Octave Tuning

[David Ilvedson]

What is the test for a perfect 12th?

David I.



----- Original message ---------------------------------------->
From: Richard Brekne <Richard.Brekne@grieg.uib.no>
To: Pianotech <pianotech@ptg.org>
Received: Thu, 23 Sep 2004 09:25:51 +0100
Subject: Re: Octave Tuning

>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

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