47zpi: Difference between revisions

Latest revision as of 20:34, 24 September 2024

47 zeta peak index (abbreviated 47zpi), is the equal-step tuning system obtained from the 47th peak of the Riemann zeta function. It is very close to 15edo, just with compressed octaves.

Approximation of harmonics in 47zpi
Harmonic		2	3	4	5	6	7	8	9	10	11	12	13	14	15
Error	Absolute (¢)	-4.3	+11.2	-8.5	+3.7	+7.0	-20.8	-12.8	+22.4	-0.5	-6.1	+2.7	+23.6	-25.0	+15.0
Error	Relative (%)	-5.3	+14.1	-10.7	+4.7	+8.7	-26.0	-16.0	+28.2	-0.7	-7.7	+3.4	+29.5	-31.4	+18.8
Step		15	24	30	35	39	42	45	48	50	52	54	56	57	59

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 '''47 zeta peak index''' (abbreviated '''47zpi'''), is the [[Equal-step tuning|equal-step]] [[tuning system]] obtained from the 47th [[Zeta peak index|peak]] of the [[The Riemann zeta function and tuning|Riemann zeta function]]. It is very close to [[15edo]], just with compressed octaves.
+== Harmonics ==
+{{harmonics in cet|79.7157343943591|columns=14|title=Approximation of harmonics in 47zpi}}
+== Intervals ==
+* 79.716
+* 159.431
+* 239.147
+* 318.863
+* 398.579
+* 478.294
+* 558.01
+* 637.726
+* 717.442
+* 797.157
+* 876.873
+* 956.589
+* 1036.305
+* 1116.02
+* 1195.736
 == Scales ==