TTRM is a program written by Alexandros Droseltis that


As the program starts, the main window opens. On the top of there are two input fields and under it two cards, the "Export" and the "Search & Find" card. In the first you can type a row an in the second field, a title for it. The notation of the row must be the german one, for example (from Alban Berg's Lulu):

c1 e1 f1 d1 g1 a1 fis1 gis1 h1 ais1 dis1 cis1

The non-numerical part of the notes indicates the pitch class, and the numerical the octave (a1=440Hz). Mind that "h" is the german name for "b" and that the german "b" means "b flat"!

Further Options:


After you have given the row, you can view the respective tables through the "View" Menu. Notice that the "Verticals" option is disabled, unless you select the option "verticals" in the "Export" card, with the respective form and transposition.


On the generated table the title of the row can be seen, and the four forms of the row in their twelve transpositions. The letter "P" indicates the prime forms, the letter "R" indicates the retrograde forms, the letter "I" indicates the inverted forms and the letters "RI" indicate the retrograde forms of the inverted forms.

The numbers at the left of the matrix indicate the first note of the P- and I-transpositions. 0 means C, 1 means C sharp (or D flat), 2 means D etc. For example, P7 is the prime form that starts from G, I8 is the inverted form that starts from G sharp or A flat. Rx or RIx are the retrograte forms of the respective Px or Ix. e.g. R9 is the retrograde form of P9, RI2 is the retrograde form of I2. This notation is widely used for the twelve-tone analysis.

The program will arrange the octave place around the trable clef, so the octave number in the row field indicates only the internal intervals of the tones of the row, and not the absolute pitch of them.


These kinds of matrices are used too at the twelve-tone analysis. The square matrix consists horizontally of the twelve transpositions of the prime form of the row and vertically of the twelve transpositions of the inverted form of it. The opposite directions build the retrograde and retrograde-inversion respectively. The advantage of this matrix is that the whole network can be seen with one glance.

The square matrix has sense only if the row is a twelve-tone one (without repetitions); otherwise not all of the forms will be printed (if the row has repetitions, some of the forms will be printed at least twice).

The square matrix can consist of the german names of the notes or of the pitch classes (0 for C, 1 for C sharp etc.) The content of the above generated arrays can be influenced from the export card (s. below).


The presentation of the stravinskian verticals is very complex, so I would better suggest the following literature:


On the export card the type of the exported file can be selected: a TeX file for the row matrix and the vertical table, and/or text files for the square matrices (nummerical and german). The box "Other Options" includes the following options:

The selected options on the export card affect the exported file, as well as the viewed tables through the "View" menu.


On this card a set of notes can be entered, that must be searched in the row matrix. The set must have at most eleven tones. The set can be ordered (its tones must me searched in the order they appear) or not ordered (all possible combinations of its tones must be searched). In the square below the "order" buttons appear the forms of the row and the exact position in it, in which the given set has been found. Rotation cases are included, as well as independent hexachords. For example, if the set has five tones and the resutls are:

that means that the given set exists at the notes:


In order to run TTRM at 100%, you must have the following files and programs:


I started writing this program in June 2001 during the editing of my thesis on the twelve-tone works of Igor Stravinsky. It helped me very much generating the twelve-tone matrices. I hope it will be useful to other people too, for analytical as well as compositional purposes.