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

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Synthesized/MIDI

 MIDI-sequenced, Movement 1  
#173332 - 0.00MB - 36 seconds -  0.0/10 2 4 6 8 10 (0) - - !N/!N/!N - 93x

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

 MIDI-sequenced, Movement 2  
#173333 - 0.01MB - 39 seconds -  0.0/10 2 4 6 8 10 (0) - - !N/!N/!N - 47x

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

TN-dreadful 0.jpg
Performer Pages:

Peter McKenzie Armstrong (Composer)

Publisher Info.:

Composer

Copyright:

Creative Commons Attribution Non-commercial No Derivatives 3.0 [tag/del]

Misc. Notes:

Output via Rosegarden matrix editor

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Sheet Music

Scores

 Movement 1: Full score (10 tracks)
#173302 - 0.21MB, 9 (11x17, landscape) pp. -  10.0/10 2 4 6 8 10 (1) - !N/!N/!N - 346x

PDF typeset by Peter M. Armstrong
Composer (2012/1/23)

 Movement 2: Individual parts (42 tracks)
#173303 - 0.39MB, 51 (A4, landscape) pp. -  10.0/10 2 4 6 8 10 (1) - !N/!N/!N - 114x

PDF typeset by Peter M. Armstrong
Composer (2012/1/23)

TN-dreadful 0.jpg
Publisher Info.:

Composer

Copyright:

Creative Commons Attribution Non-commercial No Derivatives 3.0 [tag/del]

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/Sections 2 movements
Year/Date of Composition 2011
Average Duration 78 seconds
Piece Style Modern
Instrumentation Sequenced MIDI piano


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.

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