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.
