56/45
Jump to navigation
Jump to search
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]\text{d4}^{7}_{5}[/math]
Special properties
reduced
Tenney height (log2 nd)
11.2992
Weil height (log2 max(n, d))
11.6147
Wilson height (sopfr(nd))
24
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~4.06864 bits
[sound info]
open this interval in xen-calc
| Interval information |
marvelous major third
(Shannon, [math]\sqrt{nd}[/math])
[sound info]
56/45, the septimal narrow major third, or marvelous major third, is the interval between various 9-odd-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 to 5/4.