temperament

[Don]

Hi Martin,

I thought I would answer your private question on the listserv--so that
others might jump in to help explain:

Martin asked
>there are a several language problems.  could you explain what

>coincident partials 
>parials
>Inharmonicity 
>contiguous

Contiguous means that two intervals (usually thought of as the same size)
share a note in common.

For example these major thirds

f3 to a3 : a3 to c#4 : c#4 to f4

Partials:

Any note when played will sound at the fundimental and at other pitches
based on the 1/2 length, the 1/3 length, 1/4, etc.

so:

a1 a2 e3 a3 c#4 e4 etc.

coincident partials:

When you play two notes together their partial series will often match at a
higher partial than the fundimental. For example this major third has a
contigiuous partial at:

f3        f4     c4    f5   a5
     a3        a4     d5    a5

This means the beating will be heard at a5 for the f3 a3 major third which
corresponds to the ratio (rough numbers not totally accurate) 5:4 for a
major 3rd.

It is important to know the (rough) ratios of the various intervals. Unison
is 1:1; octave 2:1, fifth 3:2, fourth 4:3, major 3rd 5:4; major 6th 5:3 and
etc.
 

Inharmonicity is a factor that causes the harmonic series of a note to be
lower than the partial series. There seem to be more factors that affect
inharmonicity than might be expected. For example in theory a note might
have a harmonic series in hertz of:

100	200	300	400	500
But in real life it might be
100	201	305	416	535

And I wish I *could* explain inharmonicity fully--but so far no one has
been able to totally understand it *grin*. We just deal with it






Regards,
Don Rose, B.Mus., A.M.U.S., A.MUS., R.M.T., R.P.T.

Tuner for the Saskatchewan Centre of the Arts

mailto:drose@dlcwest.com
http://donrose.xoasis.com/

3004 Grant Rd.
REGINA, SK
S4S 5G7
306-352-3620 or 1-888-29t-uner