1400edo

← 1399edo

1400edo

1401edo →

Prime factorization	23 × 52 × 7
Step size	0.857143 ¢
Fifth	819\1400 (702 ¢) (→ 117\200)
Semitones (A1:m2)	133:105 (114 ¢ : 90 ¢)
Consistency limit	5
Distinct consistency limit	5

Theory

1400edo is consistent in the 5-limit, where provides the optimal patent val for the 5-limit vishnuzmic temperament. Aside from that it is poor at simple harmony. In higher limits, it is good at the 2.3.19.23.29.31 subgroup. . It also tempers out the linus comma and the barium comma.

Aside from the patent val, there is a number of mappings to be considered. 1400cd val uses the 28edo mapping for 5 and gives a tuning close to the POTE tuning for the 11-limit oquatonic temperament. 1400ccdd val is a tuning for the 11-limit silicon temperament. It is worth noting, patent val can be considered a tuning for the 2.3.11 subgroup silicon - for which it conveniently provides a 70-tone mos reaching 3/2 in 1 generator up and 11/8 in 3 generators down. 1400bbbc val is a tuning for the manganese temperament.

Prime harmonics

Approximation of prime harmonics in 1400edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.045	+0.258	-0.254	-0.175	+0.329	-0.384	-0.084	+0.011	-0.149	+0.107
	Relative (%)	+0.0	+5.2	+30.1	-29.7	-20.4	+38.4	-44.8	-9.9	+1.3	-17.3	+12.5
Steps (reduced)		1400 (0)	2219 (819)	3251 (451)	3930 (1130)	4843 (643)	5181 (981)	5722 (122)	5947 (347)	6333 (733)	6801 (1201)	6936 (1336)

Subsets and supersets

1400edo has subset edos 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700.

One step of 1400edo is the relative cent for 14edo.

Regular temperament properties

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	Associated ratio*	Temperaments
1	317\1400	271.714	[66 -23 -9 -3⟩	Counterorson
2	83\1400	71.143	25/24	Vishnu (5-limit)
8	86\1400	73.714	24/23	Octium (2.3.19.23.29.31)
14	581\1400 (81\1400)	498.000 (69.429)	4/3 (?)	Silicon (2.3.11)
28	581\1400 (31\1400)	498.000 (26.571)	4/3 (126/125)	Oquatonic (1400cd)
56	581\1400 (6\1400)	498.000 (5.143)	4/3 (126/125)	Barium

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

Scales

• Silicon[70]: (19 24 19 19 19)x14

Music

Mercury Amalgam

• Apple In Your Mouth – silicon[70], oxygen[24], magnesium[175], vishnu[34]