173 (57) |
179 (63) | |