Least common multiple: Difference between revisions

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-The '''least common multiple''' ('''lcm''') or its logarithm (for example [[log2|Log2]]) can be used as a [[dissonance_measure|dissonance measure]] for [[intervals|intervals]] and [[Chords|chords]].
+{{Wikipedia}}
+The '''least common multiple''' ('''LCM''') or its logarithm (for example [[log2]]) can be used as a [[complexity]] measure for [[interval]]s and [[chord]]s.
+In terms of harmonic series, it represents the location of the first shared harmonic between all of the notes.
+Note that, for dyads, this is the same as [[Benedetti height]], since a ratio in lowest terms has no shared factors between its numerator and denominator.
-==Examples==
+== Examples ==
-{| class="wikitable"
+{| class="wikitable center-all"
 |-
-! | interval/
+! Interval/chord
+! LCM
-chord
+|-
-! | lcm
+| 7:5
+| 35
+|-
+| 8:5
+| 40
 |-
-| | 7:5
+| 4:5:6
-| | 35
+| 60
 |-
-| | 8:5
+| 10:12:15
-| | 40
+| 60
 |-
-| | 5:6:7
+| 6:7:8
-| | 210
+| 168
 |-
-| | 6:7:8
+| 5:6:7
-| | 168
+| 210
 |}
-==See also==
+[[Category:Interval complexity measures]]
-[http://en.wikipedia.org/wiki/Least_common_multiple http://en.wikipedia.org/wiki/Least_common_multiple]      [[Category:consonance]]
+[[Category:Complexity]]
-[[Category:dissonance]]
-[[Category:harmonic_entropy]]
+{{stub}}