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

[Porritt, David]

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

 

 

David M. Porritt, RPT

dporritt at smu.edu

 

-----Original Message-----
From: caut-bounces at ptg.org [mailto:caut-bounces at ptg.org] On Behalf Of
Richard Brekne
Sent: Tuesday, October 14, 2008 6:08 PM
To: caut at ptg.org
Subject: [CAUT] P-12ths was: Tuning a Steinway D and aBosendorfer
Imperial together

 

David... Google has it different.

 

The 12th root of 2 is 1.05946309

The 19th root of 3 is 1.05952606

 

Which I think you will find are the correct figures.  If you take even a


low number like  220hz and multiply that out over an octave range by 

each value... you'll end up with a 3rd of a bps difference at 440.  Add 

in all the intervals we need to take consideration to its clear that 

imposing a P 12th system will yield a significantly different, that is 

to say discernible to the ear should one take the time to notice, 

result.  That said... given the famous temperament tests of a decade or 

more ago... I'll go along ways down any road with you that implies it 

doesnt make all that much difference.  At least not to most people and 

not all that consciously to most of those who on some level or another 

do "notice"

 

Fred... excellent post... I have to read it a couple times on the morrow


and reply.   But off hand I'd agree that we are very much more on the 

same page then not. Tho to be sure, and as is my wont, I differ here and


there :)  Late here... I'm 56 today... and off to bed

 

Cheers !

RicB

 

 

    Fred:

 

    The 12th root of 2.0012 is the equivalent of the 19th root of 3 to 4

    decimal places (1.059516053 rather than 1.059526065).

 

    dp

 

 

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