Acoustic pi: Difference between revisions

Line 7:

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 this interval might have.

Intervals that are close to it 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.

{| class="wikitable"

Line 51:

== 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 ==

@@ 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 this interval might have.
 Intervals that are close to it 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.
 {| class="wikitable"
@@ Line 51: / Line 51: @@
 == 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 ==