Note C Db D Eb E F Gb G Ab A Bb B
Key
Gb (6b) 278.123 309.026 347.654 370.831 417.185 463.539 494.442
=======
Db (5b) 260.741 278.123 312.889 347.654 370.831 417.185 463.539
=======
Ab (4b) 260.741 278.123 312.889 347.654 391.111 417.185 469.333
=======
Eb (3b) 260.741 293.333 312.889 352 391.111 417.185 469.333
=======
Bb (2b) 264 293.333 312.889 352 391.111 440 469.333
=======
F (1b) 264 293.333 330 352 396 440 469.333
===
C (0) 264 297 330 352 396 440 495
===
G (1#) 264 297 330 371.25 396 445.5 495
===
D (2#) 278.438 297 334.125 371.25 396 445.5 495
===
A (3#) 278.438 297 334.125 371.25 417.656 445.5 501.188
=====
E (4#) 278.438 313.242 334.125 375.891 417.656 445.5 501.188
=======
B (5#) 281.918 313.242 334.125 375.891 417.656 469.863 501.188
=======
F# (6#) 281.918 313.242 352.397 375.891 422.877 469.863 501.188
=======
Note C C# D D# E F F# G G# A A# B
E.T. 261.626 277.183 293.665 311.127 329.628 349.228 369.994 391.995 415.305 440.000 466.164 493.883
Incidentals tuning must be worked out on a case by case basis. Often the
minor third and minor seventh take the ratios 28 and 42 when the tonic
is taken as 24, so that in C the tuning for Eb and Bb would be 308 Hz and
462 Hz. These frequencies allow dominant seventh chords with frequency
ratios of 4:5:6:7.
The line labeled "E.T." is the frequencies used for the equitempered scale in which each semitone has a ratio of the 12th root of 2 or 1.0594631.
There is a difference between Gb and F# which amounts to a ratio of (3^12)/(2^19) = 1.0136433 as discovered by Pythagoras.
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