S-expression: Difference between revisions

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For completeness, all the intervals of this form are included, because of their structural importance for JI, and for the possibility of (in)consistency of mappings when tempered for the above reason.

Below is a table of all [[31-limit]] triangle-particulars:<ref group="note">~~after~~ 75, 76, 77, 78, streaks of four consecutive harmonics in the 23-limit become very sparse. The last few streaks are deeply related to the consistency and structure of [[311edo]], as [[311edo]] can be described as the unique 23-limit temperament that tempers all triangle-particulars from [[595/594]] up to [[21736/21735]]. It also tempers all the square-particulars composing those triangle-particulars with the exception of S169 and S170. It also maps the corresponding intervals of the 77-odd-limit consistently. 170/169 is the only place where the logic seems to 'break' as it is mapped to 2 steps instead of 3 meaning the mapping of that superparticular is inconsistent.</ref>

Below is a table of all [[31-limit]] triangle-particulars:<ref group="note">After 75, 76, 77, 78, streaks of four consecutive harmonics in the 23-limit become very sparse. The last few streaks are deeply related to the consistency and structure of [[311edo]], as [[311edo]] can be described as the unique 23-limit temperament that tempers all triangle-particulars from [[595/594]] up to [[21736/21735]]. It also tempers all the square-particulars composing those triangle-particulars with the exception of S169 and S170. It also maps the corresponding intervals of the 77-odd-limit consistently. 170/169 is the only place where the logic seems to "break" as it is mapped to 2 steps instead of 3 meaning the mapping of that superparticular is inconsistent.</ref>

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@@ Line 527: / Line 527: @@
 For completeness, all the intervals of this form are included, because of their structural importance for JI, and for the possibility of (in)consistency of mappings when tempered for the above reason.
-Below is a table of all [[31-limit]] triangle-particulars:<ref group="note">after 75, 76, 77, 78, streaks of four consecutive harmonics in the 23-limit become very sparse. The last few streaks are deeply related to the consistency and structure of [[311edo]], as [[311edo]] can be described as the unique 23-limit temperament that tempers all triangle-particulars from [[595/594]] up to [[21736/21735]]. It also tempers all the square-particulars composing those triangle-particulars with the exception of S169 and S170. It also maps the corresponding intervals of the 77-odd-limit consistently. 170/169 is the only place where the logic seems to 'break' as it is mapped to 2 steps instead of 3 meaning the mapping of that superparticular is inconsistent.</ref>
+Below is a table of all [[31-limit]] triangle-particulars:<ref group="note">After 75, 76, 77, 78, streaks of four consecutive harmonics in the 23-limit become very sparse. The last few streaks are deeply related to the consistency and structure of [[311edo]], as [[311edo]] can be described as the unique 23-limit temperament that tempers all triangle-particulars from [[595/594]] up to [[21736/21735]]. It also tempers all the square-particulars composing those triangle-particulars with the exception of S169 and S170. It also maps the corresponding intervals of the 77-odd-limit consistently. 170/169 is the only place where the logic seems to "break" as it is mapped to 2 steps instead of 3 meaning the mapping of that superparticular is inconsistent.</ref>
 {| class="wikitable center-all