From Xenharmonic Wiki
Jump to navigation Jump to search
Interval information
Ratio 25/16
Factorization 2-4 × 52
Monzo [-4 0 2
Size in cents 772.62743¢
Names classic(al) augmented fifth,
diptolemaic augmented fifth
Color name yy5, yoyo 5th
FJS name [math]\text{A5}^{5,5}[/math]
Special properties reduced
Tenney height (log2 nd) 8.64386
Weil height (log2 max(n, d)) 9.28771
Wilson height (sopfr (nd)) 18
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~4.21803 bits

[sound info]
open this interval in xen-calc

25/16, the classic(al) augmented fifth is the interval obtained by stacking two 5/4 major thirds, however, it gains additional isoharmonic identity from its position between 11/8 and 7/4, so it can frequently be used in conjunction with those, even in chords. It is 100/99 sharp of 99/64, and tempering out 100/99 makes 1-5/4-25/16 into a ptolemismic chord.

While this interval has been referred to as the classic augmented fifth or classical augmented fifth for some time, the term diptolemaic was coined on Discord by Flora Canou while discussing a proposal for a consistent naming scheme for different 5-limit intervals with Aura. Specifically, since "diptolemaic" intervals have two instances of prime 5 in their factorization, this interval is also referred to as the diptolemaic augmented fifth.

See also