Should scales start on 4th natural?
The Pythagorean system of tuning produces, via succeeding 3/2 multiples of a base note (e.g., C), the following set of successive tone ratios:
C to D: 9/8
D to E: 9/8
E to F: 256/243
F to G: 9/8
G to A: 9/8
A to B: 9/8
B to C: 256/243
However, in order to obtain the value for F, one must either drop down a fourth (i.e., multiply C by 2/3) or continue around the circle of fifths for eleven steps. Would it instead make sense to begin the scale at F or, if it begins at C, to end it on F-sharp? In other words, would it be better, on a keyboard, to start the scale with four white notes rather than the current three? If so, the ratios would be as follows:
9/8
9/8
9/8
256/243
9/8
9/8
256/243
This seems to be where the math leads. Any thoughts are welcome. Thanks!
-Burch
(1)1 Comments
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What would be the advantage?
F# is the tritone in C, which sounds quite dissonant to most people, so that's a pretty good reason, possibly the primary one.
Keep in mind that you're talking about using the Lydian mode instead of the Ionian mode or major scale, and some pieces do use the Lydian mode. The Ionian mode/major scale is more popular, probably because of the way it sounds.
Personally, I love the fourth scale degree being 5 half steps above the tonic, and I like having a whole step between the fourth and fifth degrees.
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