Acoustic pi: Difference between revisions
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Created page with "{{Wikipedia|Pi}} '''Pi''', the ratio of a circle's circumference to its octave, is equal to about 3.14159. When used as an equivalence interval, it becomes a rather minor thi..." |
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== Equal divisions == | == Equal divisions == | ||
Using 3.14159.../1 as an interval of equivalence results in an interesting nonoctave tuning. | Using 3.14159.../1 as an interval of equivalence results in an interesting nonoctave tuning. | ||
{| class="wikitable" | |||
|+EDπ-ED2 correspondence | |||
!N | |||
!Description | |||
|- | |||
|2edπ | |||
|A stack of two minor sevenths, represents a problem of squaring the circle | |||
|- | |||
|3edπ | |||
|A stack of three compressed fifths, vaguely equivalent to [[2edo]] | |||
|- | |||
|4edπ | |||
|Close to equal multiplication of 4/3 | |||
|- | |||
|5edπ | |||
|Close to equal multiplication of 5/4, [[3edo]] | |||
|- | |||
|6edπ | |||
|Close to equal multiplication of 6/5, [[4edo]] | |||
|- | |||
|20edπ | |||
|Close to [[12edo]]. | |||
|} | |||
== Temperaments of interest == | |||
Engineer's temperament, tempering out π/3, the engineer's comma. | |||
Revision as of 15:08, 17 February 2022
Pi, the ratio of a circle's circumference to its octave, is equal to about 3.14159. When used as an equivalence interval, it becomes a rather minor thirteenth of 1981.795 cents.
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 results in an interesting nonoctave tuning.
| N | Description |
|---|---|
| 2edπ | A stack of two minor sevenths, represents a problem of squaring the circle |
| 3edπ | A stack of three compressed fifths, vaguely equivalent to 2edo |
| 4edπ | Close to equal multiplication of 4/3 |
| 5edπ | Close to equal multiplication of 5/4, 3edo |
| 6edπ | Close to equal multiplication of 6/5, 4edo |
| 20edπ | Close to 12edo. |
Temperaments of interest
Engineer's temperament, tempering out π/3, the engineer's comma.