PROPERTY is the term I'll use as shorthand for "ratio property," and it refers to any measurable and distinguishable feature of an irreducible ratio that relates the lengths of adjacent timespans (for short, we'll call this a timespan ratio). There are three main properties of concern: complexity, azimuth, and gravity.
PROPERTIES of timespan ratios:
- Complexity: meaning, the degree to which a given ratio (hypothetically) avoids or discourages the appreciation of an underlying pulse.
[Complexity ends up being mostly related to the size of a ratio, i.e. the sum of its irreducible parts. But, as you might expect, the question becomes somewhat more complex.]
- Azimuth: meaning, the degree of a timespan ratio's asymmetry. This is the continuum between the extremes 1:x and x:1, where x is a very large number. So, the azimuth is the property of a timespan ratio that clarifies the disparity in length between the first and second timespans.
[As x gets bigger, these ratios grow ever closer to the irrational ratios "1:0" and "0:1", so even though they're impossible, we'll use those as symbols of the extremes. 1:1 is smack-dab in the middle of the azimuth.]
- Finally, gravity is a function of these first two properties combined. Gravity is the hypothetical capacity of a ratio percept to absorb ratios that are nearby in the azimuth and greater in complexity. Hypothetically, gravity will be some function whereby the simpler a ratio is, the wider the range of its influence in the azimuth.
[Think of gravity as a metaphor, indicating the perceptual traction by which a very complex timespan ratio like 21:10 would actually be understood, to listeners, as an example of the ratio 2:1.]
But why reserve this word "property" for the description of properties assigned only to ratios, and not to the relationships among larger populations of timespans? At first it may seem counterintuitive that we put so much value on the identification of timespan pairs, rather than larger sets--after all, a timespan pair only describes the relationship between three events.
The best rejoinder to that concern can be found in the next main term, Structures of Exposure.