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Ranking Intervals by LCM of Ratio's Numbers, Harmonic Entropy and Consonance

  • 1.  Ranking Intervals by LCM of Ratio's Numbers, Harmonic Entropy and Consonance

    Posted 20 days ago
    Edited by Roshan Kakiya 17 days ago
      |   view attached

    Ranking Intervals by LCM of Ratio's Numbers + Harmonic Entropy + Consonance


    Compare the rankings below with the following chart on Harmonic Entropy



    Source: http://tonalsoft.com/enc/h/harmonic-entropy.aspx



    Rank Ratio Number 1 Number 2 LCM Number 1 + Number 2 + LCM
    1 1/1 1 1 1 3
    2 2/1 2 1 2 5
    3 3/1 3 1 3 7
    4 4/1 4 1 4 9
    5 3/2 3 2 6 11
    6 5/2 5 2 10 17
    7 4/3 4 3 12 19
    8 7/2 7 2 14 23
    9 5/3 5 3 15 23
    10 5/4 5 4 20 29
    11 7/3 7 3 21 31
    12 8/3 8 3 24 35
    13 7/4 7 4 28 39
    14 6/5 6 5 30 41
    15 10/3 10 3 30 43
    16 11/3 11 3 33 47
    17 7/5 7 5 35 47
    18 9/4 9 4 36 49
    19 8/5 8 5 40 53
    20 7/6 7 6 42 55
    21 11/4 11 4 44 59
    22 9/5 9 5 45 59
    23 13/4 13 4 52 69
    24 11/5 11 5 55 71
    25 8/7 8 7 56 71
    26 12/5 12 5 60 77
    27 15/4 15 4 60 79
    28 9/7 9 7 63 79
    29 13/5 13 5 65 83
    30 11/6 11 6 66 83
    31 10/7 10 7 70 87
    32 14/5 14 5 70 89



    Compare the rankings below with the following chart on Consonance



    Source: http://www.huygens-fokker.org/bpsite/consonance.html



    Rank Ratio Number 1 Number 2 LCM Number 1 + Number 2 + LCM
    1 1/1 1 1 1 3
    2 2/1 2 1 2 5
    3 3/1 3 1 3 7
    4 3/2 3 2 6 11
    5 5/2 5 2 10 17
    6 4/3 4 3 12 19
    7 5/3 5 3 15 23
    8 5/4 5 4 20 29
    9 7/3 7 3 21 31
    10 8/3 8 3 24 35
    11 7/4 7 4 28 39
    12 6/5 6 5 30 41
    13 7/5 7 5 35 47
    14 9/4 9 4 36 49
    15 8/5 8 5 40 53
    16 7/6 7 6 42 55
    17 11/4 11 4 44 59
    18 9/5 9 5 45 59
    19 11/5 11 5 55 71
    20 9/7 9 7 63 79


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    Roshan Kakiya
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  • 2.  RE: Ranking Intervals by LCM of Ratio's Numbers, Harmonic Entropy and Consonance

    Posted 18 days ago
    Edited by Roshan Kakiya 17 days ago
      |   view attached
    I have attached an updated Excel file to this post. I have also updated both of the tables in my original post in accordance with the details mentioned below.

    The following column has been added to both of the tables:

    • A column for Number 1 + Number 2 + LCM. This column can be used to rank the ratios that have the same LCM. For example, LCM = 30 for 6/5 and 10/3, LCM = 60 for 12/5 and 15/4 and LCM = 70 for 10/7 and 14/5.

    ------------------------------
    Roshan Kakiya
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  • 3.  RE: Ranking Intervals by LCM of Ratio's Numbers, Harmonic Entropy and Consonance

    Posted 17 days ago
    Edited by Roshan Kakiya 17 days ago

    Equations for LCM of Ratio's Numbers Ranking System


    Ratio = Number 1 / Number 2.

    Each Ratio must be reduced to its simplest form. For example, 4/2 must be reduced to 2/1.


    LCM = Number 1 × Number 2.

    LCM stands for Lowest Common Multiple. For example, the LCM of 3 and 2 is 6. The lower the LCM, the higher the rank of the Ratio.


    If LCM = LCM, use Number 1 + Number 2 + LCM.

    Some Ratios have the same LCM. For example, 6/5 and 10/3 have the same LCM because the LCM of 6 and 5 is 30 and the LCM of 10 and 3 is 30. Therefore, 6/5 and 10/3 cannot be ranked by LCM so they must be ranked by Number 1 + Number 2 + LCM instead. The lower the result of Number 1 + Number 2 + LCM, the higher the rank of the Ratio.


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    Roshan Kakiya
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