2187/1250

2187/1250, the tetraptolemaic diminished seventh, is a 5-limit interval very closely approximating 7/4. It is sharp of the Pythagorean diminished seventh by four syntonic commas, hence the name. It can also be created by stacking two 27/25 and 3/2.

Interval information

Ratio	2187/1250
Factorization	2-1 × 37 × 5-4
Monzo	[-1 7 -4⟩
Size in cents	968.4302¢
Names	tetraptolemaic diminished seventh, ragismic 5-limit harmonic seventh
Color name	g47, quadgu 7th
FJS name	[math]\displaystyle{ \text{d7}_{5,5,5,5} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	21.3824
Weil norm (log2 max(n, d))	22.1895
Wilson norm (sopfr(nd))	43
Open this interval in xen-calc

It is a ragisma below 7/4, a kleisma below the diptolemaic augmented sixth 225/128, and 250/243 below 9/5. In the ragismic temperament, it is equated with 7/4. As such, it can also be called the ragismic 5-limit harmonic seventh.

Approximation

57edo contains a very accurate approximation of 2187/1250 at its 46th step (46\57), which is only 0.009 ¢ flat of 2187/1250.

Temperaments

2187/1250 is the eigenmonzo of 4/9-comma meantone, and further equating it to 7/4 gives a tuning of flattone.

See also

• 2500/2187 – its octave complement