2187/1250: Difference between revisions

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{{Infobox Interval|2187/1250
{{Infobox Interval
| Ratio = 2187/1250
| Name = tetraptolemaic diminished seventh, ragismic 5-limit harmonic seventh
| Name = tetraptolemaic diminished seventh, ragismic 5-limit harmonic seventh
| Color name = g<sup>4</sup>7, quadgu 7th
| Color name = g<sup>4</sup>7, quadgu 7th
}}
}}
'''2187/1250''', the '''tetraptolemaic diminished seventh''' or '''ragismic 5-limit harmonic seventh''', is a [[5-limit]] interval very closely approximating [[7/4]]. It can be created by stacking two [[27/25]] and [[3/2]]. It is a [[4375/4374|ragisma]] below 7/4, a [[15625/15552|kleisma]] below the marvel 5-limit harmonic seventh [[225/128]], and [[250/243]] below [[9/5]]. In the [[ragismic]] temperament, it is equated with 7/4.
'''2187/1250''', the '''tetraptolemaic diminished seventh''', is a [[5-limit]] interval very closely approximating [[7/4]]. It is sharp of the [[32768/19683|Pythagorean diminished seventh]] by four [[81/80|syntonic commas]], hence the name. It can also be created by stacking two [[27/25]] and [[3/2]].  
 
It is a [[4375/4374|ragisma]] below 7/4, a [[15625/15552|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 ==
== Approximation ==
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== See also ==
== See also ==
* [[2500/2187]] its [[octave complement]]
* [[2500/2187]] its [[octave complement]]


[[Category:Ragismic]]
[[Category:Seventh]]
[[Category:Diminished seventh]]

Latest revision as of 09:08, 18 January 2026

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

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.

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