16767/16384

Interval information

Ratio	16767/16384
Subgroup monzo	2.3.23 [-14 6 1⟩
Size in cents	40.00435¢
Name	23 small diesis
Color name	L23o1, latwetho 1sn
FJS name	[math]\displaystyle{ \text{d}{-2}^{23} }[/math]
Special properties	reduced, reduced harmonic
Tenney norm (log2 nd)	28.0333
Weil norm (log2 max(n, d))	28.0667
Wilson norm (sopfr(nd))	69
Comma size	medium
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16767/16384 is a 2.3.23 subgroup comma. It is the amount by which the octave-reduced 23rd harmonic 23/16 exceeds the Pythagorean diminished fifth (1024/729).

Notation

This interval is significant in color notation as the formal comma to translate a Pythagorean interval to a nearby 23-limit (vicesimotertial) interval.

It is used in the Sagittal notation in the Promethean extension, whose name is the 23 small diesis or 23S (  / ).

Approximation

This interval is extremely close to one step of 30edo, though 30edo actually maps it to four steps by patent val. It is represented consistently as 1\30 in 270edo and 330edo.