2129edo

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2129edo

2130edo →

Prime factorization	2129 (prime)
Step size	0.563645 ¢
Fifth	1245\2129 (701.738 ¢)
Semitones (A1:m2)	199:162 (112.2 ¢ : 91.31 ¢)
Dual sharp fifth	1246\2129 (702.302 ¢)
Dual flat fifth	1245\2129 (701.738 ¢)
Dual major 2nd	362\2129 (204.039 ¢)
Consistency limit	5
Distinct consistency limit	5

Theory

2129et tempers out 95703125/95664294, 5767168/5764801, 47265625/47258883, 67110351/67108864 and 43923/43904 in the 11-limit; 33792000/33787663, 200000/199927, 34034175/34027136, 2250423/2249390, 78125/78078, 1449459/1449175, 1990656/1990625, 67392/67375, 4225/4224, 8858304/8857805, 59319/59290 and 4084223/4084101 in the 13-limit.

Odd harmonics

Approximation of odd harmonics in 2129edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-0.217	-0.217	+0.080	+0.129	-0.073	-0.133	+0.130	-0.117	+0.091	-0.137	+0.190
	Relative (%)	-38.5	-38.5	+14.1	+23.0	-13.0	-23.6	+23.0	-20.8	+16.2	-24.4	+33.7
Steps (reduced)		3374 (1245)	4943 (685)	5977 (1719)	6749 (362)	7365 (978)	7878 (1491)	8318 (1931)	8702 (186)	9044 (528)	9351 (835)	9631 (1115)

Subsets and supersets

2129edo is the 320th prime edo. 4258edo, which doubles it, gives a good correction to the harmonics 3 and 5.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.9	[-6749 2129⟩	⟨2129 6749]	-0.0204	0.0204	3.62
2.9.15	[37 29 -33⟩, [209 -61 -4⟩	⟨2129 6749 8318]	-0.0247	0.0177	3.14
2.9.15.7	24414062500/24407490807, 13841287201/13839609375, 2199023255552/2197176384375	⟨2129 6749 8318 5977]	-0.0256	0.0154	2.73
2.9.15.7.11	9800/9801, 5767168/5764801, 104857600/104825259, 13841287201/13839609375	⟨2129 6749 8318 5977 7365]	-0.0162	0.0232	4.12
2.9.15.7.11.13	10648/10647, 9801/9800, 196625/196608, 36924979/36905625, 304117528/303807105	⟨2129 6749 8318 5977 7365 7878]	-0.0075	0.0288	5.11
2.9.15.7.11.13.17	2431/2430, 10648/10647, 9801/9800, 845325/845152, 297440/297381, 11275335/11275264, 15980544/15978655	⟨2129 6749 8318 5977 7365 7878 8702]	-0.0024	0.0295	5.2

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	Associated Ratio	Temperaments
1	884\2129	498.262	4/3	Helmholtz

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

Music

Francium

• Brid Dance (2023) – hemischis in 2129edo tuning