*** taken from

http://www.precisionstrobe.com/apps/pianotemp/temper.html
Appendix A, The Equation of Pitch of the Equal Tempered Scale.

The octave is divided into twelve intervals to form the chromatic scale. Each of these intervals is further divided into 100 cents. Cents are used to describe small differences in pitch in terms of percentage of a semi tone.

Intervals of pitch are described in terms of the ratios of the frequencies, not absolute difference in frequencies. An octave interval is always twice, or half the frequency, of the first note. In the equal tempered scale, the twelve intervals are spread evenly between the octaves. If the ratio of each semi-tone is the inverse of the twelfth root of two (1.059463), this condition will be met. The frequency of each note in the scale can be figured by multiplying each successive note by this number to get the next. The frequency of any note can also be figured from:

f(N) = 27.5*2^(N/12)

where N is an index into the chromatic scale notes starting with 0 for A0, the lowest note on the keyboard. N increases by 1 for each note on the keyboard. Note that the actual key on the keyboard is N + 1. Table 1 shows the index and corresponding frequencies for all of the keyboard notes based on A4 = 440 Hz. To find the frequency of a note 12 cents sharp from A4, a value of n = 48.12 would be used. Sometimes it is useful to convert a frequency into N, solving for N:

N(f) = (12/ln(2))*ln(f/27.5)

This formula can be used to determine the note corresponding to a given frequency. Once N is figured, the integer value closest to it can be looked up in the following table. This equation also tells you the cents error from the corresponding note by taking the difference from it to the closest integer and multiplying by 100.

Oct 0 1 2 3 4 5 6 7

Note N f N f N f N f N f N f N f N f

A 0 27.5000 12 55.0000 24 110.0000 36 220.0000 48 440.0000 60 880.0000 72 1760.000 84 3520.000

Bb 1 29.1352 13 58.2705 25 116.5409 37 233.0819 49 466.1638 61 932.3275 73 1864.655 85 3729.310

B 2 30.8677 14 61.7354 26 123.4708 38 246.9417 50 493.8833 62 987.7666 74 1975.533 86 3951.066

C 3 32.7032 15 65.4064 27 130.8128 39 261.6256 51 523.2511 63 1046.502 75 2093.005 87 4186.009

Db 4 34.6478 16 69.2957 28 138.5913 40 277.1826 52 554.3653 64 1108.731 76 2217.461 88 4434.922

D 5 36.7081 17 73.4162 29 146.8324 41 293.6648 53 587.3295 65 1174.659 77 2349.318 89 4698.636

Eb 6 38.8909 18 77.7817 30 155.5635 42 311.1270 54 622.2540 66 1244.508 78 2489.016 90 4978.032

E 7 41.2034 19 82.4069 31 164.8138 43 329.6276 55 659.2551 67 1318.510 79 2637.020 91 5274.041

F 8 43.6535 20 87.3071 32 174.6141 44 349.2282 56 698.4565 68 1396.913 80 2793.826 92 5587.652

Gb 9 46.2493 21 92.4986 33 184.9972 45 369.9944 57 739.9888 69 1479.978 81 2959.955 93 5919.911

G 10 48.9994 22 97.9989 34 195.9977 46 391.9954 58 783.9909 70 1567.982 82 3135.963 94 6271.927

Ab 11 51.9131 23 103.8262 35 207.6523 47 415.3047 59 830.6094 71 1661.219 83 3322.438 95 6644.875

Thats the long answer to why it goes directly from "B" to "C" and again from "E" to "F".