Golden sequences and tuning: Difference between revisions

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== Golden operations and MOS height ==
== Golden operations and MOS height ==
Any MOS may be constructed from 1L 1s using two "golden operations": chromaticizing (taking the soft child of the MOS) and inverting (inverting the number of large and small steps). In effect, this makes taking the hard child "cost" 2 instead of 1. This table shows the number of such operations required to reach any MOS under 15 notes (that MOS' "height"): The total number of MOSes at each height corresponds to the Fibonacci sequence.
Any MOS may be constructed from 1L 1s using two "golden operations": chromaticizing (taking the soft child of the MOS, thus continuing the golden sequence) and inverting (inverting the number of large and small steps, switching to a new golden sequence). In effect, this makes taking the hard child "cost" 2 instead of 1. This table shows the number of such operations required to reach any MOS under 15 notes (that MOS' "height"): The total number of MOSes at each height corresponds to the Fibonacci sequence.
{| class="wikitable sortable mw-collapsible mw-collapsed"
{| class="wikitable sortable mw-collapsible mw-collapsed"
|+MOS height for MOSes under 15 notes
|+MOS height for MOSes under 15 notes