Helmholtz did a calculation of the frequencies of the musical scale. Like him we can start out with the ratios of Ptolemy's scale. Using the numerators, n, and denominators, d, below the ratios are n/d. If we want to adjust these numbers so the all the denominators are the same, the smallest denominator that will accomplish this task is D = 24. The corresponding numerators are N = 24, 27, 30, 32, 36, 40, 45, 48. These numbers are the harmonics of a fundamental frequency whose value is 1/24th that of Middle C and are part of a harmonic series.
On multiplying these numbers by the number 11 we find that the frequency corresponding to the note A is exactly 440 cycles per second. A440 is now the standard frequency for the musical scale. Helmhotz arrives at the same set of numbers in On the Sensation of Tone and attributes the scale to Scheibler.