Septimal enneadeca

[-37 57 0 -19⟩, the septimal enneadeca or 19-tone-comma, is an interval of 2.816 cents which is the amount by which nineteen 28/27's fall short of an octave, that is, 2/(28/27)¹⁹.

Interval information

Factorization	2-37 × 357 × 7-19
Monzo	[-37 57 0 -19⟩
Size in cents	3.742826¢
Name	septimal enneadeca
FJS name	[math]\displaystyle{ \text{13d}{-13}_{7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	180.683
Weil norm (log2 max(n, d))	180.686
Wilson norm (sopfr(nd))	378
Comma size	small
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Temperaments

Septimal enneadecal

This temperament is a no-5's temperament in the 7-limit; contrast with 7-limit enneadecal, which adds a mapping for 5 by tempering the enneadeca.

Subgroup: 2.3.7

Mapping: [⟨19 0 -37], ⟨0 1 3]]

CTE generators: ~28/27 = 1\19, ~3 = 1901.906

Patent val EDOs < 400: 19, 152, 171, 190, 323

Enneadecal

Subgroup: 2.3.5.7

Mapping: [⟨19 0 14 -37], ⟨0 1 1 3]]

See: Enneadecal

See also

• Unnoticeable comma
• Septimal enneadeca