Acoustic pi: Difference between revisions
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{{Novelty}} | |||
{{Infobox Interval | {{Infobox Interval | ||
| Ratio = \pi | | Ratio = \pi | ||
| Cents = 1981.7953553667824 | | Cents = 1981.7953553667824 | ||
| Name = | | Name = acoustic pi | ||
}} | }} | ||
{{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 these intervals might have. | ||
Intervals that are close to | Intervals that are close to the acoustic pi are [[3/1]], [[22/7]], and [[355/113]]. | ||
== Equal divisions == | == Equal divisions == | ||
Using 3. | 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" | {| class="wikitable" | ||
|+ | |+Selected edπ–edo correspondence | ||
!N | ! ''N'' | ||
!Description | ! Description | ||
|- | |- | ||
|[[2edπ]] | | [[2edπ]] | ||
|A stack of two minor sevenths, represents a problem of squaring the circle | | A stack of two minor sevenths, represents a problem of squaring the circle | ||
|- | |- | ||
|[[3edπ]] | | [[3edπ]] | ||
|A stack of three compressed fifths, vaguely equivalent to [[2edo]] | | A stack of three compressed fifths, vaguely equivalent to [[2edo]] | ||
|- | |- | ||
|[[4edπ]] | | [[4edπ]] | ||
|Close to equal multiplication of 4/3 | | Close to equal multiplication of 4/3 | ||
|- | |- | ||
|[[5edπ]] | | [[5edπ]] | ||
|Close to equal multiplication of 5/4, [[3edo]] | | Close to equal multiplication of 5/4, [[3edo]] | ||
|- | |- | ||
|[[6edπ]] | | [[6edπ]] | ||
|Close to equal multiplication of 6/5, [[4edo]] | | Close to equal multiplication of 6/5, [[4edo]] | ||
|- | |- | ||
|[[20edπ]] | | [[20edπ]] | ||
|Close to [[12edo]]. | | Close to [[12edo]]. | ||
|- | |- | ||
[[30edπ]] | | [[30edπ]] | ||
|Close to [[18edo]], but sets fractional temperaments to 4:5:6 triad. | | Close to [[18edo]], but sets fractional temperaments to 4:5:6 triad. | ||
|- | |- | ||
|[[38edπ]] | | [[38edπ]] | ||
|Very close to [[23edo]] | | Very close to [[23edo]] | ||
|- | |- | ||
|71edπ | | 71edπ | ||
|Very close to [[43edo]] | | Very close to [[43edo]] | ||
|- | |- | ||
|109edπ | | 109edπ | ||
|Extremely close to [[66edo]] | | Extremely close to [[66edo]] | ||
|} | |} | ||
== 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 the 3:4:5 triad with a fractional-octave temperament just as 12edo does with the 4:5:6 triad. | |||
== See also == | |||
* [[Lucy tuning]] | |||
* [[Pi-edo]] | |||
* [[Radian]] | |||
* [[Acoustic phi]] | |||
* [[Acoustic e]] | |||
* [[Edϕ]] | |||
* [[EDe]] | |||
* [[User:Eliora/Phi to the phi]] | |||
== External links == | |||
* [http://tonalsoft.com/enc/p/pi.aspx pi, π] on [[Tonalsoft Encyclopedia]] | |||
[[Category:Transcendental]] | |||