octave partials

Ron Koval drwoodwind@hotmail.com
Wed, 28 May 2003 16:36:12 +0000


Looking back at what David asked:
<<<<<<<
So my question is, for example when tuning an F octave what is
the distinction between 4:2, and say a 6:3 octave tuning?
I have searched the archives, and reviewed my potter course manual, and
still a little confused!
Thanks in advance!!
David West
Roscoe , IL.
>>>>>>>>>>>


Hi David, welcome to the list.  I'm wondering if you meant what is the 
resulting cents difference in a tuning calculated using the differing 
partials?  If so, I just did a little experiment.  I used A4,A3,A2 and A1.  
A4 will always have the first partial set to 0 cents, or A 440.  Here is  
how a full upright (Thompson) matching of the octaves looks: (A4 and A3, use 
first partial, A2 use 2nd partial, A1 use 3rd partial... no I don't use 
these for tuning, I just wanted to use those for this example)

A4____0
A3___-1.65
A2___-2.82
A1___-8.52

This gives a pleasing matching of the octaves and double octaves.
Now, here is the same piano with strict 4:2 octaves going down from A4

A4____0
A3___-1.29
A2___-1.41
A1___-4.22

And the same piano with a strict 6:3 tuning

A4____0
A3___-1.96
A2___-3.44
A1___-11.82

Here is the same experiment on a 9' Steinway D
"normal"
A4____0
A3___-2.09
A2___-2.05
A1___-5.33

4:2
A4____0
A3___-.60
A2___-1.07
A1___-5.94

6:3
A4____0
A3___-2.12
A2___-3.66
A1___-7.08

And just to show the unpredictability of the partials in a smaller piano, 
here is a Kimball spinet.  Notice on all the previous examples, the lower 
notes are tuned in negative values to stretch the octave so it appears 
"beatless".  Look at the values for A3-A2 on this piano!  A 6:3 matching 
produces a narrower octave than a 4:2........

normal (if there is such a thing on these)
A4____0
A3___1.21
A2___-2.01
A1___-9.88

4:2
A4____0
A3___1.21
A2___-2.26
A1___-6.49

6:3
A4____0
A3___2.22
A2___-.92
A1___-7.99


Help any?

Ron Koval
Chicagoland

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