Octave Tuning

[Richard Brekne]

BobDavis88@aol.com wrote:

> In a message dated 9/22/2004 8:13:28 PM Pacific Standard Time, 
> pianotuna@accesscomm.ca writes:
>
>     the Accutuner site offers information on octave types here:
>
>     http://www.accu-tuner.com/SATIIImanual/aph.html
>
> Good, compact chart. However, be aware that the test listed for the 
> 4:2 is incorrect - it should be the 3rd-10th, not the 3rd-17th.


I think the idea there was that if you tune the 3rd-10th AND the 
3rd-17th such that both the 10th and 17th have the same beat rate speed 
as the 3rd... then you get a just 4:2:1 pair of octaves and double 
octave. The problem with this is that it doesnt yeild a good tuning if 
strictly employed all the way up, and is indeed impossible to executer 
to begin with.  You can try this with Tunelab by directly referencing 
the 4th partial of the lowest note of double octaves and tuning all 
octaves and double octaves directly to that.  You will find that as soon 
as you have progressed chromatically one whole octave and have reached 
your first already tuned single octave that things go astray.  You will 
need to retune the 4:2 that was previously a 2:1... but then that screws 
up what the origional 4:2:1 was...

Example... C3:C4:C5 get tuned as a perfect 4:2:1. Progress chromatically 
til you are addressing C4:C5:C6.  Now C4 and C5 are already tuned notes 
referenced to C3(4).  But now you want C4(4) = C5(2) = C6(1), which of 
course you cant have.  There is no natural way within the octave tuning 
perspective to deal with this problem, and we are told to just <<smooth 
out>> the difference... a vague and undefined concept at best.  ETDs 
approach the problem by simply spreading the whole treble range evenly 
based on ETD settings and partials information.  However... P 12ths 
tunings simply take care of the whole problem automatically, and a very 
smooth transition from 4:2 to 2:1s is accomplished quite naturally... in 
addition to providing a solid harmonic foundation of just coincidents 
for 12ths throughout the whole treble.

Indeed.. the P12ths concept completely eliminates the need (or 
desirablitiy) for generated tuning curves to begin with. It represents a 
natural <<built in>> "curve" that is very easily reference either 
aurally or with the help of an ETD used to reference already tuned notes. 

Cheers
RicB