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Absement: The time-ingeral if displacement --- Examples
Wheras pianos respond to velocity (hit the key faster to make it louder) and organs respond to displacement (position of the key), hydraulophones respond to absement.

Absement is the time-integral of displacement

The word "absement" derives from the words "absence" and "displacement". I will attempt to explain the concept of absement by way of the following simple example:

Consider a 5-hour train ride that takes you 500 miles directly away from your home, in a straight line, to another destination where you stay for 5 hours and then return. Suppose you want to stay wirelessly glogged into your home computer at a "roaming" communications cost of $1/mile/hour. For simplicity, assume a linear long-distance rate, i.e. $1/hour when you're 1 mile away, $2/hour when you're 2 miles away, $3.14/hour when you're 3.14 miles away, etc.. The total cost of your online communications is $5000, since the absement (time-integral of displacement) is 5000 mile hours (1250 mile hours on the way to your destination, plus 500 miles * 5 hours stay = 2500 mile hours, plus 1250 mile hours of absement during the return trip).

The middle plot shows Displacement. The first 5 hours are spent in the train going at velocity 100mph (miles per hour) away from home. The area under this triangular part is 1/2 five times 500 mile hours, which is 1/2 times 2500 mile hours, i.e. 1250 mile hours. The next 5 hours are spent at your destination, 500miles from your home, where you pay $500/hour for 5 hours, for a cost of $2500. Staying online during your return trip costs you another $1250.

Your total cumulative running cost is the area under the middle plot up to a particular point in time. This integral is called absement and is shown on the top plot.

Each of the three plots is the time-derivative of the plot above it:

Absement-responsive musical instruments: Gallery of hydraulophone pictures

Hydraulophone in Experimental Musical Instruments publication

See and hear a musical composition for hydraulophone and orchestra: