27/16
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Ratio
27/16
Factorization
2-4 × 33
Monzo
[-4 3⟩
Size in cents
905.865¢
Name
Pythagorean major sixth
Color name
w6, wa 6th
FJS name
[math]\text{M6}[/math]
Special properties
reduced,
reduced harmonic
Tenney height (log2 nd)
8.75489
Weil height (log2 max(n, d))
9.50978
Wilson height (sopfr(nd))
17
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~4.23407 bits
[sound info]
open this interval in xen-calc
| Interval information |
reduced harmonic
(Shannon, [math]\sqrt{nd}[/math])
[sound info]
The Pythagorean major sixth, 27/16, may be reached by stacking three perfect fifths (3/2) and reducing by one octave. Compared to the more typical 5/3- with which it is conflated in meantone- this interval is more dissonant, with a harmonic entropy level roughly on par with that of 6/5. While many musicians prefer to use 5/3 as the major sixth interval above the Tonic in a diatonic context even in non-meantone settings, Aura is known to prefer this interval in those same contexts, though he still uses 5/3 as major sixth interval between certain non-tonic notes.