The reciprocal function which will result in Two types of fractions can be determined - one that will yield indexes larger than 1, or Quantitative device is used by Wallace Berry and is described in his book A convenient nomenclature for such a density ForĮxample, the first chord's four elements are distributed over a range ofġ51 2, chord #2 over 1161, chord #3 overġ521, and chord #4 over 1211. Simultaneity may mean little, if anything, in analysis.Īn account of pitch-range compression in analysis will yieldĪ more precise description of the chord. It is clear that the number of voices present in the Obviously representative of disparate constructionalįeatures and share in common only the fact that they are allįour-voice sonorities. For example, it isįour-note event, or a five-note event, as aspects of register, compression,Īnd chordal quality are not taken into account.Ĭonsider the four-note chords below (Example 1). Nature with a minimal distinction afforded between sonorities considerably from each other. Vertical texture in the past have been of a general Conditional statements regarding analysis of Same intervals in a different order (i.e., permutationalĭensity, I feel, is a parameter capable of being precisely defined throughĪn accurate and logical means of analysis. His numerical representationsĭensity) fail to differentiate between degrees of consonance or dissonance, the spacing of the chord, the effect ofĮvent, the effect of transposition upon the chord, and the use of the Number of parts present in the musical texture. Measure density in both the concurrent aspect as well as in the linear unfolding and accrual or decrease in the Wallace Berry, on the other hand, attempts to His vertical structures in procedures which are only incidental toĬonsiderations of density. In the compositional process as they are to this writer. The vertical or concurrent aspects of density (e.g., a chord), are Utilizes it as a function of time (i.e., the lannis Xenakis, for example, measures density and It is at this point that I differ mostįrom others who have dealt with density inĮither a compositional or analytical manner. Lastly, time will not be considered essential in density analysis. The amplitude of a pitch will have no bearing whatsoever upon the density. Secondly, dynamics will not be of importance in assessing density. This discussion of density will discount theĮffect of instrumentation upon the sound (i.e.,įor this paper, how the sound is produced is not of concern to the measurement). Limitations have been imposed from the outset. Range, distribution, dynamics, instrumentation, etc., in a numerical representation, is impossible. Musical parameters, i.e., pitch compression, Of density, one that will exemplify the interdependence of all of the A comprehensive definition and assessment Will outline this writers attempts at defining density in music, deriving quantitative measurements of density, andĪnalytical and compositional manner.
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