Metallic MOS: Difference between revisions

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</math>

Now find any ''L'' in the horogram and observe how it gets split up as we iterate through the scale sequence. In the next iteration, <math>L</math> will be replaced with an ''L'' and an ''s''. After two iterations, the original ''L'' interval is now represented by two ''L''{{'}}s and an ''s''. And so forth.

Now find any ''L'' in the horogram and observe how it gets split up as we iterate through the scale sequence. In the next iteration, <math>L</math> will be replaced with an ''L'' and an ''s''. After two iterations, the original ''L'' interval is now represented by two ''L''{{'s}} and an ''s''. And so forth.

The same will hold for the right side of the interval pattern, for ''s'':

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Find any <math>s</math> in the horogram and observe how it gets split up as we iterate through the scale sequence. In the next iteration, ''s'' will be replaced with ''L''. After two iterations, the original ''s'' interval is now represented by an ''L'' and an ''s''. And so forth.

Every MOS scale contains every scale earlier in its scale sequence. In other words, any interval that existed in an earlier scale will remain in all later scales. These earlier L's and s's that remain—only now spanning many ''L''{{'}}s and ''s''{{'}}s each—are precisely the larger intervals in the scale that also exhibit the φ ratio to each other.

Every MOS scale contains every scale earlier in its scale sequence. In other words, any interval that existed in an earlier scale will remain in all later scales. These earlier L's and s's that remain—only now spanning many ''L''{{'s}} and ''s''{{`s}} each—are precisely the larger intervals in the scale that also exhibit the φ ratio to each other.

=== Beyond golden cases ===

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* '''Generator, aristocratic:''' A generator which is found using the weighted mediant formula on a non-period Stern–Brocot tree interval with a beyond golden mean.

* '''Generator, bronze:''' The generator found using the weighted mediant formula on the period interval with the golden mean, equal to {{nowrap|[0; 4, {{overline|3}}] ≈ 0.232408}}.

* '''Generator, complement:''' A generator ''g''{{'}}s complement generator is equal to {{nowrap|1 − ''g''}}.

* '''Generator, complement:''' A generator ''g''{{'s}} complement generator is equal to {{nowrap|1 − ''g''}}.

* '''Generator, golden:''' The generator found using the weighted mediant formula on the period interval with the golden mean, equal to {{nowrap|[0; 4, {{overline|3}}] ≈ 0.381966}}.

* '''Generator, isotopic:''' A generator found using the weighted mediant formula on the period interval with any isotope of a beyond golden mean.

@@ Line 743: / Line 743: @@
 </math>
-Now find any ''L'' in the horogram and observe how it gets split up as we iterate through the scale sequence. In the next iteration, <math>L</math> will be replaced with an ''L'' and an ''s''. After two iterations, the original ''L'' interval is now represented by two ''L''{{'}}s and an ''s''. And so forth.
+Now find any ''L'' in the horogram and observe how it gets split up as we iterate through the scale sequence. In the next iteration, <math>L</math> will be replaced with an ''L'' and an ''s''. After two iterations, the original ''L'' interval is now represented by two ''L''{{'s}} and an ''s''. And so forth.
 The same will hold for the right side of the interval pattern, for ''s'':
@@ Line 758: / Line 758: @@
 Find any <math>s</math> in the horogram and observe how it gets split up as we iterate through the scale sequence. In the next iteration, ''s'' will be replaced with ''L''. After two iterations, the original ''s'' interval is now represented by an ''L'' and an ''s''. And so forth.
-Every MOS scale contains every scale earlier in its scale sequence. In other words, any interval that existed in an earlier scale will remain in all later scales. These earlier L's and s's that remain&mdash;only now spanning many ''L''{{'}}s and ''s''{{'}}s each&mdash;are precisely the larger intervals in the scale that also exhibit the &phi; ratio to each other.
+Every MOS scale contains every scale earlier in its scale sequence. In other words, any interval that existed in an earlier scale will remain in all later scales. These earlier L's and s's that remain&mdash;only now spanning many ''L''{{'s}} and ''s''{{`s}} each&mdash;are precisely the larger intervals in the scale that also exhibit the &phi; ratio to each other.
 === Beyond golden cases ===
@@ Line 1,282: / Line 1,282: @@
 * '''Generator, aristocratic:''' A generator which is found using the weighted mediant formula on a non-period Stern&ndash;Brocot tree interval with a beyond golden mean.
 * '''Generator, bronze:''' The generator found using the weighted mediant formula on the period interval with the golden mean, equal to {{nowrap|[0; 4, {{overline|3}}] &#x2248; 0.232408}}.
-* '''Generator, complement:''' A generator ''g''{{'}}s complement generator is equal to {{nowrap|1 &minus; ''g''}}.
+* '''Generator, complement:''' A generator ''g''{{'s}} complement generator is equal to {{nowrap|1 &minus; ''g''}}.
 * '''Generator, golden:''' The generator found using the weighted mediant formula on the period interval with the golden mean, equal to {{nowrap|[0; 4, {{overline|3}}] &#x2248; 0.381966}}.
 * '''Generator, isotopic:''' A generator found using the weighted mediant formula on the period interval with any isotope of a beyond golden mean.