Tridecimal eighth-octave comma

Interval information

Ratio	17303/17280
Factorization	2-7 × 3-3 × 5-1 × 113 × 13
Monzo	[-7 -3 -1 0 3 1⟩
Size in cents	2.302772 ¢
Name	Tridecimal eighth-octave comma
Color name	3o1o3g1 thotrilo-agu unison
FJS name	[math]\displaystyle{ \text{dd1}^{11,11,11,13}_{5} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	28.1556
Weil norm (log2 max(n, d))	28.1575
Wilson norm (sopfr(nd))	74
Comma size	unnoticeable
S-expression	S11/S12
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17303/17280, the tridecimal eighth-octave comma, is an unnoticable 13-limit (specifically no-7 13-limit) comma. As an ultraparticular, it is the difference between a stack of three 12/11 and 13/10. In terms of commas, it is also:

• (1331/1296)/(40/39)
• (24167/24000)/(3042/3025)
• (35035/34992)·(9801/9800)
• (41503/41472)·(1716/1715)

The latter two expressions are derivable from the fact that an alternate S-expression is S49·S55·S64·S65·S69.

Temperaments

As its name suggests, it is tempered out in low EDOs that are a multiple of 8 (specifically 8, 16, 24, 32, 40, 56, 64, 72, 80, 96, 120…).

As its S-expression suggests, it is tempered out in gariwizmic since all of its constituents are commas of it. It is also tempered out in tertiaschis, tritikleismic, artoneutral, porcupinefowl and wizard - which means the edos 7, 15, 22f, 87, 94, 159, 166, 253, 270, 364… also temper it out by extension.

Etymology

17303/17280's name is derived from the fact that it can coincidentally be expressed as an eighth root of two 8th-octave commas. Specifically, ⁸√(214990848/214358881)³·815730721/800000000.