144/125
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Ratio
144/125
Factorization
24 × 32 × 5-3
Monzo
[4 2 -3⟩
Size in cents
244.9689¢
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
| Interval information |
triptolemaic diminished third
(Shannon, [math]\sqrt{nd}[/math])
[sound info]
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.
Approximation
This interval is especially close to the 10th step of 49edo.
Temperaments
In any kleismic system, it is tuned to an exact semifourth, tempered together with 125/108. The university temperament treats it as a comma.