Golden sequences and tuning: Difference between revisions
No edit summary |
No edit summary |
||
| Line 87: | Line 87: | ||
== 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). This table shows the number of such operations required to reach any MOS under 15 notes (that 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. | ||
{| 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 | ||