2187/1250: Difference between revisions
Jump to navigation
Jump to search
m fix typo |
+1 |
||
| (One intermediate revision by the same user not shown) | |||
| Line 1: | Line 1: | ||
{{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 | '''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 == | ||
| Line 12: | Line 15: | ||
== See also == | == See also == | ||
* [[2500/2187]] | * [[2500/2187]] – its [[octave complement]] | ||
[[Category: | [[Category:Seventh]] | ||
[[Category:Diminished seventh]] | |||
Latest revision as of 09:08, 18 January 2026
| Interval information |
ragismic 5-limit harmonic seventh
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
- 2500/2187 – its octave complement