Friday, May 22, 2015

Scientific Even and Just Temperament

Medical Tuning forks are based on octaves 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 Hz.  All modern music is even temperment based on a concert A4 = 440Hz. This is just an arbitrary assignment. Music should be based on a C4 = 256 Hz.  After deciding the proper starting pitch, we need to decide on temperment. 3 major temperments are Even, Just, and Pythagorean. Pathagorean temperment leads to the popular alternative 432 pitch.  Even and Just frequencies are listed below. 

Even Temperment:
F(n) = 2 ^ ( n / 12 ) * 256 Hz

C4 = 256.0 Hz
C#4 = 271.2 Hz
D4 = 287.3 Hz
D#4 = 304.4 Hz
E4 = 322.5 Hz
F4 = 341.7 Hz
F#4 = 362.0 Hz
G4 = 383.6 Hz
G#4 = 406.4 Hz
A4 = 430.5 Hz **********
A#4 = 456.1 Hz
B4 = 483.3 Hz
C5 = 512.0 Hz

Just Temperment:

C4 = 1/1 = 256 Hz
C#4 = 25/24 = 266.7 Hz
D4 = 9/8 = 
288 Hz
D#4 = 6/5 = 307.2 Hz
E4 = 5/4 = 320 Hz
F4 = 4/3 = 341.3 Hz
F#4 = 45/32 = 360 Hz
G4 = 3/2 = 384 Hz
G#4 = 8/5 = 409.6 Hz
A4 = 5/3 = 426.7 Hz **********
A#4 = 9/5 = 460.8 Hz
B4 = 15/8 = 480 Hz
C5 = 2/1 = 512 Hz

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