Pi-edo

This page presents a novelty topic. It may contain ideas which are less likely to find practical applications in music, or numbers or structures that are arbitrary or exceedingly small, large, or complex. Novelty topics are often developed by a single person or a small group. As such, this page may also contain idiosyncratic terms, notation, or conceptual frameworks.

← 0ed697/559

1ed697/559

2ed697/559 →

Prime factorization	n/a
Step size	381.972 ¢
Octave	3\1ed697/559 (1145.92 ¢)
Twelfth	5\1ed697/559 (1909.86 ¢)
Consistency limit	7
Distinct consistency limit	4
Special properties	Highly composite

π-edo, 1ed2^1/π, or APS(1/π oct) is a nonoctave equal-step tuning in which π steps occur per octave. It does not approximate any simple harmonics well, except for the 3rd harmonic. In fact, it is nearly identical to 5edt. This lends the tuning to use with custom inharmonic timbres. It has the potential to facilitate music far removed from any conventional harmonic or melodic traditions.

Harmonics

Approximation of harmonics in π-edo

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-54.1	+7.9	-108.2	-112.5	-46.2	+68.9	-162.3	+15.8	-166.6	+50.4	-100.3
	Relative (%)	-14.2	+2.1	-28.3	-29.5	-12.1	+18.0	-42.5	+4.1	-43.6	+13.2	-26.2
Steps		3	5	6	7	8	9	9	10	10	11	11