Maximum variety: Difference between revisions
No edit summary |
|||
| Line 4: | Line 4: | ||
Any scale with all equal steps (such as an [[EDO|EDO]]) has maximum variety 1. All [[MOSScales|MOS]] scales have maximum variety 2. An example of a scale with high max variety is the [[harmonic_series|harmonic series]], because the steps get gradually smaller as you go up the scale, and none of them are equal. | Any scale with all equal steps (such as an [[EDO|EDO]]) has maximum variety 1. All [[MOSScales|MOS]] scales have maximum variety 2. An example of a scale with high max variety is the [[harmonic_series|harmonic series]], because the steps get gradually smaller as you go up the scale, and none of them are equal. | ||
== Mathematical | == Mathematical overview == | ||
A standard academic counterpart to this xen term is the '''''abelian complexity''' of a [[word]]''. | |||
* A [[balanced]] word or [[necklace]] in ''N'' letters has a maximum variety bound of <math> N \choose {\lceil N/2 \rceil}</math>. | * A [[balanced]] word or [[necklace]] in ''N'' letters has a maximum variety bound of <math> N \choose {\lceil N/2 \rceil}</math>. | ||
==Max-variety-3 scales== | ==Max-variety-3 scales== | ||