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. 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.

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

== Approximations ==

{| class="wikitable"

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== Temperaments of interest ==

Engineer's temperament, tempering out π/3, the engineer's comma.

Engineer's temperament, tempering out π/3, the [[engineer's comma]].

20edπ can be used to set 3:4:5 triad with a fractional-octave temperament just as 12edo does with the 4:5:6 triad.

20edπ can be used to set the 3:4:5 triad with a fractional-octave temperament just as 12edo does with the 4:5:6 triad.

== See also ==

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* [[Pi-edo]]

* [[Radian]]

* [[Acoustic phi]]

* [[Acoustic e]]

* [[Edϕ]]

* [[EDe]]

* [[User:Eliora/Phi to the phi]]

== External links ==

@@ 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. 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.
+Using 3.14159…/1 as an interval of equivalence (known as the "'''pitave'''") results in some interesting [[nonoctave]] tunings.
+== Approximations ==
+{{interval edo approximation|interval=355/113}}
 {| class="wikitable"
@@ Line 51: / Line 54: @@
 == Temperaments of interest ==
-Engineer's temperament, tempering out π/3, the engineer's comma.
+Engineer's temperament, tempering out π/3, the [[engineer's comma]].
-edπ can be used to set 3:4:5 triad with a fractional-octave temperament just as 12edo does with the 4:5:6 triad.
+edπ can be used to set the 3:4:5 triad with a fractional-octave temperament just as 12edo does with the 4:5:6 triad.
 == See also ==
@@ Line 59: / Line 62: @@
 * [[Pi-edo]]
 * [[Radian]]
+* [[Acoustic phi]]
+* [[Acoustic e]]
+* [[Edϕ]]
+* [[EDe]]
+* [[User:Eliora/Phi to the phi]]
 == External links ==