Pianotech

Expand all | Collapse all

Roshan Kakiya's 12-Tone Equal Temperament (RK 12-TET)

  • 1.  Roshan Kakiya's 12-Tone Equal Temperament (RK 12-TET)

    Posted 05-09-2019 12:35
      |   view attached

    Roshan Kakiya's 12-Tone Equal Temperament (RK 12-TET)


    Fifth = 700.98 cents.

    Octave = 1201.68 cents.

    12 Fifths = 8411.73 cents.

    7 Octaves = 8411.73 cents.

    Note Cents
    C 0.00
    C# 100.14
    D 200.28
    D# 300.42
    E 400.56
    F 500.70
    F# 600.84
    G 700.98
    G# 801.12
    A 901.26
    A# 1001.40
    B 1101.54
    C 1201.68

    Pythagorean Comma


    12 Pure Fifths = 8423.46 cents.

    7 Pure Octaves = 8400.00 cents.

    12 Pure Fifths ≠ 7 Pure Octaves.

    Pythagorean Comma = 12 Pure Fifths − 7 Pure Octaves = 8423.46 cents − 8400.00 cents = 23.46 cents.

    Solution: Meet in the Middle


    Average = (8423.46 cents + 8400.00 cents) / 2 = 16823.46 cents / 2 = 8411.73 cents.

    12 Tempered Fifths = 8411.73 cents.

    7 Tempered Octaves = 8411.73 cents.

    The Pythagorean Comma has been eliminated.

    Verification: 12 Tempered Fifths 
    − 7 Tempered Octaves = 8411.73 cents − 8411.73 cents = 0.00 cents.


    ------------------------------
    Roshan Kakiya
    ------------------------------


  • 2.  RE: Roshan Kakiya's 12-Tone Equal Temperament (RK 12-TET)

    Posted 05-09-2019 20:54
    One of these days you're going to see the beauty of the perfect 12th. This octave that you propose is too wide. Go ahead and try to tune it.

    ------------------------------
    Jason Kanter
    Lynnwood WA
    425-830-1561
    ------------------------------



  • 3.  RE: Roshan Kakiya's 12-Tone Equal Temperament (RK 12-TET)

    Posted 05-09-2019 21:25
    RK 12-TET lies exactly in the middle between Pure Octave 12-TET and Pure 5th 12-TET.


  • 4.  RE: Roshan Kakiya's 12-Tone Equal Temperament (RK 12-TET)

    Posted 05-09-2019 22:35
    You include no rationale for the temperament. The fifth is tempered by half the amount that it is tempered in pure octave ET? Is that all? So?

    Sent from my iPhone




  • 5.  RE: Roshan Kakiya's 12-Tone Equal Temperament (RK 12-TET)

    Posted 05-12-2019 22:45
    Inharmonicity causes the overtones of the fundamental frequency to become sharp.

    Source: http://daffy.uah.edu/piano/page4/page8/index.html


    Inharmonicity has been accounted for to some extent by RK 12-TET because its intervals are slightly sharper than each overtone of the fundamental frequency:

    1st harmonic (Ratio: 1/1) = 0.00 cents.
    RK 12-TET = 0.00 cents.

    2nd harmonic (Ratio: 2/1) = 1200.00 cents.
    RK 12-TET = 1201.68 cents.

    3rd harmonic (Ratio: 3/1) = 1901.96 cents.
    RK 12-TET = 1902.65 cents.

    4th harmonic (Ratio: 4/1) = 2400.00 cents.
    RK 12-TET = 2403.35 cents.

    ------------------------------
    Roshan Kakiya
    ------------------------------