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Sagittal notation for Sunvar24 (19/16) system - The Sagittal forum

Sagittal notation for Sunvar24 (19/16) system

mschulter
Posts: 3
Joined: Thu Jul 27, 2017 10:05 am

Sagittal notation for Sunvar24 (19/16) system

Postby mschulter » Mon Jul 31, 2017 10:33 am

This is a lattice for Sunvar-19, a variation on Scott Dakota's Sun 19 Constant Structure (CS) tuning. My idea was inspired by Scott's observation that his Sun-19 theme could have variations where the goal was to set the regular minor third (-3 fifths) to a just or near-just 19/16 (297.513 cents).

Starting from this premise, I came up with the idea of two chains of fifths at 701.350 cents, spaced at 64.171 cents so that the tempered 9/8 (202.700 cents) plus this spacing yields a pure 7/6 (266.871 cents).

The spacing can represent either 28/27 (62.961 cents), as in the first lattice with D-E/|\ (9/8-7/6); or 27/26 (65.337 cents), as in the second lattice with E\|/-E (13/12-9/8). These JI thirdtone steps differ by 729/728 (2.376 cents). The spacing may also represent the complex ratio of 256/247 (61.959 cents), curiously smaller than 28/27 by 1729/1728 (1.002 cents), or almost exactly a cent, e.g. in the first lattice F-F/|\ (19/16-16/13); and in the second lattice, F#\|/-F# (39/32-24/19).

To find a counterpart to Scott's 19-note set, I have indicated on the lattice diagrams below a 10-note subset of the lower chain of fifths (Eb-F# in the first lattice, Eb\|/-F#\|/ in the second) and a 9-note subset of the upper chain (C/|\-G#/|\ and C-G# respectively) which together would yield such a 19-note subset.

This Sunvar-19 shading has close approximations for 19/16 and related ratios, while keeping ratios of 2-3-7 (e.g. 7/6, 9/7, 7/4) near-just, as well as some basic ratios of 13 (e.g. 13/9-13/12-13/8-39/32-117/64).

I should add that the original JI form of Scott's Sun-19 may be derived from two chains of pure 3:2 fifths (701.955 cents) at a pure 7:6 apart. He encourages all kinds of variations, just and tempered.


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