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

| Color name = g<sup>4</sup>7, quadgu 7th

}}

'''2187/1250''', the '''tetraptolemaic diminished seventh''', is a [[5-limit]] interval very closely approximating [[7/4]]~~, being only a~~ [[~~4375~~/~~4374~~|~~ragisma~~]] ~~(4375/4374) below 7/4. In the~~ [[~~ragismic~~]] ~~temperament~~, ~~it is equated with 7/4~~. It ~~is very accurately approximated~~ by ~~the 46th step of~~ [[~~57edo~~]] ~~(46\57), as 46\57 is only 0.009{{cent}} flat of this interval~~.

'''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]].

[[Category:~~Ragismic~~]]

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 ==

[[57edo]] contains a very accurate approximation of 2187/1250 at its 46th step (46\57), which is only 0.009{{cent}} 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]]

[[Category:Seventh]]

[[Category:Diminished seventh]]

@@ Line 1: / Line 1: @@
-{{Infobox Interval|2187/1250
+{{Infobox Interval
+| Ratio = 2187/1250
 | Name = tetraptolemaic diminished seventh, ragismic 5-limit harmonic seventh
+| Color name = g<sup>4</sup>7, quadgu 7th
 }}
-'''2187/1250''', the '''tetraptolemaic diminished seventh''', is a [[5-limit]] interval very closely approximating [[7/4]], being only a [[4375/4374|ragisma]] (4375/4374) below 7/4. In the [[ragismic]] temperament, it is equated with 7/4. It is very accurately approximated by the 46th step of [[57edo]] (46\57), as 46\57 is only 0.009{{cent}} flat of this interval.
+'''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]].
-[[Category:Ragismic]]
+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 ==
+[[57edo]] contains a very accurate approximation of 2187/1250 at its 46th step (46\57), which is only 0.009{{cent}} flat of 2187/1250.
+== Temperaments ==
+/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]]
+[[Category:Seventh]]
+[[Category:Diminished seventh]]