Cents vs Hertz, was HT query clari:

[pianoman]

Hi,
My point was if you change each note of the temperament by this solid
amount (say+2c) because of inharmonicity being different from note to note
it seems like this is another case where close is good enough and is still
superior to exact placement of ET?  The other way would be to calculate the
exact amount of difference rather than the same amount.  Do you not know
what I mean.  It is really hard to explain.

James Grebe
R.P.T. of the P.T.G. from St. Louis, MO. USA, Earth
Piano Service and Piano Periperals
pianoman@inlink.com            May I listen as well as I hear.

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> From: Jim Coleman, Sr. <pianotoo@imap2.asu.edu>
> To: pianoman <pianoman@inlink.com>
> Cc: pianotech@ptg.org
> Subject: Cents vs Hertz, was HT query
> Date: Monday, June 22, 1998 11:37 PM
> 
> Hi James:
> 
> Many of us have wondered the same thing. However, it simplifies when you 
> think of 2 cents as being a very small interval, just like a half step 
> is a small interval (just not so small). Now, 2 cents at the 10th partial
> WILL make more difference in Hertz than 2 cents at the fundamental. Just 
> like a half step at A440 fundamental makes a difference of a little over
> 26 Hertz, but a half step 2 octaves higher makes well over 100 Hertz
> difference. Remember, the Hertz doubles each octave starting with A0 at
> theoretically 27.5, the A1 at 55, then 110 then 220 then 440, then 880,
> then 1760, then 3520 for the A7.
> 
> Lets just think of A4=440. To get to 441, you must make almost 4 cents
> change. Therefore 1 cent equal approx. 1/4 Hertz. At 880 Hertz, if you
make
> a 1 cent change, it changes to approx. 880.5 or a half Hertz change.
That's
> twice the Hertz change that 1 cent makes at 440.
> 
> Therefore, we get better accuracy listening to higher partials than 
> listening to lower partials. We can get better accuracy tuning by 3rds
than
> by tuning by 5ths which use lower partial numbers. Trying to tune by
> pure 2:1 octaves gives the least accuracy, unless one listens only to
> fundamentals while tuning unisons (I always suggest listening to the 
> highest partials you can hear when tuning unisons). In tuning by higher
> partials, you get a micrometer adjustment on the fundamentals. I think
> the mud is clearing isn't it?
> 
> Jim Coleman, Sr.
> 
> On Mon, 22 Jun 1998, pianoman wrote:
> 
> > Hi ,
> > Just a point.  I read that the directions for setting up an HT over an
> > existing tuning is a process of altering the cents values of the
calculated
> > tuning by +2c, -2c, whatever.  Question is, since you are changing
whatever
> > partial the device is listening to , is that not changing the
fundamentals
> > placement more than the amount you are changing the tuning partials. 
Is
> > this as clear as mud or can you tell what I am saying?
> > James Grebe
> > R.P.T. of the P.T.G. from St. Louis, MO. USA, Earth
> > Piano Service and Piano Periperals
> > pianoman@inlink.com            May I listen as well as I hear.
> >