[CAUT] P-12ths was: Tuning a Steinway D and aBosendorfer Imperial together

[Richard Brekne]

Hi Dave... I did tho perhaps I should have been a bit more clear about 
it.. My point was that in not looking at what the actual difference 
between the 12th root of 2 and the 19th root of three you miss the 
practical results that end up differing. Ok.. a 1/3 of a bps in a 2:1 
octave is not so much... but if you apply the same math to more relevant 
frequency ranges and more relevant intervals you begin to see rather 
larger bps rates. This all actually does translate one way or another 
into beat rates we actually do hear differences in... which is why I 
suppose many of us actually end up liking the 3:1 approach.  I'd say in 
the end you probably end up tuning to quite a bit more close to the 
<<maths>> accuracies  then perhaps you give yourself credit for.

Then the other part of how this all ends up translating into audible 
(which directly implies controllable) frequency relationships is the 
overall effect the whole arrangement imparts to the instrument. This 
should really not surprise anyone as we constantly discuss the different 
effects of octave stretches in both bass and treble. Sure... this can 
all be in the end re-analyzed in terms of an octave stretch... perhaps 
it might be an interesting exercise to do so.  It might shed some 
clearer light on why the  range from around f5 to f6  has a generally 
flatter curve in an octave priority scheme then a P-12ths scheme does 
while the P-12th usually ends up at the fairly well more conservatively 
stretched at the top.  Jim Coleman commented on this saying that the 
result was kind of like saying the tuning seemed like it had quite a bit 
more stretch then it really did.  He particularly liked that f5-f6 area. 

Cheers
RicB


    Read it all.  I said the 12th root of 2.0012 was 1.059516053 (or
    essentially the same as 19th root of 3) not 2.0.  I was pointing out
    the small difference in the 12th root of 2 and the 19th root of 3.
    Differences which are mathematically significant (if you're looking
    at decimals to the 5th digit) but insignificant if you're tuning real
    pianos with real inharmonicity with contemporary tools.  The pitch
    change from start to 4 seconds later is much wider than that.  When
    in the decay cycle are you measuring this to 5 digit accuracy? 
     
    I too am a 3:1 tuner and I like the sound I get tuning that way I just
    can't claim that kind of accuracy.

     

    dp