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Encyclopedia of Microtonal Music Theory

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frequency

[Joe Monzo]

The rate at which a periodic sound wave (or any type of periodic vibration) repeats, usually expressed as Hertz (abbr. Hz) or cycles-per-second (abbr. cps), which mean the same thing.

Frequencies are compared either digitally, as ratios of actual vibration-numbers, or in an analog fashion, as equally-spaced degrees of some logarithmic division (such as equal temperament), or possibly a combination of the two.

Below is a table giving the reference frequencies for all key tonics in a variety of chain-of-5th tunings, in which A always equals 440 Hz and is always the highest frequency:

note  generator 19-edo     31-edo     55-edo     12-edo     53-edo

A ....... 0 ... 440 ...... 440 ...... 440 ...... 440.0 .... 440
Ab ..... -7 ... 424.24 ... 420.76 ... 418.37 ... 415.3 .... 412.15
Abb ... -14 ... 409.04 ... 402.36 ... 397.8 .... 392.0 .... 386.06
Gx ..... 12 ... 424.24 ... 430.27 ... 434.49 ... 440.0 .... 222.9
G# ...... 5 ... 409.04 ... 411.45 ... 413.13 ... 415.3 .... 417.57
G ...... -2 ... 394.39 ... 393.46 ... 392.82 ... 392.0 .... 391.14
Gb ..... -9 ... 380.26 ... 376.25 ... 373.51 ... 369.99 ... 366.38
Gbb ... -16 ... 366.64 ... 359.8 .... 355.15 ... 349.23 ... 343.19
Fx ..... 10 ... 380.26 ... 384.76 ... 387.9 .... 392.0 .... 396.29
F# ...... 3 ... 366.64 ... 367.93 ... 368.83 ... 369.99 ... 371.21
F ...... -4 ... 353.5 .... 351.84 ... 350.7 .... 349.23 ... 347.71
Fb .... -11 ... 340.84 ... 336.45 ... 333.46 ... 329.63 ... 325.7
E# ...... 8 ... 340.84 ... 344.06 ... 346.31 ... 349.23 ... 352.29
E ....... 1 ... 328.63 ... 329.01 ... 329.28 ... 329.63 ... 329.99
Eb ..... -6 ... 316.85 ... 314.62 ... 313.09 ... 311.13 ... 309.1
Ebb ... -13 ... 305.5 .... 300.87 ... 297.7 .... 293.66 ... 289.53
Dx ..... 13 ... 316.85 ... 321.74 ... 325.16 ... 329.63 ... 334.33
D# ...... 6 ... 305.5 .... 307.67 ... 309.17 ... 311.13 ... 313.17
D ...... -1 ... 294.56 ... 294.21 ... 293.97 ... 293.66 ... 293.34
Db ..... -8 ... 284.01 ... 281.35 ... 279.52 ... 277.18 ... 274.78
Dbb ... -15 ... 273.83 ... 269.04 ... 265.78 ... 261.63 ... 257.38
Cx ..... 11 ... 284.01 ... 287.71 ... 290.29 ... 293.66 ... 297.21
C# ...... 4 ... 273.83 ... 275.12 ... 276.02 ... 277.18 ... 278.39
C ...... -3 ... 264.02 ... 263.09 ... 262.45 ... 261.63 ... 260.77
Cb .... -10 ... 254.56 ... 251.59 ... 249.55 ... 246.94 ... 244.26
Bx ...... 9 ... 254.56 ... 257.27 ... 259.16 ... 261.63 ... 264.2
B ....... 2 ... 245.44 ... 246.02 ... 246.42 ... 246.94 ... 247.48
Bb ..... -5 ... 236.65 ... 235.26 ... 234.31 ... 233.08 ... 231.82
Bbb ... -12 ... 228.17 ... 224.97 ... 222.79 ... 440.0 .... 434.28
Ax ..... 14 ... 236.65 ... 240.58 ... 243.34 ... 246.94 ... 250.74
A# ...... 7 ... 228.17 ... 230.06 ... 231.37 ... 233.08 ... 234.87
		
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