Guide frame
Guide frames [idiosyncratic term] 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 version of a MOS scale which may be 1-period or multiperiod; the MOS scale is the "frame".
Complexity of a guide frame (first attempt)
The complexity of a guide frame is defined as multiplicity * the length of the GGS.
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.