Pitch vs Frequency


(Note name)
Frequency (in Hz) MIDI # Comments:
Bass: E string (E0) 41.2 28
Bass: A string (A0) 55.0 33
Bass: D string (D1) 73.4 38
Bass: G string (G1) 98.0 43
Low E string (E1)
82.4 40
Guitar A string (A1) 110.0 45
Guitar D string D2) 146.8 50
Guitar G string (G2) 196.0 55
Guitar B string (B2) 246.9 59
Guitar E string (E3) 329.6 64
E0 20.6 16 Fifth below lowest note on piano,
nominal lower limit of hearing (20 Hz)
A0 27.5 21 Lowest note on a piano
G1 98.0 43 Closest pitch to 100 Hz
C3 (Middle C) 261.6 60 40th note from the lowest on a piano
A3 440 69 Used as a standard tuning reference
B4 987.7 83 B above treble clef; closest pitch to 1 kHz
C6 2,093.0 96 Closest pitch to 2 kHz
C7 4,186 108 Highest note on a piano
D#7 4,978 111 Minor 3rd above highest piano note,
closest pitch to 5 kHz
D#8 9,956 123 Octave + m3 higher than highest piano note,
closest pitch to 10 kHz
C9 19,912 NA 2 octaves + m3 higher than highest piano note,
nominal upper limit of hearing (20 kHz)

Fig. 1. A table showing common musical pitches, their frequency, MIDI #’s, and comments. In the extreme upper and lower pitch ranges, the frequencies comprise the meaningful information; the pitches are less useful.

A One-octave Chromatic Scale in C

C 130.8
C# 1386
D 146.8
D# 155.6
E 164.8
F 174.6
F# 184.9
G 195.9
G# 207.7
A 220.0
A# 233.1
B 246.9
C 261.6

Fig. 2. A one-octave chromatic scale from the C below middle C to middle C. With these 12 frequencies, you can derive any pitch in the musical universe, simply by multiplying or dividing by 2 the the frequency of the desired note.

There are two ways to derive the frequency of any pitch in the chromatic scale. One is simply have handy a list of 12 notes (one octave) of the chromatic scale in any octave (see above).

You then just multiply (if ascending) or divide (if descending) by 2 successively, depending on the octave, to get the desired pitch. Or you can memorize one number: 1.059463.

That’s the 12th root of 2, which enables you to derive any pitch by simply multiplying or dividing by that number in succession.

For example, A440 times 1.059463 = Bb466.16; Bb466.16 x 1.058463=B493.87; and so on.

If you do this 12 times, you’ll arrive at the octave, A880. Divide by 1.059463, and you'll descend the chromatic scale. (Do it 12 times and you end up with A110.)

The advantage of the 12th-root method over the chart is that you can calculate a pitch from a base frequency of other than A440 — if your reference tuning note is 446, for example.

And if you lose the chart, you always have your brain — if your memory serves you, that is!


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