Core concepts¶

Perllan and trees.¶

Perllan is a welsh word for “orchard.” When object modelling music notation, it becomes clear that most models take the graph form of a tree. The Perllan network of Python packages which wrap Abjad represents a location and a set of tools designed for the purpose of cultivating these trees.

An analysis of a score tree can help in understanding the implications of parameter parentage. Traditional Western music notation is rooted firmly in Medieval formal architectures. Pitch notation is resolutely diatonic, non-power-of-two-denominator durations can only be represented with the assistance of a prolating tuplet bracket or time signature, and duration chains of prime-number-numerator durations greater than 3 can only be notated via tie-chained notes.

A parent score can hold children as staves or staff-groups, staves hold children as voices. Staff groups may hold staves as well. A staff may hold one or more voices, but a voice, while not distinctly notated with unique symbols, is always implied. A voice may hold children as tuplet-prolated containers or (explicit or implied) tie-chained duration events. Tuplet-prolated containers may also hold tie-chained events. Abjad refers to these tie-chained events as Logical Ties. Logical ties may hold children as single-symbol (prime-number-numerator durations less than 3) leaves. While a pitch value persists through the duration of a logical tie, the notation of pitch is represented through the positioning of the note head of a leaf and when applicable, the affixing of an accidental symbol preceding the initial leaf of a logical tie. Since the positioning of note heads is required on a leaf-by-leaf basis within a logical tie, it can be implied that within the tree-structure of a musical score, the pitch value of a given note is not at the same depth as the duration value, rather pitch is a child of duration or at least a subordinate sibling. Another form of parentage increases the child-like nature of the pitch parameter. In abjad, leaves are object-modelled with an abstract base class abjad.Leaf() which has duration but no pitch. The classes which inherit from leaf are abjad.Skip(), abjad.Rest(), and abjad.Note(). Note is the only class which carries a pitch attribute. Since the child class has an attribute which the parent class does not have, this attribute is a child of the parent class.

There are several ramifications of this structure:

• A voice (explicit or implied) is always present as the lowest level of context containers, even in abstract manipulations of structures like pitch and duration.

• Regardless of when it is conceived by the composer, the tree of a score must be populated in a top-down fashion, gradually filling each parent with its children. Therefore, logical tie and leaf values must exist before pitch values can be affixed within a score.

Perllan interfaces to pitch transforms require a selection of logical ties in order to apply pitch values. Not only is this consistent with the parentage model described above, the decoupling of parameters allows for a greater number of transformational possibilities, including those which would be possible if pitch and rhythm were not decoupled.

Pitch rounding.¶

The pitch utilities in abjad-ext-microtones do not coerce number rounding. The et package only models scales of eighth, tenth, and twelfth divisions of the octave. The ji package only models 23-limit interval ratios. It is the composer’s responsibility to round pitch numbers before deployment.

Personal libraries.¶

Personal libraries such as evans can provide users with useful programming solutions, while holding a slightly less officially published quality.