Music Programming - Serial Matrix Display (Help needed)

This is a discussion on Music Programming - Serial Matrix Display (Help needed) within the C Programming forums, part of the General Programming Boards category; Hi I have the following assignment to do for a music programming class but I'm a brutal programmer so need ...

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    Music Programming - Serial Matrix Display (Help needed)

    Hi

    I have the following assignment to do for a music programming class but I'm a brutal programmer so need some help with C. I don't expect someone to do the whole thing for me, but any help with the following problem would be greatly appreciated. If anyone can help with some parts of this, I would really appreciate it.

    Matrices are a major problem so help with the matrix elements would be particularly great.

    Thanks

    The program is to: Write a program that, given a certain series of 12 unique pitch-classes
    (notes), prints out the 12x12 serial matrix. Here’s an algorithm:

    and the info is given below:


    Serial Matrix Display

    Serial Music is one of the names given to the technique of composition developed by
    Arnold Schoenberg in the early decades of the 20th Century. It consists on using a tone
    row of 12 different pitch-classes (C, C#, ..., B) in four different versions (original,
    inverted, retrograde and retrograde of inversion) as the basis for a piece. The tone row
    can have pitch-classes in any order, but without any repetition (as a plain introduction,
    see Twelve-tone Technique in the Wikipedia or, for more details, Serialism in the online
    Grove Dictionay of Music).

    In order to assist the process of composition or analysis of 12-tone music, a 12x12 serial
    matrix can be built. The first row of the matrix will receive the original 12 notes, from the
    left to the right. The inversion of the series will fill the first column of the matrix, from
    the top to the bottom. To complete the matrix, the other rows will receive transposed
    versions of the original series, each one starting with the note in the first column. When
    the matrix is completed, all the transposition forms of the original series can be read in
    the rows from left to right, the retrograde forms in the same rows from right to left, the
    inversions in the columns from top to bottom and the retrograde of inversion forms in the
    opposite sense.

    Write a program that, given a certain series of 12 unique pitch-classes
    (notes), prints out the 12x12 serial matrix. Here’s an algorithm:

    (a) substitute the notes for integers in an ordered form from 0 to 11, i.e. representing
    pitch-class C by the number 0, the pitch-class D-flat (or C-sharp) by the number 1 and
    so on, up to the pitch-class B, which will be represented by the number 11.

    (b) all the manipulations with the serial forms can be treated by arithmetical formulas. In
    this case, the formulas for the creation of the first column inverse form could be
    Pm,1 = [(Pm-1,1+ (P1,m-1 - P1, m)] mod12

    (c) and the subsequent transposition of the original series
    Pm,n = [(P1,n + (Pm,1 - P1,1)] mod12

    For this assignment, you will write a program that takes in a user-defined tone-row as
    input and then build a serial matrix and display it at the terminal (see notes below).

    Example:

    1 Original series: B B-flat D E-flat G G-flat A-flat E F C D-flat (Webern , op. 24)
    2 Numerical representation: 11 10 2 3 7 6 8 4 5 0 1 9
    3 First column inverse form:

    P2,1 = [(P1,1+ (P1,1 - P1, 2)] mod12 = [(11 + ( 11 - 10)] mod12 = 12 mod12 = 0
    P3 1 = [(P2,1+ (P1,2 - P1, 3)] mod12 = [(0 + ( 10 -2)] mod12 = 8 mod12 = 8
    P4 1 = [(P3,1+ (P1,3 - P1, 4)] mod12 = [(8 + ( 2 - 3)] mod12 = 7 mod12 = 7
    ...
    P12 ,1 = [(P11,1+ (P1,11 - P1, 12)] mod12 = [(9 + ( 1 - 9)] mod12 = 1 mod12 = 1

    4 First row transposed original form:

    P2,2 = [(P1,2+ (P2,1 - P1, 1)] mod12 = [(10 + ( 0 - 11)] mod12 = [-1] mod12 = 11
    P2,3 = [(P1,3+ (P2,1 - P1, 1)] mod12 = [(2 + ( 0 - 11)] mod12 = [-9] mod12 = 3
    ....
    P2,12 = [(P1,12+ (P2,1 - P1, 1)] mod12 = [(9 + ( 0 - 11)] mod12 = [-3] mod12 = 9

    5 The 12x12 serial matrix:

    11 10 2 3 7 6 8 4 5 0 1 9
    0 11 3 4 8 7 9 5 6 1 2 10
    8 7 11 0 4 3 5 1 2 9 10 6
    7 6 10 11 3 2 4 0 1 8 9 5
    3 2 6 7 11 10 0 8 9 4 5 1
    4 3 7 8 0 11 1 9 10 5 6 2
    2 1 5 6 10 9 11 7 8 3 4 0
    6 5 9 10 2 1 3 11 0 7 8 4
    5 4 8 9 1 0 2 10 11 6 7 3
    10 9 1 2 6 5 7 3 4 11 0 8
    9 8 0 1 5 4 6 2 3 10 11 7
    1 0 4 5 9 8 10 6 7 2 3 11

    Notes:

    1. mod12 = is the generalized modulus-12 operation (defined for both positive and
    negative numbers), and not simply the ‘%’ remainder operator. Eg.: 5mod12 = 5;
    12mod12=0; -5mod12=7; 15mod12=3; -10mod12=2, etc. It is up to you to implement
    this operation as best as possible.
    2. The program should ideally take pitch-class names (C,c,C#,c#, Db,db,D,d etc...),
    which will then be translated into numeric form. For the matrix display, you should also
    print pitch-class names. Remember that C and c should be equally good inputs for pitchclass
    C and that certain notes have the same pitch class (eg. Db and C#) and should also
    be allowed.
    3. The program should do all the checks for wrong inputs etc.
    4. As a suggestion, write the program in incremental steps, implementing one
    functionality at a time. If you do not manage to implement everything, at least you have
    something that works partially.
    5. The mode of input should be interactive (ie. the user should be queried for input).
    6. As an extra, if you are on Windows would be to playback the series or one of its
    variants (say a column or a row of the matrix) using MIDI (see the website for a sample
    code).

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