Finding a finite set of values for variables for a musical composition

silly · #1 $Old$ August 30th, 2009, 10:09 PM

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. $\sqrt{x_{i}+\mathit{n_{i}q_{i}}}=58\frac{9}{16}+\sqrt{x_{i}}$
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 $\neg \existsV=(x_{v},n_{v},q_{v},s_{v})(V\notin W\wedge V\text{ satisfies 1{}-8})$

Any help solving for W would be appreciated.

Thanks,

Silly