8/3: Difference between revisions

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Found this out a few weeks ago
 
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'''8/3''', the '''perfect eleventh''', is the ratio between the 3rd and 8th [[harmonic]]s; one octave above [[4/3]]. See also [[ed8/3]].
'''8/3''', the '''perfect eleventh''', is the ratio between the 3rd and 8th [[harmonic]]s; one octave above [[4/3]]. See also [[ed8/3]].
== Chord construction ==
Notably, 8/3 can be used as a framework for chords, but the usage of 8/3 as a framework for chords is intimately connected with the use of [[perfect fifth]]s in the same capacity- at least in [[Octave #Octave equivalence|octave-equivalent]] systems- due to the same pitch classes being involved in both 4:5:6 and 3:5:8 where 5 is kept as the same note, thus rendering the two chords as different voicings of the same underlying harmonic unit.


[[Category:Tritave-reduced harmonics]]
[[Category:Tritave-reduced harmonics]]

Latest revision as of 16:28, 29 November 2025

Interval information
Ratio 8/3
Factorization 23 × 3-1
Monzo [3 -1
Size in cents 1698.045¢
Name perfect eleventh
Color name w11, wa 11th
FJS name [math]\displaystyle{ \text{P11} }[/math]
Tenney norm (log2 nd) 4.58496
Weil norm (log2 max(n, d)) 6
Wilson norm (sopfr(nd)) 9

[sound info]
Open this interval in xen-calc

8/3, the perfect eleventh, is the ratio between the 3rd and 8th harmonics; one octave above 4/3. See also ed8/3.

Chord construction

Notably, 8/3 can be used as a framework for chords, but the usage of 8/3 as a framework for chords is intimately connected with the use of perfect fifths in the same capacity- at least in octave-equivalent systems- due to the same pitch classes being involved in both 4:5:6 and 3:5:8 where 5 is kept as the same note, thus rendering the two chords as different voicings of the same underlying harmonic unit.