Pianotech

  • 1.  Roshan Kakiya's Practical Just Intonation (Alternative Tritone)

    Posted 08-13-2018 04:29

    Roshan Kakiya's Practical Just Intonation (Alternative Tritone)

    Unison (C, Ratio: 1/1) = 0.00 cents

    Minor Second (C#, Ratio: 18/17) = 98.95 cents

    Major Second (D, Ratio: 9/8) = 203.91 cents

    Minor Third (D#, Ratio: 19/16) = 297.51 cents

    Major Third (E, Ratio: 24/19) = 404.44 cents

    Perfect Fourth (F, Ratio: 4/3) = 498.04 cents

    Tritone (F#, Ratio: 17/12) = 603.00 cents

    Perfect Fifth (G, Ratio: 3/2) = 701.96 cents

    Minor Sixth (G#, Ratio: 27/17) = 800.91 cents

    Major Sixth (A, Ratio: 27/16) = 905.87 cents

    Minor Seventh (A#, Ratio: 16/9) = 996.09 cents

    Major Seventh (B, Ratio: 17/9) = 1101.05 cents

    Octave (C, Ratio: 2/1) = 1200.00 cents

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    Roshan Kakiya
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    Attachment(s)

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    Roshan Kakiya's Practical Just Intonation (Alternative Tr...xlsx   10 KB 1 version


  • 2.  RE: Roshan Kakiya's Practical Just Intonation (Alternative Tritone)

    Posted 08-14-2018 13:15
    This is a very harmonious tuning. Here is a breakdown of its intervals from Scala (a program for creating musical scales):

    C (Ratio: 1/1) = Unison, perfect prime.
    C# (Ratio: 18/17) = Arabic lute index finger.
    D (Ratio: 9/8) = Major whole tone.
    D# (Ratio: 19/16) = 19th harmonic.
    E (Ratio: 24/19) = Smaller undevicesimal major third.
    F (Ratio: 4/3) = Perfect fourth.
    F# (Ratio: 17/12) = 2nd septendecimal tritone.
    G (Ratio: 3/2) = Perfect fifth.
    G# (Ratio: 27/17) = Septendecimal minor sixth.
    A (Ratio: 27/16) = Pythagorean major sixth.
    A# (Ratio: 16/9) = Pythagorean minor seventh.
    B (Ratio: 17/9) = Septendecimal major seventh.
    C (Ratio: 2/1) = Octave.

    Further Breakdown of Intervals

    Unison and Octave

    1/1 and 2/1.


    3-Limit Just Intonation (Pythagorean Tuning)

    3/2, 4/3, 9/8, 16/9 and 27/16.

    Source: https://en.wikipedia.org/wiki/Pythagorean_tuning#Method


    17-Limit Just Intonation

    17/9, 17/12 and 18/17.

    Source: http://xenharmonic.wikispaces.com/17-limit

    27/17 because 33 / 17 = 27/17.


    19-Limit Just Intonation

    19/16 and 24/19.

    Source: http://xenharmonic.wikispaces.com/19-limit

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    Roshan Kakiya
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    Original Message


  • 3.  RE: Roshan Kakiya's Practical Just Intonation (Alternative Tritone)

    Member
    Posted 08-15-2018 14:58
    Here are the rollingball.com images of Roshan Kakiya's two versions of this "just intonation."
    First: the "Just" version without the later modified tritone. It is basically a reverse well, its mildest M3 at A-C#, and its two full Pythagorean thirds on Bb and F. It has six perfect fifths and the waste gathered into the other six fifths, the narrowest at -5.35 cents:


    Second, the "alternate tritone" version. The F# has been flattened by about 3.5 cents. 
    You can see that in effect it is still a "reverse well". The mildest M3s are A and F#; the noisiest (full Pythagorean M3) are Bb and F.
    A bit irregular. This has seven perfect fifths, with the waste gathered into the fifths on A, E, F# (6 cents narrowed), Ab and Eb:


    Note about these charts: the methodology is explained on rollingball.com. The colored bars represent the widths (in cents) of the intervals that make up the major triad. So for example, at the left, on C3, we see the three intervals that occur in the major triad C3-E3-G3. The M3 (C3-E3) is red; the fifth (C3-G3) is blue; the m3 (E3-G3) is green. The numbers overlaid over the bars represent the beats of the major and minor thirds. The beats of the fifths are not on the chart but can be found in the data section below the chart.
    Feel free to ask any questions.


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    jason's cell 425 830 1561


    On Tue, Aug 14, 2018 at 10:15 AM, Roshan Kakiya via Piano Technicians Guild




    Original Message


  • 4.  RE: Roshan Kakiya's Practical Just Intonation (Alternative Tritone)

    Member
    Posted 08-15-2018 15:02
    I should note that the CMaj triad at the left only shows two components, the M3 and the m3; the C-G blue fifth does not show because it is a perfect fifth, therefore set at zero cents and therefore invisible.
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    jason's cell 425 830 1561


    On Wed, Aug 15, 2018 at 11:58 AM, Jason Kanter <jkanter@rollingball.com> wrote:
    Here are the rollingball.com images of Roshan Kakiya's two versions of this "just intonation."
    First: the "Just" version without the later modified tritone. It is basically a reverse well, its mildest M3 at A-C#, and its two full Pythagorean thirds on Bb and F. It has six perfect fifths and the waste gathered into the other six fifths, the narrowest at -5.35 cents:


    Second, the "alternate tritone" version. The F# has been flattened by about 3.5 cents. 
    You can see that in effect it is still a "reverse well". The mildest M3s are A and F#; the noisiest (full Pythagorean M3) are Bb and F.
    A bit irregular. This has seven perfect fifths, with the waste gathered into the fifths on A, E, F# (6 cents narrowed), Ab and Eb:


    Note about these charts: the methodology is explained on rollingball.com. The colored bars represent the widths (in cents) of the intervals that make up the major triad. So for example, at the left, on C3, we see the three intervals that occur in the major triad C3-E3-G3. The M3 (C3-E3) is red; the fifth (C3-G3) is blue; the m3 (E3-G3) is green. The numbers overlaid over the bars represent the beats of the major and minor thirds. The beats of the fifths are not on the chart but can be found in the data section below the chart.
    Feel free to ask any questions.


    | || ||| || ||| || ||| || ||| || ||| || ||| || |||
    jason's cell 425 830 1561


    On Tue, Aug 14, 2018 at 10:15 AM, Roshan Kakiya via Piano Technicians Guild





    Original Message