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Interval information
Ratio 144/125
Factorization 24 × 32 × 5-3
Monzo [4 2 -3
Size in cents 244.96886¢
Names classic(al) diminished third,
triptolemaic diminished third
Color name g33, trigu 3rd
FJS name [math]\text{d3}_{5,5,5}[/math]
Special properties reduced
Tenney height (log2 nd) 14.1357
Weil height (log2 max(n, d)) 14.3399
Wilson height (sopfr (nd)) 29
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~4.23158 bits

[sound info]
open this interval in xen-calc

144/125, the classic diminished third, about 245 cents in size, is a just interval in the 5-limit. It can be obtained by subtracting 6/5, the classic minor third, by 25/24, the classic chroma. It is also the Pythagorean diminished third (65536/59049) flattened by three syntonic commas, which lends itself to the term triptolemaic.

In any kleismic system, it is tuned to an exact semifourth, tempered together with 125/108. The university temperament treats it as a comma.


This interval is especially close to the 10th step of 49edo.

See also