Acoustic pi - Revision history

Hotcrystal0 at 00:10, 18 February 2026

2026-02-18T00:10:49Z

← Older revision		Revision as of 00:10, 18 February 2026
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	* [[Pi-edo]]		* [[Pi-edo]]
	* [[Radian]]		* [[Radian]]
			* [[Acoustic phi]]
			* [[Acoustic e]]
	* [[Edϕ]]		* [[Edϕ]]
	* [[EDe]]		* [[EDe]]

Overthink: /* Approximations */ even this is much closer

2026-01-22T05:50:34Z

Approximations: even this is much closer

← Older revision		Revision as of 05:50, 22 January 2026
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	== Approximations ==		== Approximations ==
	{{interval edo approximation\|interval=~~314159~~/~~100000~~}}		{{interval edo approximation\|interval=355/113}}

	{\| class="wikitable"		{\| class="wikitable"

FloraC at 18:18, 21 January 2026

2026-01-21T18:18:16Z

← Older revision		Revision as of 18:18, 21 January 2026
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	{{Wikipedia\|Pi}}		{{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 ==		== 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==		== Approximations ==
	{{interval edo approximation \| interval = 314159/100000}}		{{interval edo approximation\|interval=314159/100000}}

	{\| class="wikitable"		{\| class="wikitable"

Pailiaq at 00:29, 27 November 2025

2025-11-27T00:29:09Z

← Older revision		Revision as of 00:29, 27 November 2025
Line 13:		Line 13:
	== Equal divisions ==		== 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 = 314159/100000}}

	{\| class="wikitable"		{\| class="wikitable"

BudjarnLambeth: /* See also */

2025-05-19T03:44:21Z

BudjarnLambeth: Added links

2025-03-27T01:46:17Z

Added links

← Older revision		Revision as of 01:46, 27 March 2025
Line 7:		Line 7:
	{{Wikipedia\|Pi}}		{{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]].		Intervals that are close to it are [[3/1]], [[22/7]], and [[355/113]].

	== Equal divisions ==		== 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"		{\| class="wikitable"
Line 51:		Line 51:

	== Temperaments of interest ==		== 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 ==		== See also ==

Sintel: math -> novelty

2025-03-26T18:40:55Z

math -> novelty

← Older revision		Revision as of 18:40, 26 March 2025
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	{{~~Mathematical interest~~}}		{{Novelty}}
	{{Infobox Interval		{{Infobox Interval
	\| Ratio = \pi		\| Ratio = \pi

BudjarnLambeth: Niche -> mathematical interest (feel free to revert if you disagree)

2025-03-26T05:58:27Z

Niche -> mathematical interest (feel free to revert if you disagree)

← Older revision		Revision as of 05:58, 26 March 2025
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	{{~~Niche~~}}		{{Mathematical interest}}
	{{Infobox Interval		{{Infobox Interval
	\| Ratio = \pi		\| Ratio = \pi

VectorGraphics at 05:57, 26 March 2025

2025-03-26T05:57:12Z

← Older revision		Revision as of 05:57, 26 March 2025
Line 7:		Line 7:
	{{Wikipedia\|Pi}}		{{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 this interval might have.

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

BudjarnLambeth: Niche

2025-03-18T02:59:11Z

Niche

← Older revision		Revision as of 02:59, 18 March 2025
Line 1:		Line 1:
	{{~~Novelty~~}}		{{Niche}}
	{{Infobox Interval		{{Infobox Interval
	\| Ratio = \pi		\| Ratio = \pi

← Older revision		Revision as of 03:44, 19 May 2025
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	* [[Pi-edo]]		* [[Pi-edo]]
	* [[Radian]]		* [[Radian]]
			* [[Edϕ]]
			* [[EDe]]
			* [[User:Eliora/Phi to the phi]]

	== External links ==		== External links ==