\documentclass[12pt]{article}

\usepackage{bj,txfonts}

\begin{document}


Multi-level:

\def\c#1{\mbox{\scriptsize\it #1}}
\begin{eqnarray*}
\mbox{Classical}_i & = & \alpha_{0j[i]} + 
\alpha_{\c{guitar},j[i]} \cdot 1_{\{\c{Instrument}_i=\c{guitar}\}} + 
\alpha_{\c{piano},j[i]} \cdot 1_{\{\c{Instrument}_i=\c{piano}\}} + 
\alpha_{\c{string},j[i]} \cdot 1_{\{\c{Instrument}_i=\c{string}\}} + \\ & &  
\alpha_{\c{contrary},j[i]} \cdot 1_{\{\c{Voice}_i=\c{contracy}\}} + 
\alpha_{\c{par3rd},j[i]} \cdot 1_{\{\c{Voice}_i=\c{par3rd}\}} + 
\alpha_{\c{par5th},j[i]} \cdot 1_{\{\c{Voice}_i=\c{par5th}\}} + \\ & & 
\alpha_{\c{I-IV-V},j[i]} \cdot 1_{\{\c{Harmony}_i=\c{I-IV-V}\}} + 
\alpha_{\c{I-V-IV},j[i]} \cdot 1_{\{\c{Harmony}_i=\c{I-V-IV}\}} + \\ & & 
\alpha_{\c{I-V-VI},j[i]} \cdot 1_{\{\c{Harmony}_i=\c{I-V-VI}\}} + 
\alpha_{\c{IV-I-V},j[i]} \cdot 1_{\{\c{Harmony}_i=\c{IV-I-V}\}} + \epsilon_i ~,~~ \epsilon_i \stackrel{iid}{\sim} N(0,\sigma^2)\\
\alpha_{0j} & = & \beta_0 + \eta_{0j} ~,~~ \eta_{0j} \stackrel{iid}{\sim} N(0,\tau_0^2) \\
\alpha_{\c{guitar},j} & = & \beta_{\c{guitar}} + \eta_{\c{guitar},j}~,~~ 
   \eta_{\c{guitar},j} \stackrel{iid}{\sim} N(0,\tau_{\c{guitar}}^2) \\
\alpha_{\c{piano},j} & = &  \beta_{\c{piano}} + \eta_{\c{piano},j}~,~~ 
   \eta_{\c{piano},j} \stackrel{iid}{\sim} N(0,\tau_{\c{piano}}^2) \\
\alpha_{\c{string},j} & = & \beta_{\c{string}} + \eta_{\c{string},j}~,~~ 
   \eta_{\c{string},j} \stackrel{iid}{\sim} N(0,\tau_{\c{string}}^2) \\
\alpha_{\c{contrary},j} & = & \beta_{\c{contrary}} + \eta_{\c{contrary},j}~,~~ 
   \eta_{\c{contrary},j} \stackrel{iid}{\sim} N(0,\tau_{\c{contrary}}^2) \\
\alpha_{\c{par3rd},j} & = & \beta_{\c{par3rd}} + \eta_{\c{par3rd},j}~,~~ 
   \eta_{\c{par3rd},j}  \stackrel{iid}{\sim} N(0,\tau_{\c{par3rd}}^2) \\
\alpha_{\c{par5th},j} & = & \beta_{\c{par5th}} + \eta_{\c{par5th},j}~,~~ 
   \eta_{\c{par5th},j}  \stackrel{iid}{\sim} N(0,\tau_{\c{par5th}}^2) \\
\alpha_{\c{I-IV-V},j} & = & \beta_{\c{I-IV-V}} + \eta_{\c{I-IV-V},j}~,~~ 
   \eta_{\c{I-IV-V},j} \stackrel{iid}{\sim} N(0,\tau_{\c{I-IV-V}}^2) \\
\alpha_{\c{I-V-IV},j} & = & \beta_{\c{I-V-IV}} + \eta_{\c{I-V-IV},j}~,~~ 
   \eta_{\c{I-V-IV},j} \stackrel{iid}{\sim} N(0,\tau_{\c{I-V-IV}}^2) \\
\alpha_{\c{I-V-VI},j} & = & \beta_{\c{I-V-VI}} + \eta_{\c{I-V-VI},j}~,~~ 
   \eta_{\c{I-V-VI},j} \stackrel{iid}{\sim} N(0,\tau_{\c{I-V-VI}}^2) \\
\alpha_{\c{IV-I-V},j} & = & \beta_{\c{IV-I-V}} + \eta_{\c{IV-I-V},j}~,~~ 
   \eta_{\c{IV-I-V},j} \stackrel{iid}{\sim} N(0,\tau_{\c{IV-I-V}}^2) 
\end{eqnarray*}

Hierarchical:

It's actually somewhat difficult (or at least tedious) to write the Hierarchical model efficiently.  One way would be to define
\begin{eqnarray*}
m_i & = & \alpha_{0j[i]} + 
\alpha_{\c{guitar},j[i]} \cdot 1_{\{\c{Instrument}_i=\c{guitar}\}} + 
\alpha_{\c{piano},j[i]} \cdot 1_{\{\c{Instrument}_i=\c{piano}\}} + 
\alpha_{\c{string},j[i]} \cdot 1_{\{\c{Instrument}_i=\c{string}\}} + \\ & &  
\alpha_{\c{contrary},j[i]} \cdot 1_{\{\c{Voice}_i=\c{contracy}\}} + 
\alpha_{\c{par3rd},j[i]} \cdot 1_{\{\c{Voice}_i=\c{par3rd}\}} + 
\alpha_{\c{par5th},j[i]} \cdot 1_{\{\c{Voice}_i=\c{par5th}\}} + \\ & & 
\alpha_{\c{I-IV-V},j[i]} \cdot 1_{\{\c{Harmony}_i=\c{I-IV-V}\}} + 
\alpha_{\c{I-V-IV},j[i]} \cdot 1_{\{\c{Harmony}_i=\c{I-V-IV}\}} + \\ & & 
\alpha_{\c{I-V-VI},j[i]} \cdot 1_{\{\c{Harmony}_i=\c{I-V-VI}\}} + 
\alpha_{\c{IV-I-V},j[i]} \cdot 1_{\{\c{Harmony}_i=\c{IV-I-V}\}}
\end{eqnarray*}
and then write, ignoring the correlations again,
\begin{eqnarray*}
Classical_i & \sim & N(m_i,\sigma^2)\\
\alpha_{0j} & \sim & \beta_0 + \eta_{0j} ~,~~ \eta_{0j} \stackrel{iid}{\sim} N(0,\tau_0^2) \\
\alpha_{\c{guitar},j} & \sim & N(\beta_{\c{guitar}},\tau_{\c{guitar}}^2) \\
\alpha_{\c{piano},j} & \sim &  N(\beta_{\c{piano}},\tau_{\c{piano}}^2) \\
\alpha_{\c{string},j} & \sim & N(\beta_{\c{string}},\tau_{\c{string}}^2) \\
\alpha_{\c{contrary},j} & \sim & N(\beta_{\c{contrary}},\tau_{\c{contrary}}^2) \\
\alpha_{\c{par3rd},j} & \sim & N(\beta_{\c{par3rd}},\tau_{\c{par3rd}}^2) \\
\alpha_{\c{par5th},j} & \sim & N(\beta_{\c{par5th}},\tau_{\c{par5th}}^2) \\
\alpha_{\c{I-IV-V},j} & \sim & N(\beta_{\c{I-IV-V}},\tau_{\c{I-IV-V}}^2) \\
\alpha_{\c{I-V-IV},j} & \sim & N(\beta_{\c{I-V-IV}},\tau_{\c{I-V-IV}}^2) \\
\alpha_{\c{I-V-VI},j} & \sim & N(\beta_{\c{I-V-VI}},\tau_{\c{I-V-VI}}^2) \\
\alpha_{\c{IV-I-V},j} & \sim & N(\beta_{\c{IV-I-V}},\tau_{\c{IV-I-V}}^2) 
\end{eqnarray*}
A fully correct specification would express the random vector of $\alpha$'s as a multivariate normal, like this for the model with random effects \verb/(Instrument + Voice + Harmony || Subject)/, for example:

\small
\[
\hspace*{-0.5in}\left[\begin{array}{c}
\alpha_{0j} \\
\alpha_{\c{guitar},j} \\
\alpha_{\c{piano},j}  \\
\alpha_{\c{string},j} \\
\alpha_{\c{contrary},j} \\
\alpha_{\c{par3rd},j} \\
\alpha_{\c{par5th},j} \\
\alpha_{\c{I-IV-V},j} \\
\alpha_{\c{I-V-IV},j} \\
\alpha_{\c{I-V-VI},j} \\
\alpha_{\c{IV-I-V},j} 
\end{array}\right] 
\stackrel{iid}{\sim}
N\left(
\left[\begin{array}{c}
\beta_{0j} \\
\beta_{\c{guitar}} \\
\beta_{\c{piano}} \\
\beta_{\c{string}} \\
\beta_{\c{contrary}} \\
\beta_{\c{par3rd}} \\
\beta_{\c{par5th}} \\
\beta_{\c{I-IV-V}} \\
\beta_{\c{I-V-IV}} \\
\beta_{\c{I-V-VI}} \\
\beta_{\c{IV-I-V}} 
\end{array}\right] ,
\left[\begin{array}{ccccccccccc}
\tau_{0j}  \\
0 & \tau_{\c{guitar}}^2  \\
0 & \rho_{gp} & \tau_{\c{piano}}^2  \\
0 & \rho_{gs} &\rho_{ps} & \tau_{\c{string}}^2 & \multicolumn{7}{c}{\mbox{\em(symmetric)}} \\
0 & 0 & 0 & 0 & \tau_{\c{contrary}}^2 \\
0 & 0 & 0 & 0 & \rho_{c3} & \tau_{\c{par3rd}}^2 \\
0 & 0 & 0 & 0 & \rho_{c5} & \rho_{35} & \tau_{\c{par5th}}^2 \\
0 & 0 & 0 & 0 & 0 & 0 & 0 & \tau_{\c{I-IV-V}}^2 \\
0 & 0 & 0 & 0 & 0 & 0 & 0 & \rho_{145,154} & \tau_{\c{I-V-IV}}^2 \\
0 & 0 & 0 & 0 & 0 & 0 & 0 & \rho_{145,156} & \rho_{154,156} & \tau_{\c{I-V-VI}}^2 \\
0 & 0 & 0 & 0 & 0 & 0 & 0 & \rho_{145,415} & \rho_{154,415} & \rho_{156,415} & \tau_{\c{IV-I-V}}^2 
\end{array}\right] 
\right)
\]
\normalsize

\noindent
and the model with random effects \verb/(Instrument + Voice + Harmony | Subject)/ would look the same, except the 0's in the variance-covariance matrix above would be replaced with additional correlations. 

\end{document}