![[Index:]](../img/index.gif){kind=small}
Note Frequencies
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Frequency and Wavelength Note Frequencies |
Just-tempered Equal-tempered
Name of interval Note ratio ratio Diff
---------------- ---- ------------- -------------- ------
Unison C 1.00000 1.00000 0
Min2 as chrom.sem. C# 1.05469 1.05946 +0.45%
Minor 2 Db 1.06667
Maj2 as minor D 1.11111 1.12246 +1.02%
Maj2 as major D 1.12500
Dim 3rd Ebb 1.13778
Minor 3rd D# 1.17188 1.18921 +1.48%
Minor 3rd Eb 1.20000
Major 3rd E 1.25000 1.25992 +0.79%
Perfect 4th F 1.33333 1.33484 +0.11%
Aug. 4th F# 1.40625 1.41421 +0.57%
Dim. 5th Gb 1.42222
Perfect 5th G 1.50000 1.49831 -0.11%
Aug. 5th G# 1.56250 1.58740 +1.59%
Minor 6th Ab 1.60000
Major 6th A 1.66667 1.68179 +0.91%
Dim. 7th Bbb 1.68560
Minor 7th A# 1.75000 1.78180 +1.82%
Minor 7th Bb 1.77778
Major 7th B 1.87500 1.88775 +0.68%
8va C 2.00000 2.00000 0
----------------------------------------------------------------
This table assumes A = 440 and equal temperment. The ratio of
adjacent notes is the 12th root of 2, or about 1.05946. [Note:
This table is for piano. Handbells ring one octave higher.]
NOTE FREQUENCIES (Hz)
+---------------------------------------------------------+
| OCTAVE |
+-----+---------------------------------------------------------+
|NOTE | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+-----+---------------------------------------------------------+
| A |27.5| 55.0|110.0|220.0|440.0| 880.0|1760.0|3520.0| 7040.0|
|A#/Bb|29.1| 58.3|116.5|233.1|466.2| 932.4|1864.7|3729.4| 7458.9|
| B |30.9| 61.7|123.5|247.0|493.9| 987.8|1975.7|3951.3| 7902.7|
| C |32.7| 65.4|130.8|261.6|523.3|1046.6|2093.2|4186.5| 8372.9|
|C#/Db|34.6| 69.3|138.6|277.2|554.4|1108.8|2217.7|4435.5| 8871.1|
| D |36.7| 73.4|146.8|293.7|587.4|1174.8|2349.7|4699.5| 9398.9|
|D#/Eb|38.9| 77.8|155.6|311.2|622.4|1244.8|2489.5|4979.1| 9958.1|
| E |41.2| 82.4|164.9|329.7|659.4|1318.8|2637.7|5275.3|10550.6|
| F |43.7| 87.3|174.7|349.3|698.7|1397.3|2794.6|5589.2|11178.4|
|F#/Gb|46.2| 92.5|185.1|370.1|740.2|1480.4|2960.8|5921.8|11843.5|
| G |49.0| 98.0|196.1|392.1|784.3|1568.2|3137.1|6274.1|12548.2|
|G#/Ab|51.9|103.9|207.7|415.5|830.9|1661.9|3323.7|6647.4|13294.8|
+-----+---------------------------------------------------------+
Written by:
Michael Kesti Grass Valley Group, Inc. | "And like, one and one don't make
mrk@gvgspd.GVG.TEK.COM | two, one and one make one."
!tektronix!gvgpsa!gvgspd!mrk | - The Who, Bargain
Archived original can be found at: Re: Frequency/Wavelength
The fundamental unit of measurement for frequency is Hertz (abbreviated "Hz") which is equivalent to "cycles per second". "kHz" means "kilo-Hertz" or "1000 cycles per second". "MHz" means "Mega-Hertz" or "1000000 cycles per second". Audio frequencies (sound which humans can hear) range from 20Hz to 20kHz (20 cycles per second to 20000 cycles per second). For the purposes of music, we will limit the unit of measurement to simple "Hz".
The frequencies relative to "Middle C" depend on whether you are discussing the piano (and other "non-bell" instruments) or talking about bells in particular. For the piano, the A above Middle C is indeed 440Hz, but for handbells the A *below* Middle C (as written) is 440Hz. For handbells, the easy way to remember is that "A4" is "440Hz" (my favorite frequency). For an "equally tempered scale" the factor inbetween adjacent pitches (e.g., A4 to A#4) is exactly the 12th root of 2 (approximately 1.059463094359295264561825294). If you take 440Hz and sucessively multiply it (and its products) by this number 12 times you will end up with 880Hz which is the frequency of A5 (the A above Middle C as written for handbells).
The intermediate frequencies are calculated thusly (rounded to 10 decimal places, all values are in Hz):
A4 440.0
A#4 466.1637615181
B4 493.8833012561
C5 523.2511306012
C#5 554.3652619537
D5 587.3295358348
D#5 622.2539674442
E5 659.2551138257
F5 698.456462866
F#5 739.9888454233
G5 783.9908719635
G#5 830.6093951599
A5 880.0
To get the frequency for the next series up or down, take the
corresponding note and multiply or divide by 2, respectively.
For example, to obtain the frequency for the C6 multiply the
frequency given for a C5 by 2 to obtain 1046.5022612024Hz.
The frequency of an A3 is 220.0Hz (440.0Hz divided by 2).
Here now, for your amusement, are the frequencies for any handbell you can imagine, from the absolutely subsonic to ultrasonic. Either you feel the floor shake or your hound dog goes berzerk: [Table shortened. Go to archive for complete list. - ed]
Index Name Oct Fundamental -Twelfth-
27 C 2 65.4063 196.2191 28 C#/Db 2 69.2956 207.8869 29 D 2 73.4161 220.2485 30 D#/Eb 2 77.7817 233.3452 31 E 2 82.4068 247.2206 32 F 2 87.3070 261.9211 33 F#/Gb 2 92.4986 277.4958 34 G 2 97.9988 293.9965 35 G#/Ab 2 103.8261 311.4785 36 A 2 110 330 37 A#/Bb 2 116.5409 349.6228 38 B 2 123.4708 370.4124
VVV -- Typical five octave set -- VVV
39 C 3 130.8127 392.4383 40 C#/Db 3 138.5913 415.7739 41 D 3 146.8323 440.4971 42 D#/Eb 3 155.5634 466.6904 43 E 3 164.8137 494.4413 44 F 3 174.6141 523.8423 45 F#/Gb 3 184.9972 554.9916 46 G 3 195.9977 587.9931 47 G#/Ab 3 207.6523 622.9570 48 A 3 220 660 49 A#/Bb 3 233.0818 699.2456 50 B 3 246.9416 740.8249 51 C 4 261.6255 784.8766 52 C#/Db 4 277.1826 831.5478 53 D 4 293.6647 880.9943 54 D#/Eb 4 311.1269 933.3809 55 E 4 329.6275 988.8826 56 F 4 349.2282 1047.6846 57 F#/Gb 4 369.9944 1109.9832 58 G 4 391.9954 1175.9863 59 G#/Ab 4 415.3046 1245.9140 60 A 4 440 1320 61 A#/Bb 4 466.1637 1398.4912 62 B 4 493.8833 1481.6499 63 C 5 523.2511 1569.7533 <-- Middle C (as writen) 64 C#/Db 5 554.3652 1663.0957 65 D 5 587.3295 1761.9886 66 D#/Eb 5 622.2539 1866.7619 67 E 5 659.2551 1977.7653 68 F 5 698.4564 2095.3693 69 F#/Gb 5 739.9888 2219.9665 70 G 5 783.9908 2351.9726 71 G#/Ab 5 830.6093 2491.8281 72 A 5 880 2640 73 A#/Bb 5 932.3275 2796.9825 74 B 5 987.7666 2963.2998 75 C 6 1046.5022 3139.5067 76 C#/Db 6 1108.7305 3326.1915 77 D 6 1174.6590 3523.9772 78 D#/Eb 6 1244.5079 3733.5238 79 E 6 1318.5102 3955.5306 80 F 6 1396.9129 4190.7387 81 F#/Gb 6 1479.9776 4439.9330 82 G 6 1567.9817 4703.9452 83 G#/Ab 6 1661.2187 4983.6563 84 A 6 1760 5280 85 A#/Bb 6 1864.6550 5593.9651 86 B 6 1975.5332 5926.5996 87 C 7 2093.0045 6279.0135 88 C#/Db 7 2217.4610 6652.3831 89 D 7 2349.3181 7047.9544 90 D#/Eb 7 2489.0158 7467.0476 91 E 7 2637.0204 7911.0613 92 F 7 2793.8258 8381.4775 93 F#/Gb 7 2959.9553 8879.8661 94 G 7 3135.9634 9407.8904 95 G#/Ab 7 3322.4375 9967.3127 96 A 7 3520 10560 97 A#/Bb 7 3729.3100 11187.9302 98 B 7 3951.0664 11853.1992 99 C 8 4186.0090 12558.0271
^^^ -- Typical five octave set -- ^^^
100 C#/Db 8 4434.9220 13304.7662 101 D 8 4698.6362 14095.9088 102 D#/Eb 8 4978.0317 14934.0952 103 E 8 5274.0409 15822.1227 104 F 8 5587.6517 16762.9551 105 F#/Gb 8 5919.9107 17759.7322 106 G 8 6271.9269 18815.7809 107 G#/Ab 8 6644.8751 19934.6254 108 A 8 7040 21120 109 A#/Bb 8 7458.6201 *ultrasonic* 110 B 8 7902.1328 *ultrasonic* 111 C 9 8372.0180 *ultrasonic*
Written by:
Helmuth R. Litfin
helmuth@magicbells.com
The Magic Bells Project
http://www.magicbells.com
4 Jan 1999
Archived original can be found at: Note Frequencies (Long Posting!)