Hexany: Difference between revisions
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== Example == | == Example == | ||
Here is a step-by-step construction of the canonical 1-3-5-7 hexany (i.e. using [[1/1]], [[3/1]], [[5/1]], and [[7/1]] with the smallest product as the root): | Here is a step-by-step construction of the canonical 1-3-5-7 hexany (i.e. using [[1/1]], [[3/1]], [[5/1]], and [[7/1]] with the smallest product as the root): | ||
# Multiply together each pair of intervals (to find the combinations):<br>{1 × 3, 1 × 5, 1 × 7, 3 × 5, 3 × 7, 5 × 7}<br> = {3, 5, 7, 15, 21, 35}; | # Multiply together each pair of intervals (to find the combinations):<br>{1 × 3, 1 × 5, 1 × 7, 3 × 5, 3 × 7, 5 × 7}<br> = {3, 5, 7, 15, 21, 35}; | ||
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# Sort the elements in ascending order:<br>{1/1, 7/6, 5/4, 35/24, 5/3, 7/4}; | # Sort the elements in ascending order:<br>{1/1, 7/6, 5/4, 35/24, 5/3, 7/4}; | ||
# Replace the unison (1/1) by the octave ([[2/1]]) for a Scala-compatible octave-repeating scale:<br>{7/6, 5/4, 35/24, 5/3, 7/4, 2/1}. | # Replace the unison (1/1) by the octave ([[2/1]]) for a Scala-compatible octave-repeating scale:<br>{7/6, 5/4, 35/24, 5/3, 7/4, 2/1}. | ||
== Pages for individual hexanies == | |||
''See [[:Category:Hexanies]].'' | |||
== External links == | == External links == | ||