The content of books V–XII of the Schillinger System has not been used in either of the modules due to the restricted scope of this thesis. Additionally, several aspects
5This is not to suggest that single-note melodies cannot be musically interesting. In this case however, they will certainly be trivial.
§3.7 Parts of Schillinger’s Theories Not Utilised 63
of books I–IV have also been omitted from the project for various reasons. These are listed below to help give a clear idea of the extent and limitation of the current work, and also as a reference for future work.
• The use of tertiary generators, variation techniques and algebraic expansions for producing poly-rhythmic textures has not been included because the system does not currently incorporate a notion of polyphony. Polyphony is central to the construction of more complex compositions, requiring the context of books V–XII.
• The application of resultants and synchronisation to ‘instrumental forms’ is omit- ted because it pertains to instrumentation and orchestration, which are discussed in later books.
• Rests are not incorporated into the rhythmic generator for want of a more so- phisticated method determining their placement. Schillinger offers minimal ad- vice on the placement of rests.
• Rhythmic accents are not incorporated because they are only covered extremely briefly and fall partly into the realm of Schillinger’s Theory of Dynamics.
• Schillinger’s ‘evolution of rhythm styles’ is omitted because it consists primarily of an analytical discussion with reference to popular musical styles of his time of writing, rather than any explicit generative procedures.
• The discussion of ‘rhythms of variable velocities’ is relevant to the field of ex- pressive performance rather than to algorithmic composition as such. The prob- lem of expressive performance is mentioned in chapter 4 of this thesis.
• The use of synchronisation to produce simple looping melodic forms from pitch- scales has not been incorporated into the melodic module because it does not fit with the melodic axis paradigm, which is what the current melodic module is built around. As it is presented, it also produces absolute rhythmic monotony, which has been avoided for this system’s melodies.
• Schillinger’s ‘evolution of pitch-scale families’ refers to the use of interference, subdivision, circular permutation and transposition to build a set of supposedly related scales which may bring unity to a longer form piece. As both modules in this system are focussed on smaller compositions, this concept has been aban- doned for the present time.
• The concept of ‘melodic modulation’, as discussed in the Theory of Pitch-scales; that is, concatenating the synchronised melodic forms mentioned above into longer sequences using multiple pitch-scales with pivot sequences at the con- nection points, has not so far been incorporated into the melodic module. Again this is due to it being largely incongruous with the axis paradigm. Schillinger’s method of identifying and reusing motifs using this concept should also be noted.
• Producing melodic continuity from symmetric pitch-scale ‘contractions’ has been omitted for the same reasons as above.
• The accompaniment of the simple harmonic procedures in section 3.3.4 with melodic forms derived from the same pitch-scale has been omitted from the cur- rent implementation, because without significant human intervention it places too many restrictions on the current method for harmonic generation used in the harmonic module.
• The concatenation of short melodies into longer melodies using only geometri- cal inversions has been avoided as a technique in itself, because the equivalent functionality exists in the melody builder as part of the somewhat more sophis- ticated melodic module.
• Geometrical expansions in the temporal domain have been left out of the melodic module for the time being because they produce quite drastic incongruities in what are currently short-form compositions. It may be more appropriate to in- clude this once more explicit concepts of form and higher-level structure have been incorporated from later books.
• The geometrical expansion of harmonies is not currently performed, because it has the effect of simply projecting a chord progression from the 12√
2 tuning sys- tem into whole-tone (√6 2), diminished (√4 2), augmented (√3 2) and tritone (√2 2) systems. This technique was deemed unnecessarily limiting for short harmonic passages, but could be viable in the context of longer compositions.
• No attempt has been made to automate Schillinger’s notion of musical seman- tics because it is mostly in the form of philosophical discussion. The section on climax and resistance in relation to a ‘psychological dial’ is particularly note- worthy because in the past it has been referred to by successful film composers [Degazio 1988]. As explained in section 3.6.2, the user is currently in control of ‘seeding’ the melodic module with a set of abstract axis types, but no explicit musical meaning is drawn from their combination when building a composi- tion.
• Schillinger’s application of melodic trajectories to generate short embellishments has not been used in the current system, but is fairly amenable to being added in the short term.
• The very brief discussion on melodic modulation in the context of axis systems is omitted because it was felt that it would be better considered in the future alongside Schillinger’s other discussions of melodic modulation in the context of pitch-scales.
• Finally, the use of ‘organic forms’ (melodic motifs or entire passages generated using number sequences related to the Fibonacci series) in melody generation