Português | English

Partitional Operators (Partops)

Partitional Operators (Partops) is a tool for assistance in compositional or analytical musical tasks using Partitional Analysis. It is a program aimed at composers, music researchers, mainly texture and analysis, and those interested in better understanding of Partitional Analysis and its derived theories.Version 1.35 Beta is now in test phase and is offered as open source software.

Basic Instructions

Partops program interface consists of a table with time points (first column), and partitions (remaining columns, one part per column). The panels on the left can function as a calculator that applies partitional operators to integer partitions for selection and insertion in the table.

Interface Elements

1. Table

By default, the table has 16 rows and 11 columns, but the program can load tables with other dimensions. The size can also be changed while working.

• To edit the cell values:
  1. Click or double-click on any numeric value and type.
  2. Alternatively, it is possible to insert the partition directly, using Selection and Control Panels (items 2 and 5).
  3. Time points accept decimal values.
  4. Partitions fields (parts) accept integer values only (the interface ignores decimal values).
• To add a new row to the table:
  1. Select a row by clicking on a value or a cell.
  2. Click the Dupl button, inside Control Panel (item 5). The selected line duplicate and its values are available for editing.
  3. The selected line appears in the sel. row field, inside Control Panel (item 5).

• To delete a row
  1. Select a row by clicking on a value or a cell.
  2. Click the Del button, inside Control Panel (item 5). The row goes away, and the interface rearranges the subsequent ones.
  3. The selected row number appears in the sel. row field, inside Control Panel (item 5).
• To reset the table
  1. In the main menu, select Table> Reset. The table returns to the default state.
• To save the table
  1. In the main menu, select Table> Save or use the shortcut Ctrl+S
• To load a table previously saved or produced through the Parsemat program
  1. In the main menu, select Table> Open or use the shortcut Ctrl+O.

2. Selection Panel

The Selection window shows the result of applying the partitional operators - resizing (m), revariance (v), and transfer (t) to the current partition. This window is not editable and only serves to monitor results and insert them into the table using the Ins button. When opening the program, the Selection window initializes with partition [1].

When the result of the application of the operator generates more than one partition, a list of partitions is displayed. The one selected is always the first in the list; to access the next ones, use the Rot button, inside Control Panel (item 5).

3. Indices

This panel displays the indices of agglomeration (a), dispersion (d), and the global number of internal relations (T), referring to the partition in the Selection window.

• The agglomeration index (a) reflects the degree of dependence or internal convergence between components of the partition. Musically, this can mean more massive vertical situations, more dependent melodic lines, or more homogeneous instrumentations, and many other meanings, depending on the type of application.
• The dispersion index (d) indicates the degree of diversity or distinction between the internal components of the partition. Musically, this can mean explicit or implicit polyphonies (melodic), more colorful instruments, and many other meanings, depending on the type of application.
• The total index of relations (T) is the sum of the indexes (a, d). It corresponds to the number of total interactions between components involved in the integer partition, given by all pairwise combinations.

4. Operators

Six basic operations are available, coming from Partitional Analysis: three operators, in positive and negative forms.

• Resizing (m): quantitative unitary change of one of the parts. Positive, when the part thickens (+ m). Negative, when the part tapers (-m).
• Revariance (v): addition (+ v) or subtraction (-v) of a unitary part to the integer partition.