Guide frame - Revision history

TallKite: corrected "dyad" to "interval"

2024-10-26T05:56:54Z

corrected "dyad" to "interval"

← Older revision		Revision as of 05:56, 26 October 2024
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	'''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:		'''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 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).		# 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.

Inthar at 10:03, 17 September 2024

2024-09-17T10:03:23Z

← Older revision		Revision as of 10:03, 17 September 2024
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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:		'''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 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).		# 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).

Inthar at 09:50, 17 September 2024

2024-09-17T09:50:14Z

← Older revision		Revision as of 09:50, 17 September 2024
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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:		'''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 ''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.		#* 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.

Inthar at 09:48, 17 September 2024

2024-09-17T09:48:01Z

← Older revision		Revision as of 09:48, 17 September 2024
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	'''Guide frames'''{{idiosyncratic}} are the most recent formulation of "nice" scales in Inthar's contribution to ~~[[aberrismic~~ theory]]. A guide frame consists of:		'''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 ''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).

Inthar at 18:16, 9 August 2024

2024-08-09T18:16:18Z

← Older revision		Revision as of 18:16, 9 August 2024
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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]]

Inthar at 13:46, 9 August 2024

2024-08-09T13:46:37Z

← Older revision		Revision as of 13:46, 9 August 2024
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	'''Guide frames''' are the most recent formulation of "nice" scales in Inthar's contribution to [[aberrismic theory]]. A guide frame consists of:		'''Guide frames'''{{idiosyncratic}} 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 ''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).

Inthar: /* Complexity of a guide frame */

2024-08-09T13:46:19Z

Complexity of a guide frame

← Older revision		Revision as of 13:46, 9 August 2024
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	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".		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 ==		== Complexity of a guide frame (first attempt) ==
	The ''complexity'' of a guide frame is defined as multiplicity * the length of the GGS.		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.		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.

Inthar: /* Complexity of a guide frame */

2024-08-09T13:45:49Z

Complexity of a guide frame

← Older revision		Revision as of 13:45, 9 August 2024
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	== Complexity of a guide frame ==		== Complexity of a guide frame ==
	The ''complexity'' of a guide frame is defined as multiplicity * the length of the GS.		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.		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.

Inthar at 13:45, 9 August 2024

2024-08-09T13:45:11Z

← Older revision		Revision as of 13:45, 9 August 2024
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	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".		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 ==
			The ''complexity'' of a guide frame is defined as multiplicity * the length of the GS.

			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.

Inthar at 13:38, 9 August 2024

2024-08-09T13:38:48Z

← Older revision		Revision as of 13:38, 9 August 2024
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	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 version of a MOS scale which may be 1-period or multiperiod; the MOS scale is the "frame".