about Study 1    ( capella score and original recordings )

This score was originally written (2005) in CapXML format using the programming language Python.
Having read the resulting file into capella, I inserted line breaks, removed superflous dynamics and added Moritz control texts. Otherwise, the score is exactly as it was when capella first read it.
Generally, capella's automatic spacing was very good (see the score at the above link), but in extreme situations like this, noteheads and accidentals sometimes collided and/or overlapped. Capella omitted accidentals if they were already in force. The colours mark structural positions in the performed krystals (see below).

capella’s performance
was set up using it's performance options. Capella had (has) an advanced set of these, and could play many different standard instructions (pizz., accel., rit., accents, dynamics, ornaments etc.).

Moritz’ original performance: Moritz' original (desktop) Assistant Performer used special performance instructions in the CapXML. For example: t250 at the top of the score set the duration of a normal crotchet to 60/250 seconds. A small number attached to a dynamic (see the first instance of each) sets its MIDI velocity, as a percentage of the possible values, until further notice.

Assistant Performer: The piece was transcribed for my Assistant Performer web application in March 2016. It can now be played there too. The MIDI velocity values have been preserved, though Moritz transcribes these values differently. For example, the quietest chords ( ppp in the capella score) have MIDI velocity 29 (ca. 23*1.27), but Moritz transcribes this value as pp.
The following screen recording (using the Arachno soundFont on the Resident Sf2 Synth) was made in May 2017: View online (with comments) / right-click to download mp4 (for better rendering).

Construction: Study 1 is controlled by two related krystals, having the same shape and size. Krystal 1 controls the base pitch of each chord in the sequence. Krystal 2 controls the four chord parameters: dynamic, duration, inversion (shape) and density (number of pitches), so these are fixed together, always in parallel.
The durations are fractions of the standard crotchet duration (set by the “tempo” indication at the top of the score).
These are “tuplet” durations, and the only values that could be set for different crotchets having the same tempo in capella. The milliseconds value is the corresponding duration used in the transcription for Assistant Performer.
In principle, the Assistant Performer can use any millisecond duration for chord symbols.
dynamic duration inversion density milliseconds
fff 8/8 (5) 1 240
ff 8/9 6 2 213
f 8/10 7 3 192
mf 8/11 8 4 175
mp 8/12 9 5 160
p 8/13 10 6 148
pp 8/14 11 7 137
ppp 8/15 12 8 128

The inversion numbers denote chords in the following table. (The numbers are the number of semitones between neighbouring notes in the chord.) Inversion 1 is like the harmonic series, inversion 12 is inversion 1 upside-down.
The inversions between these extremes are derived using a linear krystal field:

1 1 1 1 1 1 12 12 12 12 12 12
2 2 2 2 2 12 1 7 7 7 7 7
3 3 3 3 12 2 7 1 5 5 5 5
4 4 4 12 3 7 2 5 1 4 4 4
5 5 12 4 7 3 5 2 4 1 3 3
7 12 5 7 4 5 3 4 2 3 1 2
12 7 7 5 5 4 4 3 3 2 2 1
1 2 3 4 5 6 7 8 9 10 11 12
        fff ff f mf mp p pp ppp

Krystals: The two level 4 krystals that directly control the chords are:
Krystal 1: The base pitches of the chords.
In the capella score, 1 is middle C# and 8 is the G# above. The Assistant Performer’s transcription is a semitone lower: 1 is middle C and 8 is the G above.

Krystal 2: The density, shape and inverse dynamic (velocity) of the chords.




Both the above krystals were constructed using the following density krystal hierarchy:
Number of paragraphs: 9

Number of blocks per paragraph (level 1):


Number of lines per block (level 2):


Number of values per line (level 3);

Unfortunately, I have no access to the original krystals. Possibly they have been lost completely. The above values have been recreated by reading the original, coloured capella score, and checking this against the binary files that the original Python program read. The level 4 krystals’ hierarchy and eccentricity inputs can therefore only be inferred.