25/16

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 the ptolemismic augmented triad.

Interval information

Ratio	25/16
Factorization	2-4 × 52
Monzo	[-4 0 2⟩
Size in cents	772.6274¢
Names	classic(al) augmented fifth, diptolemaic augmented fifth
Color name	yy5, yoyo 5th
FJS name	[math]\displaystyle{ \text{A5}^{5,5} }[/math]
Special properties	reduced, reduced harmonic
Tenney norm (log2 nd)	8.64386
Weil norm (log2 max(n, d))	9.28771
Wilson norm (sopfr(nd))	18
[sound info]
Open this interval in xen-calc

While this interval has been referred to as the classic 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

• 32/25 – its octave complement