Dapper '1' and Dreadful '0'for 10-track autopiano[1:22]Dapper '1'
Tinkering one day with the Fibonacci series, I wondered what might happen if, rather than summing at each step only the most recent pair, I were to sum internally all pairs thus-far generated, placing each sum between (not after) its pair elements:By its 9th iteration my impromptu generating script output all integers between 1 and 88 (the piano range) at least once and up to 10 times. With this data reserved as pitch source, I shaped a progression of equal durations, as follows:starting with 1 2
one iteration giving 1 3 2
the next 1 4 3 5 2
and so on.at each instance, a term (MIDI key number) within range is allocated to one of 10 unique-volumed tracks, according to the term's occurrence tally at that instance;The movement is written in full score, as it has few enough tracks to fit a 11x17" page.for each term so assigned, a rest is correspondingly positioned on all other tracks (i.e., its time component is preserved);
an additional track, a copy of #1 but with the rest slots filled in by extension of their just-previous notes, integrates and highlights the pattern of first occurrences.
Dreadful '0'
Then, a comeuppance. Browsing at the "On-Line Encyclopedia of Integer Sequences" (OEIS), I encountered for the first time Stern's Biatomic array. Run for two iterations beyond the series I had improvised, this one clearly subsumed that former's output!The difference, Stern's 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. My reseeded script generated the sequence as follows:
Running this way well into its 11th iteration, 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 akin to movement 1, called for selective re-specifying, as follows:starting with 0 1
one iteration giving 0 1 1
the next 0 1 1 2 1
and so on.there are now 42 unique-volume-specific tracks, necessarily at much narrower volume differences;This movement, with too many tracks to fit the page, is written as separate parts.
tempo is now 4-fold, to put so many more events into a time span compatible with Dapper '1';
a 3-second coda cascades the first occurrences.Neither score is intended to facilitate human performance. The music is for auto-sequencer, with scoring intended simply as a reasonably patterned read-along image. It uses alto clef exclusively, sparing the eye an incessant disruption of clef changes.
The movements are named for what strikes me as their "character" -- ultimately their comfy-vs-jagged patterns of volume distribution.