Tuning Curves

Richard Brekne Richard.Brekne@grieg.uib.no
Fri, 10 May 2002 23:06:31 +0200


Ok... so there was a big mistake in this.... actually I have been tuning by
taking the 3rd of D3 and A4 and useing those offsets to set that octave 5th,
and then repeating the process for the  3rd of A4 and E6. I assumed that
this was going to be the same as just taking the offsets for D3 and E6 and
setting the whole area at once... but nooooooo no no no...

What essentially is happening is that in an octave 5th Tune Lab figures the
exact relationship between the two notes... (something in excess of 3 to 1 )
and then takes the 19th root of that quotient. Then starting with the lowest
note in the range it just multiplies that result times the each successive
frequency to give you the offsets. But if you do this from E6 to D3 which
then is like the 38th root of a roughly 9 to 1 relationship then you end up
with a totally different picture. For example A4's 3rd changes from about 5
cents offset to about 14 cents. Of course this makes for a pretty wild
tuning...grin... so you have to take each section for itself.

What I am not clear on here is why there is such a big difference here... I
mean spliting an octave into 12 evenly spaced segments or spliting 3 octaves
into evenly spaced turns out not to be the same...  like the distance
between intervals then simply has to fit into an exponetial
curve........ok... so we sort of already know this... but..... so why do we
use a linear equation to define the ET temperament ?? as in Cents ??

If I tune an octave (with any given partial) slavically with this linear way
of dividing up any given actual octave... then what the heck does that do to
all the other partial relationships....they want to increase exponetially
... beat rates are going to get out of wack this way or what ???..

Grin... maybe I am thinking too much.

--
Richard Brekne
RPT, N.P.T.F.
Bergen, Norway
mailto:rbrekne@broadpark.no
http://home.broadpark.no/~rbrekne/ricmain.html




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