DuPont analysis

This is a list of the absolute frequencies in hertz (cycles per second) of the keys of a standard modern 88-key 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 1.05946...). For example, to get the frequency a semitone up from A4 (ATemplate:Music4), 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. 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 Template:Mvar of the Template:Mvar^th key, as shown in the table:

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

(a' 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

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

A printable version of the chart below.

Key number	Helmholtz name	Scientific name	Frequency (Hz)	Corresponding Open Strings
				Violin	Viola	Cello	Bass	Guitar
88	c′′′′′ 5-line octave	C8 Eighth octave	4186.01
87	b′′′′	B7	3951.07
86	aTemplate:Music′′′′/bTemplate:Music′′′′	ATemplate:Music7/BTemplate:Music7	3729.31
85	a′′′′	A7	3520.00
84	gTemplate:Music′′′′/aTemplate:Music′′′′	GTemplate:Music7/ATemplate:Music7	3322.44
83	g′′′′	G7	3135.96
82	fTemplate:Music′′′′/gTemplate:Music′′′′	FTemplate:Music7/GTemplate:Music7	2959.96
81	f′′′′	F7	2793.83
80	e′′′′	E7	2637.02
79	dTemplate:Music′′′′/eTemplate:Music′′′′	DTemplate:Music7/ETemplate:Music7	2489.02
78	d′′′′	D7	2349.32
77	cTemplate:Music′′′′/dTemplate:Music′′′′	CTemplate:Music7/DTemplate:Music7	2217.46
76	c′′′′ 4-line octave	C7 Double high C	2093.00
75	b′′′	B6	1975.53
74	aTemplate:Music′′′/bTemplate:Music′′′	ATemplate:Music6/BTemplate:Music6	1864.66
73	a′′′	A6	1760.00
72	gTemplate:Music′′′/aTemplate:Music′′′	GTemplate:Music6/ATemplate:Music6	1661.22
71	g′′′	G6	1567.98
70	fTemplate:Music′′′/gTemplate:Music′′′	FTemplate:Music6/GTemplate:Music6	1479.98
69	f′′′	F6	1396.91
68	e′′′	E6	1318.51
67	dTemplate:Music′′′/eTemplate:Music′′′	DTemplate:Music6/ETemplate:Music6	1244.51
66	d′′′	D6	1174.66
65	cTemplate:Music′′′/dTemplate:Music′′′	CTemplate:Music6/DTemplate:Music6	1108.73
64	c′′′ 3-line octave	C6 Soprano C (High C)	1046.50
63	b′′	B5	987.767
62	aTemplate:Music′′/bTemplate:Music′′	ATemplate:Music5/BTemplate:Music5	932.328
61	a′′	A5	880.000
60	gTemplate:Music′′/aTemplate:Music′′	GTemplate:Music5/ATemplate:Music5	830.609
59	g′′	G5	783.991
58	fTemplate:Music′′/gTemplate:Music′′	FTemplate:Music5/GTemplate:Music5	739.989
57	f′′	F5	698.456
56	e′′	E5	659.255	E
55	dTemplate:Music′′/eTemplate:Music′′	DTemplate:Music5/ETemplate:Music5	622.254
54	d′′	D5	587.330
53	cTemplate:Music′′/dTemplate:Music′′	CTemplate:Music5/DTemplate:Music5	554.365
52	c′′ 2-line octave	C5 Tenor C	523.251
51	b′	B4	493.883
50	aTemplate:Music′/bTemplate:Music′	ATemplate:Music4/BTemplate:Music4	466.164
49	a′	A4 A440	440.000	A	A			High A (Optional)
48	gTemplate:Music′/aTemplate:Music′	GTemplate:Music4/ATemplate:Music4	415.305
47	g′	G4	391.995
46	fTemplate:Music′/gTemplate:Music′	FTemplate:Music4/GTemplate:Music4	369.994
45	f′	F4	349.228
44	e′	E4	329.628					High E
43	dTemplate:Music′/eTemplate:Music′	DTemplate:Music4/ETemplate:Music4	311.127
42	d′	D4	293.665	D	D
41	cTemplate:Music′/dTemplate:Music′	CTemplate:Music4/DTemplate:Music4	277.183
40	c′ 1-line octave	C4 Middle C	261.626
39	b	B3	246.942					B
38	aTemplate:Music/bTemplate:Music	ATemplate:Music3/BTemplate:Music3	233.082
37	a	A3	220.000			A
36	gTemplate:Music/aTemplate:Music	GTemplate:Music3/ATemplate:Music3	207.652
35	g	G3	195.998	G	G			G
34	fTemplate:Music/gTemplate:Music	FTemplate:Music3/GTemplate:Music3	184.997
33	f	F3	174.614				F (7 string)
32	e	E3	164.814
31	dTemplate:Music/eTemplate:Music	DTemplate:Music3/ETemplate:Music3	155.563
30	d	D3	146.832			D		D
29	cTemplate:Music/dTemplate:Music	CTemplate:Music3/DTemplate:Music3	138.591
28	c small octave	C3 Low C	130.813	C (5 string)	C		C (6 string)
27	B	B2	123.471
26	ATemplate:Music/BTemplate:Music	ATemplate:Music2/BTemplate:Music2	116.541
25	A	A2	110.000					A
24	GTemplate:Music/ATemplate:Music	GTemplate:Music2/ATemplate:Music2	103.826
23	G	G2	97.9989			G	G
22	FTemplate:Music/GTemplate:Music	FTemplate:Music2/GTemplate:Music2	92.4986
21	F	F2	87.3071	F (6 string)
20	E	E2	82.4069					Low E
19	DTemplate:Music/ETemplate:Music	DTemplate:Music2/ETemplate:Music2	77.7817
18	D	D2	73.4162				D
17	CTemplate:Music/DTemplate:Music	CTemplate:Music2/DTemplate:Music2	69.2957
16	C great octave	C2 Deep C	65.4064			C
15	B͵	B1	61.7354					B (7 string)
14	ATemplate:Music͵/BTemplate:Music͵	ATemplate:Music1/BTemplate:Music1	58.2705	BTemplate:Music (7 string)
13	A͵	A1	55.0000				A
12	GTemplate:Music͵/ATemplate:Music͵	GTemplate:Music1/ATemplate:Music1	51.9131
11	G͵	G1	48.9994
10	FTemplate:Music͵/GTemplate:Music͵	FTemplate:Music1/GTemplate:Music1	46.2493					FTemplate:Music (8 string)
9	F͵	F1	43.6535
8	E͵	E1	41.2034				E
7	DTemplate:Music͵/ETemplate:Music͵	DTemplate:Music1/ETemplate:Music1	38.8909
6	D͵	D1	36.7081
5	CTemplate:Music͵/DTemplate:Music͵	CTemplate:Music1/DTemplate:Music1	34.6478					CTemplate:Music (9 string)
4	C͵ contra-octave	C1 Pedal C	32.7032
3	B͵͵	B0	30.8677				B (5 string)
2	ATemplate:Music͵͵/BTemplate:Music͵͵	ATemplate:Music0/BTemplate:Music0	29.1352
1	A͵͵ sub-contra-octave	A0 Double Pedal A	27.5000

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.

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