Pianotech

  • 1.  Why does the Major 17th break the pattern?

    Posted 05-03-2019 19:32

    UPDATE


    https://my.ptg.org/communities/community-home/digestviewer/viewthread?GroupId=43&MessageKey=67b6d4f7-737f-451d-965e-5d2797234896&CommunityKey=6265a40b-9fd2-4152-a628-bd7c7d770cbf



    I was ranking the intervals of just intonation via the following ranking system (lowest common multiple of ratio's numbers):

    https://my.ptg.org/communities/community-home/digestviewer/viewthread?GroupId=43&MessageKey=82c96d81-b20a-41fb-93c8-12d8e0f06c60&CommunityKey=6265a40b-9fd2-4152-a628-bd7c7d770cbf

    However, this system breaks down for the Major 17th. I have shown how this system breaks down for the Major 17th in one of my replies to this discussion.


    Why does this ranking system break down for the Major 17th?


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    Roshan Kakiya
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  • 2.  RE: Why does the Major 17th break the pattern?

    Registered Piano Technician
    Posted 05-04-2019 09:04
    Probably because it's a false premise that harmonicity always increases as the LCM decreases.

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    Anthony Willey, RPT
    Willey Piano Tuning
    Easy Piano Tuner
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    Original Message


  • 3.  RE: Why does the Major 17th break the pattern?

    Posted 05-04-2019 15:48
      |   view attached

    Ranking Intervals by LCM of Ratio's Numbers, Harmonic Entropy and 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
    1 1/1 1 1 1
    2 2/1 2 1 2
    3 3/1 3 1 3
    4 4/1 4 1 4
    5 3/2 3 2 6
    6 5/2 5 2 10
    7 4/3 4 3 12
    8 7/2 7 2 14
    9 5/3 5 3 15
    10 5/4 5 4 20
    11 7/3 7 3 21
    12 8/3 8 3 24
    13 7/4 7 4 28
    14 6/5 6 5 30
    15 10/3 10 3 30
    16 11/3 11 3 33
    17 7/5 7 5 35
    18 9/4 9 4 36
    19 8/5 8 5 40
    20 7/6 7 6 42
    21 11/4 11 4 44
    22 9/5 9 5 45
    23 13/4 13 4 52
    24 11/5 11 5 55
    25 8/7 8 7 56
    26 12/5 12 5 60
    27 15/4 15 4 60
    28 9/7 9 7 63
    29 13/5 13 5 65
    30 11/6 11 6 66
    31 10/7 10 7 70
    32 14/5 14 5 70



    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
    1 1/1 1 1 1
    2 2/1 2 1 2
    3 3/1 3 1 3
    4 3/2 3 2 6
    5 5/2 5 2 10
    6 4/3 4 3 12
    7 5/3 5 3 15
    8 5/4 5 4 20
    9 7/3 7 3 21
    10 8/3 8 3 24
    11 7/4 7 4 28
    12 6/5 6 5 30
    13 7/5 7 5 35
    14 9/4 9 4 36
    15 8/5 8 5 40
    16 7/6 7 6 42
    17 11/4 11 4 44
    18 9/5 9 5 45
    19 11/5 11 5 55
    20 9/7 9 7 63


    ------------------------------
    Roshan Kakiya
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    Original Message