The Seven Proportion   Melodic Proportions  
  Harmonic of the whole***   Intervals, as Fractions  
  Intervals as fractions   and the  
  and tones   tertiary unmelodic intervals  
     
  First (non interval) 1          Major Whole Tone 8/9  
  semi-tone *   Minor Whole Tone (24/25 + 15/16) 9/10  
  two tones combined (15/16)*+(8/9)**=5/6   Semi-Tone   15/16  
  major tone **    
  1. Minor Third 5/6   The Diesis almost ceases to be melodic  
  diesis 24/25    
  2. Major Third    4/5    Diesis (or "slackening of the string") 24/25  
  semi-tone 15/16    
  3. Diatessaron 3/4   The following are considered "unmelodic"  
  major tone 8/9   Major Diesis or Limma (8/9) / (15/16) 128/135  
  4. Diapente 2/3   Comma or (8/9) / (9/10) "common" 80/81  
  semi-tone 15/16   Double Comma (24/25) / (15/16) 125/128 or ~42/43  
  5. Minor Sixth 5/8   Triple Comma ( 42/43 + 80/81 ) 625/648 or ~27/28  
  diesis 24/25   Narrow Diesis (24/25 - 80/81) 243/250 or ~35/36  
  6. Major Sixth 3/5   Platonic Limma ( 15/16 * 80/81) 243/256 or  25/27  
  semi-tone *   Wide Semi-Tone ( 8/9 * 8/9)?? 64/81 ???  
  two tones combined (15/16)*+(8/9)**=5/6    
  major tone **   Platonic Apotome (128/135 * 80/81) 9.36442615454961E-01  
  7. Octave 1/2   two-thousand-forty-eight  
    over-  
  ***in this case the   two-thousand-one-hundred-eightyseven  
  tones are intervals    
  between the harmonic    
  intervals, not proportions    
  of the whole.