deletions | additions       diff --git a/ChordTheory.tex b/ChordTheory.tex  index 51a6700..da86cb2 100644  --- a/ChordTheory.tex  +++ b/ChordTheory.tex 
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A chord consists of a combination of notes sounding simultaneously or close enough in succession to resemble a texture. The \textit{Harvard Dictionary of Music} defines a chord as consisting of at least three notes\cite{harvdict}. A chord perceptually describes the notes that are contained within.  Chords are commonly labeled with qualities, which describe the intervals between the pitches involved. A \textit{root note} describes the base upon which successive intervals are based. For example, given a specified root, a \textit{major} chord consists of notes 3 4  semitones above the root and 6 7  semitones above the root, invariant of octave. This means that notes in a major chord must be 3 4  and 6 7  semitones above the root modulus 12. See figure~\ref{fig:qualitytable} for a sample of commonly named chord qualities and the associated intervals. \begin{figure}[h!]  \begin{center} 
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\toprule  Chord Quality & Shorthand & Intervals from Root (mod 12) \\  \midrule  Major & & +3, +6 +4, +7  \\ Major 6th & 6 & +3, +6, +4, +7,  +8 \\ Major 7th & maj7 & +3, +6, +10\\ +4, +7, +11\\  Minor & m & +2, +6 +3, +7  \\ Minor 6th & m6 & +2, +6, +8 +3, +7, +9  \\ Minor 7th & m7 & +2, +6, +9 \\ +3, +7, +10\\  Dominant 7th & 7 & +3, +6, +9 \\ +4, +7, +10\\  Augmented & aug & +3, +7 +4, +8  \\ Diminished & dim & +2, +5 +3, +6  \\ Diminished 7th & dim7 & +2, +5, +8 +3, +6, +9  \\ Half-diminished 7th & m7b5 & +2, +5, +9 \\ +3, +6, +10\\  \bottomrule  \end{tabular}  \caption{Common chord qualities and associated intervals}