169/144 and 169/128

169/144 is the difference between 16/13 and 13/9.

This is 277¢, which happens to be very close to 7/6 (which is 267¢)

6/5 (minor 3rd) is the “next” higher interval (at this resolution) at 314¢

Normally the range is expanded by 8/7 (231¢) and 9/8 (204¢ major 2nd), as opposed to between 7/6 and 6/5, with which 13/11 is usually common (as 7/6 < (7+6)/(6+5) < 6/5 and (7+6)/(6+5) = 13/11.

13/11 is 289¢

and then the different between 16/13 and 13/8 is 169/128 which is 481¢, a nicely flat 4, quite sharp from the supermajor 3 of 9/7 that is 495¢

What makes this interesting more is that 16/13 and 13/8 are inverses as 16/13 * 13/8 = 2

On the Rhodes I have retuned, this 1/1 is D, and the 16/13 is the F#, the 13/9 the G# and the 13/8 the A#.   This is based of the idea that this pentatonic scale of F# (major pentatonic scape) has a very tonicizing property to it, even though the 1/1 is not played in the set.

The full note set being 1/1, 14/13, 15/13, 13/11, 16/13, 13/10, 13/9, 3/2, 13/8, 22/13, 26/15, and 13/7.

So, the F# pentatonic set of F# G# A# C# and D# are

14/13, 16/13, 13/9, 13/8, 13/7

D#,      F#,      G#,      A#,   C#

between D# and F# is 8/7

so the step sizes are, sequentially: 8/7, 169/144, 9/8, 8/7, 196/169 (between C# and D#)

196/169 is 256¢, also very much between 8/7 and 7/6

Hear this pentatonic scale at the end of the end of the 13-limit demo posted recently at https://www.patreon.com/noahdeanjordan and also the full scale, this time in “”Cminor”” at the Tribute to Phillip Glass recording (which will eventually be completed more fully with this scale)

 

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