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Isometric tunings based om just versions of standard guitar tuning intervals.

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  • January 19, 2018, 09:17:27 PM
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Author Topic: Isometric tunings based om just versions of standard guitar tuning intervals.  (Read 1533 times)

Mark Allan Barnes

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(5n)ed4 and (4n)ed3, for example 15ed2 and 12ed3 are special tunings for guitar because they take an interval found in standard guitar tuning, make it just and then divide it into equal parts in such a way that the interval between pairs of adjacent strings can be the same for every pair, allowing isometric guitar tunings that strongly resemble standard guitar open string tunings. Please suggest other examples that have interesting intervals in them. For example, what good ed(4/3)s, ed(7/2)s and ed(12/5)s are there?
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Gedankenwelt

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The standard guitar tuning divides 2 ovtaves into 5 intervals of similar size, so the closest we can get to standard guitar tuning is by stacking 2\5 intervals (= 2 steps in 5ed2, or 480 cents).

53ed2 has an interval that is slightly smaller, and 72ed2 has an interval that is slightly larger. It might be interesting to stack those intervals, find suitable just intervals that approximate these ratios, and use those, or just intervals that lie between the ones generated by 21\53 and 29\72:

53ed2:
21\53 = 475.47.. ~ 21/16
42\53 = 950.94.. ~ 26/15
63\53 = 1426.41.. ~ 16/7
84\53 = 1901.88.. ~ 3/1
105\53 = 2377.35.. ~ 160/81 (< 4/1)
...

72ed2:
29\72 = 483.33.. ~ 33/25
58\72 = 966.66.. ~ 7/4
87\72 = 1450 ~ 30/13
116\72 = 1933.33.. ~ 64/21
145\72 = 2416.66.. ~ 81/40 (> 4/1)
...

For example, 53ed2 gives us (4n)ed3 (one of your examples), as well as (3n)ed(16/7). 72ed2 offers (2n)ed(7/4).

Exploring only one sequence will lead to very similar results, so in order to find actually new results it might be better to focus on intervals between (or beyond) both sequences, but not too close to the sequence generated by stacking 2\5s.
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Gedankenwelt

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You may also try some of the following, derived from 12\31: (2n)ed(12/7), (3n)ed(9/4), (6n)ed5.
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