Relative frequencies of the first eight harmonics for five octaves of chromatic pitches
|
c |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
|
|
1.059463 |
2.118926 |
3.178389 |
4.237852 |
5.297315 |
6.356779 |
7.416242 |
8.475705 |
|
d |
1.122462 |
2.244924 |
3.367386 |
4.489848 |
5.61231 |
6.734772 |
7.857234 |
8.979696 |
|
|
1.189207 |
2.378414 |
3.567621 |
4.756828 |
5.946036 |
7.135243 |
8.32445 |
9.513657 |
|
e |
1.259921 |
2.519842 |
3.779763 |
5.039684 |
6.299605 |
7.559526 |
8.819447 |
10.07937 |
|
f |
1.33484 |
2.66968 |
4.00452 |
5.339359 |
6.674199 |
8.009039 |
9.343879 |
10.67872 |
|
|
1.414214 |
2.828427 |
4.242641 |
5.656854 |
7.071068 |
8.485281 |
9.899495 |
11.31371 |
|
g |
1.498307 |
2.996614 |
4.494921 |
5.993228 |
7.491535 |
8.989842 |
10.48815 |
11.98646 |
|
|
1.587401 |
3.174802 |
4.762203 |
6.349604 |
7.937005 |
9.524406 |
11.11181 |
12.69921 |
|
a |
1.681793 |
3.363586 |
5.045378 |
6.727171 |
8.408964 |
10.09076 |
11.77255 |
13.45434 |
|
|
1.781797 |
3.563595 |
5.345392 |
7.12719 |
8.908987 |
10.69078 |
12.47258 |
14.25438 |
|
b |
1.887749 |
3.775497 |
5.663246 |
7.550995 |
9.438743 |
11.32649 |
13.21424 |
15.10199 |
|
c |
2 |
4 |
6 |
8 |
10 |
12 |
14 |
16 |
|
|
2.118926 |
4.237852 |
6.356779 |
8.475705 |
10.59463 |
12.71356 |
14.83248 |
16.95141 |
|
d |
2.244924 |
4.489848 |
6.734772 |
8.979696 |
11.22462 |
13.46954 |
15.71447 |
17.95939 |
|
|
2.378414 |
4.756828 |
7.135243 |
9.513657 |
11.89207 |
14.27049 |
16.6489 |
19.02731 |
|
e |
2.519842 |
5.039684 |
7.559526 |
10.07937 |
12.59921 |
15.11905 |
17.63889 |
20.15874 |
|
f |
2.66968 |
5.339359 |
8.009039 |
10.67872 |
13.3484 |
16.01808 |
18.68776 |
21.35744 |
|
|
2.828427 |
5.656854 |
8.485281 |
11.31371 |
14.14214 |
16.97056 |
19.79899 |
22.62742 |
|
g |
2.996614 |
5.993228 |
8.989842 |
11.98646 |
14.98307 |
17.97968 |
20.9763 |
23.97291 |
|
|
3.174802 |
6.349604 |
9.524406 |
12.69921 |
15.87401 |
19.04881 |
22.22361 |
25.39842 |
|
a |
3.363586 |
6.727171 |
10.09076 |
13.45434 |
16.81793 |
20.18151 |
23.5451 |
26.90869 |
|
|
3.563595 |
7.12719 |
10.69078 |
14.25438 |
17.81797 |
21.38157 |
24.94516 |
28.50876 |
|
b |
3.775497 |
7.550995 |
11.32649 |
15.10199 |
18.87749 |
22.65298 |
26.42848 |
30.20398 |
|
c |
4 |
8 |
12 |
16 |
20 |
24 |
28 |
32 |
|
|
4.237852 |
8.475705 |
12.71356 |
16.95141 |
21.18926 |
25.42711 |
29.66497 |
33.90282 |
|
d |
4.489848 |
8.979696 |
13.46954 |
17.95939 |
22.44924 |
26.93909 |
31.42894 |
35.91879 |
|
|
4.756828 |
9.513657 |
14.27049 |
19.02731 |
23.78414 |
28.54097 |
33.2978 |
38.05463 |
|
e |
5.039684 |
10.07937 |
15.11905 |
20.15874 |
25.19842 |
30.23811 |
35.27779 |
40.31747 |
|
f |
5.339359 |
10.67872 |
16.01808 |
21.35744 |
26.6968 |
32.03616 |
37.37552 |
42.71488 |
|
|
5.656854 |
11.31371 |
16.97056 |
22.62742 |
28.28427 |
33.94113 |
39.59798 |
45.25483 |
|
g |
5.993228 |
11.98646 |
17.97968 |
23.97291 |
29.96614 |
35.95937 |
41.9526 |
47.94583 |
|
|
6.349604 |
12.69921 |
19.04881 |
25.39842 |
31.74802 |
38.09763 |
44.44723 |
50.79683 |
|
a |
6.727171 |
13.45434 |
20.18151 |
26.90869 |
33.63586 |
40.36303 |
47.0902 |
53.81737 |
|
|
7.12719 |
14.25438 |
21.38157 |
28.50876 |
35.63595 |
42.76314 |
49.89033 |
57.01752 |
|
b |
7.550995 |
15.10199 |
22.65298 |
30.20398 |
37.75497 |
45.30597 |
52.85696 |
60.40796 |
|
c |
8 |
16 |
24 |
32 |
40 |
48 |
56 |
64 |
|
|
8.475705 |
16.95141 |
25.42711 |
33.90282 |
42.37852 |
50.85423 |
59.32993 |
67.80564 |
|
d |
8.979696 |
17.95939 |
26.93909 |
35.91879 |
44.89848 |
53.87818 |
62.85787 |
71.83757 |
|
|
9.513657 |
19.02731 |
28.54097 |
38.05463 |
47.56828 |
57.08194 |
66.5956 |
76.10926 |
|
e |
10.07937 |
20.15874 |
30.23811 |
40.31747 |
50.39684 |
60.47621 |
70.55558 |
80.63495 |
|
f |
10.67872 |
21.35744 |
32.03616 |
42.71488 |
53.39359 |
64.07231 |
74.75103 |
85.42975 |
|
|
11.31371 |
22.62742 |
33.94113 |
45.25483 |
56.56854 |
67.88225 |
79.19596 |
90.50967 |
|
g |
11.98646 |
23.97291 |
35.95937 |
47.94583 |
59.93228 |
71.91874 |
83.9052 |
95.89165 |
|
|
12.69921 |
25.39842 |
38.09763 |
50.79683 |
63.49604 |
76.19525 |
88.89446 |
101.5937 |
|
a |
13.45434 |
26.90869 |
40.36303 |
53.81737 |
67.27171 |
80.72606 |
94.1804 |
107.6347 |
|
|
14.25438 |
28.50876 |
42.76314 |
57.01752 |
71.2719 |
85.52628 |
99.78066 |
114.035 |
|
b |
15.10199 |
30.20398 |
45.30597 |
60.40796 |
75.50995 |
90.61193 |
105.7139 |
120.8159 |
|
c |
16 |
32 |
48 |
64 |
80 |
96 |
112 |
128 |
|
|
16.95141 |
33.90282 |
50.85423 |
67.80564 |
84.75705 |
101.7085 |
118.6599 |
135.6113 |
|
d |
17.95939 |
35.91879 |
53.87818 |
71.83757 |
89.79696 |
107.7564 |
125.7157 |
143.6751 |
|
|
19.02731 |
38.05463 |
57.08194 |
76.10926 |
95.13657 |
114.1639 |
133.1912 |
152.2185 |
|
e |
20.15874 |
40.31747 |
60.47621 |
80.63495 |
100.7937 |
120.9524 |
141.1112 |
161.2699 |
|
f |
21.35744 |
42.71488 |
64.07231 |
85.42975 |
106.7872 |
128.1446 |
149.5021 |
170.8595 |
|
|
22.62742 |
45.25483 |
67.88225 |
90.50967 |
113.1371 |
135.7645 |
158.3919 |
181.0193 |
|
g |
23.97291 |
47.94583 |
71.91874 |
95.89165 |
119.8646 |
143.8375 |
167.8104 |
191.7833 |
|
|
25.39842 |
50.79683 |
76.19525 |
101.5937 |
126.9921 |
152.3905 |
177.7889 |
203.1873 |
|
a |
26.90869 |
53.81737 |
80.72606 |
107.6347 |
134.5434 |
161.4521 |
188.3608 |
215.2695 |
|
|
28.50876 |
57.01752 |
85.52628 |
114.035 |
142.5438 |
171.0526 |
199.5613 |
228.0701 |
|
b |
30.20398 |
60.40796 |
90.61193 |
120.8159 |
151.0199 |
181.2239 |
211.4278 |
241.6318 |
|
c |
32 |
64 |
96 |