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 The Equal Temp

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An equal temperament is amusical temperament - asystem of tuning, in which

every pair of adjacent pitchesis separated by the sameinterval. n other words, thepitches of an equaltemperament can be producedby repeating a generatinginterval. Equal intervals also

means equal ratios betweenthe frequencies of any adjacentpair, and, since pitch isperceived roughly as the

logarithm of frequency, equal! !

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n twelve-tone equal temperament, which dividesthe octave into "# equal parts, the width of asemitone, i.e. the frequency ratio of the intervalbetween two adjacent notes, is the twelfth root oftwo$

%nly twelfth root of two ma&es the octavesconsonanse.'i(rence between frequencies must be li&e " $ #to ma&e octave tuned.

)hen we try to tune piano using major thirds wehave to ma&e di(rence between them li&e * $ +.

n one octave we have three major thirds, so $

requency of rst tone */+ */+ */+ 0".1*2"3

t is not #.

 The same happends when we use another

4o we have "# semitones in octave $

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5efore the equal temperat hascreated in use were unequaltemperaments, where the

di(rence of frequencies werenational numbers. 5ecause ofthis some &eys sounds betterthan the others. %ne of the rst

equal temperaments was madeby 6incen7o 8alilei 9"*#:-"*1",plays lute; - rst twelve-tonescale, still rational numbers.<enricus 8rammateus - "*"= ,the most simillar to todaystemperament. 4imon 4tevin -

made it in ">:*, but published"==+. ?athematician. <e didn@t

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 .4 5ach@s 'as )ohltemperirte Blavier