Least common multiple: Difference between revisions
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The '''least common multiple''' (''' | {{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/chord | ||
! LCM | |||
|- | |||
| 7:5 | |||
| 35 | |||
|- | |||
| 8:5 | |||
| 40 | |||
|- | |- | ||
| | | 4:5:6 | ||
| | | 60 | ||
|- | |- | ||
| | | 10:12:15 | ||
| | | 60 | ||
|- | |- | ||
| | | 6:7:8 | ||
| | | 168 | ||
|- | |- | ||
| | | 5:6:7 | ||
| | | 210 | ||
|} | |} | ||
[[Category:Interval complexity measures]] | |||
[[Category:Complexity]] | |||
[[Category: | |||
{{stub}} | |||
Latest revision as of 21:46, 24 April 2025
The least common multiple (LCM) or its logarithm (for example log2) can be used as a complexity measure for intervals and chords. 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
| Interval/chord | LCM |
|---|---|
| 7:5 | 35 |
| 8:5 | 40 |
| 4:5:6 | 60 |
| 10:12:15 | 60 |
| 6:7:8 | 168 |
| 5:6:7 | 210 |
|
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