Structures of ratio exposure considered in conjunction with ratio properties:
In conjunction with ratio properties, structures of ratio exposure will acquire a new level of distinction. In the first place, we distinguished conditions of segregation/aggregation from the condition of non-segregation; now, we'll further distinguish stream aggregation into two kinds: unilateral and multilateral. Unilateral segregation is the condition in which a single cue (such as "accent") is responsible for the aggregation of a rhythmic stream. In such cases, all accented notes are members of a stream, of which no unaccented notes can be members. Multilateral segregation is the condition in which streaming depends upon a variety of cooperating, but independent, cues. For example, accented notes may be members of a stream only on the condition that they are followed immediately a downward leap in pitch; and some unaccented notes that are followed immediately by such leaps are also members, provided the leap is large enough. (These combined conditions for stream membership could also be mitigated by any number of other conditions, reinforcing or undermining one another in a stream that defies any one consistent threshold of membership.)
Given the above, consider how a timespan-pair's azimuth (the disparity between values) and complexity (the size of a ratio) must be imagined differently under each of these conditions of "stream aggregation/segregation.":
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Azimuth (value disparity) |
Complexity (ratio size) |
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Structure: |
Unitary/unsegregated |
The (a)symmetry of adjacent timespan pairs is assessed neutrally. We assess degrees of "swing" or "inegal" abstractly, but without any fixed inference of how short and long imply strong or weak, nor any place in a metric structure. |
Ratios of differing complexity (but similar azimuth) like 11:5 and 2:1, taken in isolation, seem to be equivalent experiences.
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Unilateral aggregation |
Perceive distinctions of short and long timespans (in motives) as layered contours of emphasis, or (in ostinati) as metrically weak and strong, across structures like meters, beats, and subdivisions. |
Distinctions in ratio complexity suggest 'pulse' or 'unpulsedness.' Even without metric reinforcement, these distinctions increase in salience, as degree of 'exposure' by stream segregation increases. (Carson 2007).
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Multilateral aggregation |
Varieties of swing and 'inegale' in metric hierarchy can be articulated further with syncopation; varieties of long/short distinction in rhythmic motive can be articulated further with ornamentation. Thus, the multilateral aggregation of distinctions in the azimuth property allows syncopation as a construct separate from meter, and ornamentation as a construct separate from motive. |
Distinctions in ratio "complexity" (suggestive of pulse or unpulsedness) are salient in multilaterally-aggregated streams, and the competition among aggregation cues makes possible contrasting properties within a single stream; one cue distinguishes an event-stream that is rhythmically simple, while another distinguishes one that is rhythmically complex; contrasting properties can thus coexist simultaneously in a single line.
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