729/640

Interval information

Ratio	729/640
Factorization	2-7 × 36 × 5-1
Monzo	[-7 6 -1⟩
Size in cents	225.4163¢
Names	acute whole tone, retroptolemaic whole tone
Color name	Lg2, lagu 2nd
FJS name	[math]\text{M2}_{5}[/math]
Special properties	reduced
Tenney height (log2 nd)	18.8317
Weil height (log2 max(n, d))	19.0196
Wilson height (sopfr(nd))	37
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~4.19121 bits
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729/640, the retroptolemaic whole tone, is the interval that results from stacking 16/15 (classical diatonic semitone) and 2187/2048 (Pythagorean apotome), or 27/25 (large limma) and 135/128 (major limma). It is equal to 9/8 raised by a syntonic comma, about 225.4 cents in size.

Approximation

This interval is well approximated by three steps of 16edo, and 16 of them exceed three octaves by the comma (729/640)¹⁶/2³ = 3⁹⁶/(2¹¹⁵×5¹⁶) = [-115 96 -16⟩ (lela-quadquadgu negative 6th, ~6.66 cents). In addition, this interval differs from 256/225 (Neapolitan diminished third) by the schisma.

See also

• 1280/729 – its octave complement
• Gallery of just intervals