56/45: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Name = septimal narrow major third, marvelous major third
| Name = septimal narrow major third, marvelous major third
| Color name = zg4, zogu 4th
| Sound = jid_56_45_pluck_adu_dr220.mp3
| Sound = jid_56_45_pluck_adu_dr220.mp3
}}
}}

Revision as of 02:50, 4 December 2022

Interval information
Ratio 56/45
Factorization 23 × 3-2 × 5-1 × 7
Monzo [3 -2 -1 1
Size in cents 378.6022¢
Names septimal narrow major third,
marvelous major third
Color name zg4, zogu 4th
FJS name [math]\displaystyle{ \text{d4}^{7}_{5} }[/math]
Special properties reduced
Tenney norm (log2 nd) 11.2992
Weil norm (log2 max(n, d)) 11.6147
Wilson norm (sopfr(nd)) 24

[sound info]
Open this interval in xen-calc

56/45, the septimal narrow major third, or marvelous major third, is the interval between various 9-limit consonances- 5/4 and 14/9, 9/7 and 8/5, 9/8 and 7/5, and 10/7 and 16/9- with it also being 6/5 away from the marvelous fifth, 112/75. Marvel tempering makes all of these intervals into major thirds like any other, and turns chords like 1-5/4-8/5 or 1-5/4-14/9 into essentially tempered dyadic chords. It is a third of a cent flatter than the 6\19 major third of 19edo, however, it functionally doubles as a type of diminished fourth. According to Ozan Yarman, the perde segah of Turkish maqam music should range from 56/45.

See also