<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML><HEAD> <META http-equiv=Content-Type content="text/html; = charset=iso-8859-1"> <META content="MSHTML 6.00.2600.0" name=GENERATOR> <STYLE></STYLE> </HEAD> <BODY bgColor=#ffffff> <DIV> <DIV>Hi List,</DIV> <DIV> </DIV> <DIV>My exercise for the day is what is narrow and what is wide. (In = tuning of course)</DIV> <DIV> </DIV> <DIV>I have a Yamaha U1 Tuning Accuracy Graph in my possession so I = copied (roughly) the cents readings for all notes.</DIV> <DIV> </DIV> <DIV>Both narrow and wide measurements vary only below note 15 "B" and = above note 64 "C".</DIV> <DIV> </DIV> <DIV>From this one would assume that the narrowing and widening of a = piano should only happen above and below those notes.</DIV> <DIV> </DIV> <DIV>So with my trusty Tunelab Pro I set up a series of files set on = </DIV> <DIV>6:3 in the bass & 4:2 in the treble</DIV> <DIV>4:2 in the bass & 2:1 in the treble</DIV> <DIV>C1 on 6, C2 on 6, C3 on 4, C4 on 2 & 4:1 in the treble. When = setting scale use top scale only and set all C's on zero cents.</DIV> <DIV> </DIV> <DIV>The results are below.</DIV> <DIV>Personal preference of course but I find that the 6:3  4:2 is = to wide and the 4:2 2:1 is too narrow.</DIV> <DIV> </DIV> <DIV>Anybody wants the 3 Tunelab files I will send them privately.</DIV> <DIV> </DIV> <DIV>PS I did not include C1 or A0 inharmonicity  measurements as = if these measurements are included the inharmonicity of  the fundamental of = A0 will go down to -33 cents which is a bit flat.</DIV> <DIV> </DIV> <DIV> </DIV> <DIV>All are fundamental measurements.</DIV>   YAMAHA TUNING ACCURACY GRAPH & TUNELAB         &n= bsp;           &nb= sp;                       &nbs= p;           &nbsp= ;                    &nbs= p;                    &nbs= p;         GRAPH           &nbs= p;    PRO  TUNELAB = No.   Note     Narrow Wide  6:3 / 4:2  4:2 / 2:1 C'sLevel        &= nbsp;           &n= bsp;     1          A         -7         -12       -21       -11       -15 2          A#       -7         -11       -19       -10       -14 3          B          -6         -10       -18       -9         = -13 4          C         -5         -10       -16       -8         = -12 5          C#       -5         -9         -15       -8         = -11 6          D         -4         -8         -14       -7         = -10 7          D#       -4         -7         -13       -7         = -9 8          E          -3         -6         -12       -6         = -9 9          F          -3         -5         -11       -6         = -8 10        F#        -3         -4         -10       -6         = -7 11        G         -2         -4         -9         = -5         -7 12        G#       -2         -3         -9         = -5         -6 13        A         -2         -3         -8         = -5         -6 14        A#       -2         -3         -7         = -4         -6 15        B          -2         -3         -7         = -4         -5 16        C         -2         -2         -6         = -4         -5 17        C#       -2         -2         -6         = -4         -5 18        D         -1         -1         -6         = -3         -4 19        D#       -1         -1         -5         = -3         -4 20        E          -1         -1         -5         = -3         -4 21        F          -1         -1         -5         = -3         -4 22        F#        -1         -1         -4         = -3         -3 23        G         -1         -1         -4         = -3         -3 24        G#       -1         -1         -4         = -2         -3 25        A         -1         -1         -4         = -2         -3 26        A#       -1         -1         -3         = -2         -3 27        B          -1         -1         -3         = -2         -2 28        C         -1         -1         -3         = -2         -2 29        C#       -1         -1         -3         = -2         -2 30        D         0          0          -3         = -2         -2 31        D#       0          0          -2         = -2         -2 32        E          0          0          -2         = -2         -2 33        F          0          0          -2         = -2         -2 34        F#        0          0          -2         = -2         -2 35        G         0          0          -2         = -1         -2 36        G#       0          0          -2         = -1         -2 37        A         0          0          -2         = -1         -1 38        A#       0          0          -2         = -1         -1 39        B          0          0          -1         = -1         -1 40        C         0          0          -1         = -1         -1 41        C#       0          0          -1         = -1         -1 42        D         1          1          -1         = -1         -1 43        D#       1          1          -1         = -1         -1 44        E          1          1          -1         = -1         -1 45        F          1          1          -1         = -1         -1 46        F#        1          1          -1         = -1         -1 47        G         1          1          -1         = 0          0 48        G#       1          1          0          0          0 49        A         1          1          0          0          0 50        A#       2          2          0          0          0 51        B          2          2          0.5       0          0 52        C         2          2          0.5       0.5       0.5 53        C#       2          2          0.5       0.5       0.5 54        D         3          3          1          0.5       1 55        D#       3          3          1          1          1 56        E          3          3          1.5       1          1 57        F          4          4          1.5       1          1.5 58        F#        4          4          2          1.5       1.5 59        G         4          4          2          2          2 60        G#       5          5          2.5       2          2 61        A         5          5          3          2.5       2.5 62        A#       5          5          3          3          3 63        B          5          5          3.5       3          3 64        C         5          6          4          3.5       3.5 65        C#       5          6          5          4          4 66        D         6          6          5          4.5       4.5 67        D#       6          7          6          5          5 68        E          7          9          6.5       5.5       5.5 69        F          7          10        7          6          6.5 70        F#        8          10        8          7          7 71        G         8          11        9          7.5       8 72        G#       9          12        10        8.5       8.5 73        A         10        13        11        9.5       9.5 74        A#       12        14        12        10.5     10.5 75        B          13        15        13        11.5     11.5 76        C         15        17        14        12.5     13 77        C#       16        18        16        14        14 78        D         17        19        17        15        16 79        D#       18        20        19        17        17 80        E          20        23        21        18.5     19 81        F          22        25        23        20        21 82        F#        23        26        25        22        23 83        G         25        28        27        24.5     25 84        G#       27        30        30.5     27        28 85        A         29        34        33.5     29        30 86        A#       33        37        37        32        33 87        B          36        40        40        35.5     37 88        C         40        45        44        39        40<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" /><o:p></o:p></DIV></BODY></HTML>