2:1, 4:2, 6:3 octaves

[Matthew Todd]

Thank you Gene!
   
  Very useful info.

Gene Nelson <nelsong at pbic.net> wrote:
          Hi Todd,
  The discription of the octaves speak for themselfs. In the 4:2 example the 4th partial of the lower note coincides with the 2nd partial of the upper note. Same explaination for 2:1 and 6:3
  I think I would say yes, the 4:2 dominates in the temperament area as well as just above and below it slightly.
  The way I tune the 4:2 octave is first by tuning the octave close - getting it to sound beatless - I am not focusing my hearing at this time on any particular partial. Then I use the 3rd 10th test (this is the test for the 4:2 octave) the third should beat equal to the 10th.
  Next I like to listen to the 2:1 and 6:3 octave tests for greater confirmation. 
  If I have tuned f3 to f4 and the 3rd 10th tests about equal beating then I listen to the 10th 17th (2:1 octave test). If the octave that I just tuned is correct at 4:2 then the 2:1 should test wide - the 10th should be slower than the 17th.
  Also I will listen to the 6:3 which is the minor 3rd major 6th test. This test should have the minor 3rd beating faster than the major 6th. The 6:3 should test narrow.
  So - at f3-f4 I have set the octave to get it beatless, tuned a 4:2 and used the 4:2 test - if it is correct the 2:1 partials of f3-f4 octave are wide and the 6:3 partials of f3-f4 octave are norrow - you cannot go wrong.
  One thing that you can experiment with while tuning f3-f4 is to widen the octave so that the 6:3 minor 3rd-major 6th tests equal beating and listen to the octave. Does it sound good or bad. Do the same thing with f3-f4 but now tune the 2:1 partials so that the 10th 17th are equal beating. Does it sound good or bad?
  Gene Nelson
    ----- Original Message ----- 
  From: Matthew Todd 
  To: pianotech at ptg.org 
  Sent: Tuesday, August 21, 2007 8:11 PM
  Subject: 2:1, 4:2, 6:3 octaves
  

  I have been really, really studying tonight.
   
  Can someone please explain the system they use to tune 2:1, 4:2 and 6:3 octaves.  I am so close to grasping this concept, but I think I need another tech to explain it to me besides Reblitz.
   
  In the octave interval, if I were to tune a 4:2, the fourth partial of the lower note theoretically has the same frequency as the 2nd partial of the upper note.  Do those partials normally dominate each octave?  How can I tell whether to tune a 4:2 or a 6:3?
   
  Oh, and lets leave inharmonicity for another post.  I am just trying to grasp this main theoretical concept.
   
  Thank you!
Matthew
    
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