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Ranking Intervals by (A+B) / AB: Analysis of Consonance and Harmonic Entropy Graphs

  • 1.  Ranking Intervals by (A+B) / AB: Analysis of Consonance and Harmonic Entropy Graphs

    Posted 01-06-2020 10:16
      |   view attached

    Ranking Intervals by (A+B) / AB: Analysis of Consonance and Harmonic Entropy Graphs


    Compare the rankings below with the following graph on Consonance



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



    Rank Ratio (A/B) A B (A+B) / AB
    1 1/1 1 1 2.000
    2 2/1 2 1 1.500
    3 3/1 3 1 1.333
    4 3/2 3 2 0.833
    5 5/2 5 2 0.700
    6 4/3 4 3 0.583
    7 5/3 5 3 0.533
    8 7/3 7 3 0.476
    9 8/3 8 3 0.458
    10 5/4 5 4 0.450
    11 7/4 7 4 0.393
    12 6/5 6 5 0.367
    13 9/4 9 4 0.361
    14 7/5 7 5 0.343
    15 11/4 11 4 0.341
    16 8/5 8 5 0.325
    17 9/5 9 5 0.311
    18 7/6 7 6 0.310
    19 11/5 11 5 0.291
    20 9/7 9 7 0.254



    Compare the rankings below with the following graph on Harmonic Entropy



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



    Rank Ratio (A/B) A B (A+B) / AB
    1 1/1 1 1 2.000
    2 2/1 2 1 1.500
    3 3/1 3 1 1.333
    4 4/1 4 1 1.250
    5 3/2 3 2 0.833
    6 5/2 5 2 0.700
    7 7/2 7 2 0.643
    8 4/3 4 3 0.583
    9 5/3 5 3 0.533
    10 7/3 7 3 0.476
    11 8/3 8 3 0.458
    12 5/4 5 4 0.450
    13 10/3 10 3 0.433
    14 11/3 11 3 0.424
    15 7/4 7 4 0.393
    16 6/5 6 5 0.367
    17 9/4 9 4 0.361
    18 7/5 7 5 0.343
    19 11/4 11 4 0.341
    20 13/4 13 4 0.327
    21 8/5 8 5 0.325
    22 15/4 15 4 0.317
    23 9/5 9 5 0.311
    24 7/6 7 6 0.310
    25 11/5 11 5 0.291
    26 12/5 12 5 0.283
    27 13/5 13 5 0.277
    28 14/5 14 5 0.271
    29 8/7 8 7 0.268
    30 11/6 11 6 0.258
    31 9/7 9 7 0.254
    32 10/7 10 7 0.243


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    Roshan Kakiya
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