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Accumulated Errors In Different Keys. |
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Temperament Errors Table
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TEMPERAMENT |
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C |
C# |
D |
Eb |
E |
F |
F# |
G |
G# |
A |
Bb |
B |
TOTALL |
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JUST
INTONATION |
|
MAJOR |
MAJOR |
0 |
20 |
63 |
43 |
123 |
22 |
119 |
22 |
22 |
125 |
65 |
121 |
743 |
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"R" |
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MINOR |
MINOR |
0 |
102 |
106 |
125 |
41 |
0 |
80 |
43 |
104 |
63 |
41 |
39 |
743 |
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WERCKMEISTER
III |
|
MAJOR |
MAJOR |
29 |
64 |
53 |
47 |
53 |
23 |
70 |
47 |
59 |
53 |
29 |
59 |
587 |
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"UR" |
|
MINOR |
MINOR |
65 |
53 |
47 |
47 |
35 |
53 |
53 |
59 |
47 |
29 |
47 |
53 |
587 |
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KIRNBERGER
III |
|
MAJOR |
MAJOR |
22 |
66 |
52 |
48 |
64 |
22 |
63 |
38 |
59 |
61 |
32 |
61 |
587 |
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"UR" |
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MINOR |
MINOR |
59 |
57 |
52 |
50 |
30 |
48 |
50 |
59 |
55 |
41 |
46 |
38 |
587 |
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VALLOTTI |
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MAJOR |
MAJOR |
33 |
61 |
45 |
41 |
65 |
29 |
65 |
37 |
53 |
57 |
33 |
68 |
587 |
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"UR" |
|
MINOR |
MINOR |
53 |
49 |
45 |
53 |
45 |
57 |
45 |
49 |
53 |
45 |
53 |
41 |
587 |
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EQUAL
TEMPERAMENT |
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MAJOR |
MAJOR |
49 |
49 |
49 |
49 |
49 |
49 |
49 |
49 |
49 |
49 |
49 |
49 |
587 |
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"UR" |
|
MINOR |
MINOR |
49 |
49 |
49 |
49 |
49 |
49 |
49 |
49 |
49 |
49 |
49 |
49 |
587 |
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1/5 COMMA
MEAN TONE |
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MAJOR |
MAJOR |
30 |
126 |
30 |
50 |
58 |
30 |
115 |
30 |
145 |
30 |
30 |
86 |
760 |
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"R" |
|
MINOR |
MINOR |
58 |
69 |
30 |
106 |
58 |
86 |
58 |
30 |
89 |
30 |
86 |
58 |
760 |
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1/4 COMMA
MEAN TONE |
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MAJOR |
MAJOR |
32 |
164 |
32 |
63 |
63 |
32 |
145 |
32 |
195 |
32 |
32 |
104 |
927 |
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"R" |
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MINOR |
MINOR |
73 |
82 |
32 |
145 |
63 |
114 |
63 |
32 |
113 |
32 |
114 |
63 |
927 |
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1/3 COMMA
MEAN TONE |
|
MAJOR |
MAJOR |
50 |
230 |
50 |
98 |
84 |
50 |
196 |
50 |
278 |
50 |
50 |
133 |
1320 |
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"R" |
|
MINOR |
MINOR |
99 |
118 |
50 |
210 |
84 |
162 |
84 |
50 |
167 |
50 |
162 |
84 |
1320 |
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YOUNG II |
|
MAJOR |
MAJOR |
29 |
65 |
37 |
53 |
57 |
33 |
68 |
33 |
61 |
45 |
41 |
65 |
587 |
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"UR" |
|
MINOR |
MINOR |
57 |
45 |
49 |
53 |
45 |
53 |
41 |
53 |
49 |
45 |
53 |
45 |
587 |
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18th C.
ENGLISH |
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MAJOR |
MAJOR |
25 |
76 |
42 |
67 |
56 |
27 |
69 |
32 |
82 |
49 |
47 |
59 |
632 |
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"UR" |
|
MINOR |
MINOR |
73 |
56 |
52 |
57 |
32 |
58 |
49 |
63 |
58 |
39 |
57 |
39 |
632 |
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PYTHAGOREAN |
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MAJOR |
MAJOR |
65 |
65 |
25 |
65 |
29 |
65 |
88 |
45 |
65 |
6 |
65 |
63 |
634 |
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(VAN ZWOLLE)
"R" |
|
MINOR |
MINOR |
65 |
25 |
45 |
45 |
68 |
65 |
49 |
45 |
25 |
45 |
65 |
92 |
634 |
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Errors in cents:
each key compared to just ratio's. |
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Blue:
good; Yellow: satisfactory; Red:intolerable |
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JUST INTONATION |
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C |
C# |
D |
Eb |
E |
F |
F# |
G |
G# |
A |
Bb |
B |
c |
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Ratio's |
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1 |
(16/15) |
(9/8) |
(6/5) |
(5/4) |
(4/3) |
(45/32) |
(3/2) |
(8/5) |
(5/3) |
(16/9) |
(15/8) |
2 |
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Intervals in
cents |
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0 |
112 |
204 |
316 |
386 |
498 |
590 |
702 |
814 |
884 |
996 |
1088 |
1200 |
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