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The Shrutar

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

11/30/2000 2:51:05 PM

As I've been developing quite a bit in the direction of playing raga-style
music on the acoustic guitar tuned to an open drone fifth (often accompanied
by didjeridoo and djembe), I've been spending considerable time pondering
the question of a refretted acoustic guitar. The best solution I can see
right now would be along the lines of the 22-tone "well temperament" in my
paper (Figure 7 and Table 5), but with the "Indian Fifths" tuned twice as
close to Just than 705.75 cents, and the other fifths farther from Just than
711 cents. For example, if the "Indian" fifths are tuned to 703.3 cents, the
other fifths (unlikely to occur harmonically in this style) would increase
to 712.4 cents, resulting in the following tuning:

Shruti Pitch
0 0
1 47.1
2 103.3
3 159.5
4 206.6
5 271.9
6 319
7 384.3
8 422.3
9 496.7
10 534.7
11 590.9
12 647.1
13 703.3
14 759.5
15 815.7
16 871.9
17 909.9
18 984.3
19 1022.3
20 1087.6
21 1134.7
22 1200

The "Modern Indian Gamut" of 0 3/sqrt(2) 9/8 6/5 5/4 4/3 45/32 3/2 8/5 27/16
9/5 15/8 2/1 is represented very accurately, and other important ratios like
5/3, 7/6, and 7/4 are not too far off. Also present is a very
Arabian-sounding neutral second. Using a bit of bending, 5/3 can be brought
into better tune and 11/8 too. There would also be some 8.9-cent-lower
variants available on the dominant string if this were tuned 703.3 cents
higher than the tonic string:

tonic dominant
string string

47.1 38
103.3 94.2
159.5 150.4
206.6 206.6
271.9 262.8
319 319
384.3 375.2
422.3 413.2
496.7 487.6
534.7 525.6
590.9 590.9
647.1 638
703.3 703.3
759.5 750.4
815.7 806.6
871.9 862.8
909.9 909.9
984.3 975.2
1022.3 1022.3
1087.6 1087.6
1134.7 1125.6
1200 1200

The closest frets are a manageable 38 cents apart. What I want is to get an
acoustic guitar as good as my Martin D1-R (a $900 guitar) refretted in this
way. Probably an expensive proposition!