Fifive comma: Difference between revisions

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The '''fifive comma''' is a [[5-limit]] interval with a width of about a third of a semitone. It is the amount that a stack of 5 [[27/25]]s exceeds [[3/2]] by, and also the amount by which a stack of 10 [[5/3]]s exceeds harmonic 162.
The '''fifive comma''' is a [[5-limit]] interval with a width of about a third of a semitone. It is the amount that a stack of 5 [[27/25]]s falls short of [[3/2]] by, and also the amount by which a stack of 10 [[5/3]]s exceeds harmonic 162.


Tempering out this interval leads to the [[Fifive family|fifive family]] of temperaments, where the perfect fifth is divided into 5 equal parts and the octave is split in half. [[26edo]] and [[34edo]] are two notable examples of [[EDO|edo]]s that support the basic 5-limit temperament in this family, simply known as [[Fifive family#Fifive|fifive]].
Tempering out this interval leads to the [[Fifive family|fifive family]] of temperaments, where the perfect fifth is divided into 5 equal parts and the octave is split in half. [[26edo]] and [[34edo]] are two notable examples of [[EDO|edo]]s that support the basic 5-limit temperament in this family, simply known as [[Fifive family#Fifive|fifive]].

Revision as of 18:56, 30 March 2025

Interval information
Ratio 9765625/9565938
Factorization 2-1 × 3-14 × 510
Monzo [-1 -14 10
Size in cents 35.76713¢
Name fifive comma
Color name sy10-2,
saquinbiyo negative 2nd
FJS name [math]\displaystyle{ \text{ddd}{-2}^{5,5,5,5,5,5,5,5,5,5} }[/math]
Special properties reduced
Tenney height (log2 nd) 46.4088
Weil height (log2 max(n, d)) 46.4386
Wilson height (sopfr(nd)) 94
Comma size medium
Open this interval in xen-calc

The fifive comma is a 5-limit interval with a width of about a third of a semitone. It is the amount that a stack of 5 27/25s falls short of 3/2 by, and also the amount by which a stack of 10 5/3s exceeds harmonic 162.

Tempering out this interval leads to the fifive family of temperaments, where the perfect fifth is divided into 5 equal parts and the octave is split in half. 26edo and 34edo are two notable examples of edos that support the basic 5-limit temperament in this family, simply known as fifive.