1759edo

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1759edo

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Prime factorization	1759 (prime)
Step size	0.682206 ¢
Fifth	1029\1759 (701.99 ¢)
Semitones (A1:m2)	167:132 (113.9 ¢ : 90.05 ¢)
Consistency limit	23
Distinct consistency limit	23

Theory

1759edo is consistent to the 23-odd-limit, tempering out 3025/3024, 2500/2499, 5985/5984, 4225/4224, 6175/6174, 3520/3519, 14875/14872 and 256000/255879. It supports etampesic. Essentially tempered chords in 1759et include vicetertismic chords.

Prime harmonics

Approximation of prime harmonics in 1759edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.035	-0.185	-0.094	-0.096	-0.050	+0.104	-0.071	+0.037	-0.129	-0.294
	Relative (%)	+0.0	+5.1	-27.2	-13.7	-14.0	-7.3	+15.3	-10.4	+5.5	-18.9	-43.1
Steps (reduced)		1759 (0)	2788 (1029)	4084 (566)	4938 (1420)	6085 (808)	6509 (1232)	7190 (154)	7472 (436)	7957 (921)	8545 (1509)	8714 (1678)

Subsets and supersets

1759edo is the 274th prime EDO.

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
2.3	[2788 -1759⟩	[⟨1759 2788]]	−0.0110	0.0110	1.61
2.3.5	[-68 18 17⟩, [-4 -59 42⟩	[⟨1759 2788 4084]]	+0.0193	0.0437	6.41
2.3.5.7	420175/419904, 48828125/48771072, [44 -28 5 -4⟩	[⟨1759 2788 4084 4938]]	+0.0228	0.0383	5.61
2.3.5.7.11	3025/3024, 420175/419904, 1953125/1951488, 645922816/645700815	[⟨1759 2788 4084 4938 6085]]	+0.0238	0.0343	5.03
2.3.5.7.11.13	3025/3024, 4225/4224, 256000/255879, 4100625/4100096, 420175/419904	[⟨1759 2788 4084 4938 6085 6509]]	+0.0221	0.0316	4.63
2.3.5.7.11.13.17	3025/3024, 2500/2499, 4225/4224, 56595/56576, 14875/14872, 256000/255879	[⟨1759 2788 4084 4938 6085 6509 7190]]	+0.0153	0.0336	4.93
2.3.5.7.11.13.17.19	3025/3024, 2500/2499, 5985/5984, 4225/4224, 6175/6174, 14875/14872, 256000/255879	[⟨1759 2788 4084 4938 6085 6509 7190 7472]]	+0.0155	0.0315	4.62

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	Associated ratio*	Temperaments
1	164\1759	111.882	16/15	Vavoom

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

Music

Francium

• "Regret" from Naughty Girl Era (2024) – Spotify | Bandcamp | YouTube – etampesic in 1759edo
• 1759 (2025) – Spotify | Bandcamp | YouTube – 4-piece EP in 1759edo