25/16
25/16, the classic(al) augmented fifth or diptolemaic 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 |
diptolemaic augmented fifth
reduced harmonic
[sound info]
Names
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. The concept of "diptolemaic" intervals builds on the concept of "ptolemaic"[1] intervals, with "diptolemaic" intervals being those that have two factors of 5 in their monzo and differ from their Pythagorean counterparts by two instances of 81/80 in the direction of ratio simplicity— for instance, 25/16 differing from 6561/4096—, while 5-limit intervals that differ from their Pythagorean counterparts by a single instance of 81/80 in the same direction are simply called "ptolemaic" intervals.
See also
- 32/25 – its octave complement
References
- ↑ Fundamental Principles of Just Intonation and Microtonal Composition by Thomas Nicholson and Marc Sabat —"'Ptolemaic' refers to intervals combining only the primes 2, 3, and 5."