Inharmonicity other than n^2

[Richard Moody]

Since no one responded to Robert Scott's suggestion of using a value other
than n^2, (the square of the partial number) I would like to ask for a
little clarification of the information below.

"instead of n^2, the
| following lookup table:
|
| n C[n] (instead of n^2)
|      --------------
| 1 1.000
| 2 4.000
| 3 8.450
............."

The line that says n C[n]   ,   I wonder what the letters mean.   [n] ,   I
take to mean to use the values you give instead of n^2.   For example for
the 3rd partial, instead of 3^2 or 9, you give 8.450.  However  "n C"  of
n C[n]   I don't understand.  Could you elucidate?

I enjoyed reading the original pubublications of the experments
inhnarmonicity.  I am looking forward to reading about modern experiments
with modern machines.
---ric











`
----- Original Message -----
From: Robert Scott <rscott@wwnet.net>
To: <caut@ptg.org>
Sent: Thursday, February 14, 2002 11:04 AM
Subject: RE: frequencies


| In answer to Richard's question, Denis Brassard writes:
|
|  >>>>>
| One equation used to find the frequency of a note is the following:
|
| I took the next 2 formulas  from Dr. Albert Sanderson:
|
| (1.b)     I=Bn^2
| B is the inharmonicity constant and n is the partial number.
| <<<<<
|
|  From my own empirical studies, I have found that the n^2 term
| in the equation for inharmonicity does not agree with
| actual measurements.  I suggest using, instead of n^2, the
| following lookup table:
|
| n C[n] (instead of n^2)
|      --------------
| 1 1.000
| 2 4.000
| 3 8.450
| 4 13.18
| 5 19.72
| 6 27.27
| 7 35.53
| 8 46.25
| 9 57.12
| 10 69.43
| 11 83.22
| 12 96.60
| 13 109.8
| 14 125.4
| 15 139.5
| 16 156.1
|
| This is, in fact, what is used by TuneLab Pro and TuneLab Pocket.
|
| -Robert Scott
|   Real-Time Specialties
|