RESULTS of chord-grammar test

[Martin Braun <nombraun@xxxxxxxxxxxxxxx>]

Before the results, you'll see the test again.
After the results, you'll see by whom, when and where the piece was written.
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THE TEST (as mailed to this list on 2001-4-29):

A piece, which is well known and appreciated in many parts of the world, has
the following sequence of chords in its final 10 bars:

1) D-A-C
2) D-F
3) G-minor
4) C-Eb
5) D-major
6) G-D-Bb-A
7) G-minor
8) D-major
9) G-D-A-Bb
10) G-minor
11) D-major
12) G-A-D-Bb
13) G-minor
14) D-major
15) G-minor
16) G-E-C#-B
17) D-major
18) D-major
19) D-F#-A-E
20) D-major
21) D-major
22) D-major

Questions of the test:

A) Which syntactical expectations could be SATISFIED by this chord sequence?

B) Which syntactical expectations could be VIOLATED by this chord sequence?

C) Can you guess from the chord sequence which musical style this piece
belongs to and at which time about it may have been written?
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RESULTS (as mailed to me on 2001-4-30):

1) Any syntax of chords is associated with style - therefore you cannot
answer  A) and B) without knowing the style of the music.
2) The harmonic repertoire consists in essence of these chords (number of
times in parenthesis):
- G minor,  line 3,7,10,13,15 (n = 5)
- G minor add 9, line 6,9,12 (n = 3)
- D minor omit 5, line 2 (n = 1)
- D major, line 5,8,11,14,17,18,20,21,22 (n = 9)
- D major add 9, line 19 (n = 1)
- D 7 omit 3, line 1 (n = 1)
- C# minor 7 b5, line 16 (n = 1)

To recapitulate; there are 8 G minor chords, 10 D major chords, 1 D minor
chord, a D7 chord omit 3 and a
C# minor 7 b5 which functions as V of V (V9 omit 1).
I = 8
V = 12
V of V = 1
(Granted that the melody line is incorporated into the description of tones
that Braun presented). ["Yes, of course it is." Martin Braun]

The progression is circular. There is one modulation.

The chords and the sequence in which they appear could be from a number of
styles. The problem is that you cannot for certain exclude a style because
this could be an untypical example of that style. This could have been made
in the romantic period, but "as a rule" (defined earlier in this discussion)
the harmonic progressions in the romantic period is often characterized as
linear. The modulation point sounds rather "romantic" though. This could
also have been a song by Mariah Carey whose music often employs a kind of
simplified romantic harmony. It could even be a song by Grieg.
This can be a typical or an untypical piece, regarding its harmony, of the
style it represents.
The thing is that a piece of music - as a multidimensional object -
compensates for its untypical parameters by employing parameters that are
prototypical to the style the composer associates with.

To sum up: the harmonic rules of a certain style is extracted from a vast
number of pieces in that style. These rules can be regarded as harmonic
schematas based on statistical occurrences. This means that no style can
provide a harmonic repertoire that is completely homogeneous - there will
always be "outliers" that muddles the picture. There is nowhere in the real
world where you find 100% conformity between objects and "rules".
This I don't know for sure, but maybe a statistical occurence between 50 and
100% is needed to consider some harmonic progression to be typical to a
style? Also, the more central the harmonic parameter is in a particular
style, the higher the statistical occurence of a specific harmonic
progression needs to be in a song in order for that song to be associated
with that style. If there is a style whose harmonic parameters are subdued
for the benefit of timbre or rhythm, I suspect that we might find very low
consistency in the harmonic parameters. The techno genre drum'n'bass could
employ all sorts of harmonic relations without distorting the stylistic
impression - this is because harmony is of minor importance in this genre.
This is not the case with the chorals of J.S. Bach.

As I see it, this test is not a test on the existence of syntax or rules in
harmony. It is rather a test on our knowledge of different harmonic rules in
different styles around the world. Many of these relations are still waiting
to be unveiled.

Odd Torleiv
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Odd Torleiv Furnes
Department of Musicology
University of Oslo
Norway
oddtf@imt.uio.no
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THE PIECE WAS:

Final 10 bars of the second movement of Anton Bruckner's Symphony No. 5.
It was written 1875-1878 in Austria, and it has been an international
success right from the first performance 1894 until today.

The Symphony No. 5 is often regarded as Bruckner's best symphony.

I should add that I picked this piece at random. The finale of this movement
was all that I looked at. I did NOT search for anything particularly
uncommon or strange.
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Martin