2100edo: Difference between revisions

Revision as of 11:06, 30 October 2023

Prime factorization

2² × 3 × 5² × 7

Step size

0.571429 ¢

Fifth

1228\2100 (701.714 ¢) (→ 307\525)

Semitones (A1:m2)

196:160 (112 ¢ : 91.43 ¢)

Dual sharp fifth

1229\2100 (702.286 ¢)

Dual flat fifth

1228\2100 (701.714 ¢) (→ 307\525)

Dual major 2nd

357\2100 (204 ¢) (→ 17\100)

Consistency limit

7

Distinct consistency limit

7

The patent val tempers out 32805/32768 in the 5-limit and 2401/2400 in the 7-limit, and thereby provides an excellent tuning for 5-limit schismatic aka helmholtz temperament, and the 7-limit sesquiquartififths temperament. As with any equal division of this size, it supports a number of possible meantone tunings, but ⟨2100 3319 4876 5890] is notable for being nearly identical to quarter-comma meantone.

Approximation of odd harmonics in 2100edo
Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-0.241	-0.028	-0.254	+0.090	+0.111	+0.044	-0.269	+0.187	+0.201	+0.076	-0.274
Error	Relative (%)	-42.1	-4.9	-44.5	+15.7	+19.4	+7.7	-47.0	+32.8	+35.2	+13.3	-48.0
Steps (reduced)		3328 (1228)	4876 (676)	5895 (1695)	6657 (357)	7265 (965)	7771 (1471)	8204 (1904)	8584 (184)	8921 (521)	9224 (824)	9499 (1099)

Since 2100 factors into 2² × 3 × 5² × 7, 2100edo has subset edos 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 50, 60, 70, 75, 84, 100, 105, 140, 150, 175, 210, 300, 350, 420, 525, 700, and 1050.

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 {{EDO intro|2100}}
-The [[patent val]] [[Tempering out|tempers out]] [[32805/32768]] in the 5-limit and [[2401/2400]] in the 7-limit, and thereby provides an excellent tuning for 5-limit schismatic aka [[Schismatic family|helmholtz]] temperament, and the 7-limit [[sesquiquartififths]] temperament. As with any equal division of this size, it [[support]]s a number of possible meantone tunings, but {{val| 2100 3319 4876 5890 }} is notable for being nearly identical to [[quarter-comma meantone]].
+The [[patent val]] [[Tempering out|tempers out]] [[32805/32768]] in the 5-limit and [[2401/2400]] in the 7-limit, and thereby provides an excellent tuning for 5-limit [[schismatic|schismatic aka helmholtz]] temperament, and the 7-limit [[sesquiquartififths]] temperament. As with any equal division of this size, it [[support]]s a number of possible meantone tunings, but {{val| 2100 3319 4876 5890 }} is notable for being nearly identical to [[quarter-comma meantone]].
+=== Odd harmonics ===
+{{Harmonics in equal|2100}}
+=== Subsets and supersets ===
+Since 2100 factors into {{factorization|2100}}, 2100edo has subset edos {{EDOs| 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 50, 60, 70, 75, 84, 100, 105, 140, 150, 175, 210, 300, 350, 420, 525, 700, and 1050 }}.