Dapper '1' and Dreadful '0' (Armstrong, Peter McKenzie)

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Performances

Recordings

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Synthesized/MIDI

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Peter M. Armstr... (2015/11/26)

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Peter M. Armstr... (2015/11/26)

Performer Pages Peter McKenzie Armstrong (Rosegarden & Pianoteq)
Publisher Info. Edition Ottaviano Petrucci
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MID file (audio/video)
Composer (2012/1/23)

MID file (audio/video)
Composer (2012/1/23)

Performer Pages Peter McKenzie Armstrong (Rosegarden)
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Sheet Music

Scores

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Composer (2012/1/23)

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Composer (2012/1/23)

Publisher. Info. Edition Ottaviano Petrucci
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Misc. Notes Engraved with LilyPond 2.13.32.
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General Information

Work Title Dapper '1' and Dreadful '0', for sequenced MIDI piano
Alternative. Title
Composer Armstrong, Peter McKenzie
Movements/SectionsMov'ts/Sec's 2 movements
Year/Date of CompositionY/D of Comp. 2011
Average DurationAvg. Duration 78 seconds
Composer Time PeriodComp. Period Modern
Piece Style Modern
Instrumentation Autopiano


Misc. Comments

COMPOSITION NOTES

Dapper '1'

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:

starting with                1   2
one iteration giving     1   3   2
the next                      1   4   3   5   2
and so on.

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:

  • at each instance, a term within key range is allocated to one of 10 unique-volumed tracks, according to the term's occurrence tally at that instance;
  • for each term (MIDI key number) so assigned, a rest is placed in corresponding position on all other tracks;
  • terms above range are realized as rests on all tracks (i.e., their time component is preserved);
  • an additional track, a copy of #1 but with its rest slots filled in by extension of their just-previous notes, integrates and highlights the pattern of first occurrences.

Dreadful '0'

Then, comeuppance! Browsing at the "Online Encyclopedia of Integer Sequences" (OEIS), I encountered for the first time Stern's biatomic array (http://oeis.org/A002487). 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:

starting with                0   1
one iteration giving     0   1   1
the next                      0   1   1   2   1
and so on.

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:

  • there are now 42 unique-volume-specific tracks, necessarily at much narrower volume differences;
  • 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.

Scores

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.