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|Work Title||Dapper '1' and Dreadful '0', for sequenced MIDI piano|
|Composer||Armstrong, Peter McKenzie|
|I-Catalogue NumberI-Cat. No.||IPA 17|
|Year/Date of CompositionY/D of Comp.||2011|
|Average DurationAvg. Duration||78 seconds|
|Composer Time PeriodComp. Period||Modern|
Tinkering one day with the Fibonacci series, I wondered what might happen if, instead of adding always just the most recent two terms to get the one following, I were to add every pair of terms to get for each pair a new term in between:
I wrote a short generator (J-language script) and ran it to the point (in iteration #9) where it had output all integers between 1 and 88 -- the piano range -- at least once. Except for this sampling's unique final term, all its terms within range had occurred from 2 to 10 times each, with a few dozen others exceeding it. Given these circumstances, I shaped a progression of equal durations, as follows:
Then, comeuppance! Browsing at the "Online Encyclopedia of Integer Sequences" (OEIS), I encountered for the first time Stern's biatomic array (). When run for two iterations beyond the series I had improvised, this one clearly subsumed the latter's output. The difference, Stern seeds "0 1" replacing my hazarded "1 2", exposes something extraordinary at work: with this "0 1" start, every generator iteration first replicates the just-previous one, before appending then a continuation of its own. OEIS presents several offshoots. My improvised script output the sequence as follows:
Run this way well unto its 11th iteration (to build up from 0), the procedure now filled the 88-slot range only after 1276 terms, accumulating an occurrence-frequency maximum of 42. Musical realization here, to be conceptually as before, called for selective re-specifying, as follows:
Dapper '1' is written in full score, as it has few enough tracks to fit a 11x17-inch page. Dreadful '0' , with too many to fit, is written instead as separate parts. In any case, neither score is intended to facilitate human performance. The music is for auto-sequencer. I did, however, want to give its overall patterning visual realization. Hence this style, with alto clef exclusively (Middle-C in the middle!) to spare the eye an incessant disruption of clef changes. The LilyPond files rework drafts I had initially exported from Rosegarden.
These pieces are named for what strikes me as their "character" -- ultimately their comfy vs jagged patterns of volume distribution.