音樂中泛音純律之研究－未來人類最完美之律　　　　2001.02.15訂1991傅國權著

六.以基音C=261.63 HZ 為起音,推算各頻率值.
泛音序列 頻率值 音名 12平均律
1 261.63x1=261.63 /1=261.63 C 261.63
2 261.63x2=523.26 /2=261.63 C
3 261.63x3=784.89 /2=392.445 G 392.00
4 261.63x4=1046.52 /4=261.63 C
5 261.63x5=1308.15 /4=327.0375 E 329.63
6 261.63x6=1569.78 /4=392.445 G
7 261.63x7=1831.41 /4=457.8525 bB 466.16
8 261.63x8=2093.04 /8=261.63 C
9 261.63x9=2354.67 /8=294.3375 D 293.66
10 261.63x10=2616.3 /8=327.0375 E
11 261.63x11=2877.93/8=359.74125 #F 349.23
12 261.63x12=3139.56/8=392.445 G 392.00
13 261.63x13=3401.19/8=425.14875
14 261.63x14=3662.82/8=457.8525
15 261.63x15=3924.45/8=490.55625
16 261.63x16=4186.08/16=261.63
17 261.63x17=4447.71/16=277.981875
18 261.63x18=4709.34/16=294.33375
19 261.63x19=4970.97/16=310.685625
20 261.63x20=5232.6 /16=327.0375
21 261.63x21=5494.23/16=343.389375
22 261.63x22=5755.86/16=359.74125
23 261.63x23=6017.49/16=376.093125
24 261.63x24=6279.12/16=392.445 G
25 261.63x25=6540.75/16=408.796875
26 261.63x26=6802.38/16=425.14875
27 261.63x27=7064.01/16=441.500625 A 440
28 261.63x28=7325.64/16=457.8525
29 261.63x29=7587.27/16=474.204375
30 261.63x30=7848.9 /16=490.55625
七.以基音C=261.25 HZ 為起音,推算各頻率值.
泛音序列 頻率值 音名 12平均律
1 261.25x 1 261.25 /1=261.25 C 261.63
2 261.25x 2 522.50 /2=261.25 C
3 261.25x 3 783.75 /2=391.875 G 392.00
4 261.25x 4 1045.00 /4=261.25 C
5 261.25x 5 1306.25 /4=326.5625 E 329.63
6 261.25x 6 1567.50 /4=391.875 G
7 261.25x 7 1828.75 /4=457.1875 bB 466.16
8 261.25x 8 2090.00 /8=261.25 C
9 261.25x 9 2351.25 /8=293.90625 D 293.66
10 261.25x 10 2612.50 /8=326.5625 E
11 261.25x 11 2873.75 /8=359.21875 #F 349.23
12 261.25x 12 3135.00 /8=391.875 G 392.00
13 261.25x 13 3396.25 /8=424.53125
14 261.25x 14 3657.50 /8=457.1875
15 261.25x 15 3918.75 /8=489.84375
16 261.25x 16 4180.00 /16=261.25
17 261.25x 17 4441.25 /16=277.578125
18 261.25x 18 4702.50 /16=293.90625
19 261.25x 19 4963.75 /16=310.234375 #D=bE
20 261.25x 20 5225.00 /16=326.5625
21 261.25x 21 5486.25 /16=342.890625
22 261.25x 22 5747.50 /16=359.21875
23 261.25x 23 6008.75 /16=375.546875
24 261.25x 24 6270.00 /16=391.875
25 261.25x 25 6531.25 /16=408.203125
26 261.25x 26 6792.50 /16=424.53125
27 261.25x 27 7053.75 /16=440.859375
28 261.25x 28 7315.00 /16=457.1875
29 261.25x 29 7576.25 /16=473.515625
30 261.25x 30 7837.50 /16=489.84375
31 261.25x 31 8098.75 /32=506.171875
32 261.25x 32 8360.00 /32=261.25
33 261.25x 33 8621.25 /32=269.4140625
34 261.25x 34 8882.50 /32=277.578125
35 261.25x 35 9143.75 /32=285.7421875
36 261.25x 36 9405.00 /32=293.90625
37 261.25x 37 9666.25 /32=302.0703125
38 261.25x 38 9927.50 /32=310.234375
39 261.25x 39 10188.75/32=318.3984375
40 261.25x 40 10450.00/32=326.5625
41 261.25x 41 10711.25/32=334.7265625
42 261.25x 42 10972.50/32=342.890625
43 261.25x 43 11233.75/32=351.0546875
44 261.25x 44 11495.00/32=359.21875
45 261.25x 45 11756.25/32=367.3828125
46 261.25x 46 12017.50/32=375.546875
47 261.25x 47 12278.75/32=383.7109375
48 261.25x 48 12540.00/32=391.875
49 261.25x 49 12801.25/32=400.0390625
50 261.25x 50 13062.50/32=408.203125
51 261.25x 51 13323.75/32=416.3671875
52 261.25x 52 13585.00/32=424.53125
53 261.25x 53 13846.25/32=432.6953125
54 261.25x 54 14107.50/32=440.859375
55 261.25x 55 14368.75/32=449.0234375
56 261.25x 56 14630.00/32=457.1875
57 261.25x 57 14891.25/32=465.3515625
58 261.25x 58 15152.50/32=473.515625
59 261.25x 59 15413.75/32=481.6796875
60 261.25x 60 15675.00/32=489.84375
61 261.25x 61 15936.25/32=498.0078125
62 261.25x 62 16197.50/64=253.0859375
63 261.25x 63 16458.75/64=257.15625
64 261.25x 64 16720.00/64=261.25
65 261.25x 65 16981.25/64=265.33203125
66 261.25x 66 17242.50/64=269.4140625
67 261.25x 67 17503.75/64=273.49609375
68 261.25x 68 17765.00/64=277.578125
69 261.25x 69 18026.25/64=281.66015625
70 261.25x 70 18287.50/64=285.7421875
71 261.25x 71 18548.75/64=289.82421875
72 261.25x 72 18810.00/64=293.90625
73 261.25x 73 19071.25/64=297.98828125
74 261.25x 74 19332.50/64=302.0703125
75 261.25x 75 19593.75/64=306.15234375
76 261.25x 76 19855.00/64=310.234375
77 261.25x 77 20116.25/64=314.31640625
78 261.25x 78 20377.50/64=318.3984375
79 261.25x 79 20638.75/64=322.48046875
80 261.25x 80 20900.00/64=326.5625
81 261.25x 81 21161.25/64=330.64453125
82 261.25x 82 21422.50/64=334.7265625
83 261.25x 83 21683.75/64=338.80859375
84 261.25x 84 21945.00/64=342.890625
85 261.25x 85 22206.25/64=346.97265625
86 261.25x 86 22467.50/64=351.0546875
87 261.25x 87 22728.75/64=355.13671875
88 261.25x 88 22990.00/64=359.21875
89 261.25x 89 23251.25/64=363.30078125
90 261.25x 90 23512.50/64=367.3828125
91 261.25x 91 23773.75/64=371.45703125
92 261.25x 92 24035.00/64=375.546875
93 261.25x 93 24296.25/64=379.62890625
94 261.25x 94 24557.50/64=383.7109375
95 261.25x 95 24818.75/64=387.79296875
96 261.25x 96 25080.00/64=391.875
97 261.25x 97 25341.25/64=395.95703125
98 261.25x 98 25602.50/64=400.0390625
99 261.25x 99 25863.75/64=404.12109375
100 261.25x 100 26125.00/64=408.203125
1.基音D=293.33時第17泛音 #D=bE=311.66 3cent
2.基音D=440.00時第23泛音 #D=bE=316.25
3.基音F=352.00時第14泛音 bE=308.00 -14cent
4.基音C=261.25時第19泛音 #D=bE=310.234375
5 基音C=261.63時第19泛音 #D=bE=310.685625
A=440Hz 泛音純律與十二平均律之比教
HARMORICA-PURE TEMPERAMENT & EQUAL TEMPERAMENT RATIO
C 19泛音261.25 #F 27泛音371.25
293.33-261.25=32.08 412.75-371.25=41.25
200/32.08=6.2344 200/41.25=4.84
(261.25-261.63)=-0.38 (371.25-369.99)=1.26
-0.38x6.2344=-2.36cent 4.84x1.26=6.09 cent
C 261.25 = -2 cent #F 371.25 = 6 cent
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#C 5泛音275 * G 57泛音391.88
312.81-275=37.81 440-391.88=48.12
200/37.81=5.29 200/48.12=4.1562
(275-277.18)=-2.18 (391.88-392)=-0.12
-2.18x5.29=-11.53 cent -0.12x4.1562=0.4987 cent
#C 275 = -12 cent G 391.88 = -0.5 cent
─────────── ──392 =0cent ───
D 為A下屬音 293.33 #G 15泛音412.5
330-293.33=36.67 467.5-412.5=55
200/36.67=5.4540 200/55=3.63
(293.33-293.66)=-0.33 (412.5-415.3)=-2.8
-0.33x5.4540=-1.7998ent -2.8x3.63=-10.16 cent
D 293.33 = - 2 cent #G 412.5 = -10 cent
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#D 91泛音312.81 A
349.23-311.13=38.1
200/38.1 =5.28
312.81-311.13 = 1.68 Ａ＝４４０
1.68 x5.25= 8.82 cent
#D 312.81 = 9 cent A 440 = 0 cent
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E 6泛音330 #A 17泛音467.5
371.25-330=41.25 522.5-467.5=55
200/41.25=4.84 200/55=3.63
(330-329.63)=0.37 (467.5-466.16)=1.34
0.37x4.84=1.79 cent 1.34x3.63=4.86 cent
E 330 = 2 cent #A 467.5 = 5 cent
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F 51泛音350.63 B 9泛音495
391.86-350.63=41.23 550-495=55
200/41.23=4.85 200/55=3.63
(350.63-349.23)=1.4 (495-493.88)=1.12
1.4x4.85=6.79 cent 1.12x3.63=4.07 cent
F 350.63 = 7 cent B 495 = 4 cent