Enneadeca

Interval information

Factorization	2-14 × 3-19 × 519
Monzo	[-14 -19 19⟩
Size in cents	2.815547¢
Names	enneadeca, 19-tone-comma
Color name	y19-4, Neyo comma
FJS name	[math]\displaystyle{ \text{8d}{-4}^{5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} }[/math]
Special properties	reduced
Tenney height (log2 nd)	88.2309
Weil height (log2 max(n, d))	88.2333
Wilson height (sopfr(nd))	180
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~1.27353 bits
Comma size	unnoticeable
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[-14 -19 19⟩, the enneadeca or 19-tone-comma, is an unnoticeable 5-limit comma of 2.816 cents which is the amount by which nineteen classical minor thirds fall short of five octaves, that is, 2⁵/(6/5)¹⁹.

Temperament

Tempering out the enneadeca leads to the enneadecal temperament, supported by equal divisions divisible by 19 such as 19edo, 38edo, 57edo, 76edo, 114edo, 152edo, 171edo, 190edo and 228edo.

Etymology

This comma was named by Gene Ward Smith in 2001 in terms of the corresponding temperament, enneadecal, for the temperament has 19 periods per octave. The comma was at one point dubbed enneadecima, though it was enneadeca that stuck.

See also

• Septimal enneadeca