Piano key frequencies

Template:Short description Template:More citations needed This is a list of the fundamental frequencies in hertz (cycles per second) of the keys of a modern 88-key standard or 108-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).<ref name=":0">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref><ref name=":1">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> Every octave is made of twelve steps called semitones. A jump from the lowest semitone to the highest semitone in one octave doubles the frequency (for example, the fifth A is 440 Hz and the sixth A is 880 Hz). The frequency of a pitch is derived by multiplying (ascending) or dividing (descending) the frequency of the previous pitch by the twelfth root of two (approximately 1.059463).<ref name=":0" /><ref name=":1" /> For example, to get the frequency one semitone up from A₄ (ATemplate:Music₄), multiply 440 Hz by the twelfth root of two. To go from A₄ up two semitones (one whole tone) to B₄, multiply 440 twice by the twelfth root of two (or once by the sixth root of two, approximately 1.122462). To go from A₄ up three semitones to C₅ (a minor third), multiply 440 Hz three times by the twelfth root of two (or once by the fourth root of two, approximately 1.189207). 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.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> This deviation from equal temperament is called the Railsback curve.

The following equation gives the frequency Template:Mvar (Hz) of the Template:Mvar^th key on the idealized standard piano with the 49th key tuned to A₄ at 440 Hz:

<math>

f(n) = \left(\sqrt[12]{2}\,\right)^{n-49} \times 440 \,\text{Hz}\, = 2^{\frac{n-49}{12}} \times 440 \,\text{Hz}\, </math> where Template:Mvar is shown in the table below.<ref name=":0" />

Conversely, the key number of a pitch with a frequency Template:Mvar (Hz) on the idealized standard piano is:

<math>

n = 12 \, \log_2\left({\frac{f}{440 \,\text{Hz}}}\right) + 49 </math>

List

File:Piano Frequencies.svg

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

File:Piano key frequencies.png

A printable version of the standard key frequencies (only including the 88 keys on a standard piano)

Values in bold are exact on an idealized standard piano. Keys shaded gray are rare and only appear on extended pianos. The normal 88 keys were numbered 1–88, with the extra low keys numbered 89–97 and the extra high keys numbered 98–108. A 108-key piano that extends from C₀ to B₈ was first built in 2018 by Stuart & Sons.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> (Note: these piano key numbers 1–108 are not the Template:Mvar keys in the equations or the table.)

Piano key number	MIDI note number	Helmholtz name<ref name=":2">{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	Scientific pitch name<ref name=":2" />	Template:Mvar	Frequency Template:Mvar(Template:Mvar) (Hz) (Equal temperament) <ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	Corresponding open strings on other instruments						Vocal Ranges
			width="5%" Template:Vert header				width="6%" Template:Vert header	width="7%" Template:Vert header	width="7%" Template:Vert header	width="9%" Template:Vert header	width="5%" Template:Vert header	width="5%" Template:Vert header	width="6%" Template:Vert header	width="7%" Template:Vert header	width="7%" Template:Vert header	width="9%" Template:Vert header	width="5%" Template:Vert header
108	119	b′′′′′	B8	99	7902.133
107	118	aTemplate:Music′′′′′/bTemplate:Music′′′′′	ATemplate:Music8/BTemplate:Music8	98	7458.620
106	117	a′′′′′	A8	97	7040.000
105	116	gTemplate:Music′′′′′/aTemplate:Music′′′′′	GTemplate:Music8/ATemplate:Music8	96	6644.875
104	115	g′′′′′	G8	95	6271.927
103	114	fTemplate:Music′′′′′/gTemplate:Music′′′′′	FTemplate:Music8/GTemplate:Music8	94	5919.911
102	113	f′′′′′	F8	93	5587.652
101	112	e′′′′′	E8	92	5274.041
100	111	dTemplate:Music′′′′′/eTemplate:Music′′′′′	DTemplate:Music8/ETemplate:Music8	91	4978.032
99	110	d′′′′′	D8	90	4698.636
98	109	cTemplate:Music′′′′′/dTemplate:Music′′′′′	CTemplate:Music8/DTemplate:Music8	89	4434.922
88	108	c′′′′′ 5-line octave	C8 Eighth octave	88	4186.009
87	107	b′′′′	B7	87	3951.066
86	106	aTemplate:Music′′′′/bTemplate:Music′′′′	ATemplate:Music7/BTemplate:Music7	86	3729.310
85	105	a′′′′	A7	85	3520.000
84	104	gTemplate:Music′′′′/aTemplate:Music′′′′	GTemplate:Music7/ATemplate:Music7	84	3322.438
83	103	g′′′′	G7	83	3135.963
82	102	fTemplate:Music′′′′/gTemplate:Music′′′′	FTemplate:Music7/GTemplate:Music7	82	2959.955
81	101	f′′′′	F7	81	2793.826
80	100	e′′′′	E7	80	2637.020
79	99	dTemplate:Music′′′′/eTemplate:Music′′′′	DTemplate:Music7/ETemplate:Music7	79	2489.016
78	98	d′′′′	D7	78	2349.318
77	97	cTemplate:Music′′′′/dTemplate:Music′′′′	CTemplate:Music7/DTemplate:Music7	77	2217.461
76	96	c′′′′ 4-line octave	C7 Double high C	76	2093.005
75	95	b′′′	B6	75	1975.533
74	94	aTemplate:Music′′′/bTemplate:Music′′′	ATemplate:Music6/BTemplate:Music6	74	1864.655
73	93	a′′′	A6	73	1760.000
72	92	gTemplate:Music′′′/aTemplate:Music′′′	GTemplate:Music6/ATemplate:Music6	72	1661.219
71	91	g′′′	G6	71	1567.982
70	90	fTemplate:Music′′′/gTemplate:Music′′′	FTemplate:Music6/GTemplate:Music6	70	1479.978
69	89	f′′′	F6	69	1396.913
68	88	e′′′	E6	68	1318.510
67	87	dTemplate:Music′′′/eTemplate:Music′′′	DTemplate:Music6/ETemplate:Music6	67	1244.508
66	86	d′′′	D6	66	1174.659
65	85	cTemplate:Music′′′/dTemplate:Music′′′	CTemplate:Music6/DTemplate:Music6	65	1108.731
64	84	c′′′ 3-line octave	C6 Soprano C (High C)	64	1046.502							rowspan="25" Template:Yes C
63	83	b′′	B5	63	987.7666
62	82	aTemplate:Music′′/bTemplate:Music′′	ATemplate:Music5/BTemplate:Music5	62	932.3275
61	81	a′′	A5	61	880.0000							rowspan="25" Template:Yes C
60	80	gTemplate:Music′′/aTemplate:Music′′	GTemplate:Music5/ATemplate:Music5	60	830.6094
59	79	g′′	G5	59	783.9909
58	78	fTemplate:Music′′/gTemplate:Music′′	FTemplate:Music5/GTemplate:Music5	58	739.9888							rowspan="25" Template:Yes C
57	77	f′′	F5	57	698.4565
56	76	e′′	E5	56	659.2551	E	E (5 String Viola)
55	75	dTemplate:Music′′/eTemplate:Music′′	DTemplate:Music5/ETemplate:Music5	55	622.2540
54	74	d′′	D5	54	587.3295
53	73	cTemplate:Music′′/dTemplate:Music′′	CTemplate:Music5/DTemplate:Music5	53	554.3653							rowspan="25" Template:Yes C
52	72	c′′ 2-line octave	C5 Tenor C	52	523.2511
51	71	b′	B4	51	493.8833					High B (Optional for 12 String Guitar)
50	70	aTemplate:Music′/bTemplate:Music′	ATemplate:Music4/BTemplate:Music4	50	466.1638
49	69	a′	A4 A440	49	440.0000	A	A			High A (Optional)	A	rowspan="25" Template:Yes C
48	68	gTemplate:Music′/aTemplate:Music′	GTemplate:Music4/ATemplate:Music4	48	415.3047				High Ab (12 Single String Bass)
47	67	g′	G4	47	391.9954						High G
46	66	fTemplate:Music′/gTemplate:Music′	FTemplate:Music4/GTemplate:Music4	46	369.9944
45	65	f′	F4	45	349.2282
44	64	e′	E4	44	329.6276			High E (5 String Cello)		High E	E	rowspan="25" Template:Yes C
43	63	dTemplate:Music′/eTemplate:Music′	DTemplate:Music4/ETemplate:Music4	43	311.1270				High Eb (12 String Single String Bass)
42	62	d′	D4	42	293.6648	D	D
41	61	cTemplate:Music′/dTemplate:Music′	CTemplate:Music4/DTemplate:Music4	41	277.1826
40	60	c′ 1-line octave	C4 Middle C	40	261.6256						C
39	59	b	B3	39	246.9417					B
38	58	aTemplate:Music/bTemplate:Music	ATemplate:Music3/BTemplate:Music3	38	233.0819
37	57	a	A3	37	220.0000			A
36	56	gTemplate:Music/aTemplate:Music	GTemplate:Music3/ATemplate:Music3	36	207.6523
35	55	g	G3	35	195.9977	G	G			G	Low G
34	54	fTemplate:Music/gTemplate:Music	FTemplate:Music3/GTemplate:Music3	34	184.9972
33	53	f	F3	33	174.6141				High F (7 String)
32	52	e	E3	32	164.8138				High E (5th tuning, 5 String Bass)
31	51	dTemplate:Music/eTemplate:Music	DTemplate:Music3/ETemplate:Music3	31	155.5635
30	50	d	D3	30	146.8324			D		D
29	49	cTemplate:Music/dTemplate:Music	CTemplate:Music3/DTemplate:Music3	29	138.5913
28	48	c small octave	C3	28	130.8128	C (5 String)	C		C (6 string)
27	47	B	B2	27	123.4708
26	46	ATemplate:Music/BTemplate:Music	ATemplate:Music2/BTemplate:Music2	26	116.5409
25	45	A	A2	25	110.0000				A (5th tuning Upright)	A
24	44	GTemplate:Music/ATemplate:Music	GTemplate:Music2/ATemplate:Music2	24	103.8262
23	43	G	G2	23	97.99886			G	G
22	42	FTemplate:Music/GTemplate:Music	FTemplate:Music2/GTemplate:Music2	22	92.49861
21	41	F	F2	21	87.30706	Low F (6 String)	Low F (6 String)
20	40	E	E2	20	82.40689					Low E
19	39	DTemplate:Music/ETemplate:Music	DTemplate:Music2/ETemplate:Music2	19	77.78175
18	38	D	D2	18	73.41619				D
17	37	CTemplate:Music/DTemplate:Music	CTemplate:Music2/DTemplate:Music2	17	69.29566
16	36	C great octave	C2 Deep C	16	65.40639			C
15	35	B͵	B1	15	61.73541					Low B (7 string)
14	34	ATemplate:Music͵/BTemplate:Music͵	ATemplate:Music1/BTemplate:Music1	14	58.27047
13	33	A͵	A1	13	55.00000				A
12	32	GTemplate:Music͵/ATemplate:Music͵	GTemplate:Music1/ATemplate:Music1	12	51.91309
11	31	G͵	G1	11	48.99943				G (5th tuning Upright)
10	30	FTemplate:Music͵/GTemplate:Music͵	FTemplate:Music1/GTemplate:Music1	10	46.24930					Low FTemplate:Music (8 string)
9	29	F͵	F1	9	43.65353			Low F (6 String)
8	28	E͵	E1	8	41.20344				E
7	27	DTemplate:Music͵/ETemplate:Music͵	DTemplate:Music1/ETemplate:Music1	7	38.89087
6	26	D͵	D1	6	36.70810
5	25	CTemplate:Music͵/DTemplate:Music͵	CTemplate:Music1/DTemplate:Music1	5	34.64783					Low C#(9 String)
4	24	C͵ contra-octave	C1 Pedal C	4	32.70320				C (Upright Extension or 5th tuning)
3	23	B͵͵	B0	3	30.86771				B (5 string)
2	22	ATemplate:Music͵͵/BTemplate:Music͵͵	ATemplate:Music0/BTemplate:Music0	2	29.13524
1	21	A͵͵	A0	1	27.50000
97	20	GTemplate:Music͵͵/ATemplate:Music͵͵	GTemplate:Music0/ATemplate:Music0	0	25.95654					Low G# (10 String)
96	19	G͵͵	G0	−1	24.49971
95	18	FTemplate:Music͵͵/GTemplate:Music͵͵	FTemplate:Music0/GTemplate:Music0	−2	23.12465
94	17	F͵͵	F0	−3	21.82676
93	16	E͵͵	E0	−4	20.60172
92	15	DTemplate:Music͵͵/ETemplate:Music͵͵	DTemplate:Music0/ETemplate:Music0	−5	19.44544
91	14	D͵͵	D0	−6	18.35405
90	13	CTemplate:Music͵͵/DTemplate:Music͵͵	CTemplate:Music0/DTemplate:Music0	−7	17.32391
89	12	C͵͵ sub-contra-octave	C0 Double Pedal C	−8	16.35160

See also

• Piano tuning
• Scientific pitch notation
• Music and mathematics

References

<references />

Template:Musical keyboards Template:Pitch (music)