15/14

Interval information

Ratio	15/14
Factorization	2-1 × 3 × 5 × 7-1
Monzo	[-1 1 1 -1⟩
Size in cents	119.4428¢
Name	septimal diatonic semitone
Color name	ry1, ruyo semitone
FJS name	[math]\displaystyle{ \text{A1}^{5}_{7} }[/math]
Special properties	superparticular, reduced
Tenney norm (log2 nd)	7.71425
Weil norm (log2 max(n, d))	7.81378
Wilson norm (sopfr(nd))	17
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15/14 is a superparticular ratio with a numerator which is the fifth triangular number.

It may be found as the interval between many 7-limit ratios, including:

• 16/15 and 8/7
• 14/13 and 15/13
• 7/6 and 5/4
• 6/5 and 9/7
• 14/11 and 15/11
• 4/3 and 10/7
• 7/5 and 3/2
• 22/15 and 11/7
• 14/9 and 5/3
• 8/5 and 12/7
• 26/15 and 13/7
• 7/4 and 15/8

Although called septimal diatonic semitone for its proximity (and conflation in systems such as septimal meantone) with the classic diatonic semitone 16/15, 15/14 is a chromatic semitone in both Helmholtz-Ellis notation and Functional Just System because it is 5120/5103 larger than the apotome 2187/2048.

In combination with 19/17 it forms a good approximation of golden meantone.

See also

• 28/15 – its octave complement
• 7/5 – its fifth complement
• List of superparticular intervals
• Gallery of Just Intervals
• Septimal diatonic semitone - Wikipedia