144/125: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = classic(al) diminished third, triptolemaic diminished third | |||
| Color name = g<sup>3</sup>3, trigu 3rd | |||
| Name = classic diminished third | |||
| Color name = | |||
| Sound = jid_144_125_pluck_adu_dr220.mp3 | | Sound = jid_144_125_pluck_adu_dr220.mp3 | ||
}} | }} | ||
'''144/125''', the '''classic diminished third''', about 245 [[cent]]s in size, is a just interval in the [[5-limit]]. [[ | '''144/125''', the '''classic diminished third''', about 245 [[cent]]s 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 [[81/80|syntonic commas]], which lends itself to the term ''triptolemaic''. | ||
This interval is especially close to the 10th step of [[49edo | == Approximation == | ||
This interval is especially close to the 10th step of [[49edo]]. | |||
== Temperaments == | |||
In any [[kleismic]] system, it is tuned to an exact semifourth, tempered together with [[125/108]]. The [[university]] temperament treats it as a [[comma]]. | |||
== See also == | == See also == | ||
* [[125/72]] – its [[octave complement]] | * [[125/72]] – its [[octave complement]] | ||
* [[125/96]] – its [[fifth complement]] | * [[125/96]] – its [[fifth complement]] | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
[[Category:Third]] | [[Category:Third]] | ||
[[Category:Diminished third]] | [[Category:Diminished third]] | ||
[[Category:Interseptimal]] | [[Category:Interseptimal intervals]] | ||
[[Category: | [[Category:Semifourth]] | ||
[[Category: | [[Category:University]] | ||
Latest revision as of 10:24, 1 January 2025
| Interval information |
triptolemaic diminished third
[sound info]
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.
Approximation
This interval is especially close to the 10th step of 49edo.
Temperaments
In any kleismic system, it is tuned to an exact semifourth, tempered together with 125/108. The university temperament treats it as a comma.