| Deutsche Version |  |
 |
• Keyboard, frequencies = naming of notes, piano keys •
Music frequencies of equal temperament tuning
The English and American scientific system versus the German system
The standard tuning pitch is A4 (A above middle C) - in German-speaking countries it is called a’.
The notes have different names. The German system is used also in many other countries, as there
are e.g. Poland, Czech Republic, and Russia. The frequencies of the 88-key piano keyboard are:
| Note number Key number |
Note names English |
Note names German |
Frequency in Hz |
| 88 | C8 | c''''' | 4186,01 |
| 87 | B7 | h'''' | 3951,07 |
| 86 | A 7/B 7 |
ais''''/b'''' | 3729,31 |
| 85 | A7 | a'''' | 3520,00 |
| 84 | G7/A7 |
gis''''/ges'''' | 3322,44 |
| 83 | G7 | g'''' | 3135,96 |
| 82 | F7/G7 |
fis''''/ges'''' | 2959,96 |
| 81 | F7 | f'''' | 2793,83 |
| 80 | E7 | e'''' | 2637,02 |
| 79 | D7/E7 |
dis''''/es'''' | 2489,02 |
| 78 | D7 | d'''' | 2349,32 |
| 77 | C7/D7 |
cis''''/des'''' | 2217,46 |
| 76 | C7 | c'''' | 2093,00 |
| 75 | B6 | h''' | 1975,53 |
| 74 | A6/B6 |
ais'''/b''' | 1864,66 |
| 73 | A6 | a''' | 1760,00 |
| 72 | G6/A6 |
gis'''/as''' | 1661,22 |
| 71 | G6 | g''' | 1567,98 |
| 70 | F6/G6 |
fis'''/ges''' | 1479,98 |
| 69 | F6 | f''' | 1396,91 |
| 68 | E6 | e''' | 1318,51 |
| 67 | D6/E6 |
dis'''/es''' | 1244,51 |
| 66 | D6 | d''' | 1174,66 |
| 65 | C6/D6 |
cis'''/des''' | 1108,73 |
| 64 | C6 | c''' | 1046,50 |
| 63 | B5 | h'' | 987,767 |
| 62 | A5/B5 |
ais''/b'' | 932,328 |
| 61 | A5 | a'' | 880,000 |
| 60 | G5/A5 |
gis''/as'' | 830,609 |
| 59 | G5 | g' | 783,991 |
| 58 | F5/G5 |
fis''/ges'' | 739,989 |
| 57 | F5 | f' | 698,456 |
| 56 | E5 | e' | 659,255 |
| 55 | D5/E5 |
dis''/es'' | 622,254 |
| 54 | D5 | d'' | 587,330 |
| 53 | C5/D5 |
cis''/des'' | 554,365 |
| 52 | C5 | c'' | 523,251 |
| 51 | B4 | h' | 493,883 |
| 50 | A4/B4 |
ais'/b' | 466,164 |
| 49 | A4 concert pitch | a' Kammerton | 440,000 |
| 48 | G4/A4 |
gis'/as' | 415,305 |
| 47 | G4 | g' | 391,995 |
| 46 | F4/G4 |
fis'/ges' | 369,994 |
| 45 | F4 | f' | 349,228 |
| 44 | E4 | e' | 329,628 |
| 43 | D4/E4 |
dis'/es' | 311,127 |
| 42 | D4 | d' | 293,665 |
| 41 | C4/D4 |
cis'/des' | 277,183 |
| 40 | C4 (middle C) | c' (Schloss-C) | 261,626 |
| 39 | B3 | h | 246,942 |
| 38 | A3/B3 |
ais/b | 233,082 |
| 37 | A3 | a | 220,000 |
| 36 | G3/A3 |
gis/as | 207,652 |
| 35 | G3 | g | 195,998 |
| 34 | F3/G3 |
fis/ges | 184,997 |
| 33 | F3 | f | 174,614 |
| 32 | E3 | e | 164,814 |
| 31 | D3/E3 |
dis/es | 155,563 |
| 30 | D3 | d | 146,832 |
| 29 | C3/D3 |
cis/des | 138,591 |
| 28 | C3 | c | 130,813 |
| 27 | B2 | H | 123,471 |
| 26 | A2/B2 |
Ais/B | 116,541 |
| 25 | A2 | A | 110,000 |
| 24 | G2/A2 |
Gis/As | 103,826 |
| 23 | G2 | G | 97,9989 |
| 22 | F2/G2 |
Fis/Ges | 92,4986 |
| 21 | F2 | F | 87,3071 |
| 20 | E2 | E | 82,4069 |
| 19 | D2/E2 |
Dis/es | 77,7817 |
| 18 | D2 | D | 73,4162 |
| 17 | C2/D2 |
Cis/Des | 69,2957 |
| 16 | C2 | C | 65,4064 |
| 15 | B1 | H1 | 61,7354 |
| 14 | A1/B1 |
Ais1/b1 | 58,2705 |
| 13 | A1 | A1 | 55,0000 |
| 12 | G1/A1 |
Gis1/As1 | 51,9130 |
| 11 | G1 | G1 | 48,9995 |
| 10 | F1/G1 |
Fis1/Ges1 | 46,2493 |
| 9 | F1 | F1 | 43,6536 |
| 8 | E1 | E1 | 41,2035 |
| 7 | D1/E1 |
Dis1/Es1 | 38,8909 |
| 6 | D1 | D1 | 36,7081 |
| 5 | C1/D1 |
Cis1/Des1 | 34,6479 |
| 4 | C1 | C1 | 32,7032 |
| 3 | B0 | H2 | 30,8677 |
| 2 | A0/B0 |
Ais2/B2 | 29,1353 |
| 1 | A0 | A2 | 27,5000 |
Some manufacturers label 440 Hz not correct as A3.
| Frequencies of the equal temperament | |||||||||||
| C / B# | 16.352 | 32.703 | 65.406 | 130.813 | 261.626 | 523.251 | 1046.502 | 2093.005 | 4186.009 | 8372.018 | 16744.036 |
| C# / Db | 17.324 | 34.648 | 69.296 | 138.591 | 277.183 | 554.365 | 1108.731 | 2217.461 | 4434.922 | 8869.844 | 17739.688 |
| D | 18.354 | 36.708 | 73.416 | 146.832 | 293.665 | 587.330 | 1174.659 | 2349.318 | 4698.636 | 9397.273 | 18794.545 |
| D# / Eb | 19.445 | 38.891 | 77.782 | 155.563 | 311.127 | 622.254 | 1244.508 | 2489.016 | 4978.032 | 9956.063 | 19912.127 |
| E / Fb | 20.602 | 41.203 | 82.407 | 164.814 | 329.628 | 659.255 | 1318.510 | 2637.020 | 5274.041 | 10548.082 | - |
| F / E# | 21.827 | 43.654 | 87.307 | 174.614 | 349.228 | 698.456 | 1396.913 | 2793.826 | 5587.652 | 11175.303 | - |
| F# / Gb | 23.125 | 46.249 | 92.499 | 184.997 | 369.994 | 739.989 | 1479.978 | 2959.955 | 5919.911 | 11839.822 | - |
| G | 24.500 | 48.999 | 97.999 | 195.998 | 391.995 | 783.991 | 1567.982 | 3135.963 | 6271.927 | 12543.854 | - |
| G# / Ab | 25.957 | 51.913 | 103.826 | 207.652 | 415.305 | 830.609 | 1661.219 | 3322.438 | 6644.875 | 13289.750 | - |
| A | 27.500 | 55.000 | 110.000 | 220.000 | 440.000 | 880.000 | 1760.000 | 3520.000 | 7040.000 | 14080.000 | - |
| A# / Bb | 29.135 | 58.270 | 116.541 | 233.082 | 466.164 | 932.328 | 1864.655 | 3729.310 | 7458.620 | 14917.240 | - |
| B / Cb | 30.868 | 61.735 | 123.471 | 246.942 | 493.883 | 987.767 | 1975.533 | 3951.066 | 7902.133 | 15804.266 | - |
Comparing the Frequency Ratios for Equal Temperament and Pure Harmonic Series |
MIDI note numbers (midi files)
Octave notation is given here in the international standard ISO system, formerly known as the ASA (Acoustical
Society of America) or ANSI system. In this system, middle C (MIDI note number 60) is C4; octaves start
with C, so the B just below (MIDI number 59) is B3. The lowest note of the normal modern piano is A0 (MIDI 21),
though Boesendorfer Imperials go down to F0 or even C0. The highest note of the piano is C8 (MIDI 108).
| Octave # | MIDI Note Numbers | |||||||||||
| C | C# | D | D# | E | F | F# | G | G# | A | A# | B | |
| -1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| 0 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 |
| 1 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 |
| 2 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 |
| 3 | 48 | 49 | 50 | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 |
| 4 | 60 | 61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 | 70 | 71 |
| 5 | 72 | 73 | 74 | 75 | 76 | 77 | 78 | 79 | 80 | 81 | 82 | 83 |
| 6 | 84 | 85 | 86 | 87 | 88 | 89 | 90 | 91 | 92 | 93 | 94 | 95 |
| 7 | 96 | 97 | 98 | 99 | 100 | 101 | 102 | 103 | 104 | 105 | 106 | 107 |
| 8 | 108 | 109 | 110 | 111 | 112 | 113 | 114 | 115 | 116 | 117 | 118 | 119 |
| 9 | 120 | 121 | 122 | 123 | 124 | 125 | 126 | 127 | ||||
Note: The MIDI specification only defines note number 60 as "Middle C", and all other notes
are relative. The absolute octave number designations shown here are based on
Middle C = C4, which is an arbitrary assignment.
|
Method for finding the corresponding MIDI note number for a given frequency: Original expression f = 440 × 2(n − 69) / 12 Simplification step 1: f / 440 = 2(n − 69) / 12 Simplification step 2: log2 (f / 440) = (n − 69) / 12 Simplification step 3: 12 × log2 (f / 440) = n – 69 Formula for finding a MIDI note number given the frequency in Hz of the MIDI note: n = (12 × log2 (f / 440)) + 69 Given the frequency f for a note in Hz, it is possible to find the corresponding |
Interval conversions - Frequency ratio to cents and vice versa
back  |
Google  |
home  |