Text: Intervals: Any tone can succeed any other tone, any tone can sound simulataneously with any other tone or tones, and any group of tones can be followed by any other group of tones, just as any degree of tension or naunce can occur in any medium under any kind of stress or duration. Successful projection will depend upon the contextual and formal conditions that prevail, and upon the skill and the soul of the composer. An understanding of the harmonic process may begin with an understanding of the melodic and harmonic intervals of sound. Construction: An interval, like any other musical sound, may have different meanings for different composers. While its physical properties are constant, its usage changes with the working context to which it belongs. For centuries theorists have, through the science of acoustics, observed degrees of interval tension and from this has been evolved a concept of the relative consonant-dissonant qualities of intervals. Although this consonant-dissonant concept is affected by countless factors within any given style, and may vary considerably from one age to another, the notes of an isolated interval - whether sounded simultaneously or successively - do have a basic quality. This quality is determined by the interval's own particular physical properties of sound waves and overtones. An isolated tone, when sounded, generates a series of overtones which form intervals that relate to each other by mathematical ratio. Generally, in the tempered scale, consonant intervals are considered to be those formed from the lower tones of the overtone series, the upper overtones producing dissonant intervals. In practice, these tone-to-tone relationships have been reduced by the use of the chromatic tempered scale from an unlimited number of intervals to 12 intervals which retain the characteristics of their counterparts in the overtone series. Their textual characteristics are as follows: Perfect fifth and Octave - open consonance, C G C Major and minor thirds and sixths - soft consonance D# E, G# A Minor seconds and Major sevenths - sharp dissonance C# B Major seconds and minor sevenths - mild dissonance D Bb Perfect fourth -consonant or dissonant F Tri-tone -(augmented fourth or diminished fifth) - ambiguous, can be either neutral or restless F# It is difficult to classify the perfect fourth and the tri-tone out of musical context. The tri-tone divides the octave at its halfway point and is the least stable of the intervals. It sounds primarily neutral in chromatic passages and restless in diatonic passages. The perfect fourth sounds consonant in dissonant surroundings and dissonant in consonant surroundings. Luigi Martino, 6/16/02 quoting from unknown musical text

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