ALCHEMICAL OCTAVES
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SOUND WAVES

OCTAVE RATIOS AND TUNINGS

Note C D E F G A B
True Ratios 1:1 9:8 5:4 4:3 3:2 5:3 15:8
Phythagoran 1:1 9:8 81:64 4:3 3:2 27:16 243:128
Justified Ratios 1:1 55:49 63:50 578:433 433:289 37:22 185:98
Justified Tuning 261.62 293.66 329.63 349.23 391.99 440 493.84
Alchemical Tuning 256.00 288.00 320.00 341.333 384.00 426.666 480.00

TRUE OCTAVE FREQUENCIES IN CPS

C 1:1 D 9:8 E 5:4 F 4:3 G 3:2 A 5:3 B 15:8
1.00 1.125 1.25 1.333 1.50 1.666 1.875
2.00 2.250 2.50 2.666 3.00 3.333 3.750
4.00 4.50 5.00 5.333 6.00 6.666 7.50
8.00 9.00 10.00 10.666 12.00 13.333 15.00
16.00 18.00 20.00 21.333 24.00 26.666 30.00
32.00 36.00 40.00 42.666 48.00 53.333 60.00
64.00 72.00 80.00 85.333 96.00 106.666 120.00
128.00 144.00 160.00 170.666 192.00 213.333 240.00
256.00 288.00 320.00 341.333 384.00 426.666 480.00
512.00 576.00 640.00 682.666 768.00 853.333 960.00
1024.00 1152.00 1280.00 1365.333 1536.00 1706.666 1920.00
2048.00 2304.00 2560.00 2730.666 3072.00 3413.333 3840.00
4096.00 4608.00 5120.00 5461.333 6144.00 6826.666 7680.00
8192.00 9216.00 10240.0 10922.66 12288.0 13653.33 15360.0
16384.0 18432.0 20480.0 21845.33 24576.0 27306.66 30720.0
32768.0 36864.0 40960.0 43690.66 49152.0 54613.33 61440.0
65536.0 73728.0 81920.0 87381.33 98304.0 109226.6 122880
131072 147456 163840 174762.6 196608 218453.3 245760
262144 294912 327680 439525.3 393216 439606.6 491520
524288 589824 655360 699050.6 786432 873813.3 983040

Original justified tuning was at "A"=435 CPS, quite close to the true ratio. It was recently changed to the modern standard of "A"=440 CPS, taking modern instruments farther away from the natural frequencies of the universe. Justified tuning was designed to be dissharmonious. Notice that with the justified "A" at 400 CPS it's the only note with a whole number of waves per second. With the natural Alchenical tuning the "F" and "A" are the only ones that don't. Compare this with the natural human brain waves. Modern digital instruments may be tuned to these natural frequencies without the side effects that bothered the old masters.