32/27: Difference between revisions

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The '''Pythagorean minor third''' of '''32/27''' is the interval between [[9/8]] and [[4/3]] which arises naturally in [[3-limit]] just intonation.  Compared to the more typical [[6/5]]- with which it is conflated in [[meantone]]- this interval is more dissonant, with a [[harmonic entropy]] level roughly on par with that of [[9/8]].
The '''Pythagorean minor third''' of '''32/27''' is the interval between [[9/8]] and [[4/3]] which arises naturally in [[3-limit]] just intonation.  Compared to the more typical [[6/5]]- with which it is conflated in [[meantone]]- this interval is more dissonant, with a [[harmonic entropy]] level roughly on par with that of 9/8.


It is 352/351 sharp of [[13/11]], and tempering 352/351 out equates it with 13/11 and leads to [[minthmic chords]].
It is 352/351 sharp of [[13/11]], and tempering 352/351 out equates it with 13/11 and leads to [[minthmic chords]].

Revision as of 17:48, 4 November 2021

Interval information
Ratio 32/27
Factorization 25 × 3-3
Monzo [5 -3
Size in cents 294.135¢
Name Pythagorean minor third
Color name w3, wa 3rd
FJS name [math]\displaystyle{ \text{m3} }[/math]
Special properties reduced,
reduced subharmonic
Tenney norm (log2 nd) 9.75489
Weil norm (log2 max(n, d)) 10
Wilson norm (sopfr(nd)) 19

[sound info]
Open this interval in xen-calc

The Pythagorean minor third of 32/27 is the interval between 9/8 and 4/3 which arises naturally in 3-limit just intonation. Compared to the more typical 6/5- with which it is conflated in meantone- this interval is more dissonant, with a harmonic entropy level roughly on par with that of 9/8.

It is 352/351 sharp of 13/11, and tempering 352/351 out equates it with 13/11 and leads to minthmic chords.

See also