27/16: Difference between revisions

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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, [[User:Aura|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.
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.


== See also ==
== See also ==

Revision as of 03:22, 14 October 2024

Interval information
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]\displaystyle{ \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

[sound info]
Open this interval in xen-calc

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.

See also