Guide frame: Difference between revisions
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'''Guide frames''' are the most recent formulation of " | '''Guide frames'''{{idiosyncratic}} are the most recent formulation of "detempered MOS" scales in Inthar's contribution to the theory of generator sequences. A guide frame consists of: | ||
# a ''guided [[generator sequence]]'' (GGS) GS(g1, g2, ...), where each generator subtends the same fixed number of steps in the scale; | # a ''guided [[generator sequence]]'' (GGS) GS(g1, g2, ...), where each generator subtends the same fixed number of steps in the scale; | ||
# a ''polyoffset'' (offset chord) for that generator sequence where every copy of the generator sequence has the same length. This is the unison for scales with only one GGS chain and | # a ''polyoffset'' (offset chord) for that generator sequence where every copy of the generator sequence has the same length. This is the unison for scales with only one GGS chain and an interval for scales with two GGS chains. ssLssLssLssMssLssLssM has three GGS chains with a polyoffset of 0, s, 2s; note that the polyoffset is also GS(s). | ||
#* The size of the polyoffset is called the ''multiplicity'' of the guide frame. [[Diasem]] and [[diamech]] have multiplicity 1, and achiral [[diachrome]] and [[blackdye]] have multiplicity 2. Diachrome and blackdye illustrate two ways that a scale can have multiplicity 2. In the language of [[interleaved scale]]s, achiral diachrome has a 2-note strand and a 6-note interleaving polyoffset that is generated by 3/2, and blackdye has two copies of a 5-note strand. | #* The size of the polyoffset is called the ''multiplicity'' of the guide frame. [[Diasem]] and [[diamech]] have multiplicity 1, and achiral [[diachrome]] and [[blackdye]] have multiplicity 2. Diachrome and blackdye illustrate two ways that a scale can have multiplicity 2. In the language of [[interleaved scale]]s, achiral diachrome has a 2-note strand and a 6-note interleaving polyoffset that is generated by 3/2, and blackdye has two copies of a 5-note strand. | ||
Scales that consist of an offset but where the two chains have different lengths can be formulated as a modification of a guide-frame scale. An example is chiral diachrome which can be modified from achiral diachrome by moving one note from one GGS chain to the other. | Scales that consist of an offset but where the two chains have different lengths can be formulated as a modification of a guide-frame scale. An example is chiral diachrome which can be modified from achiral diachrome by moving one note from one GGS chain to the other. | ||
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If the scale can be viewed as a guide frame in multiple ways, the complexity of such a scale is defined as the smallest of the complexities. One important caveat is that the simplest guide frame may not agree with the guide frame given by the [[MOS substitution]] scale structure. | If the scale can be viewed as a guide frame in multiple ways, the complexity of such a scale is defined as the smallest of the complexities. One important caveat is that the simplest guide frame may not agree with the guide frame given by the [[MOS substitution]] scale structure. | ||
[[Category:Aberrismic theory]] | |||