Acoustic pi: Difference between revisions

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The '''acoustic pi''', the transcendental number equal to the [[ratio]] of a circle's circumference to the diameter, is about 3.14159, a rather minor thirteenth of 1981.795 [[cent]]s. Octave-[[equivalent]] intervals include '''acoustic tau''' (3181.795 [[cent]]s) and '''reduced acoustic pi''' (781.795 cents). It is unclear what psychoacoustic significance ~~this interval~~ might have.

The '''acoustic pi''', the transcendental number equal to the [[ratio]] of a circle's circumference to the diameter, is about 3.14159, a rather minor thirteenth of 1981.795 [[cent]]s. Octave-[[equivalent]] intervals include '''acoustic tau''' (3181.795 [[cent]]s) and '''reduced acoustic pi''' (781.795 cents). It is unclear what psychoacoustic significance these intervals might have.

Intervals that are close to it are [[3/1]], [[22/7]], and [[355/113]].

Intervals that are close to the acoustic pi are [[3/1]], [[22/7]], and [[355/113]].

== Equal divisions ==

Using 3.14159…/1 as an interval of equivalence (known as the "'''pitave'''") results in some interesting [[nonoctave]] tunings.

==Approximations==

== Approximations ==

{{interval edo approximation | interval = ~~314159~~/~~100000~~}}

{| class="wikitable"

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* [[Pi-edo]]

* [[Radian]]

* [[Acoustic phi]]

* [[Acoustic e]]

* [[Edϕ]]

* [[EDe]]

@@ Line 7: / Line 7: @@
 {{Wikipedia|Pi}}
-The '''acoustic pi''', the transcendental number equal to the [[ratio]] of a circle's circumference to the diameter, is about 3.14159, a rather minor thirteenth of 1981.795 [[cent]]s. Octave-[[equivalent]] intervals include '''acoustic tau''' (3181.795 [[cent]]s) and '''reduced acoustic pi''' (781.795 cents). It is unclear what psychoacoustic significance this interval might have.
+The '''acoustic pi''', the transcendental number equal to the [[ratio]] of a circle's circumference to the diameter, is about 3.14159, a rather minor thirteenth of 1981.795 [[cent]]s. Octave-[[equivalent]] intervals include '''acoustic tau''' (3181.795 [[cent]]s) and '''reduced acoustic pi''' (781.795 cents). It is unclear what psychoacoustic significance these intervals might have.
-Intervals that are close to it are [[3/1]], [[22/7]], and [[355/113]].
+Intervals that are close to the acoustic pi are [[3/1]], [[22/7]], and [[355/113]].
 == Equal divisions ==
 Using 3.14159…/1 as an interval of equivalence (known as the "'''pitave'''") results in some interesting [[nonoctave]] tunings.
-==Approximations==
+== Approximations ==
-{{interval edo approximation | interval = 314159/100000}}
+{{interval edo approximation|interval=355/113}}
 {| class="wikitable"
@@ Line 62: / Line 62: @@
 * [[Pi-edo]]
 * [[Radian]]
+* [[Acoustic phi]]
+* [[Acoustic e]]
 * [[Edϕ]]
 * [[EDe]]