Octave-reduce: Difference between revisions

Revision as of 19:08, 8 December 2018

Octave-reducing a fraction r means to make it fit into the range from 1 (the unison) to (excluding) 2 (the octave):

1 <= r < 2

If r does not satisfy this inequality, it has to be

3/4 is less than 1, so multiply by 2 to get 3/2
7/2 is greater than 2, so divide by 2 to get 7/4
4/2 is greater than 2, so divide by 2 to get 2, which is equal to 2, so divide by 2 to get 1

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-'''Octave-reducing''' a fraction ''r'' means to make it fit into the range from 1 (the [[unisone|unisone]]) to (excluding) 2 (the [[Octave|octave]]):
+'''Octave-reducing''' a fraction ''r'' means to make it fit into the range from 1 (the [[unison]]) to (excluding) 2 (the [[octave]]):
 <span style="font-family: monospace; font-size:150%">1 &lt;= r &lt; 2</span>
 If ''r'' does not satisfy this inequality, it has to be
+* multiplied by 2 while less than 1 or
+* divided by 2 while greater than or equal to 2
-<ul><li>multiplied by 2 while less than 1 or</li><li>divided by 2 while greater than or equal to 2</li></ul>
+== Examples ==
+* 3/4 is less than 1, so multiply by 2 to get [[3/2]]
+* 7/2 is greater than 2, so divide by 2 to get [[7/4]]
+* 4/2 is greater than 2, so divide by 2 to get 2, which is equal to 2, so divide by 2 to get 1
-== Examples ==
+== See also ==
-<ul><li>3/4 is less than 1, so multiply by 2 to get [[3/2|3/2]]</li><li>7/2 is greater than 2, so divide by 2 to get [[7/4|7/4]]</li><li>4/2 is greater than 2, so divide by 2 to get 2, which is equal to 2, so divide by 2 to get 1</li></ul>      [[Category:howto]]
+* [[Octave reduction]]
+[[Category:howto]]
 [[Category:interval_measure]]
 [[Category:method]]
 [[Category:octave]]
 [[Category:term]]