722edo

← 721edo

722edo

723edo →

Prime factorization	2 × 192
Step size	1.66205 ¢
Fifth	422\722 (701.385 ¢) (→ 211\361)
Semitones (A1:m2)	66:56 (109.7 ¢ : 93.07 ¢)
Dual sharp fifth	423\722 (703.047 ¢)
Dual flat fifth	422\722 (701.385 ¢) (→ 211\361)
Dual major 2nd	123\722 (204.432 ¢)
Consistency limit	5
Distinct consistency limit	5

722edo is a strong 2.7.19.23 subgroup tuning, with 179\722 being a semiconvergent to the log₂(19/16). Despite having a strong approximation of 7, it is only consistent upwards to the 5-limit.

Using the 421\722 fifth, it supports a variant of fifth-stacked tuning that divides 38th harmonic into 9 parts, meaning that C - D# in this system is equal to 19/16, creating a peculiar violation of Western harmony which would require spelling the minor triad as C-D#-G instead of C-Eb-G.

Aside from this, 722bc val tempers out the hemifamity comma and is a tuning for the undecental temperament. Since 722 is divisible by 19, the 722dg val is a tuning for the kalium temperament in the 19-limit.

Odd harmonics

Approximation of odd harmonics in 722edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-0.570	-0.718	+0.149	+0.522	+0.483	+0.470	+0.374	-0.246	-0.006	-0.421	-0.019
	Relative (%)	-34.3	-43.2	+9.0	+31.4	+29.0	+28.3	+22.5	-14.8	-0.4	-25.3	-1.2
Steps (reduced)		1144 (422)	1676 (232)	2027 (583)	2289 (123)	2498 (332)	2672 (506)	2821 (655)	2951 (63)	3067 (179)	3171 (283)	3266 (378)

Subsets and supersets

722edo has subset edos 1, 2, 19, 38, 361.