1289edo

← 1288edo

1289edo

1290edo →

Prime factorization	1289 (prime)
Step size	0.930954 ¢
Fifth	754\1289 (701.939 ¢)
Semitones (A1:m2)	122:97 (113.6 ¢ : 90.3 ¢)
Consistency limit	9
Distinct consistency limit	9

1289 equal divisions of the octave (abbreviated 1289edo or 1289ed2), also called 1289-tone equal temperament (1289tet) or 1289 equal temperament (1289et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1289 equal parts of about 0.931 ¢ each. Each step represents a frequency ratio of 2^1/1289, or the 1289th root of 2.

Theory

1289edo is consistent to the 9-odd-limit. As an equal temperament, it tempers out [-16 35 -17⟩ (minortone comma) in the 5-limit. Using the patent val, it tempers out 3025/3024, 180224/180075, 2460375/2458624 and 50014503/50000000 in the 11-limit; 1716/1715, 4096/4095, 91125/91091 and 5282739/5281250 in the 13-limit. In the 2.3.13.23.29.31 subgroup it tempers out 19344/19343, in the 2.3.5.7.11.23.31 subgroup 19251/19250.

Prime harmonics

Approximation of prime harmonics in 1289edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	-0.016	+0.032	+0.297	-0.193	+0.124	+0.242	+0.392	+0.120	+0.058	+0.038
	Relative (%)	+0.0	-1.7	+3.5	+32.0	-20.7	+13.3	+26.0	+42.1	+12.9	+6.2	+4.1
Steps (reduced)		1289 (0)	2043 (754)	2993 (415)	3619 (1041)	4459 (592)	4770 (903)	5269 (113)	5476 (320)	5831 (675)	6262 (1106)	6386 (1230)

Subsets and supersets

1289edo is the 209th prime edo.

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
2.3	[-2043 1289⟩	[⟨1289 2043]]	+0.0049	0.0049	0.53
2.3.5	[-16 35 -17⟩, [91 -12 -31⟩	[⟨1289 2043 2993]]	−0.0014	0.0097	1.04
2.3.5.7	2460375/2458624, 78125000/78121827, 12884901888/12867859375	[⟨1289 2043 2993 3619]]	−0.0275	0.0461	4.95
2.3.5.7.11	3025/3024, 180224/180075, 2460375/2458624, 50014503/50000000	[⟨1289 2043 2993 3619 4459]]	−0.0109	0.0530	5.69
2.3.5.7.11.13	3025/3024, 1716/1715, 4096/4095, 91125/91091, 5282739/5281250	[⟨1289 2043 2993 3619 4459 4770]]	−0.0146	0.0491	5.27
2.3.5.7.11.13.17	3025/3024, 1716/1715, 4096/4095, 2500/2499, 37180/37179, 3536379/3536000	[⟨1289 2043 2993 3619 4459 4770 5269]]	−0.0210	0.0481	5.17
2.3.5.7.11.13.17.19	3025/3024, 1716/1715, 2376/2375, 4096/4095, 2500/2499, 270864/270725, 75735/75712	[⟨1289 2043 2993 3619 4459 4770 5269 5476]]	−0.0299	0.0508	5.46

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	Associated ratio*	Temperaments
1	142\1289	132.196	[-38 5 13⟩	Astro
1	196\1289	182.467	10/9	Minortone
1	238\1289	221.567	8388608/7381125	Fortune

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

Music

Francium

• "Baking With Honey" from The Scallop Disco Accident (2025) – Spotify | Bandcamp | YouTube – in Honeybrookic, 1289edo tuning
• "Those Peas, With That Hat?" from Questions, Vol. 2 (2025) – Spotify | Bandcamp | YouTube