1248/1225

1248/1225, the wowma, is a diesis-sized interval. It appears as the difference between 36/35 and 105/104, or between 35/32 and 39/35.

Interval information

Ratio	1248/1225
Factorization	25 × 3 × 5-2 × 7-2 × 13
Monzo	[5 1 -2 -2 0 1⟩
Size in cents	32.20342¢
Names	wowma, hemimean sixthtone
Color name	thobirugu unison, 3orrgg1
FJS name	[math]\displaystyle{ \text{d1}^{13}_{5,5,7,7} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	20.544
Weil norm (log2 max(n, d))	20.5708
Wilson norm (sopfr(nd))	50
Open this interval in xen-calc

It appears as almost exactly a fraction of many useful intervals. Namely, 1/2 of 27/26 (0.93c), 1/4 of 14/13 (0.51c), 1/6 of 19/17 (0.662c), 1/9 of 13/11 (0.621c), 1/11 of 27/22 (0.30c), 1/12 of 5/4, (0.127c), 1/13 of 14/11 (1.136c).

It also appears as fractions of more complex intervals, like 1/5 of 34/31, 1/7 of 33/29 (1.728c), 1/8 of 29/25 (0.677c),

Less accurately, it appears as 1/3 of 18/17 (2.344c), 1/10 of 6/5 (6.392), 1/14 of 13/10 (3.366), 1/22 of 3/2 (6.22)... etc.

Temperaments

As a generator

Due its great approximation of 19/17, it can be used to generate a variant of hemimean.

As a comma

If instead treated as a comma to be tempered, it produces a temperament a rank-4 temperament with Superpyth levels of badness. If 64/63 and 351/350 are added, it produces an extension of Superpyth.

Wowmic

Subgroup: 2.3.5.7.13

Comma list: 1248/1225

Mapping: [⟨1 1 2 2 2], ⟨0 1 0 0 -1], ⟨0 0 1 0 2], ⟨0 0 0 1 2]]

Optimal tunings:

• WE: ~2 = 1198.283 ¢, ~3/2 = 702.799 ¢, ~5/4 = 393.408 ¢, ~7/4 = 977.617 ¢

error map: ⟨-1.717 -0.872 3.661 5.357 -4.710]

• CWE: ~2 = 1200 ¢, ~3/2 = 702.519 ¢, ~5/4 = 392.843 ¢, ~7/4 = 977.795 ¢

error map: ⟨-0.000 0.564 6.529, 8.969 -1.771]

Optimal ET sequence: 5, 12f, 27, 9, 7, 22, 34, 16, 31f, 43, 39df, 15f, 6, 8df, 18, 36

Badness (Sintel): 2.791