Harmonics & beats are better..(Paul E)

This message is a few days late due to a transmission hick-up.

Paul Erlich (via Manuel Op de Coul) wrote:

>Heinz Bohlen believes that difference tones to be the foundation of all
harmony.<

Close. More exact, however: Heinz Bohlen considers difference tones to be
just first order combination tones. So what he really believes is that
combination tones are the "foundation of all harmony" (thanks for that nice
expression, Paul!). And if he lives long enough he might one fine day be
going to prove it...
Slightly deviating from Paul E, and more in tune with Daniel Wolf, he also
believes that beats (like distant harmonics) add flavor to sounds (and thus
have "musical significance) but are of no harmonical importance.

(By the way, if somebody is interested enough in combination tones to try his
(her) German on Helmholtz, he (she) might find the following source even more
yielding regarding this specific issue: Husmann, H., Vom Wesen der Konsonanz.
Mueller-Thiergarten-Verlag, Heidelberg 1953.)

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The answer to Neal's question might depend on your view of the fundamentals
of mathematics. A strict finitist might very well not accept arbitrary
transposition downward, while most will be satisfied that transposing thefundmental downward until octave multiples of all the desired tones fall
within a given range is unobjectionable, even if the fundmental becomes so
low as to be a completely theoretical entity.

It is interesting to look at examples of systems where the octave is not
the basic building block but rather the fifth or another interval.
Classical harmonics used conjunct tetrachords and pentachords as well as
the octave-filling disjunct tetrachords. Xenakis suggested reviving this
technique. One way of hearing the three javanese slendro pathet is as
conjunct pentatonic tetrachords (each with four tones encompassing an
approximate acoustical fifth). A lot of melodies from very different
repertoires might be usefully analysed in these terms, where formal unitsare defined by the range of a fifth. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl
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>Those 5ths that we mathematically alter...we
>are not HEARING them in their proper place in the Universe. They are
>actually sounding at some frequency well beyond our hearing. So, just
>where are they, then?

You should not be distracted by the fact that these systems are
generally described relative to an original tonic, and the fact that the
notes you create in a stack of fifths would become ultrasonic quickly. The
point of using circles (spirals, whatever) of fifths to construct a tuning
is one of several means of lending consistency to a tuning system,
especially consistency across many keys. The point that matters is that a
tuning like meantone that is based upon a stack of fifths will always have
a consistent-sized fifth, which makes where you start unimportant.

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>It is interesting to look at examples of systems where the octave is not
>the basic building block but rather the fifth or another interval.

The 88CET system I keep droning on and on about is such a system, as is
Carlos' Alpha. 88CET has 8 steps per P5, and Alpha has 9 per P5. Bohlen's
13ET per P12 tuning obviously concentrates on twelfths instead.

At least when it comes to 88CET, I found value in considering stacks of
fifths wrapping within a 7:4, since those are two useful and very clearly
recognizable building blocks. Similarly, I found stacks of 9:7 supramajor,
and 11:9 neutral, thirds to form useful chord or chord-fragment building
blocks.

Or to put it another way, I have found stacks of many intervals to have
both harmonic and melodic meaning, whether or not we wrap them within an
octave or other interval, and regardless of what root pitch you build them
upon.

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