deletions | additions       diff --git a/section_Analysis_subsection_Octave_For__.tex b/section_Analysis_subsection_Octave_For__.tex  index a96afd2..36c0250 100644  --- a/section_Analysis_subsection_Octave_For__.tex  +++ b/section_Analysis_subsection_Octave_For__.tex 
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\subsection{Tuning System}  To assess the Slendro scale, and make an attempt at determining the theoretical basis behind the measured frequencies of Slendro instruments, we first must express the measured frequencies not as hertz, but as intervals between musical notes. In this paper we assess intervals in absolute terms\footnote{We could also compare the intervals in relative terms, meaning each interval is a comparison between one note and the prior one in the scale. I have done a preliminary relative analysis, but I have chosen to omit it from this paper. A relative analysis is more complicated, less meaningful, and would not reach conclusions independent of an absolute analysis. Most every tuning system in practice, is devised relative to a base frequency, and in the literature of musical tunings absolute comparisons are the norm.}, meaning every tone will be compared with the base frequency of the scale. In our absolute comparison, we will treat the 1 note in the Slendro scale as our base frequency\footnote{While this is something we are assuming, it is largely irrelevant as to which tone we assume is the base tone.}. Calculating absolute intervals is done by dividing every notes frequency by the frequency of the base note.  Listed below are the absolute intervals for the Barung and Demung.  \begin{table}   \begin{tabular}{ c c c }  Note & Barung & Demung \\   1 & 1 & 1 \\   2 & 1.144518589 & 1.152198853 \\   3 & 1.311725453 & 1.313193117 \\   5 & 1.530981888 & 1.52581262 \\   6 & 1.751382269 & 1.745697897 \\   1 & 2.012392755 & 2.005736138 \\   \end{tabular}   \end{table}  \subsubsection{Equal Temperament}  It is widely understood that the Slendro scale is comprised of 5 tones, that are more or less equally spaced through the octave. We call tuning systems, in which the tones are logarithmically equally distributed through the octave equal tempered scales (logarithmically, because people perceive frequency multiples as equal steps)\footnote{ Meaning, 100 to 200 hertz is an octave, a multiple of 2, and a difference of 100 hertz (200 - 100 = 100), while 800 to 1600 hertz is also an octave, also a multiple of two, but a difference of 800 hertz. People identify frequency steps by their multiple, not their integer frequency difference.}.   To calculate a musical interval in an equal tempered scale in which the octave is divided into X equal parts, one can use the following equation..  \begin{equation}  fitness \ = | (i_equal / i_measured ) \- \1|  \end{equation}