2024-July-04

mdgBookSVG4itv1.tex

@@ -204,10 +204,9 @@ \subsection{Table for finding Measure Number from Table of Measures}\label{table
 
 The table given here (Table~\ref{fig:0tab1}) combines the two (2) tables, given on page 2 of {\it Gioco Filarmonico} but the contents are exactly as given there.  The leftmost column contains the possible two-dice outcomes while the topmost row contains the bar numbers (16 in all) for the MDG minuet-to-be-generated. \\
 
-Although the body of Table~\ref{fig:0tab1} includes $11\times 16 = 176$ measure numbers, the Table of Measures for Minuets (Figures~\ref{fig:meas1} to \ref{fig:meas4}) contains only 174 different measures.  This is so since in Table~\ref{fig:0tab1}, although 11 choices are listed below each column, two choices under bar 8 (choices 30 and 123) and also under bar 16 (choices 151 and 172)) lead to identical notes in the Table of Measures for Minuets, so that only 10 different bars are under each of these two (2) columns. Consequently, the total number of different measures for minuets is $11\times 14 + 10 + 10 = 174$. These also explain why the total number of unique minuets that can be produced is about 3.8 quintillion), more precisely $$11^{14} \times 10 \times 10 = 3,797,498,335,8324,100,$$
-instead of $11^{16}$, which is the total number of minuets up to two-dice outcomes. \\
+Although the body of Table~\ref{fig:0tab1} includes $11\times 16 = 176$ measure numbers, the Table of Measures for Minuets (Figures~\ref{fig:meas1} to \ref{fig:meas4}) contains only 174 different measures.  This is so since in Table~\ref{fig:0tab1}, although 11 choices are listed below each column, two choices under bar 8 (choices 30 and 123) and also under bar 16 (choices 151 and 172)) lead to identical notes in the Table of Measures for Minuets, so that only 10 different bars are under each of these two (2) columns. Consequently, the total number of different measures for minuets is $11\times 14 + 10 + 10 = 174$. These also explain why the total number of unique minuets that can be produced is about 38 quadrillion), more precisely $$11^{14} \times 10 \times 10 = 37,974,983,358,324,100,$$ instead of $11^{16}$, which is the total number of minuets up to two-dice outcomes. \\
 
-An example of a generated minuet based on the just described rules is given below.  The same minuet and 49 other examples are given in Section~\ref{selMinuets}.
+An example of a generated minuet based on the just described rules is given below.  Other examples are given in Section~\ref{selMinuets}.
 
 \begin{figure}[H]
 	\centering