144/125
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Ratio | 144/125 |
Factorization | 2^{4} × 3^{2} × 5^{-3} |
Monzo | [4 2 -3⟩ |
Size in cents | 244.96886¢ |
Names | classic(al) diminished third, triptolemaic diminished third |
Color name | g^{3}3, trigu 3rd |
FJS name | [math]\text{d3}_{5,5,5}[/math] |
Special properties | reduced |
Tenney height (log_{2} nd) | 14.1357 |
Weil height (log_{2} 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.
Approximation
This interval is especially close to the 10th step of 49edo.