Diaschisma: Difference between revisions

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{{Infobox Interval
| JI glyph =
| Ratio = 2048/2025
| Monzo = 11 -4 -2
| Cents = 19.55257
| Name = diaschisma
| Color name =
| FJS name = d2<sub>25</sub>
| Sound =
}}
'''2048/2025''', the '''diaschisma''', an interval of 19.553 [[cent|cents]], is the difference between four perfect fifths plus two major thirds and three octaves. Tempering it out leads to [[Diaschismic_family|diaschismic temperament]]. It may also be defined as the difference between a Pythagorean minor seventh ([[16/9]]) and a just augmented sixth ([[225/128]]), as the difference between two classic diatonic semitones ([[16/15]]) and the major whole tone ([[9/8]]), that is, (9/8)/(16/15)<sup>2</sup>, or as the difference between the 5-limit tritone [[45/32]] and its enharmonic equivalent [[64/45]].
'''2048/2025''', the '''diaschisma''', an interval of 19.553 [[cent|cents]], is the difference between four perfect fifths plus two major thirds and three octaves. Tempering it out leads to [[Diaschismic_family|diaschismic temperament]]. It may also be defined as the difference between a Pythagorean minor seventh ([[16/9]]) and a just augmented sixth ([[225/128]]), as the difference between two classic diatonic semitones ([[16/15]]) and the major whole tone ([[9/8]]), that is, (9/8)/(16/15)<sup>2</sup>, or as the difference between the 5-limit tritone [[45/32]] and its enharmonic equivalent [[64/45]].
== See also ==
* [[Comma]]


[[Category:5-limit]]
[[Category:5-limit]]
[[Category:Small comma]]
[[Category:Small comma]]
[[Category:Diaschismic]]
[[Category:Diaschismic]]

Revision as of 07:20, 5 October 2020

Interval information
Ratio 2048/2025
Factorization 211 × 3-4 × 5-2
Monzo [11 -4 -2
Size in cents 19.55257¢
Name diaschisma
FJS name [math]\displaystyle{ \text{d2}_{25} }[/math]
Special properties reduced,
reduced subharmonic
Tenney norm (log2 nd) 21.9837
Weil norm (log2 max(n, d)) 22
Wilson norm (sopfr(nd)) 44
Open this interval in xen-calc

2048/2025, the diaschisma, an interval of 19.553 cents, is the difference between four perfect fifths plus two major thirds and three octaves. Tempering it out leads to diaschismic temperament. It may also be defined as the difference between a Pythagorean minor seventh (16/9) and a just augmented sixth (225/128), as the difference between two classic diatonic semitones (16/15) and the major whole tone (9/8), that is, (9/8)/(16/15)2, or as the difference between the 5-limit tritone 45/32 and its enharmonic equivalent 64/45.

See also