User:FloraC: Difference between revisions

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=== Notes ===

* For ~~any~~ temperament tempering out {{monzo| ''m''1 ''m''2 … ''m''''n'' }}, each prime ''pi'' is tuned to ~~log~~<~~sub>2</sub~~> (~~''pi''~~)(~~Σ''i'' = 1''n'' ''m''''i'' log2~~ (~~''pi''~~)~~)/(Σ''i'' = 1~~</~~sub><sup~~>~~''n'' |''m''''i''| log2 (''pi'')).~~

* For the nullity-1 temperament tempering out {{monzo| ''m''1 ''m''2 … ''m''''n'' }}, each prime ''qi'' is tuned to

* ~~For~~ ets, TOP ~~tuning~~ and TE tuning are ~~close but~~ not identical.

: <math>\log_2 (q_i) \frac {\sum m_i \log_2 (q_i)}{\sum \vert m_i \vert \log_2 (q_i)}</math>

* Even for ets, TOP and TE tuning are not identical, but close.

* The relative interval error space of equal temperaments in TOP tuning seems to be linear.

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 === Notes ===
-* For any temperament tempering out {{monzo| ''m''<sub>1</sub> ''m''<sub>2</sub> … ''m''<sub>''n''</sub> }}, each prime ''p<sub>i</sub>'' is tuned to log<sub>2</sub> (''p<sub>i</sub>'')(&Sigma;<sub>''i'' = 1</sub><sup>''n''</sup> ''m''<sub>''i''</sub> log<sub>2</sub> (''p<sub>i</sub>''))/(&Sigma;<sub>''i'' = 1</sub><sup>''n''</sup> |''m''<sub>''i''</sub>| log<sub>2</sub> (''p<sub>i</sub>'')).
+* For the nullity-1 temperament tempering out {{monzo| ''m''<sub>1</sub> ''m''<sub>2</sub> … ''m''<sub>''n''</sub> }}, each prime ''q<sub>i</sub>'' is tuned to
-* For ets, TOP tuning and TE tuning are close but not identical.
+: <math>\log_2 (q_i) \frac {\sum m_i \log_2 (q_i)}{\sum \vert m_i \vert \log_2 (q_i)}</math>
+* Even for ets, TOP and TE tuning are not identical, but close.
+* The relative interval error space of equal temperaments in TOP tuning seems to be linear.
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