34691edo: Difference between revisions
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{{Infobox ET | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
34691edo is a [[zeta peak edo]] and [[zeta peak integer edo]], [[consistent]] in the 41-odd-limit with a lower [[relative error]] than any previous equal temperaments in the 41-limit. | 34691edo is a [[zeta peak edo]] and [[zeta peak integer edo]], [[consistent]] in the 41-odd-limit with a lower [[relative error]] than any previous equal temperaments in the 41-limit. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|34691| | {{Harmonics in equal|34691|columns=9}} | ||
{{Harmonics in equal|34691|columns=9|start=10|collapsed=true|title=Approximation of prime harmonics in 34691edo (continued)}} | |||
{{Harmonics in equal|34691|columns=9|start=19|collapsed=true|title=Approximation of prime harmonics in 34691edo (continued)}} | |||
Latest revision as of 11:18, 15 January 2026
| ← 34690edo | 34691edo | 34692edo → |
34691 equal divisions of the octave (abbreviated 34691edo or 34691ed2), also called 34691-tone equal temperament (34691tet) or 34691 equal temperament (34691et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 34691 equal parts of about 0.0346 ¢ each. Each step represents a frequency ratio of 21/34691, or the 34691st root of 2.
34691edo is a zeta peak edo and zeta peak integer edo, consistent in the 41-odd-limit with a lower relative error than any previous equal temperaments in the 41-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | +0.0023 | -0.0003 | +0.0017 | -0.0049 | +0.0016 | -0.0060 | +0.0051 | +0.0039 |
| Relative (%) | +0.0 | +6.6 | -0.8 | +5.0 | -14.2 | +4.6 | -17.3 | +14.7 | +11.2 | |
| Steps (reduced) |
34691 (0) |
54984 (20293) |
80550 (11168) |
97390 (28008) |
120011 (15938) |
128372 (24299) |
141798 (3034) |
147365 (8601) |
156927 (18163) | |
| Harmonic | 29 | 31 | 37 | 41 | 43 | 47 | 53 | 59 | 61 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.0076 | -0.0008 | -0.0051 | +0.0057 | +0.0155 | -0.0084 | -0.0100 | +0.0080 | -0.0072 |
| Relative (%) | -21.9 | -2.4 | -14.7 | +16.3 | +44.9 | -24.2 | -28.8 | +23.0 | -20.9 | |
| Steps (reduced) |
168528 (29764) |
171866 (33102) |
180721 (7266) |
185859 (12404) |
188243 (14788) |
192694 (19239) |
198707 (25252) |
204075 (30620) |
205743 (32288) | |
| Harmonic | 67 | 71 | 73 | 79 | 83 | 89 | 97 | 101 | 103 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0104 | +0.0042 | -0.0070 | -0.0158 | -0.0171 | +0.0115 | +0.0147 | -0.0005 | -0.0135 |
| Relative (%) | +30.0 | +12.3 | -20.4 | -45.8 | -49.3 | +33.2 | +42.4 | -1.5 | -39.0 | |
| Steps (reduced) |
210439 (2293) |
213341 (5195) |
214731 (6585) |
218684 (10538) |
221156 (13010) |
224650 (16504) |
228958 (20812) |
230980 (22834) |
231961 (23815) | |