Equal Temperament

The equal tempered scale is the common musical scale used at present, used for the tuning of pianos and other instruments of relatively fixed scale. It divides the octave into 12 equal semitones. It is common practice to state musical intervals in cents, where 100 is defined as one equal tempered semitone. The cents notation provides a useful way to compare intervals in different temperaments and to decide whether those differences are musically significant. A useful parameter for comparison is the just noticeable difference in pitch which corresponds to about 5.

One of the advantages of the equal tempered scale is that it is the same in any musical "key", so that compositions may be freely transposed up or down without changing the musical intervals. This is such a major advantage that it has made equal temperament the standard temperament in western music for the past 200 years. The equal tempered intervals may be compared with Just and Pythagorean temperaments which maintain the exact-integer-ratio rule for the main intervals, while equal temperament departs from that standard.

The piano keyboard is the standard example of the equal tempered scale, and the frets on a modern guitar are also placed to fix the instrument into the equal tempered scale.

Equal tempered frequency list
Equal tempered octave on the piano
Equal tempered octave vs other temperaments
Index

Temperament and musical scales
 
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This table is based upon the A-440 Hz frequency standard. The note letters have a number appended which is their octave number beginning at the bottom octave on the piano. The offset frequencies are the chromatic notes (sharps and flats)

Equal temperament
Index

Temperament and musical scales
 
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The A 440 Pitch Standard

In 1939, an International Conference met in London and unanimously adopted 440 Hz as the standard frequency for the pitch A4, and that is the almost universal standard at present. It was reaffirmed in 1975 by the International Organization for Standardization. The National Institute of Standards and Technology (NIST) broadcasts a precise 440 Hz reference tone on its short wave radio station WWV.

Rossing reports Handel's tuning fork frequency to be 422.5 Hz for that A, and the eras of Hayden, Mozart, Bach and Beethoven had pitch standards around that frequency. This means that their compositions are now played about 70 cents sharper than the originals.

While the A4 440Hz is the internationally recognized pitch standard, there are some orchestra groups that specialize in the music of a given historical period. For example, some use 415Hz for the baroque period music and there are other pitch standards like "Chorton pitch" at 466Hz and "classical pitch" at 430Hz.

Equal tempered frequencies based on this standard
Index

Temperament and musical scales

Reference
Rossing
Science of Sound, 2nd ed.
Ch 7
 
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