Re: New Topic: Music Idiosyncracy

ESchluessel · Tue, 25 Apr 2000 07:24:07 -0700

Time now for an important divergence: the
Harmonic Series. The human ear in geneneral defines "good"
harmony (the technical word is 'consonant') as
constructive interference with a minimum of 'beating.' Beating
is the audible change in amplitude caused by two
pitches which are close but not exactly identical, which
occurs such that Frequency of Beat = Frequency of Source
1 - Frequency of Souce 2. The harmonic series is
that series of tones, produced naturally, which will
not interfere with one another as is defined as a
base frequency and all integer multiples of that
frequency. Make note of this list:
1st harmonic = tonic
(= C for our purposes)
2nd " " = octave
(C')
3rd " " = 8ve and a perfect 5th (G')
4th = 2
octaves (C'')
5th = 2 octaves and a major 3rd
(E'')
6th = 2 x 3rd = 2 octaves and a 5th (G'')
7th = 2
8ves and a minor 7th (Bb'')
8th = 3 8ves
(C''')
9th = 3 8ves and a major 2nd (D''')
10th = 2 x 5th
= 3 8ves and a major 3rd (E''')
11th = 3 8ves
and a tritone (F#''' or Gb''')
And so on to
infinity.

You will of course note that in the Harmonic Series,
all enharmonics come out as being the same. To return
to the discussion of odd-temperament,
then:

In an odd-tempered scale, all the 5ths are perfect,
and therefore consonant. No other interval is.
Furthermore, the degree of the discrepancy of notes, relative
to the tonic of the scale, varies from scale to
scale. In short, every key sounds different, and has a
different harmonic flavor. Classical composers, being
basically mystics at heart, ascribed each key a different
emotion; the enharmonic keys Gb and F#, Db and C#, etc.
were, since they were obtained by different series of
derivations.

Then J.S.Bach messes this whole intricately-structured
system up with "The Well-Tempered
Clavier."

Even-tempering is much easier; select a frequency, and then
define notes as Pitch = base frequency x 2^(n/12) where
n is the number of half-steps above the base
frequency. The advantage to this system is that all pieces
sound the same in all keys. The disadvantage, of
course, is that every interval deviates from the harmonic
series, and therefore from perfect consonance, including
the hallowed Perfect 5th.

If anyone should
feel like turning their computers into a little teeny
synthesizer, the recognized base pitch in the United States
and Canada is A = 440Hz. In Europe, it's A =
445Hz.

Oh, and one last thing: Just temperament is a tuning
such that all the intervals are perfect relative to a
tonic. Those ratios, if you're interested, are (from
memory, so may be sketchy)
C = 1
C# =
D =
9/8
Eb = 6/5
E = 5/4
F = 4/3
F#= 11/8
G =
3/2
Ab = 8/5
A = 5/3
Bb = 16/9
B = 
C' =
2
(The ratios for the m9 and M7 have slipped my mind and
I don't feel like deriving them)

To get to
the question of why Matt Bruce likes Ab better, then,
I present three possibilities:
1. The key of
Ab's unique series of intervals is, as the classicists
viewed it, associated with boisterous happiness
2.
Mr. Bruce listens to a lot of composers who, when
they came up with a boisterous, happy melody, wrote it
in Ab because they believed in reason 1
3. The
pitch Ab or one of its overtones resonates pleasantly
with the empty spaces in Mr. Bruce's
head.

Edmund