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¢
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 height (log2 nd)	180.683
Weil height (log2 max(n, d))	180.686
Wilson height (sopfr(nd))	378
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~1.32888 bits
Comma size	small
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The septimal enneadeca (monzo: [-37 57 0 -19⟩), is an interval of 3.743 cents which is the amount by which nineteen 28/27's fall short of an octave, that is, 2/(28/27)¹⁹.

Temperaments

Because of how accurately 19edo approximates 6/5, there is no real reason to not also temper out the enneadeca with the septimal enneadeca, leading to the 7-limit version of enneadecal.

Enneadecal

See Ragismic microtemperaments #Enneadecal.

See also

• Unnoticeable comma
• Enneadeca