Acoustic pi: Difference between revisions
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|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. | ||
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|38edπ | |||
|Very close to [[23edo]] | |||
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|71edπ | |||
|Very close to [[43edo]] | |||
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|109edπ | |||
|Extremely close to [[66edo]] | |||
|} | |} | ||
Revision as of 12:21, 6 March 2023
| Interval information |
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. |
| 30edπ | Close to 18edo, but sets fractional temperaments to 4:5:6 triad. |
| 38edπ | Very close to 23edo |
| 71edπ | Very close to 43edo |
| 109edπ | Extremely close to 66edo |
Temperaments of interest
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.