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THE TENSION/RELAXATION PRINCIPAL IN 20TH CENTURY HARMONY
Copyright - Jim Mccarthy. 26/10/95'
The performer must essentially understand the basic mechanisms involved, to most effectively execute a written part. For example, a rising melody normally associated with increasing tension is enhanced by an increase in volume, which is also associated with increased tension. If two aspects of music do not complement each other in this way, it is not necessarily an incorrect interpretation, however such devices can be used to increase the overall effect.
In Western music of the Twentieth Century, There is a large range of devices which can be used to create tension and relaxation. Wallace Berry writes: "The concept of progressive and recessive actions within confluent element structures suggests the useful basic principal that in an important sense, there are "dissonances" and "resolutions" within all of music's parameters. The clear relevance of this idea is apparent with even a little thought: thus, for example, an upward leap in the pitch-line, a highly active (perhaps imitative) texture of competing lines, relative ambiguity or (in relation to a referential norm) asymmetry of metric relations - any of these can, like other comparable conditions of instability and expectancy of restoration of "simpler" states, be conceived as "dissonant," as evocative of intense feeling and subjective involvement in potentially absorbing actions and interactions, pertinent to the elements of tonality, harmony, melody, texture, and rhythm, as to further parameters within each of these, are a principal substance of function and expression in music." (*1.)
1. BERRY, Wallace - Structural functions in music. (Prentice Hall Inc. Englewood Cliffs, New Jersey. C.1976) 13.
"One thinks of rising pitch, shrinking units (acceleration), increased textural quantity, increased compression of texture, crescendo, harmonic succession of increasing tonal distance, increase in the overall spatial field, fluctuation toward more penetrating coloration, increased rate of attack, and dissonance, among other musical states [other than increased volume] commonly associated with increased intensity." (*2.)
It is because of this overbearing range of devices, that this essay deals purely with those related to vertical structures - that is harmony. Even so limited, the range of devices available to the Western composer is ever increasing as the vertical is better understood, and further explored. As all harmony relates in some way to the acoustic facts presented in the harmonic series, this shall be our starting point.
2. BERRY. 9.
HARMONIC SERIES AND TEMPERAMENT
The intervals and hence the notes we use in Western music are derived from the harmonic series (fig 1.), the simplest interval, and first in the series being the octave. A.J. Ellis (1814-1890) introduced a system where the octave (represented in terms of frequency by the ratio 1:2) was divided into 1200 equal "cents". This makes an understanding of the smaller intervals easier. The next interval on the harmonic series, the fifth, has the ratio 2:3 and would be 702 cents. All the intervals can be seen in fig 2.
INTERVAL --------------------+ 8ve - 5th - 4th - M3 - m3 - M2 - m2 RATIO -----------------------+ 1:2 - 2:3 - 3:4 - 4:5 - 5:6 - 8:9 - 15:16 CENTS IN PURE INTERVAL ------+ 1200 - 702 - 498 - 386 - 316 - 204 - 112 CENTS IN TEMPERED INTERVAL --+ 1200 - 700 - 500 - 400 - 300 - 200 - 100 FIG. 2. REAL vs. TEMPERED INTERVALS.
If we take for example the above melody - the first two ascending intervals of a fifth and fourth, add up to a perfect octave of 1200 cents. Coming down however, the sum of four consecutive minor thirds of 386 cents (1264) would mean the final C would be 64 cents lower than that with which we started - in fact, closer to a B.
In early, more linear music, this problem was solved by the use of a "syntonic comma" - an interval made imperfect (usually a more impure interval such as a third or sixth) to adjust to a fundamental pitch.
In later music, as the vertical structure became both more complex and important, and pitch-inflexible instruments like keyboards came into more frequent use, equal temperament was introduced. This simply divides the octave into twelve equal semitones of 100 cents each. This means that every interval other than the octave is slightly imperfect according to "Natural Harmony," but by an amount which is tolerable to the ear.
In theory this means that the composer may use any tonal centre without altering the character of the intervals in their harmonic structure.
It is for these reasons that ensemble musicians talk of "Instrument length" rather than "Tuning".
For example, in any given instant that a musician is playing a Bb, the harmonic structure to which the Bb belongs to may change. As most instruments are slightly flexible in their exact intonation, a good musician may sharpen or flatten the Bb to make it more in accordance with natural harmony.
They must also take into account however the linear function of their note. There may for example be times when playing a leading tone, that the horizontal function of the note is more important than the vertical, and the tension may be increased accordingly by sharpening the note away from the "Naturally accurate" towards the destination tone.
In times before an equally tempered scale was in common use, composers would select certain keys, because of their inherent tensions. C Major was considered to be a "broad" and "relaxed" key often used for the finale of a major work. As the period instruments were constructed using naturally harmonic intervals based on C, it was easier for the musicians to play their notes according to natural harmony in C Major, producing a "fat" and "round" ensemble sound.
In keys further away from C, the increasingly inaccurate intervals produced an inherent "Natural harmonic tension" with the clash of many overtones not quite sitting together.
The first group of tension devices are only applicable to music adhering to conventional Major/minor harmonic structures.
Removal From The Tonic. - As the harmony leads further away from the current tonal centre or tonic, towards the dominant, the harmonic tension is increased. The most relaxed harmony would be unisons, open octaves and fifths on the tonic respectively. The most tense harmony would involve a dominant seventh chord. For an example of this, I have chosen bars 34-45 of the third movement from Bartok's "Concerto for Orchestra". This is the primary composition from which my examples will be taken. Fig. 3 shows a break down of the chords used. A regular modulation from tonic to dominant can quite clearly be seen.
Ascending Tonal Centre. - The tension is also increased as the tonic/tonal centre itself is raised. Bar 76 in Bartok's first movement is a good example of raising the tension by ascending modulation from Eb to F.
Increasing Harmonic Tempo. - As the rate of change of harmony increases, the tension also increases accordingly. This can work on many levels. It is possible to change the vertical structure many times without changing it in a more fundamental way. Although "Harmonic Rhythm" usually refers to the most fundamental of harmonic changes, flux of a less significant nature can also increase tension.
Use of More Dissonant Notes. - Within any single vertical instant, the tension can be increased by the use of notes that are further removed from the bass tone according to the harmonic series. If a strong overall tonal centre is present at the same point horizontally, the degree of removal from the tonal centre must also be considered; both of the individual notes, and the chordal centre or bass tone. An example of dissonant notes used to create tension, can be found in bars 6-10 and 16-20 of the first movement, where the bass tone is suddenly overlaid with a Major seventh.
Thickening Texture. - Vertical structures with a greater number of notes, in general tend to have more tension than those with less. This is a complex issue as a number of factors are involved. Without considering the number of notes in a vertical structure or their tonal implications, the question of compression and total pitch range also plays a large role in determining the vertical tension. In general, the greater the total range of pitch (interval from highest note to lowest note), the greater the tension. It is also true however, that the closer a given set of notes are together, the greater the tension produced.
Whilst these rules seem to contradict each other, they can be used together. Given a certain group of notes, one could arrange them such that there was a tight cluster of notes with at least one note a long way apart from the rest of the cluster. For reasons discussed later on, this will produce more tension if the closely positioned notes are in the lower register.
The same example (bars 6-10) can be used to show thickening texture. The C# and C are gradually added to with other notes. It is interesting to note, that the tension release in bar 11 still leaves us with some expectancy, by giving the C# in the bass a dominant function. This is confirmed in the next bar.
Increasing Independence of Lines. - Assuming a given number of lines or voices in a piece of music, the tension produced is increased as they move towards greater independence contrapuntally, or decreased as they move towards lesser independence or homophony. Although voice movement plays a large part in our perception of a lines independence, rhythmic differentiation plays the largest role.
It becomes apparent then, that some horizontal recognition becomes involved in determining the vertical tension, according to the "independence of lines". Horizontal recognition will be dealt with more thoroughly under "Horizontal Aspects in Vertical structures."
In bar 76 of the first movement where the previously discussed upwards modulation takes place, we can also see an increase of overall tension because of the increased independence of the parts. In the previous bars, virtually all the instruments are playing a unison figure, whereas at 76 the orchestra can be clearly divided into three quite distinct voices.
The third group of tension devices, relates directly to "Natural Harmonics" as determined by the harmonic series. In general they deal with the total number of overtones produced, and their dissonance or consonance.
Absolute Frequency of Notes. - The lower the frequency of a note, the greater the number of its overtones that will fall within the human's audible capability. Therefore, placing a given note at a lower octave will make that note more inherently dissonant according to the thickness of texture rule. It should also be considered that for the same reasons, placing a note in a lower octave will give the note more harmonic "weight" within a given vertical structure.
Volume Increase. - Increase of volume works in two ways that are independent of the more simple fact that higher volumes require more physical energy to produce. From a harmonic point of view, the louder a single note, the greater the number of its overtones become audible. In accordance with the pitch-range and texture rules - that note then becomes more dissonant within itself.
Volume increase also has another effect within a more complex vertical structure. If a loud bass tone is sounded with softer high notes, the high notes tend to be perceived more as overtones of the bass tone. If the bass tone is soft and the high notes are loud however, the notes are perceived to be more independent. Therefore the tension is increased according to the texture rule.
Bar 51 of the first movement is an excellent example of a sudden volume increase used to increase the tension.
Orchestration and Coloration. - One way to vary the vertical intensity of a given moment, without changing or adding notes, is to vary the orchestration. Some instruments will produce a greater number of overtones than others particularly in certain registers, so use of these instruments in preference to others, will produce a greater harmonic intensity. In general, the greater the number of different instrument types involved in a chord, also the greater the intensity.
In the same way that volume differences can change the perceived independence of notes and therefore the intensity, differing instrument types can also be used to highlight certain parts of a chord.
The proximity of a note to an instruments fundamental pitch can also vary the intensity of the note. For example take two very similar instruments, the Bb trumpet, and the trombone. If both instruments were to produce a middle C (not a difficult note for either instrument), the intensity of the notes would differ considerably. The main reason for this is that the trumpet's C is quite close to its fundamental pitch, allowing many overtones to be also produced. The trombone's C however is already using harmonics of the instrument's fundamental length that are fairly high, making it difficult for higher overtones to sound strongly.
Bars 63-76 use many devices to increase the tension throughout. As well as the more obvious acceleration and crescendo, there is also a thickening of orchestration and texture, and expansion of the total pitch range.
We have briefly touched already on the idea of separating contrapuntal lines or notes more clearly from each other to create more tension. The following section discusses the devices for creating this separation. All these devices can be used in both horizontal and vertical musical structures to separate notes, chords, voices, and tonalities.
Register Difference. - Large differences in register make our perception of the separations in musical structures easier.
Rhythmic Differentiation. - Rhythm, although a purely horizontal function of music, can play an important role in our perception of separations. Vertical separations work best when used in conjunction with consistent and contrasting horizontal structures. Unfortunately this also tends to reduce the effectiveness of horizontal tension devices in their own right.
Spatial Differentiation - One method of increasing our perception of separations that works particularly well in specially set up live performances, is that of spatial differentiation. The further the physical distance between sources of sound which we hear simultaneously, the greater the degree of separation which we tend to assign to them. Berlioz was perhaps one of the first composers to explore this area in a significant way.
HORIZONTAL ASPECTS IN VERTICAL STRUCTURES
Although we have been separating the vertical and harmonic aspects of music from the horizontal and melodic aspects so far, the two are never truly divided in real musical examples. They relate to each other on many levels, some of which have been touched upon already.
"To be sure, the understanding of single harmonies (intervals or chords) is founded on their isolated, non-collaborative harmonic qualities, but single harmonies do not cause musical effects; they must progress and thus produce the typical musical impression of streaming, of traversing spatial and temporal distances." (*3.) A purely horizontal line may at times have strong vertical implications, as in the case of arpeggios or ostinati. In these cases, a wider "vertical slice" must be looked at in order to consider the broader vertical implications, as well as the smaller, moment for moment slices.
In these situations, the horizontal and the vertical can seem to work against one another. Larger intervals tend to represent increased melodic intensity but decreased harmonic intensity. Similarly, tension is generally increased harmonically with smaller intervals, but decreased melodically.
One of the most important relationships between the horizontal and vertical aspects of music, comes from a tendency for people to recognise melodic fragments. Modern composers can often get away with a severe vertical dissonance if the dissonant element is part of a horizontal fragment recognised from earlier in the composition.
The concept of looking at the vertical within a wide horizontal slice leads inevitably to the area of tonality, which has been a significant issue in the Twentieth Century.
3. HINDEMITH, Paul. A Composer's World - Horizons and Limitations. (Harvard University Press, Cambridge. 1952.) 98.
DEVICES FOR ESCAPING TONALITY
The following is useful in terms of defining what is meant by "tonality." "The word 'tonal' is incorrectly used if it is intended in an exclusive rather than an inclusive sense. It can be valid only in the following sense: everything implied by a series of tones (tonreihe) constitues tonality, whether it be brought together by means of direct reference to a single fundamental or by more complicated connections". (*4.)
4. SCHOENBERG, Arnold. - Theory of Harmony. (Trans. Roy Carter. Faber, London. 1978.) 432.
One of the most important developments in this area was the introduction of Messian's "Modes of Limited Transposition". The purpose of his modes is to divide the octave into scales of one or two equal intervals, so that unlike traditional Major/minor scales, they can centre around more than one tonality. The beauty of the "Modes of Limited Transposition," is that they work in both horizontal and vertical aspects of a composition. They are vertically limited however, in that they still assume the entire range of possible tonality to be encompassed within a single octave. Examples of this sort of mode can be found from bar 106 of the third movement.
Some composers have explored vertical structures based on intervals which do not fit exactly into the octave such as fourths or fifths. This expands the vertical possibilities immensely, although these possibilities seem not to have yet been properly discovered. For example - take a mode of unlimited transposition: Tone, Semitone, Tone. This adds up to a perfect fourth, and repeated, to a minor seventh. In this fashion, the pattern can land on any of our twelve notes regardless of where it starts, as long as it extends far enough in one direction. This is essentially a way of dividing a five octave space into twelve equal fourths (one for each of our twelve tones), but still allowing small melodic leaps by the further dividing of the fourth.
Another method used to avoid our traditional strong tonal ties is to divide the material, and employ more than one tonal centre at any one time. The use of polytonality has been very popular with impressionist composers such as Debussy.
This trend away from the use of tonality became so strong that 12-tone compositions began to emerge. Compositions which used any device at hand to make all of our twelve tones equal within the music. Unfortunately, by doing away with the majority of methods for creating tension and relaxation, the resulting music became less communicative on all but a purely intellectual level.
"The only segment of our conventional body of theoretical musical knowledge which the dodecaphonists have deigned to admit and which, in fact, alone makes their speculations possible, is the twelve-tone tempered scale. We have already been told of this scale's weakness: because of its basic impurity it can be used only as a supplementary regulative to a tone system containing natural intervals - at least, so long as we want to save our music from total instrumental mechanization and have human voices participate in its execution." (*5.)
5. HINDEMITH. 121-122.
One of the organizational systems that came to be used for pitch events (as well as other aspects of music) was that of serialism. Whilst serialism is not, as is often misunderstood, the same thing as 12-tone music, it is important to understand that it is a result of the same trend, and in many ways, serialism exists because of the 12-tone concept.
Hindemith has a fairly popular view of such music as abandons any connection to "natural harmony" in favour of purely intellectual methods of organization.
"..... we find examples in many supercontrapuntal or otherwise overconstructed compositions, when our intellectual faculty of understanding may be carried to very high spheres, but emotionally we are left with dissatisfaction, because these structures are so involved or overburdened or unpredictable, that our activity of reconstructing them intellectually absorbs all our attention and prohibits emotional enjoyment." (*6.)
6. HINDEMITH. 41.
USE OF CLICHÉ
The use of cliché plays a very important role in producing tension and relaxation in modern music, particularly in music associated with the media. There are three main ways in which cliché can be presented.
Specific Devices. - Some devices used for creating tension or relaxation are so effective, that they have been used often enough to become stylized and easily recognized. For example, a dominant pedal tone is a well used method for sustaining expectation, and has become so cliché that if a sustained bass tone is sounded alone, we often automatically assign it to a dominant function.
Stylistic Adherence/Disturbance. - If a composition is written strictly in a style that has become by the Twentieth Century well known, such as from the late Classical period; it has an inherent lack of tension, as the listener has learnt what to expect. This is in part, why the overall level of intensity in music is continuously increasing. As tension producing devices become known or cliché, composers have had to find increasing numbers of devices of increasing effectiveness in order to create the required levels of tension.
Cliché styles can be used to intensity's advantage however through disturbance. Sudden changes of style generally have the effect of putting the listener on edge.
"... in former times the scientific roots of music were embedded in mathematics. With the continuous increase of technical knowledge in music, notably the widening aspects of harmony and tonality, mathematics proved insufficient as a foundation. Physical facts became a more reliable scientific basis, and nowadays we are on the verge of entering with our research that innermost field in which the very actions of music take place: the human mind. Thus psychology, supplementing - in due time perhaps replacing - former mathematical, physical, and physiological scientiae, will become the science that eventually illuminates the background before which the musical figures move in a state of meaningful clarity. But this science is, as a foundation for musical speculation and technique, even more suspect to the musician than was mathematics. Now it is not only the sounding form of music that is violated by nonmusical intrusion, it is the musician's own artistic self that is attacked." (*7.)
7. HINDEMITH. 24-25.