Frequencies of equal tuning
This article presents a list of the frequencies of all tones on the piano keyboard in equal tuning . In addition, the note names in German and English.
In addition to the use of superscript and subscript numbers for the octave, the notation with dashes is also used. The German pronunciation of the notation listed below is partly based on this. It is shown here using the example of the octavings of the concert pitch:
- A 2 (also A '') = Subcontra-A
- A 1 (also A ') = Contra-A
- A = capital A
- a = small A
- a 1 (also a ') = dashed A
- a 2 (also a '') = two-prime A
- a 3 (also a '' ') = three-stroke A
- a 4 (also a '' '') = four-stroke A
Note:
- The concert pitch (our a 1 ) is also referred to as A4 in the USA .
- The frequencies are calculated values and do not correspond to those of a well-tuned instrument (see stretching ).
- Based on psycho-acoustic findings, we hear sinus tones not linearly; The logarithmic frequency scale and the logarithmic Mel scale run almost proportionally up to approx. 500 Hz (100 Hz = 100 mel, 200 Hz = 200 mel); Above this, there are clear deviations (1000 Hz = 850 mel, 8000 Hz = 2100 mel). Complex musical tones are perceived up to approx. 5 kHz almost like the theoretical logarithmic frequency scale. Errors are within the barely noticeable area.
- In the twelve-step scale, the frequency of direct neighboring tones differs by a factor
- .
The following equation gives the frequency f from the key number n , as shown in the table below.
This equation can also be written as:
The key number is obtained from the frequency with the following equation:
Virtual keyboard
The keyboard of a modern piano or digital piano usually has 88 keys and includes sounds of A 2 to C 5 . The following table shows the frequencies of an equal tuning according to the above formula. A real instrument is usually tuned differently.
Key number | Notation (English) |
Notation (German) |
Frequency in Hertz (concert pitch 440 Hz) |
---|---|---|---|
88 | C8 | c 5 | 4186.01 |
87 | B7 | h 4 | 3951.07 |
86 | A # 7 / Bb7 | ais 4 / b 4 | 3729.31 |
85 | A7 | a 4 | 3520.00 |
84 | G # 7 / Ab7 | g sharp 4 / a flat 4 | 3322.44 |
83 | G7 | g 4 | 3135.96 |
82 | F # 7 / Gb7 | f sharp 4 / gt 4 | 2959.96 |
81 | F7 | f 4 | 2793.83 |
80 | E7 | e 4 | 2637.02 |
79 | D # 7 / Eb7 | dis 4 / es 4 | 2489.02 |
78 | D7 | d 4 | 2349.32 |
77 | C # 7 / Db7 | cis 4 / 4th | 2217.46 |
76 | C7 | c 4 | 2093.00 |
75 | B6 | h 3 | 1975.53 |
74 | A # 6 / Bb6 | ais 3 / b 3 | 1864.66 |
73 | A6 | a 3 | 1760.00 |
72 | G # 6 / Ab6 | g sharp 3 / a flat 3 | 1661.22 |
71 | G6 | g 3 | 1567.98 |
70 | F # 6 / Gb6 | f sharp 3 / gt 3 | 1479.98 |
69 | F6 | f 3 | 1396.91 |
68 | E6 | e 3 | 1318.51 |
67 | D # 6 / Eb6 | dis 3 / es 3 | 1244.51 |
66 | D6 | d 3 | 1174.66 |
65 | C # 6 / Qb6 | cis 3 / of 3 | 1108.73 |
64 | C6 | c 3 | 1046.50 |
63 | B5 | h 2 | 987.767 |
62 | A # 5 / Bb5 | ais 2 / b 2 | 932,328 |
61 | A5 | a 2 | 880,000 |
60 | G # 5 / Ab5 | g sharp 2 / a flat 2 | 830,609 |
59 | G5 | g 2 | 783,991 |
58 | F # 5 / Gb5 | f sharp 2 / gt 2 | 739.989 |
57 | F5 | f 2 | 698.456 |
56 | E5 | e 2 | 659.255 |
55 | D # 5 / Eb5 | dis 2 / es 2 | 622.254 |
54 | D5 | d 2 | 587,330 |
53 | C # 5 / Db5 | cis 2 / 2nd | 554,365 |
52 | C5 | c 2 | 523.251 |
51 | B4 | h 1 | 493.883 |
50 | A # 4 / Bb4 | ais 1 / b 1 | 466.164 |
49 | A4 | a 1 concert pitch | 440,000 |
48 | G # 4 / Ab4 | g sharp 1 / a flat 1 | 415,305 |
47 | G4 | g 1 | 391.995 |
46 | F # 4 / Gb4 | f sharp 1 / gt 1 | 369.994 |
45 | F4 | f 1 | 349.228 |
44 | E4 | e 1 | 329.628 |
43 | D # 4 / Eb4 | dis 1 / es 1 | 311.127 |
42 | D4 | d 1 | 293.665 |
41 | C # 4 / Db4 | cis 1 / 1st | 277.183 |
40 | C4 | c 1 | 261.626 |
39 | B3 | H | 246,942 |
38 | A # 3 / Bb3 | ais / b | 233,082 |
37 | A3 | a | 220,000 |
36 | G # 3 / Ab3 | g sharp / as | 207.652 |
35 | G3 | G | 195.998 |
34 | F # 3 / Gb3 | f sharp / total | 184.997 |
33 | F3 | f | 174.614 |
32 | E3 | e | 164.814 |
31 | D # 3 / Eb3 | dis / it | 155.563 |
30th | D3 | d | 146.832 |
29 | C # 3 / Db3 | cis / des | 138,591 |
28 | C3 | c | 130.813 |
27 | B2 | H | 123.471 |
26th | A # 2 / Bb2 | Ais / B | 116.541 |
25th | A2 | A. | 110,000 |
24 | G # 2 / Ab2 | G sharp / a flat | 103.826 |
23 | G2 | G | 97.9989 |
22nd | F # 2 / Gb2 | F sharp / Ges | 92.4986 |
21st | F2 | F. | 87,3071 |
20th | E2 | E. | 82,4069 |
19th | D # 2 / Eb2 | Dis / Es | 77.7817 |
18th | D2 | D. | 73.4162 |
17th | C # 2 / Db2 | Cis / Db | 69.2957 |
16 | C2 | C. | 65.4064 |
15th | B1 | H 1 | 61.7354 |
14th | A # 1 / Bb1 | A sharp 1 / B 1 | 58.2705 |
13 | A1 | A 1 | 55.0000 |
12 | G # 1 / Ab1 | G sharp 1 / A flat 1 | 51.9131 |
11 | G1 | G 1 | 48.9994 |
10 | F # 1 / Gb1 | Fis 1 / Ges 1 | 46.2493 |
9 | F1 | F 1 | 43.6535 |
8th | E1 | E 1 | 41.2034 |
7th | D # 1 / Eb1 | Dis 1 / Es 1 | 38.8909 |
6th | D1 | D 1 | 36.7081 |
5 | C # 1 / Db1 | Cis 1 / Des 1 | 34.6478 |
4th | C1 | C 1 | 32.7032 |
3 | B0 | H 2 | 30.8677 |
2 | A # 0 / Bb0 | A sharp 2 / B flat 2 | 29.1352 |
1 | A0 | A 2 | 27.5000 |
The following keys are only available on a few and very large concert grand pianos, see piano .
Key number | Note name (english) |
Note name (German) |
Frequency in Hertz (concert pitch 440 Hz) |
---|---|---|---|
0 | G # 0 / Ab0 | G sharp 2 / A flat 2 | 25.9565 |
−1 | G0 | G 2 | 24.4997 |
−2 | F # 0 / Gb0 | Fis 2 / Ges 2 | 23.1247 |
−3 | F0 | F 2 | 21.8268 |
−4 | E0 | E 2 | 20.6017 |
−5 | D # 0 / Eb0 | Dis 2 / Eb 2 | 19.4454 |
−6 | D0 | D 2 | 18.3540 |
−7 | C # 0 / Db0 | Cis 2 / Des 2 | 17.3239 |
−8 | C0 | C 2 | 16.3516 |
See also
Individual evidence
- ↑ Basic Concepts - Acoustic Phonetics . University of Cologne
- ^ Concert pitch in the English language Wikipedia
- ↑ Middle C in the English language Wikipedia