Harmony and Rhythm

G'day all

One day I was thinking about low notes and made the connection between
rhythm and frequency. If we are in C and suppose C=256 Hz to make it
easy on the calculations, then we have more Cs at 128, 64, 32, 16, 8 etc
except that this is too low for hearing. However 8, 4, 2, 1 Hz are
equivalent to tempos of 480, 240, 120 and 60 bpm. So if a piece is
played in C at a tempo of 120 bpm then we can say that the tempo/rhythm
is IN TUNE with the key.

Because I have this idea that after every few octaves a fifth should be
thrown in, I consider that the frequency of the key note should be
either 2^n or 3*2^n times the tempo (when converted from bpm to Hz).
In either of these cases I would say that the composer got it right.

I had a look at a number of classical composers to see whether they did
this or not and found that the good composers generally did. Some of
the not so good ones didn't. Of course sometimes we are stuck with a
tempo in words and don't know the exact rate.

I had a look at a few modern composers. I like Billy Joel and he writes
definite things like 124 bpm and leaves you with no doubt. Well I
checked his pieces and they are in tune but there is a 2% to 2.5%
difference which would be removed if A=440 was changed to A=450.
So does anyone know whether he tunes his instruments to 450? That would
explain things. If not then I think that he is picking up the natural
earth frequencies and that A=450 is the natural rate.

If it can be accepted that having the tempo and key matching is a sign
of good music then it is also true that transpositions are not a good
practice. If you transpose a piece up by a third then to keep the
balance you would need to play it 25% faster and it would sound like the
chipmunks! Any chance of conveying (the right) emotions would be gone.

OK, so all shoot me down in flames again!

There is an article on WWW (link on my pages) about a similar idea.
That is, that chords slowed down become rhythm and that certain common
chords make common drum beats etc. For example, a fifth becomes:

Low note x x x x x
High note * * * * * * *

Result # * x * # * x * #

More complicated chords become more interesting beats.

-- Ray Tomes -- rtomes@kcbbs.gen.nz -- Harmonics Theory --
http://www.kcbbs.gen.nz/users/rtomes/rt-home.htm

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Andrew Milne wrote:

''If the 7th in a dominant 7th chord is tuned to 7/4, then it loses its
dissonance and instability. Indeed such a chord can function as a tonic
(as it does, quite exceptionally for the time, in Chopin's 22nd
Prelude).''

The category ''dissonance'' is, ultmately, contextual, and may not always
be the most useful arbitrator of musical functions. James Tenney's _A
History of Consonance and Dissonance_ is very useful in beginning to sort
out how variously such terms have been used.

The most striking characteristics of a dominant seventh chord within an
otherwise triadic environment are - for me - the density of the chord (a
triad contains three interval classes, a tetrad six) and the appearance of
a new (even ''xenharmonic'') interval. These features are enhancements of
the dominant/tonic voice leading relationship: root movement by fifth, and
stepwise ''resolution'' in the remaining voices. The introduction of a
raised third in the minor dominant illustrates the classical emphasis on
acoustical contrast between the chords. When a dominant seventh chord is
suspended for a classical cadenza, it suffers little when tuned as 4:5:6:7
and indeed, the stability of the chord enhances its contrast with the tonic
triad. On the other hand, the suspension of a 16/9 (or 9/5) as the seventh
introduces a tone dissonant to the rest of the chord, but not foreign to
the scale.

One often-raised objection to the septimal tuning is the narrow semitone
(21/20) voice leading from the seventh to the third of the tonic. I find
this line of argumentation more compelling, but the interval itself is not
difficult to sing - and if melodically ''strange'', it does maximize the
contrast function.

Readers might have some fun investigating the traditional rule of thumb for
the relative density of the chords in V7 - I cadences: In four voices, if
the voice leading is correct, then one of the two chords has to be
incomplete (that is with a doubled pc). (Why this should be so I will leave
as a kind of ''Puzzler'').

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-------------------- Begin Original Message --------------------

Message text written by INTERNET:tuning@ella.mills.edu

"The category ''dissonance'' is, ultmately, contextual, and may not always
be the most useful arbitrator of musical functions. "


-------------------- End Original Message --------------------

Bingo!

Dissonance is contextual. Discord is not. 4:5:6:7 is only mildly
discordant, but I for one find it capable of, and effective at, creating a
pull to a 4:5:6 in a V7-I progression.

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