Septimal enneadeca

Interval information

Ratio	1 570 042 899 082 081 611 640 534 563 / 1 566 652 225 014 704 215 735 402 496
Factorization	2-37 × 357 × 7-19
Monzo	[-37 57 0 -19⟩
Size in cents	3.742826¢
Names	septimal enneadeca, septienneadeca
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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The septimal enneadeca or septienneadeca (monzo: [-37 57 0 -19⟩), 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.

Temperaments

Septienneadecal

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 out the enneadeca.

Subgroup: 2.3.7

Mapping: [⟨19 0 -37], ⟨0 1 3]]

mapping generators: ~28/27, ~3

Optimal tuning (CTE): ~28/27 = 1\19, ~3/2 = 701.906 (~[14 -23 0 8⟩ = 6.969)

Optimal ET sequence: 19, …, 152, 171, 494, 665, 836, 1007, 1843, 2850, 6707, 9557

Badness: 0.00146

Enneadecal

See Ragismic microtemperaments #Enneadecal.

See also

• Unnoticeable comma
• Enneadeca