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Twelve-Tone Equal-Tempered Scales

Though people commonly talk about, for instance, the C major scale or the minor scale, in practice there are many ways to define a musical scale. A musical scale is essentially just a collection of frequencies that are assigned names such as , , F, and so on—these named frequencies comprise the notes or tones of the scale and the distances between any two frequencies make up the intervals of the scale. The octave is a particularly useful interval for tuning purposes and is defined as the interval between one note and another with double or half its frequency.
When tuning a particular instrument, the frequencies to which you tune the notes have an important effect on the overall tonality of the instrument. For example, a piece written in B major may sound very harmonious when played on a piano tuned a particular way, while the same piece modulated to F major played on the same instrument might not sound as pleasant.
The most common form of tuning in contemporary Western music is the twelve-tone equal temperament (12-TET) system. This system takes a particular octave and divides it into 12 equal parts, which correspond to the 12 tones in the chromatic scale (A, , B, C, , and so on). The construction thus ensures the ratio between any two adjacent notes to be . In this Demonstration, change the starting frequency to hear the 12-tone equal-tempered octave based on this tone. Compare this 12-TET scale with the standard tuning for an ideal piano.

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