59049/32768: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Cmloegcmluin (talk | contribs)
No edit summary
No edit summary
 
(7 intermediate revisions by 4 users not shown)
Line 1: Line 1:
{{Infobox Interval
{{Infobox Interval
| Name = pentatone
| Name = Pythagorean augmented sixth, pentatone
| Color name = Lw6, lawa 6th
}}
}}
{{Redirect|Pentatone|systems with 5 note classes per octave|Pentatonic}}
The '''Pythagorean augmented sixth''', otherwise known as the '''pentatone''', 59049/32768, is the interval found by stacking five [[9/8|(Pythagorean whole) tones (9/8)]]. It exceeds the [[9/5|classical minor seventh (9/5)]] by a [[schisma]]. The Medieval music theorist {{w|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>


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>
== See also ==
* [[32768/19683]] – its [[twelfth complement]]
* [[65536/59049]] — its [[octave complement]]
 
== Notes ==

Latest revision as of 20:05, 3 February 2026

Interval information
Ratio 59049/32768
Factorization 2-15 × 310
Monzo [-15 10
Size in cents 1019.55¢
Names Pythagorean augmented sixth,
pentatone
Color name Lw6, lawa 6th
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
"Pentatone" redirects here. For systems with 5 note classes per octave, see Pentatonic.

The Pythagorean augmented sixth, otherwise known as the pentatone, 59049/32768, is the interval found by stacking five (Pythagorean whole) tones (9/8). It exceeds the classical minor seventh (9/5) by a schisma. 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]

See also

Notes

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