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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).

012345678910
A-27.50055.000110.000220.000440.000880.0001760.0003520.0007040.00014080.000
A# / Bb-29.13558.270116.541233.082466.164932.3281864.6553729.3107458.62014917.240
B / Cb-30.86861.735123.471246.942493.883987.7671975.5333951.0667902.13315804.266
C /B#-32.70365.406130.813261.626523.2511046.5022093.0054186.0098372.01816744.036
C# /Db-34.64869.296138.591277.183554.3651108.7312217.4614434.9228869.84417739.688
D-36.70873.416146.832293.665587.3301174.6592349.3184698.6369397.27318794.545
D# / Eb-38.89177.782155.563311.127622.2541244.5082489.0164978.0329956.06319912.127
E / Fb20.60241.20382.407164.814329.628659.2551318.5102637.0205274.04110548.082-
F / E#21.82743.65487.307174.614349.228698.4561396.9132793.8265587.65211175.303-
F# / Gb23.12546.24992.499184.997369.994739.9891479.9782959.9555919.91111839.822-
G24.50048.99997.999195.998391.995783.9911567.9823135.9636271.92712543.854-
G# / Ab25.95751.913103.826207.652415.305830.6091661.2193322.4386644.87513289.750-

 
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 16 years ago. efesar is responsible for keeping this article's information up to date. This page has been viewed 2908 time(s).
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