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Acoustic ϕ and ϕϕ-1: improve section title. Direct mapping -> direct approximation.
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(*) Based on 49edo's 11-limit patent val {{val| 49 78 114 138 170 }} mapping
(*) Based on 49edo's 11-limit patent val {{val| 49 78 114 138 170 }} mapping


== Acoustic ϕ and ϕ<sup>ϕ<sup>-1</sup></sup> ==
== Approximation to irrational intervals ==
=== Acoustic ϕ and ϕ<sup>ϕ<sup>-1</sup></sup> ===
49edo has a very close approximation of both [[acoustic phi]] and ϕ<sup>ϕ<sup>-1</sup></sup>, a kind of logarithmic phi that divides [[acoustic phi]] logarithmically by phi ([[Logarithmic phi|instead of dividing 2/1]]).
49edo has a very close approximation of both [[acoustic phi]] and ϕ<sup>ϕ<sup>-1</sup></sup>, a kind of logarithmic phi that divides [[acoustic phi]] logarithmically by phi ([[Logarithmic phi|instead of dividing 2/1]]).


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{| class="wikitable center-all"
{| class="wikitable center-all"
|+Direct mapping
|+Direct approximation
|-
|-
! Interval
! Interval