Frequencies of equal tuning

This article presents a list of the frequencies of all tones on the piano keyboard in equal tuning . In addition, the note names in German and English.

In addition to the use of superscript and subscript numbers for the octave, the notation with dashes is also used. The German pronunciation of the notation listed below is partly based on this. It is shown here using the example of the octavings of the concert pitch:

• A ₂ (also A '') = Subcontra-A
• A ₁ (also A ') = Contra-A
• A = capital A
• a = small A
• a ¹ (also a ') = dashed A
• a ² (also a '') = two-prime A
• a ³ (also a '' ') = three-stroke A
• a ⁴ (also a '' '') = four-stroke A

Note:

• The concert pitch (our a ¹ ) is also referred to as A4 in the USA .
• The frequencies are calculated values ​​and do not correspond to those of a well-tuned instrument (see stretching ).
• Based on psycho-acoustic findings, we hear sinus tones not linearly; The logarithmic frequency scale and the logarithmic Mel scale run almost proportionally up to approx. 500 Hz (100 Hz = 100 mel, 200 Hz = 200 mel); Above this, there are clear deviations (1000 Hz = 850 mel, 8000 Hz = 2100 mel). Complex musical tones are perceived up to approx. 5 kHz almost like the theoretical logarithmic frequency scale. Errors are within the barely noticeable area.
• In the twelve-step scale, the frequency of direct neighboring tones differs by a factor

${\displaystyle {\sqrt[{12}]{2}}\approx 1{,}0594630943593\,}$.

The following equation gives the frequency f from the key number n , as shown in the table below.

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

This equation can also be written as:

${\displaystyle f(n)=2^{\frac {n-49}{12}}\,\cdot 440\ \mathrm {Hz} }$

The key number is obtained from the frequency with the following equation:

${\displaystyle n=\log _{2}(f/440\ \mathrm {Hz} )\cdot 12+49}$

Virtual keyboard

The keyboard of a modern piano or digital piano usually has 88 keys and includes sounds of A ₂ to C ⁵ . The following table shows the frequencies of an equal tuning according to the above formula. A real instrument is usually tuned differently.

Key number	Notation (English)	Notation (German)	Frequency in Hertz (concert pitch 440 Hz)
88	C8	c 5	4186.01
87	B7	h 4	3951.07
86	A # 7 / Bb7	ais 4 / b 4	3729.31
85	A7	a 4	3520.00
84	G # 7 / Ab7	g sharp 4 / a flat 4	3322.44
83	G7	g 4	3135.96
82	F # 7 / Gb7	f sharp 4 / gt 4	2959.96
81	F7	f 4	2793.83
80	E7	e 4	2637.02
79	D # 7 / Eb7	dis 4 / es 4	2489.02
78	D7	d 4	2349.32
77	C # 7 / Db7	cis 4 / 4th	2217.46
76	C7	c 4	2093.00
75	B6	h 3	1975.53
74	A # 6 / Bb6	ais 3 / b 3	1864.66
73	A6	a 3	1760.00
72	G # 6 / Ab6	g sharp 3 / a flat 3	1661.22
71	G6	g 3	1567.98
70	F # 6 / Gb6	f sharp 3 / gt 3	1479.98
69	F6	f 3	1396.91
68	E6	e 3	1318.51
67	D # 6 / Eb6	dis 3 / es 3	1244.51
66	D6	d 3	1174.66
65	C # 6 / Qb6	cis 3 / of 3	1108.73
64	C6	c 3	1046.50
63	B5	h 2	987.767
62	A # 5 / Bb5	ais 2 / b 2	932,328
61	A5	a 2	880,000
60	G # 5 / Ab5	g sharp 2 / a flat 2	830,609
59	G5	g 2	783,991
58	F # 5 / Gb5	f sharp 2 / gt 2	739.989
57	F5	f 2	698.456
56	E5	e 2	659.255
55	D # 5 / Eb5	dis 2 / es 2	622.254
54	D5	d 2	587,330
53	C # 5 / Db5	cis 2 / 2nd	554,365
52	C5	c 2	523.251
51	B4	h 1	493.883
50	A # 4 / Bb4	ais 1 / b 1	466.164
49	A4	a 1 concert pitch	440,000
48	G # 4 / Ab4	g sharp 1 / a flat 1	415,305
47	G4	g 1	391.995
46	F # 4 / Gb4	f sharp 1 / gt 1	369.994
45	F4	f 1	349.228
44	E4	e 1	329.628
43	D # 4 / Eb4	dis 1 / es 1	311.127
42	D4	d 1	293.665
41	C # 4 / Db4	cis 1 / 1st	277.183
40	C4	c 1	261.626
39	B3	H	246,942
38	A # 3 / Bb3	ais / b	233,082
37	A3	a	220,000
36	G # 3 / Ab3	g sharp / as	207.652
35	G3	G	195.998
34	F # 3 / Gb3	f sharp / total	184.997
33	F3	f	174.614
32	E3	e	164.814
31	D # 3 / Eb3	dis / it	155.563
30th	D3	d	146.832
29	C # 3 / Db3	cis / des	138,591
28	C3	c	130.813
27	B2	H	123.471
26th	A # 2 / Bb2	Ais / B	116.541
25th	A2	A.	110,000
24	G # 2 / Ab2	G sharp / a flat	103.826
23	G2	G	97.9989
22nd	F # 2 / Gb2	F sharp / Ges	92.4986
21st	F2	F.	87,3071
20th	E2	E.	82,4069
19th	D # 2 / Eb2	Dis / Es	77.7817
18th	D2	D.	73.4162
17th	C # 2 / Db2	Cis / Db	69.2957
16	C2	C.	65.4064
15th	B1	H 1	61.7354
14th	A # 1 / Bb1	A sharp 1 / B 1	58.2705
13	A1	A 1	55.0000
12	G # 1 / Ab1	G sharp 1 / A flat 1	51.9131
11	G1	G 1	48.9994
10	F # 1 / Gb1	Fis 1 / Ges 1	46.2493
9	F1	F 1	43.6535
8th	E1	E 1	41.2034
7th	D # 1 / Eb1	Dis 1 / Es 1	38.8909
6th	D1	D 1	36.7081
5	C # 1 / Db1	Cis 1 / Des 1	34.6478
4th	C1	C 1	32.7032
3	B0	H 2	30.8677
2	A # 0 / Bb0	A sharp 2 / B flat 2	29.1352
1	A0	A 2	27.5000

The following keys are only available on a few and very large concert grand pianos, see piano .

Key number	Note name (english)	Note name (German)	Frequency in Hertz (concert pitch 440 Hz)
0	G # 0 / Ab0	G sharp 2 / A flat 2	25.9565
−1	G0	G 2	24.4997
−2	F # 0 / Gb0	Fis 2 / Ges 2	23.1247
−3	F0	F 2	21.8268
−4	E0	E 2	20.6017
−5	D # 0 / Eb0	Dis 2 / Eb 2	19.4454
−6	D0	D 2	18.3540
−7	C # 0 / Db0	Cis 2 / Des 2	17.3239
−8	C0	C 2	16.3516

See also

• Sound symbol

Individual evidence

1. ↑ Basic Concepts - Acoustic Phonetics . University of Cologne
2. ^ Concert pitch in the English language Wikipedia
3. ↑ Middle C in the English language Wikipedia