|
"Human Supervision and Control in Engineering and Music" |
| Workshop | Orchestra Concert | Ensemble Concert | About us |
Eva
Ferková
Dynamic Potential of Harmonic
Structures - The Way of Evaluation
Abstract
This
discussion contribution deals with some features and potentialities of
harmonic
structures in tonal music, that are inherent in music of 17th - 19th
century
and control feeling of ascending or descending of tension. We assume,
that
there is a way, how to enumerate experimentally this ability according
to
harmonic structures, development and relationships. The enumeration
enables the
computational procesing and graphical visualisation of the dynamical
motion and
evolution.
Some years
ago while cooperating with programmer Marian Dudek we have built up a
package
of computer programs for automatic analysis of classical music –
CACH
((1),(2), (3), (4)). Currently these programs are out of date because
of MS DOS
platform and because of non automatic input via note editor. The
musicological
question, if there is a convenient way of automatization of harmonic
analysis
and evaluation of dynamism of harmonic structures is still actual
and
open.
The situation in Slovakia
is permanent changing and it is not easy to do scientific research, and
it is
almost impossible to find programmer for cooperation (there is a
contradiction between best paid programmers and worst paid research
workers). According to this reality, we provide only meditation
or a
proposal how to find one of the possible ways to analyze harmony in
music by
computer and to find one alternative for enumeration of
tensional
changes and appropriate visualisation of development of this kind
of
tensional motion.
Harmony is the structural
quality of music, in which dynamics and tension or stress of
music
is inherent, especially in tonal music, which was dominant in Europa
through
three centuries (17th - 19th) and recently we could observe a new
comeback to
it. We suppose that the tension and stress of harmonic structures
in
tonal music is inherent and connected with listeners
feeling
in perception. This opinion confirms Nicolas Cook, too."At the
beginning
of the century, as indeed nowadays, it was harmony that was regarded as
the
most crucial aspect of musical content", ((6), p.16). We assume, that
content and tension of music are inseparable.
The measurment and
evaluation of tension in music therefore is not possible only by
acoustical
measurement of loudness or tempo (and eventually with ascending and
descending
of melody (8)), it is necessary to make harmonic analysis, too, and to
evaluate
the motion in harmony according to the structural direction and
development of
chords and according to their place in so called cadence (musical
instance – A. Dvo?ák, Symphony n.8 op.22, 1st Movement,
2´40´´)
It seems, that the
Schenkerian way of harmonic analysis (5), (6) doesn´t focus an
interest on a
fluctuation of stress, it´s oriented preliminary to find
"foreground", "middleground" and "background"
of the harmony by reduction of many chords, which are not so
important
for basic tonal key, which are only embalishing, or which are secondary
(lend
from other tonal keys) respectively which are connected more with
melody.
Listener is hearing
music from the beginning, and he doesn´t reduce no one chord in
his hearing.
Temporal stress is therefore not so important from the point of view of
Schenkerian analysis, but in progress of the full composition. In the
moment of
sounding, the tension, higher or lower, is brought by every chord
sounding
inherently with its environment (previous and next chord), by its
development
and in connection with melodical motion of individual voices. We
assume, that
the way of traditional harmonic analysis (9), (10), where every chord
has its
tonal function, is for our purpose in this project better root.
Tonal functions as tonic –
T, subdominant – S and dominant – D are representatives of various
sizes of
harmonic tension and in this sense they control psychological quality
of
hearing, too. Tonic (the triad on the I-st degree of tonal key) as a
chord of
harmonic peace, subdominant (the triad on the IV-th degree) as a chord
of
middle tension or harmonic digression and dominant (the triad on the
V-th
degree) as a chord of highest tension or maximal harmonic stress are
the basic
functions. Chords on other degrees of tonal key were used in tonal
music as
modifications or combinations of basic functions. In our opinion it
could be
useful to consider every other degree as a double function, ie. the
II-nd
degree SD function (two pitches from S and one from D), the III-rd
degree TD or
DT (two pitches from T and two from D), the VI-th degree TS or ST (2
pitches
from S, 2 from T) and the VII-th degree DS (2 pitches from D and 1 from
S). The
size of tonal tension of these chords probably depends on how much is
the chord
similar to the basic function or how is it used as (the very usual way
of using
similarity is the way of placing the chord instead of basic function in
cadence). It is well known use of II in cadence T-II-D7-T, or use of
VII as
T-S-VII-T.
We could try to
propose the evaluation (and enumeration necessary for computer
processing) of
this ability of harmonic structures for control tension in
listeners
feeling. The evaluation/enumeration should be made in three basic
levels:
Traditional music theory considered as a consonant only two chords –
major and
minor triad. (The fact, that these triads could take place like
disonances, if
they are not used as basic functions, will be satisfied in level of
tonal
functions.) The dynamics of these triad we will consider to cause
the
lowest tension. "...the major triad is in itself static..." ((6) p.
40). Other chords are more or less disonant and bring higher tension.
The most
disonant interval (of highest tension) is a major seventh and a minor
second,
then minor seventh and major second and then diminished fifth or
augmented
fourth. Two major thirds in superposition are disonant despite of that
major
third alone is a consonant interval
Perception of tonality in
European music is based on perception of chordal relation of fifth
(interval of
7 semitones) and on perception of tension of so called "leading" (8)
tones. The chord having one or more leading tones to the next one, is
strongly
directed to it. Therefore D7 (in c major this chord consists of
g-b-d-f) which
has two leading tones to the tonic (b gravitates up to c – this is
ascending
leading tone, and f gravitates to e – this is descending leading tone)
is
dominant, strongly gravitated to the tonic.
Development of every
secondary dominant seventh chord to its tonic is everytime full of
tension
caused by leading tones.
In most cases the chord directed to its tonic is built up by thirds,
but also
there is a most important intervalic distance full of tension –
diminished
fifth (or augmented fourth) – named also tritonus. It is well known
characteristic of this interval – diabolo in musica – bringing feeling
of
tension and stress. Therefore many authors consider this interval as a
dynamic
substance of chords. This interval should be the decisive one in
evaluation of dynamical size of chords.
We regard as reasonable to
divide evaluation and enumeration of above mentioned levels of tension,
and
after that to make some correlation between them. It will bring new,
graphically visualizable motion of tension or dynamics of harmony.
References:
(1)
Ferková, E. (1991). The algorithm of basic harmonic
analysis of
tonal classical music, Computers in Music Research. Conference
Handbook,
Belfast, 66 – 68.
(2) Ferková, E.
(1992). Computer analysis of classic harmonic structures,
Selfridge- Field, E. - Hewlett, W. (Eds.),
Computing in
Musicology, CCARH, Menlo Park, 85 – 89.
(3) Ferková, E., Dudek, M. (1992). CACH:
Computer analysis of classical harmony, Secondo Convegno Europeo di
Analisi Musicale, Trento, 619 – 621.
(4) Ferková, E. (1999).
Harmonic-tonal motion as a reflection of the development of musical
form,
Diderot Forum on Mathematics and Music, Vienna, 169-177.
(5) Salzer, F.
(1952). Structural hearing: tonal coherence in music., Dover
Publications, New York.
(6)Cook, N. (1987). A guide
to musical analysis, J. M. Sons & Ltd., London.
(7)Randal,. M. (1978).
Harvard Concise Dictionary of Music, Cambridge, London.
(8)Selfridge-Field, E.,
Hewlett, W. B. Eds.(1998). Melodic similarity: concepts, procedures,
and
applications, Computing in Musicology, 11, Stanford.
(9) Kresánek, J. (1982).
Tonalita, Bratislava.
(10)Filip, M. (1998). Súborné
dielo I: vývinové zákonitosti klasickej
harmónie, Bratislava.