source file: mills3.txt


Subject:  Kopie von: harmonic metrics

From:  DJWOLF_MATERIAL@compuserve.com

---------- Weitergeleitete Nachricht ----------

Von:    Daniel Wolf, 106232.3266
An:     INTERNET:tuning@eartha.mills.edu, INTERNET:tuning@eartha.mills.ed=
u
Datum:  15.07.97 11:31

Betreff:Kopie von: harmonic metrics

Thanks to Carter Scholz for an excellent, focused posting. I agree
wholeheartedly that the greater the variety of metrics (among many other
tools), the more useful they will be for a greater variety of composers
with different sensibilities, be they innate, or cultivated.

Carter wrote:

<2) Non-integers/approximations.  Small-number-ratio metrics fail with
<irrationals.  E.g. 300001/200000 is much more "dissonant" than 3/2;
<indeed, the closer the approximation, the more distant it's ranked by
<any small-number metric.  The ear has a much more adaptable threshold. =

<Some metric that describes near-misses could be quite useful.  (Again,
<by incorporating critical bandwidth, Sethares's metric avoids this
<particular pitfall.  Tenney alludes to, but does not incorporate, a
<"tolerance range" in his harmonic distance metric.)

Closely related to this - and to the question of making the graphs octave=

equivalent or not - is the inclusion of raw interval size, independent of=

its factorization. Since my own orientation as a musician includes a stro=
ng
vocal sensibility, there is a real sense that the larger the interval, th=
e
greater the effort to produce it, thus sometimes reducing or neutralizing=

the effect of harmonic distance when derived from factoring alone. =


I can well imagine harmonic situations where 5/3 and 15/8 represents
equivalent levels of harmonic distance from a given tonic, both
horizontally and vertically, but singing these intervals melodically will=
,
in most cases, override the equivalence. =



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