Guide frame: Difference between revisions
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# 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 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. LssLssLssMssLssLssMss has three GGS chains; 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 | #* 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. | ||
The term is inspired by Scott Dakota's "guide generators". The idea is that a guide frame scale is a detempered MOS. | The term is inspired by Scott Dakota's "guide generators". The idea is that a guide frame scale is a detempered MOS. | ||
Revision as of 13:36, 9 August 2024
Guide frames are the most recent formulation of "nice" scales in Inthar's contribution to aberrismic theory. 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).
- 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 scales, 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.
The term is inspired by Scott Dakota's "guide generators". The idea is that a guide frame scale is a detempered MOS.