# 15/14

 Ratio 15/14 Factorization 2-1 × 3 × 5 × 7-1 Monzo [-1 1 1 -1⟩ Size in cents 119.44281¢ Names septimal diatonic semitone,septimal major semitone Color name ry1, ruyo unison FJS name $\text{A1}^{5}_{7}$ Special properties superparticular,reduced Tenney height (log2 nd) 7.71425 Weil height (log2 max(n, d)) 7.81378 Wilson height (sopfr (nd)) 17 Harmonic entropy(Shannon, $\sqrt{nd}$) ~4.26381 bits https://en.xen.wiki/w/File:Jid_15_14_pluck_adu_dr220.mp3[sound info] open this interval in xen-calc
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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:

In combination with 19/17 it forms a good approximation of golden meantone. The untempered combination of five 19/17 and two 15/14 leads to an interval that is sharp to an octave by the mercurial comma: ((19/17)^5 * (15/14)^2 = (2/1) / (mercurial comma))

## Terminology

15/14 is traditionally called a diatonic semitone, perhaps for its proximity (and conflation in systems such as septimal meantone) with the classic diatonic semitone 16/15. However, 15/14 is a chromatic semitone in both Helmholtz-Ellis notation and Functional Just System, viewed as the apotome 2187/2048 altered by 5120/5103. Marc Sabat has taken to call it the major chromatic semitone in the same material where 21/20 is also named as the minor diatonic semitone[1].

## Approximation

15/14 is very accurately approximated by 10EDO (1\10) and all linus temperaments. The linus comma, 5.6¢, is the amount by which a stack of ten 15/14's falls short of the octave.