Hi Richard: You are right that I was measuring something beside inharmonicity when I measured 2.1 cents at the fundamental or 1st partial. I could have simply tuned the fundamental to 0.0 cents before taking the measurements, then all of the other partials would have been 2.1 cents less. I didn't bother. I thought it would be so obvious. Isn't it a strange thing that not every thing which is obvious to me is not obvious to others and vice versa? It could be a lot worse if we were communicating in different languages. If I had tuned the note first, it would not have made any difference in the straight line graph when plotted cents VS partial number squared. If I may further answer Richard Moody's question about the 8th partial, the 20.2 cents shows inharmonicity of 18.1 sharp of the fundamental raised 3 octaves. The normal usage of the word inharmonicity applies only to the amount which a partial deviates from a true harmonic for which we have formulas that figure in the stiffness factor of a string. Whatever deviates from this is now referred to as para-inharmonicity. We could have called it a non-conformity (a term used in Geology) e.g. it doesn't fit our theory. To date, there are no formulas for para-inharmonicity. We don't know enough about it yet. Obviously (at least to me), known para-inharmonicity exists. We speculate on its causes, as I have already done in previous emails. We can definitely see its affects upon our measurements which lack exponential evenness. What can we do about it? Very little without upsetting other normal things about a string in our tuning process. If it affects the tuning of a simple 2-1 type octave, our adjusting because of it would throw out other relationships. When we tune by ear, we tend to make the best compromise we can. In tuning with machine, we can minimize this problem by tuning by higher partials which are less affected by para-inharmonicity. If we give total attention to lower partials which exhibit para-inharmonicity, we do so at the expense of throwing out many other relationships. The second definition of inharmonicity which you cited has nothing to do with inharmonicity. This is just conversion factors which are needed when translating readings taken with an equal tempered machine. It was through the use of this type machine that inharmonicity was discovered in the first place. Jim Coleman, Sr. On Sun, 23 May 1999, Richard Brekne wrote: > > > Richard Moody wrote: > > > Hi Jim > > I wanted to ask you but held off, thinking it would come up. You > > mentioned.... > > > > > the cents deviations of actual octavely related partials taken from > > > my Steinway L, note C4. > > > > > > 1st partial 2nd partial 4th partial 8th partial > > > > > > 2.1 2.8 6.2 20.2 in Cents > > > > > > > If I read it right does it say the first partial has a "cents deviation" > > of 2.1 ? > > > > I can't figure out how the fundamental (commonly called the first partial) > > can deviate by more than 0.0 cents let alone 2.1. > > > > I get the idea that this must be 2.1 cents deviation in relation to the ET > theoretical value for that fundemental. In which case one is measuring here > something more then simple string inharmonicity. At least thats the only way it > makes sense to me. > > I get the feeling that the term inharmonicity is a bit loosely used. We have at > least three seperate things we refer to with this word. String Inharmonicity, > Inharmonicity with relation to ET, and finnally Para Inharmonicity which no one > seems to be quite sure what the causes are. In this last case I have a hard time > accepting that it should figure into definition for string inharmonicity as it may > turn out that it has nothing to do with strings at all. Just a thought > > Richard Brekne > >
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