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THE EQUAL TEMPERED CHROMATIC SCALE

Tech Reference by efesar
Thursday February 21, 2002

Equal Tempered Chromatic Scale
In a world of electronic music we take many things for granted. One thing we take for granted is that almost all computer sequencers, samplers, keyboards and synthesizers use the same common form of tuning. The common form of tuning that all this modern equipment uses is called Equal Tempered Chromatic Tuning. 

Equal Tempered Chromatic Tuning was created to allow stringed instruments with extremely wide ranges (ergo, the piano) to sound in-tune across the entire range. Typical western music and almost all stringed instruments are tuned according to Just Intonation Tuning -- a different type of tuning where scales are tuned based on perfect ratios (i.e. 3/2 for a perfect fifth, 5/4 for a perfect fourth).

Equal Tempered tuning is extremely easy to calculate. It is a quick exponential calculation to get from one (half-step) note to the next. Simply multiply the frequency of a note by the 12th root of 2 (which happens to be a constant at approximately 1.05946), or divide by the 12th root of 2 (again, 1.05946). Be careful though -- as I said, this is an exponential calculation meaning that for each half-step you must multiply by 1.05946 -- do not attempt to multiply the number of half steps by 1.05946 first!

So why choose Equal Tempered over Just Intonation? Because Just Intonation requires that you retune your instrument for each scale you plan to play. If you are going to play Sonata in G Major, you will tune your instrument to G Major. If you wanted to play F Major instead, you would have to return to F Major. Equal Tempered Scales might not be perfect according to (some) human ears, but they make the convenience of playing most instruments worth the loss in harmonic perfection.

Below is a chart of the Equal Tempered Chromatic Scale based on concert pitch A5 (440Hz).

0 1 2 3 4 5 6 7 8 9 10
A - 27.500 55.000 110.000 220.000 440.000 880.000 1760.000 3520.000 7040.000 14080.000
A# / Bb - 29.135 58.270 116.541 233.082 466.164 932.328 1864.655 3729.310 7458.620 14917.240
B / Cb - 30.868 61.735 123.471 246.942 493.883 987.767 1975.533 3951.066 7902.133 15804.266
C /B# - 32.703 65.406 130.813 261.626 523.251 1046.502 2093.005 4186.009 8372.018 16744.036
C# /Db - 34.648 69.296 138.591 277.183 554.365 1108.731 2217.461 4434.922 8869.844 17739.688
D - 36.708 73.416 146.832 293.665 587.330 1174.659 2349.318 4698.636 9397.273 18794.545
D# / Eb - 38.891 77.782 155.563 311.127 622.254 1244.508 2489.016 4978.032 9956.063 19912.127
E / Fb 20.602 41.203 82.407 164.814 329.628 659.255 1318.510 2637.020 5274.041 10548.082 -
F / E# 21.827 43.654 87.307 174.614 349.228 698.456 1396.913 2793.826 5587.652 11175.303 -
F# / Gb 23.125 46.249 92.499 184.997 369.994 739.989 1479.978 2959.955 5919.911 11839.822 -
G 24.500 48.999 97.999 195.998 391.995 783.991 1567.982 3135.963 6271.927 12543.854 -
G# / Ab 25.957 51.913 103.826 207.652 415.305 830.609 1661.219 3322.438 6644.875 13289.750 -

 
Next: Just Intonation vs. Equal Tempered
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This article was added to our database on February 21, 2002, and the article's information was last updated 22 years ago. efesar is responsible for keeping this article's information up to date. This page has been viewed 2588 time(s).
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