Piano key frequencies

This is a virtual keyboard showing the absolute frequencies in hertz (cycles per second), of the notes on a modern piano (typically containing 88 keys) in twelve-tone equal temperament, with the 49th key, the fifth A (called A4), tuned to 440 Hz (referred to as A440). Each successive pitch is derived by multiplying (ascending) or dividing (descending) the previous by the twelfth root of two. For example, to get the frequency a semitone up from A4 (A♯4), multiply 440 by the twelfth root of two. To go from A4 to B4 (up a whole tone), multiply 440 by the twelfth root of two squared. For other tuning schemes refer to musical tuning.

This list of frequencies is for a theoretical ideal piano. On an actual piano the ratio between semitones is slightly larger, especially at the high and low ends, due to string thickness which causes inharmonicity due to the nonzero force required to bend steel piano wire in the absence of tension. This effect is sometimes known as stretched octaves, and the pattern of deviation is called the Railsback curve.

The following equation will give the frequency F of the n^th key, as shown in the table:

$F(n)=440\ ({\sqrt[{12}]{2}}\,)^{n-49}$

Virtual keyboard

An 88-key piano, with the octaves numbered and Middle C (cyan) and A440 (yellow) highlighted.

Key number	Helmholtz name	Scientific name	Frequency (Hz)	Corresponding Open Strings
				Violin	Viola	Cello	Bass	Guitar
88	c′′′′′ 5-line 8ve	C8 Eighth octave	4186.01
87	b′′′′	B7	3951.07
86	a♯′′′′/b♭′′′′	A♯7/B♭7	3729.31
85	a′′′′	A7	3520.00
84	g♯′′′′/a♭′′′′	G♯7/A♭7	3322.44
83	g′′′′	G7	3135.96
82	f♯′′′′/g♭′′′′	F♯7/G♭7	2959.96
81	f′′′′	F7	2793.83
80	e′′′′	E7	2637.02
79	d♯′′′′/e♭′′′′	D♯7/E♭7	2489.02
78	d′′′′	D7	2349.32
77	c♯′′′′/d♭′′′′	C♯7/D♭7	2217.46
76	c′′′′ 4-line 8ve	C7 Double high C	2093.00
75	b′′′	B6	1975.53
74	a♯′′′/b♭′′′	A♯6/B♭6	1864.66
73	a′′′	A6	1760.00
72	g♯′′′/a♭′′′	G♯6/A♭6	1661.22
71	g′′′	G6	1567.98
70	f♯′′′/g♭′′′	F♯6/G♭6	1479.98
69	f′′′	F6	1396.91
68	e′′′	E6	1318.51
67	d♯′′′/e♭′′′	D♯6/E♭6	1244.51
66	d′′′	D6	1174.66
65	c♯′′′/d♭′′′	C♯6/D♭6	1108.73
64	c′′′ 3-line 8ve	C6 Soprano C	1046.50
63	b′′	B5	987.767
62	a♯′′/b♭′′	A♯5/B♭5	932.328
61	a′′	A5	880.000
60	g♯′′/a♭′′	G♯5/A♭5	830.609
59	g′′	G5	783.991
58	f♯′′/g♭′′	F♯5/G♭5	739.989
57	f′′	F5	698.456
56	e′′	E5	659.255	E
55	d♯′′/e♭′′	D♯5/E♭5	622.254
54	d′′	D5	587.330
53	c♯′′/d♭′′	C♯5/D♭5	554.365
52	c′′ 2-line 8ve	C5 Tenor C	523.251
51	b′	B4	493.883
50	a♯′/b♭′	A♯4/B♭4	466.164
49	a′	A4 A440	440.000	A	A
48	g♯′/a♭′	G♯4/A♭4	415.305
47	g′	G4	391.995
46	f♯′/g♭′	F♯4/G♭4	369.994
45	f′	F4	349.228
44	e′	E4	329.628					High E
43	d♯′/e♭′	D♯4/E♭4	311.127
42	d′	D4	293.665	D	D
41	c♯′/d♭′	C♯4/D♭4	277.183
40	c′ 1-line 8ve	C4 Middle C	261.626
39	b	B3	246.942					B
38	a♯/b♭	A♯3/B♭3	233.082
37	a	A3	220.000			A
36	g♯/a♭	G♯3/A♭3	207.652
35	g	G3	195.998	G	G			G
34	f♯/g♭	F♯3/G♭3	184.997
33	f	F3	174.614
32	e	E3	164.814
31	d♯/e♭	D♯3/E♭3	155.563
30	d	D3	146.832			D		D
29	c♯/d♭	C♯3/D♭3	138.591
28	c small 8ve	C3 Low C	130.813		C
27	B	B2	123.471
26	A♯/B♭	A♯2/B♭2	116.541
25	A	A2	110.000					A
24	G♯/A♭	G♯2/A♭2	103.826
23	G	G2	97.9989			G	G
22	F♯/G♭	F♯2/G♭2	92.4986
21	F	F2	87.3071
20	E	E2	82.4069					Low E
19	D♯/E♭	D♯2/E♭2	77.7817
18	D	D2	73.4162				D
17	C♯/D♭	C♯2/D♭2	69.2957
16	C great 8ve	C2 Deep C	65.4064			C
15	Bˌ	B1	61.7354
14	A♯ˌ/B♭ˌ	A♯1/B♭1	58.2705
13	Aˌ	A1	55.0000				A
12	G♯ˌ/A♭ˌ	G♯1/A♭1	51.9131
11	Gˌ	G1	48.9994
10	F♯ˌ/G♭ˌ	F♯1/G♭1	46.2493
9	Fˌ	F1	43.6535
8	Eˌ	E1	41.2034				E
7	D♯ˌ/E♭ˌ	D♯1/E♭1	38.8909
6	Dˌ	D1	36.7081
5	C♯ˌ/D♭ˌ	C♯1/D♭1	34.6478
4	Cˌ contra-8ve	C1 Pedal C	32.7032
3	Bˌˌ	B0	30.8677
2	A♯ˌˌ/B♭ˌˌ	A♯0/B♭0	29.1352
1	Aˌˌ sub-contra-8ve	A0 Double Pedal A	27.5000

Note Wavelengths

The wavelength of the notes is predominantly dependent upon the air temperature and somewhat on humidity in the air. Here is how you can accurately calculate the wavelength for any given musical note:

$c={\text{Temperature degrees in Celsius}}$

$h={\text{Humidity percentage in the air. e.g. use the whole number 45 to represent 45 percent humidity, not 0.45}}$

The following equation will calculate the wavelength F represented in Centimeters for the frequency (n) represented in Hz:

$F(n)={\frac {331.3*{\sqrt {{\frac {c}{273.15}}+1}}*(h*0.00006+1)}{n*100}}$

To help clarify this formula, the speed of sound (m/sec) is calculated here as the entire numerator above n * 100:

$SpeedofSound=331.3*{\sqrt {{\frac {c}{273.15}}+1}}*(h*0.00006+1)$

This is a very accurate formula for the speed of sound because it increase the speed of sound for humidity levels; e.g. 100% humidity = 0.6% overall increase in speed.

See also

• Piano tuning

External links

• interactive piano frequency table — A php script allowing the reference pitch of A4 to be altered from 440 Hz.
• PySynth — A simple Python-based software synthesizer that prints the key frequencies table and then creates a few demo songs based on that table.