4096/2187

Interval information

Ratio	4096/2187
Factorization	212 × 3-7
Monzo	[12 -7⟩
Size in cents	1086.315¢
Name	Pythagorean diminished octave
Color name	sw8, sawa 8ve
FJS name	[math]\displaystyle{ \text{d8} }[/math]
Special properties	reduced, reduced subharmonic
Tenney height (log2 nd)	23.0947
Weil height (log2 max(n, d))	24
Wilson height (sopfr(nd))	45
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~4.22567 bits
Open this interval in xen-calc

4096/2187, the Pythagorean diminished octave is the interval formed by subtracting 2187/2048, the apotome, from the octave. It differs from 15/8 by the schisma.

See also

• 2187/2048 – its octave complement
• Gallery of just intervals