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The equal temperament

The tuning or temperament of a scale is the way the frequencies of the notes are chosen. In Western music the equal temperament is most popular. Other temperaments are for example: the just intonation, the Pythagorean tuning, the mean tone temperament, the well temperament and the 31 equal temperament.

An octave is divided into 12 'proportionally increasing' distances. The ratio of the frequencies of two successive semitones is always the same (approximately 1.0594631). Because of this, all intervals (second, third, fourth, fifth, sixth, seventh), except the octave, deviate from the just tuning. They cause beating. All equally named intervals sound equally false (they beat). The advantage of this tuning is that it remains the same when switched to another tone type (a number of semitones higher or lower), and it is therefore not needed to tune the instrument differently.

Below an overview is given of the intervals and the differences of the equal and the just temperament. The just temperament is the way to construct a scale where the frequency ratios are simple integers. This produces music which is experienced as pure (not false).
Interval Equal Just
Unison1.0001.0001/10.0%
Minor second1.0591.06716/15-0.7%
Major second1.1221.1259/8-0.2%
Minor third1.1891.2006/5-0.9%
Major third1.2601.2505/4+0.8%
Fourth1.3351.3334/3+0.1%
Augmented fourth1.4141.4007/5+1.0%
Fifth1.4981.5003/2-0.1%
Minor sixth1.5871.6008/5-0.8%
Major sixth1.6821.6675/3+0.9%
Minor seventh1.7821.77816/9+0.2%
Major seventh1.8881.87515/8+0.7%
Octave2.0002.0002/10.0%

Frequency table of the notes

# Tone Octave Frequency (Hz)
0C016.3516
1C#017.3239
2D018.3540
3D#019.4454
4E020.6017
5F021.8268
6F#023.1247
7G024.4997
8G#025.9565
9A027.5000
10A#029.1352
11B030.8677
# Tone Octave Frequency (Hz)
12C132.7032
13C#134.6478
14D136.7081
15D#138.8909
16E141.2034
17F143.6535
18F#146.2493
19G148.9994
20G#151.9131
21A155.0000
22A#158.2705
23B161.7354
# Tone Octave Frequency (Hz)
24C265.4064
25C#269.2957
26D273.4162
27D#277.7817
28E282.4069
29F287.3071
30F#292.4986
31G297.9989
32G#2103.8262
33A2110.0000
34A#2116.5409
35B2123.4708
# Tone Octave Frequency (Hz)
36C3130.8128
37C#3138.5913
38D3146.8324
39D#3155.5635
40E3164.8138
41F3174.6141
42F#3184.9972
43G3195.9977
44G#3207.6523
45A3220.0000
46A#3233.0819
47B3246.9417
# Tone Octave Frequency (Hz)
48C4261.6256
49C#4277.1826
50D4293.6648
51D#4311.1270
52E4329.6276
53F4349.2282
54F#4369.9944
55G4391.9954
56G#4415.3047
57A4440.0000
58A#4466.1638
59B4493.8833
# Tone Octave Frequency (Hz)
60C5523.2511
61C#5554.3653
62D5587.3295
63D#5622.2540
64E5659.2551
65F5698.4565
66F#5739.9888
67G5783.9909
68G#5830.6094
69A5880.0000
70A#5932.3275
71B5987.7666
# Tone Octave Frequency (Hz)
72C61,046.5023
73C#61,108.7305
74D61,174.6591
75D#61,244.5079
76E61,318.5102
77F61,396.9129
78F#61,479.9777
79G61,567.9817
80G#61,661.2188
81A61,760.0000
82A#61,864.6550
83B61,975.5332
# Tone Octave Frequency (Hz)
84C72,093.0045
85C#72,217.4610
86D72,349.3181
87D#72,489.0159
88E72,637.0205
89F72,793.8259
90F#72,959.9554
91G73,135.9635
92G#73,322.4376
93A73,520.0000
94A#73,729.3101
95B73,951.0664
# Tone Octave Frequency (Hz)
96C84,186.0090
97C#84,434.9221
98D84,698.6363
99D#84,978.0317
100E85,274.0409
101F85,587.6517
102F#85,919.9108
103G86,271.9270
104G#86,644.8752
105A87,040.0000
106A#87,458.6202
107B87,902.1328
# Tone Octave Frequency (Hz)
108C98,372.0181
109C#98,869.8442
110D99,397.2726
111D#99,956.0635
112E910,548.0818
113F911,175.3034
114F#911,839.8215
115G912,543.8540
116G#913,289.7503
117A914,080.0000
118A#914,917.2404
119B915,804.2656
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