Edϕ: Difference between revisions

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-The octave-reduced 13th harmonic, 13/8 (≈840.5276618¢), is closely approximated by 7 steps of 10ed2 (840¢).
+Various equal divisions of the octave have close approximations of acoustic phi.
-/8 (1.625) is also close to acoustic phi (≈1.618033989), because 8 and 13 are sequential [[wikipedia:Fibonacci_number|Fibonacci numbers]].
+If the mth step of n-edo is a close approximation of φ, the nth step of m-edφ will be a close approximation of an octave.
-So, if we divide acoustic phi into 7 steps, then 10 of those steps will bring us quite close to an octave.
+Such m-edφ are interesting as variants of their respective n-edo, introducing some combination tone powers.
-This tuning therefore could also be thought of as 10edo with a stretched octave. Since the ratio between acoustic phi and the 10ed2 approximation of the 13th harmonic is ≈0.9917741623, the resulting stretched octave is 2^0.9917741623 = 1.988629015, or ≈1190.128995¢.
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