144/125

Interval information

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]\displaystyle{ \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]\displaystyle{ \sqrt{nd} }[/math])	~4.23158 bits
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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.

See also

• 125/72 – its octave complement
• 125/96 – its fifth complement
• Gallery of just intervals