It corresponds to the classical pedal point. In this example, the clarinet tremolo, E-G , acts like a classical pedal point, providing simple, clear, registral, rhythmic, and harmonic unity. However, the outer parts also contribute to coherence. The flute part starts the first two phrases with the same three notes which emphasize B as a stable tone. This causes the final cadence note, A , to sound like a lower neighbor. Similarly, the highest note in the first bar, A , leads stepwise to the highest note in the second bar, B. The oboe part is homorhythmic with, and has similar voice leading to, the flute part: The D and C in the first bar remain in the second bar; the E of the first bar is "ornamented" by the F in the second, and the E in the last bar seems to "resolve" the previous D.
The harp is limited to 4 notes. The last bar sounds cadential because of the less animated rhythm, the on-the-beat accent, the softer harmony which avoids semitone conflicts and the descent of the harp into a new register. While the common tones in each instrument certainly help to hold the phrase together, we can see that these various other relationships - in rhythm, voice leading, and interval tension - also help the listener to make sense of the whole. Identity relationships are thus only one aspect of a more complex coherence. However, limiting the intervals used in a given passage to one single interval and its inversion can define a strong, audible character.
Similarly, limiting a passage or a piece to material derived from a small unordered cell "unordered set" in the literature can also create fairly strong character. Note that the larger the cell, the more intervals it contains, and therefore the less 10 distinctive it becomes. If more than three or four intervals are involved, the cell will usually contain all of the chromatic intervals - being unordered, non-adjacent intervals must be counted as well.
The Principle of Harmony
This is where Forte's notion of "interval vector", i. Sets with very uneven distributions of intervals tend to have clearer characters. These techniques can be applied quite rigorously for short passages, or more flexibly over larger stretches see below for discussion of this important distinction. Flexible applications usually involve either melodic movements which create other intervals as "non-harmonic tones", or vertical stacking, which necessarily results in richer chords.
Since stacks of any one interval almost always produce additional, new intervals between non-adjacent notes, this technique allows for harmonic "shading", i. In this example, the first chord is a simple quartal sonority. The outer notes, however, form a 3rd. Thus it is easy to move from the first chord to the second one, which is triadic, via the the smooth stepwise movement from A to G. The second chord could subsequently either return to the first, acting like a neighbor chord in a generally quartal passage, or else lead into a passage of tertian harmony.
Likewise, progressions of tension, e. This example illustrates a gradual progression from gentle, open intervals to an intense climax on a major 7th m.
The dynamics and registral 11 evolution reinforce this progression. Note that the progression is not simplistically linear: Overly obvious progressions tend to be boring. The best strategy is for the overall direction to be well defined, while the details remain somewhat unpredictable: The general direction of the progression allows the listener to develop expectations, but the inability to predict the exact next note maintains interest. A family often will contain chords associated in more than one way e. This is logical, since simple voice leading tends to keep parts in one register, or at least to change register without discontinuity.
The more elements which are kept common within a harmonic family, the easier the harmonic character will be to perceive. This is yet another example of how critical it is for the composer to accurately judge degrees of salience; only in this way can he exercise subtle control over audible gradations of harmonic continuity and contrast. Linear aspects: melody and bass lines; voice leading We have pointed out above how pitch and interval limitations help define and unify harmonic character.
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Two other traditional concepts contribute significantly to harmonic coherence: leading lines, and voice leading. Even in contrapuntal textures, all parts are never of equal importance: Interest migrates from one part to another. In simpler, homophonic textures, outer parts are easier to follow than inner parts. Thus, clear linear progressions in the outer parts can clarify the music's sense of direction. For example, a melodic line which gradually attains higher and higher local peaks, leading to a sectional climax, helps give coherent shape to a musical paragraph.
In the same way, the combination of stepwise motion in the bass with occasional angular passages - often at cadences helps clarify harmonic direction. Voice leading is always a very audible force, both for harmonic continuity and for articulation. The basic principles of voice leading arise from two fundamental facts for experimental documentation, see Albert Bergman's Auditory Scene Analysis : the tendency of the ear to separate musical strands by register, and the fact that voices, and most instruments, are most at ease moving by fairly small intervals. These are facts about human hearing, and they therefore go beyond specific styles.
Constantly leaping lines are very demanding to follow and to sing.
By contrast, registral continuity, as expressed by common tones, conjunct movement, and stepwise movement between salient tones in the line, are easier to follow and provide the "glue", connecting one harmony to the next. An important consequence of the importance of registral continuity is that ornamental nonharmonic tones arise from the nature of hearing, since they are virtually always stepwise. They are not just a stylistic peculiarity of tonal music. The fact that many systems for controlling pitch in non-tonal situations do not allow for them is a serious limitation: It deprives the composer of an effective means of creating leading lines which are easy to follow.
An aside: open vs. An open system imposes audible, but not rigid, constraints, providing aural coherence, while allowing the composer's melodic imagination more freedom. Closed systems are much more mechanical, limiting the composer's options at any given moment in quite rigid ways.
The distinction is largely one of degree. Advantages of open systems include: z z Because most of them came about through evolution, rather than invention, they have usually been "survival-tested" by ear: Evolution tends to filter out approaches which are not effective. They are flexible.
They thus allow the composer's ear to work in more intuitive ways and do not automatically constrain basic linear impulses, such as conjunct lines. There is no inherent contradiction between non-harmonic tones and coherent, non-tonal music. For example, a piece using a core harmonic cell at key points could allow for non-harmonic tones between them. As long as the rhythm and phrasing make it clear which sonorities are the structural "pillars", and as long as there are enough such pillars - reference points - to stimulate the memory reasonably frequently, there is no more need for such harmony to derive every note from the basic cell than for classical harmony to insist that every non-harmonic tone be part of a triad.
This example is based on the three note unordered harmonic cell: B-C-Eb.
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The places marked "X" contain intervals not in the cell: major 2nd, perfect 4th, tritone. However, the cell is still very prominent overall, and these "exceptions" are not musically salient. They are easily heard as simple passing or other ornamental movements.http://nn.threadsol.com/map358.php
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Apart from the flexible kind of cellular harmony seen in the example above, other examples of open systems include: z Families of chords, as defined above. Stratified harmony, i. A fuller discussion of this technique will be found below. All of these techniques create recognizable harmonic worlds, while allowing the composer a great deal of local choice. Closed systems, by contrast, severely limit the choice of notes available.
Worse, they often do so to the extent that the expressive intentions of the composer cannot be fulfilled while respecting the limits of the system. Examples of closed systems include: most algorithmic, total serial, and rigid mirror procedures. The key feature of such systems is that they do not allow the composer's inner ear to follow its own impulses at every point.
If the ear is to remain paramount for both composer and listener, why waste effort creating inaudible connections, and excluding audible ones which do not weaken aural coherence?
Much serial technique has long created problems of this sort, since the "order" in question usually has nothing to do with what can be reliably heard, even by an experienced, attentive listener. Further, chords in serial music inevitably create interval combinations not inherent in the row. And in any case, what is the meaning of "order" in a chord whose notes are heard simultaneously?
Of course, these comments do not imply that no serial music is of any value, but just that serial procedures easily lead to unmusical thinking. Hierarchy, landmarks, cadences Apart from family resemblances, classical tonality provides an example of another important principle of harmonic coherence: hierarchy.
The idea of "leading lines", already discussed above, provides a simple application of this notion to simultaneous strands of the musical texture. Applied to successive phrases, sections, etc. Hierarchy, in short, makes possible richer and more complex musical structures. We will first discuss the hierarchical functions of tonality, and then discuss how similar effects can be achieved without it.
Hierarchy applies on several levels. First, tonality itself is based on scales with unequal intervals: If all intervals are equal, there is no harmonic reason why one note will sound more final than any other. Within unequal scales, differences in intervals create points of relative stability and attraction. For example, in major and minor scales, the semitones are points of attraction; the leading tone is a familiar example.
Such articulation is the function of cadences. Cadences are necessary, whatever the harmonic language used. If the listener is to follow music of any length, he requires gradations of cadence. Such variety of punctuation makes phrase divisions easier to perceive, and clarifies their relationship to one another: Hierarchical tonal cadences tell the listener how far away he is from "home", i.
In tonal music, this hierarchy of cadences is well known, and need not be listed here. On an even higher level, not only does a tonal center provide a useful point of reference, but it also allows for the creation of secondary centers, permitting still more degrees of punctuation, thus making large-scale coherence easier to grasp. This points out the necessity of audibly underlining important notes and chords, in effect treating what happens between them as ornamentation or, to use the Schenkerian term, prolongation. This kind of salient, musical "highlighting" makes it easier for the listener to parse large forms by ensuring that landmarks are easily noticed, and memorable.
These distinctions between harmonic reference points and harmonic ornamentation, and the way reference points are approached and left - in other words the way they are pointed out to the listener - are critical for understanding the interaction between harmony and form.
Even in elementary tonal harmony, the tonic will often not be recognizable after substantial harmonic digression, unless it is thus made salient, through coordination with other aspects of the music. How many people notice that many classical operas - for example, Mozart's Magic Flute - do not end in the same key in which they start? Such salience can be achieved by: z z z z z Accent: extremes of pitch, strong contrast of duration or orchestration.
Building up to such important moments, with crescendi, rising lines, gradual tempo change. Repetition, for emphasis. Directed cadential progressions.
Related Principles of Harmony
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