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Math Help - Finding a finite set of values for variables for a musical composition

  1. #1
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    Finding a finite set of values for variables for a musical composition

    Hello mathematicians,

    I am a student of musical composition and I need to solve the following problem for one of my pieces. I worked on it for a long time but I have not taken enough advanced algebra to solve it.

    I am looking for the list: W=((x_{0},n_{0},q_{0},s_{0}),(x_{1},n_{1},q_{1},s_  {1}),(x_{2},n_{2},q_{2},s_{2}),...(x_{w},n_{w},q_{  w},s_{w}))
    such that
    1. \sqrt{x_{i}+\mathit{n_{i}q_{i}}}=58\frac{9}{16}+\s  qrt{x_{i}}
    2. \sqrt{x_{i}+q_{i}}=11\frac{3}{16}+\sqrt{x_{i}}
    3. \sqrt{x_{i}+\mathit{n_{i}q_{i}}}=s_{i}+\sqrt{x_{i}  +(n_{i}-1)q_{i}}
    4. 2\le s_{i}<11\frac{3}{16}
    5. s_{i}\in \mathbb{R}
    6. n_{i}\in \mathbb{Z}
    7. x_{i}\in \mathbb{R}
    8. q_{i}\in \mathbb{R}

    where \neg \exists<br />
V=(x_{v},n_{v},q_{v},s_{v})(V\notin W\wedge V\text{ satisfies 1{}-8})

    Any help solving for W would be appreciated.

    Thanks,

    Silly
    Last edited by silly; September 5th 2009 at 07:44 AM. Reason: simplification
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