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Pure Major Third Equal Temperament

  • 1.  Pure Major Third Equal Temperament

    Posted 02-08-2020 06:49
    Cents

    C 0.00
    C# 96.58
    D 193.16
    D# 289.74
    E 386.31
    F 482.89
    F# 579.47
    G 676.05
    G# 772.63
    A 869.21
    A# 965.78
    B 1062.36
    C 1158.94



    Features

    Semitone = 1200 × 1/4 × log2(5/4) = 96.58 cents.


    Pure Major Third = 1200 × 4/4 × log2(5/4) = 1200 × log2(5/4) = 386.31 cents.

    Every Major Third is pure.


    Fifth = 1200 × 7/4 × log2(5/4) = 676.05 cents.

    Every Fifth is extremely narrow.


    Octave = 1200 × 12/4 × log2(5/4) = 1200 × 3 × log2(5/4) = 1158.94 cents.

    Every Octave is extremely narrow.



    Purpose of Pure Major Third Equal Temperament

    To prove that it is possible for every Major Third to be pure across the whole scale of a temperament.

    A hefty price in the form of extremely out of tune intervals must be paid in order to achieve this.


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    Roshan Kakiya
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