13edo: Difference between revisions
m →Phi vibes: use superscript |
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Not until [[144edo|144]] do we find a better EDO in terms of relative error on these two intervals. | Not until [[144edo|144]] do we find a better EDO in terms of relative error on these two intervals. | ||
However, it should be noted that when we are hearing logarithmic phi, we are in fact hearing 2 | However, it should be noted that when we are hearing logarithmic phi, we are in fact hearing 2<sup>ϕ</sup> ≃ 3.070. While this interval can still be used in a way or another as a useful tone in a piece of music, it doesn't correspond to anything. When it comes to acoustic phi, we are truly hearing the mathematical constant ϕ ≃ 1.6180. | ||
That being said, logarithmic phi has interesting applications as [[Metallic MOS]], and in particular the fractal-like possibilities of self-similar subdivision of musical scales. | That being said, logarithmic phi has interesting applications as [[Metallic MOS]], and in particular the fractal-like possibilities of self-similar subdivision of musical scales. | ||
| Line 1,112: | Line 1,112: | ||
! Error (abs, [[Cent|¢]]) | ! Error (abs, [[Cent|¢]]) | ||
|- | |- | ||
| 2 | | 2<sup>ϕ</sup> / ϕ | ||
| 0.858 | | 0.858 | ||
|- | |- | ||
| Line 1,118: | Line 1,118: | ||
| 2.321 | | 2.321 | ||
|- | |- | ||
| 2 | | 2<sup>ϕ</sup> | ||
| 3.179 | | 3.179 | ||
|} | |} | ||