19683/16384: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Name = Pythagorean augmented second
| Name = Pythagorean augmented second, Evadairean comma
| Color name = lw2, Lawa 2nd
| Color name = lw2, Lawa 2nd
}}
}}


The '''Pythagorean augmented 2nd''', '''19683/16384''', may be reached by stacking 9 3/2's and octave reducing. It differs from the classic minor third, [[6/5]], by the [[schisma]], and, as a result, the Pythagorean augmented second is in fact rather consonant.  According to [[User:Aura|Aura]], while 19683/16384 may take the place of the classic minor third in chords, its status as a augmented second means that it has a different function in terms of voice-leading. If it is tempered out, you set the fifth to 5/9 and divide the octave into 9 parts, although only 9edo does this in it's patent val. If it is used as a generator, it produces [[Hanson]].
The '''Pythagorean augmented 2nd''', '''19683/16384''', may be reached by stacking 9 3/2's and octave reducing. It differs from the classic minor third, [[6/5]], by the [[schisma]], and, as a result, the Pythagorean augmented second is in fact rather consonant.  According to [[User:Aura|Aura]], while 19683/16384 may take the place of the classic minor third in chords, its status as a augmented second<sup>[according to what?]</sup> means that it has a different function in terms of voice-leading.
 
== Temperaments ==
When this ratio is taken as a comma to be tempered out, it produces the [[tervenna]] temperament, and has been named the '''Evadairean comma''' (by analogy with the Pythagorean comma not sharing its name with compton temperament). Edos tempering it out include [[9edo]], as well as [[18edo]] if its flat fifth is used. If it is used as a generator, it produces [[Hanson]].


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

Revision as of 01:54, 12 July 2024

Interval information
Ratio 19683/16384
Factorization 2-14 × 39
Monzo [-14 9
Size in cents 317.595¢
Names Pythagorean augmented second,
Evadairean comma
Color name lw2, Lawa 2nd
FJS name [math]\displaystyle{ \text{A2} }[/math]
Special properties reduced,
reduced harmonic
Tenney norm (log2 nd) 28.2647
Weil norm (log2 max(n, d)) 28.5293
Wilson norm (sopfr(nd)) 55
Open this interval in xen-calc

The Pythagorean augmented 2nd, 19683/16384, may be reached by stacking 9 3/2's and octave reducing. It differs from the classic minor third, 6/5, by the schisma, and, as a result, the Pythagorean augmented second is in fact rather consonant. According to Aura, while 19683/16384 may take the place of the classic minor third in chords, its status as a augmented second[according to what?] means that it has a different function in terms of voice-leading.

Temperaments

When this ratio is taken as a comma to be tempered out, it produces the tervenna temperament, and has been named the Evadairean comma (by analogy with the Pythagorean comma not sharing its name with compton temperament). Edos tempering it out include 9edo, as well as 18edo if its flat fifth is used. If it is used as a generator, it produces Hanson.

See also