Phith root of phi: Difference between revisions
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[[49edo]] provides an exceptionally accurate approximation. Because 34 steps ≈ 832.65¢ (acoustic phi) *and* because 34 is a fibonacci number, it naturally follows that 21 steps, its previous fibonacci number, ≈ 514.29¢ (<math>\varphi^{1/\varphi}</math>). This pattern continues, creating a highly accurate golden scale of self-similar frequency relationships at step sizes 2, 3, 5, 8, 13, 21, 34. | [[49edo]] provides an exceptionally accurate approximation. Because 34 steps ≈ 832.65¢ (acoustic phi) *and* because 34 is a fibonacci number, it naturally follows that 21 steps, its previous fibonacci number, ≈ 514.29¢ (<math>\varphi^{1/\varphi}</math>). This pattern continues, creating a highly accurate golden scale of self-similar frequency relationships at step sizes 2, 3, 5, 8, 13, 21, 34. | ||
[[7edo]] approximates this interval extremely well (0.59c off), as does all edos that are multiples of 7.{{Interval Edo Approximation|interval=134636/100000|interval_name=<math>\varphi | [[7edo]] approximates this interval extremely well (0.59c off), as does all edos that are multiples of 7.{{Interval Edo Approximation|interval=134636/100000|interval_name=<math>\sqrt[\varphi]{\varphi}</math>}} | ||
== Compositions based on the golden ratio == | == Compositions based on the golden ratio == | ||
* ''[[Star Nursery]]'' - [[Sean Archibald]] (2021) | * ''[[Star Nursery]]'' - [[Sean Archibald]] (2021) | ||
* ''[https://www.youtube.com/watch?v=gXMqkyVbFmI Durationplex]'' - [[Sean Archibald]] (2025) | |||
== External links == | == External links == | ||
* [https://sevish.com/2017/golden-ratio-music-interval/ The Golden Ratio as a musical interval] by [[Sevish]] | * [https://sevish.com/2017/golden-ratio-music-interval/ The Golden Ratio as a musical interval] by [[Sevish]] | ||
[[Category:Irrational intervals]] | |||
[[Category:Golden ratio]] | |||