56/45

Interval information

Ratio	56/45
Factorization	23 × 3-2 × 5-1 × 7
Monzo	[3 -2 -1 1⟩
Size in cents	378.6022¢
Names	small septimal major third, marvelous major third
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
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56/45, the small septimal 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. 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. The 56/45 third is 6/5 away from the marvelous fifth, 112/75, and may also be called the marvelous major third. It is a third of a cent flatter than the 6\19 major third of 19et. According to Ozan Yarman, the perde segah of Turkish maqam music should range from 56/45.

See also

• 45/28 -- its octave complement
• 135/112 -- its fifth complement
• Gallery of just intervals