Piano key frequencies

This is a list of the absolute frequencies in hertz (cycles per second) of the keys of a modern 88-key standard or 102-key extended piano 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 (approximately 1.0594631...). 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, or two semitones), multiply 440 twice by the twelfth root of two (or just by the sixth root of two, approximately 1.12246204831). For other tuning schemes refer to musical tuning.

This list of frequencies is for a theoretically ideal piano. On an actual piano the ratio between semitones is slightly larger, especially at the high and low ends, where string stiffness causes inharmonicity, i.e., the tendency for the harmonic makeup of each note to run sharp. To compensate for this, octaves are tuned slightly wide, stretched according to the inharmonic characteristics of each instrument. This deviation from equal temperament is called the Railsback curve.

The following equation gives the frequency f of the n^th key, as shown in the table:

$f(n)=({\sqrt[{12}]{2}}\,)^{n-49}\times 440\,{\text{Hz}}\,$

(a' = A4 = A440 is the 49th key on the idealized piano)

Alternatively, this can be written as:

$f(n)=2^{\frac {n-49}{12}}\times 440\,{\text{Hz}}\,$

Conversely, starting from a frequency on the idealized piano tuned to A440, one obtains the key number by:

$n=12\,\log _{2}\left({{\frac {f}{440\,{\text{Hz}}}}}\right)+49$

List

A printable version of the standard key frequencies

Values in bold are exact on an ideal piano. Keys shaded gray are rare and only appear on extended pianos.

Key number	Helmholtz name	Scientific name	Frequency (Hz)	Corresponding Open Strings
				Violin	Viola	Cello	Bass	Guitar
102	f′′′′′	F8	5587.65
101	e′′′′′	E8	5274.04
100	d♯′′′′′/e♭′′′′′	D♯8/E♭8	4978.03
99	d′′′′′	D8	4698.64
98	c♯′′′′′/d♭′′′′′	C♯8/D♭8	4434.92
88	c′′′′′ 5-line octave	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 octave	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 octave	C6 Soprano C (High 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 octave	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			High A (Optional)
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 octave	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				F (7 string)
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 octave	C3	130.813	C (5 string)	C		C (6 string)
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	F (6 string)
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 octave	C2 Deep C	65.4064			C
15	B͵	B1	61.7354					B (7 string)
14	A♯͵/B♭͵	A♯1/B♭1	58.2705	B♭ (7 string)
13	A͵	A1	55.0000				A
12	G♯͵/A♭͵	G♯1/A♭1	51.9131
11	G͵	G1	48.9994
10	F♯͵/G♭͵	F♯1/G♭1	46.2493					F♯ (8 string)
9	F͵	F1	43.6535
8	E͵	E1	41.2034				E
7	D♯͵/E♭͵	D♯1/E♭1	38.8909
6	D͵	D1	36.7081
5	C♯͵/D♭͵	C♯1/D♭1	34.6478					C♯ (9 string)
4	C͵ contra-octave	C1 Pedal C	32.7032
3	B͵͵	B0	30.8677				B (5 string)
2	A♯͵͵/B♭͵͵	A♯0/B♭0	29.1352
1	A͵͵	A0	27.5000
97	G♯͵͵/A♭͵͵	G♯0/A♭0	25.9565					G♯ (10 string)
96	G͵͵	G0	24.4997
95	F♯͵͵/G♭͵͵	F♯0/G♭0	23.1247
94	F͵͵	F0	21.8268
93	E͵͵	E0	20.6017
92	D♯͵͵/E♭͵͵	D♯0/E♭0	19.4454
91	D͵͵	D0	18.3540
90	C♯͵͵/D♭͵͵	C♯0/D♭0	17.3239
89	C͵͵ sub-contra-octave	C0 Double Pedal C	16.3516

See also

• Piano tuning
• Scientific pitch notation
• Music and mathematics

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.
• "Keyboard and frequencies", SengpielAudio.com.
• Notefreqs – A complete table of note frequencies and ratios for midi, piano, guitar, bass, and violin. Includes fret measurements (in cm and inches) for building instruments.