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!