Table: A Justly-Tuned Guitar

Table: Guitar Frets. Each column represents a string (in open tuning); each line represents a fret. The ratios give the tone at that fret on that string.

    1/1        3/2        1/1        5/4        3/2        1/1    

   33/32      99/64      33/32     165/128     99/64      33/32   

   21/20      63/40      21/20      21/16      63/40      21/20   

   16/15       8/5       16/15       4/3        8/5       16/15   

   13/12      13/8       13/12      65/48      13/8       13/12   

   11/10      33/20      11/10      11/8       33/20      11/10   

   10/9        5/3       10/9       25/18       5/3       10/9    

    9/8       27/16       9/8       45/32      27/16       9/8    

    8/7       12/7        8/7       10/7       12/7        8/7    

    7/6        7/4        7/6       35/24       7/4        7/6    

   32/27      16/9       32/27      40/27      16/9       32/27   

    6/5        9/5        6/5        3/2        9/5        6/5    

   11/9       11/6       11/9       55/36      11/6       11/9    

    5/4       15/8        5/4       25/16      15/8        5/4    

   81/64     243/128     81/64     405/256    243/128     81/64   

    9/7       27/14       9/7       45/28      27/14       9/7    

   21/16      63/32      21/16     105/64      63/32      21/16   

    4/3        1/1        4/3        5/3        1/1        4/3    

   27/20      81/80      27/20      27/16      81/80      27/20   

   11/8       33/32      11/8       55/32      33/32      11/8    

    7/5       21/20       7/5        7/4       21/20       7/5    

   10/7       15/14      10/7       25/14      15/14      10/7    

   13/9       13/12      13/9       65/36      13/12      13/9    

    3/2        9/8        3/2       15/8        9/8        3/2    

   32/21       8/7       32/21      40/21       8/7       32/21   

   14/9        7/6       14/9       35/18       7/6       14/9    

   11/7       33/28      11/7       55/28      33/28      11/7    

    8/5        6/5        8/5        1/1        6/5        8/5    

   13/8       39/32      13/8       65/64      39/32      13/8    

    5/3        5/4        5/3       25/24       5/4        5/3    

   27/16      81/64      27/16     135/128     81/64      27/16   

   12/7        9/7       12/7       15/14       9/7       12/7    

    7/4       21/16       7/4       35/32      21/16       7/4    

   16/9        4/3       16/9       10/9        4/3       16/9    

    9/5       27/20       9/5        9/8       27/20       9/5    

   11/6       11/8       11/6       55/48      11/8       11/6    

   15/8       45/32      15/8       75/64      45/32      15/8    

   40/21      10/7       40/21      25/21      10/7       40/21   

    1/1        3/2        1/1        5/4        3/2        1/1    

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David Canright -- DCanright@NPS.edu