The pitch as a hertz value

The following table contains the different octave ranges and the hertz values of the tones in each octave. The first column on the left is the (imaginary) infraoctave and well outside the hearing range: its frequencies cannot be perceived as auditory sensations but as physical vibrations with one's sense of touch. The frequency of this C₃ is approximately 8 Hz, or eight beats per second, which corresponds rhythmically with sixteenth tones, when the tempo of the quarter stroke is approximately 123 bps (beats per minute). The ultraoctave on the right also extends beyond the hearing range.

The actual hearing range starts with the second column. The frequencies of the 1^st octave are given with additional precision. The official frequency of the one-lined A is 440 Hz, although current practice favours frequencies of 442443 Hz or even 446 Hz. The hertz value can be calculated using the following formula:

i is the ratio used for multiplying the original hertz value, while c is the cent value of the interval.

For calculating the frequency of a 1^st octave B, when A is 443 Hz, the formula becomes: 443 · 10^{(200 · log^2/1200)}

The difference between A and B is 200 cents. The result is 497.25 Hz.

The frequency of the 1st octave C (c = -900) can be calculated using the same formula. The result is 263.4 Hz.

The bottom line of the following table includes the American notation for octave ranges. It is commonly used in applications such as MIDI technology, where g becomes G3 and e² becomes E5.

		sub- contra	contra	great	small	one-lined	2-lined	3-lined	4-lined	5-lined	6-lined	7-lined
C	8,18	16,35	32,70	65,41	130,8	261,6	523,3	1047	2093	4186	8372	16744
C#	8,66	17,32	34,65	69,30	138,6	277,2	554,4	1109	2217	4435	8870	17740
D	9,18	18,35	36,71	73,42	146,8	293,7	587,3	1175	2349	4699	9397	18795
D#	9,72	19,45	38,89	77,78	155,6	311,1	622,3	1245	2489	4978	9956	19912
E	10,30	20,60	41,20	82,41	164,8	329,6	659,3	1319	2637	5274	10548	21096
F	10,91	21,83	43,65	87,31	174,6	349,2	698,5	1397	2794	5588	11175	22351
F#	11,56	23,12	46,25	92,50	185,0	370,0	740,0	1480	2960	5920	11840	23680
G	12,25	24,50	49,00	98,00	196,0	392,0	784,0	1568	3136	6272	12544	25088
G#	12,98	25,96	51,91	103,8	207,7	415,3	830,6	1661	3322	6645	13290	26580
A	13,75	27,50	55,00	110,0	220,0	440,0	880,0	1760	3520	7040	14080	28160
A#	14,57	29,14	58,27	116,5	233,1	466,2	932,3	1865	3729	7459	14917	29834
H	15,43	30,87	61,74	123,5	246,9	493,9	987,8	1976	3951	7902	15804	31609
	C-1	C0	C1	C2	C3	C4	C5	C6	C7	C8	C9	C10

The table below can be used for examining the approximate proportions of frequencies and pitches. The diagram only expresses frequencies within the range of the 1^st octave. The chart illustrates how, for example, a pitch with a frequency of 320 Hz is located between the 1^st octave D sharp and E. The frequencies of 160, 80, 40 and 20 Hz are, correspondingly, between the same pitch names in the lower octave ranges.

Tone frequencies (Hz)