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

[Mike Spalding]

Matthew,

First, praise and encouragement.  Keep on studying and practicing, you 
won't regret it.

Next, let me suggest some additional reference sources:  "On Pitch" by 
Rick Baldassin, available from the PTG store, also available as a series 
of articles in the '79 to '99 CD of old Journals.   The Tuning Exam 
Source Book, available from the PTG store.  Go to a convention and take 
a class from Jack Stebbins.  And there is a series of articles in the 
Journal this summer that explains these concepts quite well.

Now to answer your question:  To verify / refine a 4:2 octave, you use a 
test note which makes a beating interval with each note of the octave.  
Further, the test note must have only ONE coincident partial with each 
note of the octave, and it must coincide with the 4th partial of the 
lower note, and the 2nd partial of the upper note.   The  best test note 
for 4:2 octaves is a Major 3rd below the lower note.  For A3 - A4, the 
test note is F3.  Its 5th partial is A5, coinciding with the 4th partial 
of A3 and the 2nd of A4.  When the F3-A3 3rd beats the same as the F3-A4 
10th, you have a pure 4:2 octave from A3 to A4.  This is the Third-Tenth 
test for a 4:2 octave.  (Note:  most pianos want a wide 4:2 at A3-A4).

Similarly, for 6:3 use a minor third above the lower note.  Its 5th 
partial coincides with the 6th of the lower and the 3rd of the upper.   
For 2:1 use a tenth below the lower note.

hope this helps


Matthew Todd wrote:
> 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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