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.
In any kleismic system, it is tuned to an exact semifourth, tempered together with 125/108. The university temperament treats it as a comma.
Approximation
This interval is especially close to the 10th step of 49edo.