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.
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.
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, click on the numeric values and type.
- Time points accept decimal values.
- The parts accept integer values only (the interface ignores decimal values).
- To add a new row to the table: Select a row by clicking on a value or a cell.
- Click the Dupl button. The selected line duplicate and its values are available for editing.
- The selected line appears in the sel. row field, above the table.
- To delete a line Select a row by clicking on a value or a cell.
- Click the Del button. The line goes away, and the interface rearranges the subsequent lines.
- The selected line number appears in the sel. row field, above the table.
- At any time, it is possible to reset the table through the Table> Reset menu. The table returns to the default state.
- To save the table, use the command Table> Save or the shortcut Ctrl+S
- To load a table previously saved or produced by the Parsemat program, use the command Table> Open or the shortcut Ctrl+O.
Selection window shows the result of applying the partial operators (m, v, 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 .
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.
In this panel, three indices (a, d, T) are presented, referring to the selection window partition.
- 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 relationships between components involved in the integer partition, given by pairwise combinations.
Six basic operations are available, coming from Particular 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.
- Transfer (t): when a unitary component is transferred from one part to another, unitary or not. This operation is composed, as it comprises two simple operations (m and/or v) with opposite signs ([+ m -v] or [-m + v]; in some cases, [+ m -m]). The transfer is positive (+t) when it causes progression (movement towards more dispersed partitions) and negative (-t) when it causes recession (movement towards more agglomerated partitions).
Em alguns casos, a operação não é aplicável (não existem resultados a partir da partição que está na janela de seleção). Isso faz parte da própria estrutura subjacente aos operadores. Quando isso acontece, ao clicar no botão, a janela de seleção se manterá no mesmo estado.
The buttons on this panel help to modify or select the data produced in the selection window and the table.
- CE – resets the selection window, returning to the default partition .
- Rot – in cases where the application of the operators results in two or more partitions, the Rot button allows the selection of each one, through the vertical rotation of the list of partitions.
- Del – delete a row from the table. Clicking on a value or cell selects the corresponding row. The sel. row field, above the table, indicates line selection.
- Dupl – duplicates a row in the table. You must select a row by clicking on a value or cell in the table.
- ▲ (up) and ▼ (down) – navigation through the table lines. Navigation can also proceed by clicking on values or cells, but the up and down buttons can save mouse movements, as it stays next to the insertion button and operators. It is also possible that the insertion of partition takes place line by line, in ascending order, which gives these buttons an additional function.
- Ins – inserts the selection window partition into a row in the table. You must select a row by clicking on a value or cell in the table. Up and down buttons can also accomplish the selection.
After completion of the partition table, the program allows visualization in the form of an Indexogram and Particiogram.
- Index – produces the indexogram for the table. The opened window can be resized and brings Matlab figure commands for editing and viewing (see reference here). Indexogram shows the indexes of agglomeration and dispersion over time, forming textural curves.
- Partic – produces the partitiogram referring to the table. The opened window can be resized and brings the Matlab figure commands for editing and viewing (see reference here). Partitiogram shows all partitions used in the table with their positions defined according to their degrees of homogeneity or internal diversity.
Once the graph window is open, you can edit the table without closing it, and click the corresponding button Index or Partic again to update the graph immediately.