\section{The Grateful Dead Concert Behavior\label{sec:concert}}

Concert set lists provide the raw data from which to study the concert behavior of the Grateful Dead.\footnote{Set list data obtained from \texttt{http://www.cs.cmu.edu/People/gdead/setlists.html}. The data were cleaned to remedy various typographical alterations (e.g.~\ttt{Trucking} and \ttt{{Truckin'}} are the same song), to fix various spelling errors (e.g.~\ttt{Warf Rat} and \ttt{Wharf Rat} are the same song), and to fix various abbreviations (e.g. \ttt{China Cat} and \ttt{China Cat Sunflower} are the same song).} The data gathered include 1,590 set lists for concerts from 1972 to 1995, with 28,904 individual song plays. A typical, unmodified set list is presented below:

\begin{footnotesize}
\begin{verbatim}
Winterland Arena, San Francisco, CA (12/31/77)

Music Never Stopped
Tennessee Jed
Funiculi Funicula
Me and My Uncle
Loser
Jack Straw
Friend of the Devil
Lazy Lightnin'
Supplication

Sugar Magnolia
Scarlet Begonias
Fire on the Mountain
Truckin'
Wharf Rat
drums
Not Fade Away
Around and Around

One More Saturday Night
Casey Jones
\end{verbatim}
\end{footnotesize}
Blank lines divide the set list into 4 components. The first component is the concert venue and location along with the date that the concert was played. The second component is the first set list in the sequence in which the songs were played. For example, \ttt{Friend of the Devil} was played immediately after \ttt{Jack Straw} in the above example. The third component is the second set list of the concert. The second set of the Grateful Dead is known for fewer songs and extended improvisational sessions. Furthermore, the second set of a Grateful Dead concert is known for its ``blending'' of songs in which there exist fewer pauses between the end of one song and the beginning of the next; that is, the second set was often a large medley of sorts.  Second set medleys often featured pairs of songs that were almost always played together.  For example, \ttt{China Cat Sunflower} almost always preceded \ttt{I Know You Rider}, but never in the opposite order.  Also, \ttt{China Cat Sunflower} was very rarely played with a different song following.\footnote{A similar pattern exists for other song pairs such as \ttt{Scarlet Begonias} and \ttt{Fire on the Mountain}, \ttt{Saint of Circumstance} and \ttt{Lost Sailor}, and \ttt{Cryptic Envelopment} and \ttt{The Other One}.}  The fourth and last component, which is usually the shortest, is the encore set list. The Grateful Dead were known to typically play their concerts in this 3 set form.

A basic measure, calculated using many concert set lists, is to simply count the number of times a given song is played over all concerts.  This ranked list of songs is a rudimentary ``greatest hits'' list of sorts, but also a histogram of concert plays sheds light on the distribution of these counts.  Did most songs get approximately the same number of concert plays, or did the band play a small set of favorite songs interspersed with less popular songs to provide variety? Table~\ref{tab:plays} shows the raw counts for the 15 most played songs.  Note that of the 1,590 concerts analyzed, 1,386 of those concerts included the \ttt{Drums} improvisational rhythm sequence, which typically appeared in the second set of most concerts.  The Grateful Dead very often used \ttt{Drums} in the second set to bridge two songs that would not otherwise be simple to link as a medley.  Figure 2 presents a histogram denoting the number of songs that were played a given number of times. In summary, many songs were played only a few times and few songs were played many times.