User:BudjarnLambeth/435zpi

435zpi, the 435th zeta peak index, is a compressed-octaves version of 80edo. It can be thought of as 80ed1198.9c or as 14.986cet.

80edo tunes almost all simple harmonics slightly sharp by roughly the same amount (roughly 3 cents), so 435zpi is one possible way of correcting for this.

Harmonics

Odd

Approximation of odd harmonics in 435zpi

Harmonic		3	5	7	9	11	13	15	17	19	21	23	25	27
Error	Absolute (¢)	+1.27	+1.08	+3.02	+2.53	-0.20	-4.67	+2.35	-4.53	-2.27	+4.29	-3.34	+2.16	+3.80
	Relative (%)	+8.5	+7.2	+20.2	+16.9	-1.3	-31.2	+15.7	-30.3	-15.2	+28.6	-22.3	+14.4	+25.4
Step		127	186	225	254	277	296	313	327	340	352	362	372	381

Approximation of odd harmonics in 435zpi

Harmonic		29	31	33	35	37	39	41	43	45	47	49	51	53
Error	Absolute (¢)	-0.02	+4.41	+1.07	+4.11	-2.18	-3.40	-0.07	+7.39	+3.62	+3.26	+6.05	-3.27	+5.07
	Relative (%)	-0.2	+29.4	+7.1	+27.4	-14.6	-22.7	-0.5	+49.3	+24.1	+21.8	+40.4	-21.8	+33.8
Step		389	397	404	411	417	423	429	435	440	445	450	454	459

Prime

Approximation of prime harmonics in 435zpi

Harmonic		2	3	5	7	11	13	17	19	23	29	31	37	41
Error	Absolute (¢)	-1.12	+1.27	+1.08	+3.02	-0.20	-4.67	-4.53	-2.27	-3.34	-0.02	+4.41	-2.18	-0.07
	Relative (%)	-7.5	+8.5	+7.2	+20.2	-1.3	-31.2	-30.3	-15.2	-22.3	-0.2	+29.4	-14.6	-0.5
Step		80	127	186	225	277	296	327	340	362	389	397	417	429

Approximation of prime harmonics in 435zpi

Harmonic		43	47	53	59	61	67	71	73	79	83	89	97
Error	Absolute (¢)	+7.39	+3.26	+5.07	-0.77	+1.47	+3.89	-6.58	+5.27	+3.39	-7.19	+6.85	-7.29
	Relative (%)	+49.3	+21.8	+33.8	-5.1	+9.8	+26.0	-43.9	+35.1	+22.6	-48.0	+45.7	-48.6
Step		435	445	459	471	475	486	492	496	505	510	519	528