829edo

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829edo

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Prime factorization	829 (prime)
Step size	1.44753 ¢
Fifth	485\829 (702.051 ¢)
Semitones (A1:m2)	79:62 (114.4 ¢ : 89.75 ¢)
Consistency limit	11
Distinct consistency limit	11

Theory

829edo is consistent to the 11-odd-limit. It tempers out 4375/4374, [-25 6 -3 8⟩, and [16 -9 -8 6⟩ in the 7-limit; 41503/41472, 200704/200475, and 3750705/3748096 in the 11-limit. It supports squarschmidt, senior and acrokleismic.

Prime harmonics

Approximation of prime harmonics in 829edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.096	+0.176	-0.430	+0.190	+0.486	+0.714	+0.678	-0.048	-0.385	-0.042
	Relative (%)	+0.0	+6.6	+12.2	-29.7	+13.1	+33.5	+49.3	+46.8	-3.3	-26.6	-2.9
Steps (reduced)		829 (0)	1314 (485)	1925 (267)	2327 (669)	2868 (381)	3068 (581)	3389 (73)	3522 (206)	3750 (434)	4027 (711)	4107 (791)

Subsets and supersets

829edo is the 145th prime edo.

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
2.3	[1314 -829⟩	[⟨829 1314]]	–0.0302	0.0302	2.09
2.3.5	[39 -29 3⟩, [61 4 -29⟩	[⟨829 1314 1925]]	−0.0454	0.0327	2.26
2.3.5.7	4375/4374, [-25 6 -3 8⟩, [16 -9 -8 6⟩	[⟨829 1314 1925 2327]]	+0.0043	0.0906	6.25
2.3.5.7.11	4375/4374, 41503/41472, 200704/200475, 3750705/3748096	[⟨829 1314 1925 2327 2868]]	−0.0076	0.0844	5.83
2.3.5.7.11.13	4096/4095, 4375/4374, 4459/4455, 47432/47385, 59535/59488	[⟨829 1314 1925 2327 2868 3068]]	−0.0282	0.0898	6.20

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	Associated ratio*	Temperaments
1	218\829	315.561	6/5	Acrokleismic
1	223\829	322.799	3087/2560	Senior / seniority
1	274\829	396.622	98304/78125	Squarschmidt
1	391\829	565.983	59049/40960	Tricot

* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct

Music

Francium

• "confluencelessness" from albumwithoutspaces (2024) – Spotify | Bandcamp | YouTube – acrokleismic[19] in 829edo tuning