Guide frame: Difference between revisions

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'''Guide frames'''{{idiosyncratic}} are the most recent formulation of "nice" 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 ''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 dyad for scales with two GGS chains. ~~LssLssLssMssLssLssMss~~ has three GGS chains; note that the polyoffset is also GS(s).

# 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 dyad 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.

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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 '''Guide frames'''{{idiosyncratic}} are the most recent formulation of "nice" 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 ''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 dyad for scales with two GGS chains. LssLssLssMssLssLssMss has three GGS chains; note that the polyoffset is also GS(s).
+# 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 dyad 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.
 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.