Ternary scale theorems: Difference between revisions
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* A scale is ''primitive'' if its period is the same as its equave. A ''multiMOS'' or ''multiperiod MOS'' is a non-primitive MOS. A MOS ''a'''''L''' ''b'''''s''' is primitive iff {{nowrap|gcd(''a'', ''b'') {{=}} 1}}. This corresponds to the term ''single-period'' in common xen parlance. Any multiMOS can be constructed from a primitive MOS by repeating the MOS pattern multiple times, e.g. if 3'''L''' 2'''s''' is '''LLsLs''', then 9'''L''' 6'''s''' is '''LLsLsLLsLsLLsLs'''. | * A scale is ''primitive'' if its period is the same as its equave. A ''multiMOS'' or ''multiperiod MOS'' is a non-primitive MOS. A MOS ''a'''''L''' ''b'''''s''' is primitive iff {{nowrap|gcd(''a'', ''b'') {{=}} 1}}. This corresponds to the term ''single-period'' in common xen parlance. Any multiMOS can be constructed from a primitive MOS by repeating the MOS pattern multiple times, e.g. if 3'''L''' 2'''s''' is '''LLsLs''', then 9'''L''' 6'''s''' is '''LLsLsLLsLsLLsLs'''. | ||
* An ''n''-''ary'' scale is a scale with ''n'' different step sizes. ''Binary'' and ''ternary'' are used when {{nowrap|''n'' {{=}} 2 and 3}}, respectively. | * An ''n''-''ary'' scale is a scale with ''n'' different step sizes. ''Binary'' and ''ternary'' are used when {{nowrap|''n'' {{=}} 2 and 3}}, respectively. | ||
* For the ''well-formed generator sequence'' property, see the [[generator sequence]] article. | * For the ''well-formed generator sequence'' (WFGS) property, see the [[generator sequence]] article. | ||
* The property of having a WFGS of period 2 is important as it is equivalent to being an odd-regular MV3 scale; see below. It used to be called the "SGA property" in past versions of this article. | * The property of having a WFGS of period 2 is important as it is equivalent to being an odd-regular MV3 scale; see below. It used to be called the "SGA property" in past versions of this article. | ||
* An ''odd-step'' is a ''k''-step where ''k'' is odd; an ''even-step'' is defined similarly. | * An ''odd-step'' is a ''k''-step where ''k'' is odd; an ''even-step'' is defined similarly. | ||