59049/32768: Difference between revisions

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The '''pentatone''', 59049/32768, is the interval found by stacking five (Pythagorean whole) [[tone]]s ([[9/8]]). The Medieval music theorist Jacobus of Liège described it along with the [[ditone]], [[tritone]], [[tetratone]], and [[hexatone]].
The '''pentatone''', 59049/32768, is the interval found by stacking five (Pythagorean whole) [[tone]]s ([[9/8]]). The Medieval music theorist Jacobus of Liège described it along with the [[ditone]], [[tritone]], [[tetratone]], and [[hexatone]], and considered the pentatone to be highly discordant.<ref>''Pythagorean Tuning and Medieval Polyphony'', Margo Schulter, 10 June 1998</ref>

Revision as of 06:19, 24 June 2024

Interval information
Ratio 59049/32768
Factorization 2-15 × 310
Monzo [-15 10
Size in cents 1019.55¢
Name pentatone
FJS name [math]\displaystyle{ \text{A6} }[/math]
Special properties reduced,
reduced harmonic
Tenney norm (log2 nd) 30.8496
Weil norm (log2 max(n, d)) 31.6993
Wilson norm (sopfr(nd)) 60
Open this interval in xen-calc

The pentatone, 59049/32768, is the interval found by stacking five (Pythagorean whole) tones (9/8). The Medieval music theorist Jacobus of Liège described it along with the ditone, tritone, tetratone, and hexatone, and considered the pentatone to be highly discordant.[1]

  1. Pythagorean Tuning and Medieval Polyphony, Margo Schulter, 10 June 1998