Chad Stearns edited section_Other_Literature_Edward_C__.tex  over 8 years ago

Commit id: 43aaf15c27e97fe1ee88ff137303c46656d799d0

deletions | additions      

       

\begin{equation}  |(8/7)/1.142742| \ - \ 1 \ = \ 0.00010076  \end{equation}  \begin{equation}  |(21/16)/1.312666| \ - \ 1 \ = \ 0.00012646  \end{equation}  This is a level of exactness that would exceed anyones anyone standard for precision in tuning. For instruments in the middle range of human hearing, it would take a full 20 seconds for a beat duration between 8/7 and Carterette and Kendalls recorded average for Slendro note 2.  Kendall and Cartettes recorded interval for note 5 and note 6 deviates from what we recorded from Arizona State Universitys Javanese orchestra. Note 5 roughly corresponds to 3/2. To my knowledge, Kendall and Carterettes recorded value for note 6 has no strong similarity to a simple just interval, it sits roughly equally between just intervals 7/4 and 12/7, and is closer to the equal tempered note 6 (2 ^ 4 / 5 ). It could be that Slendro notes 6 in Gamelan orchestras, are always tuned in equal proportion to either 7/4 or 12/7.  A just intonation model for Kendall and Carterettes recorded intervals fit far better than an equal intonation model, especially with regards to notes 2, 3, and 5. Carterette and Kendalls average recorded Slendro note 6 is closer to the equal intonation value, but not to an exceptional extent, and like we mentioned above different just intonation values for note 6 in different orchestras could result in Carterette and Kendalls average.