4M - Revision history

Lhearne at 00:22, 21 March 2024

2024-03-21T00:22:59Z

← Older revision		Revision as of 00:22, 21 March 2024
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	For MOS with equave period the 4M is the [[MOS scale\|MOS]] with the second note in the [[chroma-positive]] generator chain raised by a chroma, or the second last note lowered by a chroma. Using Meantone[7] 4M as an example - the Meantone melodic scale - We start with the [[Meantone]][7] generator chain F-C-G-D-A-E-B. Replacing C with C# (moving it up 7 generators) leads to the chain F-.-G-D-A-E-B-.-C#, which is the notes of the D melodic scale D E F G A B C# D. Alternatively, replacing E with Eb (moving it down 7 generators) leads to the chain Eb-.-F-C-G-D-A-.-B, which we can see is the same scale on a different pitch, i.e., C D Eb F G A B C. The generator chain of the 4M of MOS with one period per equave always takes this shape, with a generator span length 2 generators longer than the number of notes in the scale. Like MOS, 4Ms of MOS with equave period are [[Chirality\|achiral]], or mirror-symmetric.		For MOS with equave period the 4M is the [[MOS scale\|MOS]] with the second note in the [[chroma-positive]] generator chain raised by a chroma, or the second last note lowered by a chroma. Using Meantone[7] 4M as an example - the Meantone melodic scale - We start with the [[Meantone]][7] generator chain F-C-G-D-A-E-B. Replacing C with C# (moving it up 7 generators) leads to the chain F-.-G-D-A-E-B-.-C#, which is the notes of the D melodic scale D E F G A B C# D. Alternatively, replacing E with Eb (moving it down 7 generators) leads to the chain Eb-.-F-C-G-D-A-.-B, which we can see is the same scale on a different pitch, i.e., C D Eb F G A B C. The generator chain of the 4M of MOS with one period per equave always takes this shape, with a generator span length 2 generators longer than the number of notes in the scale. Like MOS, 4Ms of MOS with equave period are [[Chirality\|achiral]], or mirror-symmetric.

	The 4M of a multi-MOS is found by raising the first note or lowering the last note of one generator chain by a chroma. For example, the pentachordal decatonic, 4M of [[Pajara]][10]: In [[22edo]], Pajara[10] has ~~gen~~ chroma-positive gen chains 0-9-7-5-3 and 11-20-18-16-14. Raising '11' by a chroma to '12' leads to the scale 0-3-5-7-9-12-14-16-18-20, or 3222322222, which is the pentachord decatonic, which has chroma-positive gen chains 0-9-7-5-3 and 20-18-16-14-12.		The 4M of a multi-MOS is found by raising the first note or lowering the last note of one generator chain by a chroma. For example, the pentachordal decatonic, 4M of [[Pajara]][10]: In [[22edo]], Pajara[10] has chroma-positive gen chains 0-9-7-5-3 and 11-20-18-16-14. Raising '11' by a chroma to '12' leads to the scale 0-3-5-7-9-12-14-16-18-20, or 3222322222, which is the pentachord decatonic, which has chroma-positive gen chains 0-9-7-5-3 and 20-18-16-14-12.

	'''Conjecture:''' Abstract 4Ms are the abstract MODMOS with the lowest variety.		'''Conjecture:''' Abstract 4Ms are the abstract MODMOS with the lowest variety.

	[[Category:MODMOS]]		[[Category:MODMOS]]

Fredg999: Categories

2024-03-14T22:20:09Z

Lhearne at 03:11, 14 March 2024

2024-03-14T03:11:46Z

← Older revision		Revision as of 03:11, 14 March 2024
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	Minimally Modified [[MODMOS scale\|MODMOS]]: '4M' because the initialism would be 4Ms, i.e., MMMM. 4Ms may be of interest as the only [[Chirality\|achiral]] (mirror-symmetric) 1-MODMOS (MODMOS through only a single chroma modification) or [[MOS scale\|MOS]] with one [[period]] per [[equave]], and as a simple way to modify Multi-MOS into scales with one period per equave.		Minimally Modified [[MODMOS scale\|MODMOS]]: '4M' because the initialism would be 4Ms, i.e., MMMM. 4Ms may be of interest as the only [[Chirality\|achiral]] (mirror-symmetric) 1-MODMOS (MODMOS through only a single chroma modification) for [[MOS scale\|MOS]] with one [[period]] per [[equave]], and as a simple way to modify Multi-MOS into scales with one period per equave.

	For MOS with equave period the 4M is the [[MOS scale\|MOS]] with the second note in the [[chroma-positive]] generator chain raised by a chroma, or the second last note lowered by a chroma. Using Meantone[7] 4M as an example - the Meantone melodic scale - We start with the [[Meantone]][7] generator chain F-C-G-D-A-E-B. Replacing C with C# (moving it up 7 generators) leads to the chain F-.-G-D-A-E-B-.-C#, which is the notes of the D melodic scale D E F G A B C# D. Alternatively, replacing E with Eb (moving it down 7 generators) leads to the chain Eb-.-F-C-G-D-A-.-B, which we can see is the same scale on a different pitch, i.e., C D Eb F G A B C. The generator chain of the 4M of MOS with one period per equave always takes this shape, with a generator span length 2 generators longer than the number of notes in the scale. Like MOS, 4Ms of MOS with equave period are [[Chirality\|achiral]], or mirror-symmetric.		For MOS with equave period the 4M is the [[MOS scale\|MOS]] with the second note in the [[chroma-positive]] generator chain raised by a chroma, or the second last note lowered by a chroma. Using Meantone[7] 4M as an example - the Meantone melodic scale - We start with the [[Meantone]][7] generator chain F-C-G-D-A-E-B. Replacing C with C# (moving it up 7 generators) leads to the chain F-.-G-D-A-E-B-.-C#, which is the notes of the D melodic scale D E F G A B C# D. Alternatively, replacing E with Eb (moving it down 7 generators) leads to the chain Eb-.-F-C-G-D-A-.-B, which we can see is the same scale on a different pitch, i.e., C D Eb F G A B C. The generator chain of the 4M of MOS with one period per equave always takes this shape, with a generator span length 2 generators longer than the number of notes in the scale. Like MOS, 4Ms of MOS with equave period are [[Chirality\|achiral]], or mirror-symmetric.

Lhearne at 03:11, 14 March 2024

2024-03-14T03:11:05Z

← Older revision		Revision as of 03:11, 14 March 2024
Line 1:		Line 1:
	Minimally Modified [[MODMOS scale\|MODMOS]]: '4M' because the initialism would be 4Ms, i.e., MMMM.		Minimally Modified [[MODMOS scale\|MODMOS]]: '4M' because the initialism would be 4Ms, i.e., MMMM. 4Ms may be of interest as the only [[Chirality\|achiral]] (mirror-symmetric) 1-MODMOS (MODMOS through only a single chroma modification) or [[MOS scale\|MOS]] with one [[period]] per [[equave]], and as a simple way to modify Multi-MOS into scales with one period per equave.

	For MOS with equave period the 4M is the [[MOS scale\|MOS]] with the second note in the [[chroma-positive]] generator chain raised by a chroma, or the second last note lowered by a chroma. Using Meantone[7] 4M as an example - the Meantone melodic scale - We start with the [[Meantone]][7] generator chain F-C-G-D-A-E-B. Replacing C with C# (moving it up 7 generators) leads to the chain F-.-G-D-A-E-B-.-C#, which is the notes of the D melodic scale D E F G A B C# D. Alternatively, replacing E with Eb (moving it down 7 generators) leads to the chain Eb-.-F-C-G-D-A-.-B, which we can see is the same scale on a different pitch, i.e., C D Eb F G A B C. The generator chain of the 4M of MOS with one period per equave always takes this shape, with a generator span length 2 generators longer than the number of notes in the scale. Like MOS, 4Ms of MOS with equave period are [[Chirality\|achiral]], or mirror-symmetric.		For MOS with equave period the 4M is the [[MOS scale\|MOS]] with the second note in the [[chroma-positive]] generator chain raised by a chroma, or the second last note lowered by a chroma. Using Meantone[7] 4M as an example - the Meantone melodic scale - We start with the [[Meantone]][7] generator chain F-C-G-D-A-E-B. Replacing C with C# (moving it up 7 generators) leads to the chain F-.-G-D-A-E-B-.-C#, which is the notes of the D melodic scale D E F G A B C# D. Alternatively, replacing E with Eb (moving it down 7 generators) leads to the chain Eb-.-F-C-G-D-A-.-B, which we can see is the same scale on a different pitch, i.e., C D Eb F G A B C. The generator chain of the 4M of MOS with one period per equave always takes this shape, with a generator span length 2 generators longer than the number of notes in the scale. Like MOS, 4Ms of MOS with equave period are [[Chirality\|achiral]], or mirror-symmetric.

Lhearne at 07:22, 13 March 2024

2024-03-13T07:22:35Z

← Older revision		Revision as of 07:22, 13 March 2024
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	Minimally Modified [[MODMOS scale\|MODMOS]]: '4M' because the initialism would be 4Ms, i.e., MMMM.		Minimally Modified [[MODMOS scale\|MODMOS]]: '4M' because the initialism would be 4Ms, i.e., MMMM.

	For MOS with equave period the 4M is the [[MOS scale\|MOS]] with the second note in the [[chroma-positive]] generator chain raised by a chroma, or the second last note ~~in the generator chain~~ lowered by a chroma. Using Meantone[7] 4M as an example - the Meantone melodic scale - We start with the [[Meantone]][7] generator chain F-C-G-D-A-E-B. Replacing C with C# (moving it up 7 generators) leads to the chain F-.-G-D-A-E-B-.-C#, which is the notes of the D melodic scale D E F G A B C# D. Alternatively, replacing E with Eb (moving it down 7 generators) leads to the chain Eb-.-F-C-G-D-A-.-B, which we can see is the same scale on a different pitch, i.e., C D Eb F G A B C. The generator chain of the 4M of MOS with one period per equave always takes this shape, with a generator span length 2 generators longer than the number of notes in the scale. Like MOS, 4Ms of MOS with equave period are [[Chirality\|achiral]], or mirror-symmetric.		For MOS with equave period the 4M is the [[MOS scale\|MOS]] with the second note in the [[chroma-positive]] generator chain raised by a chroma, or the second last note lowered by a chroma. Using Meantone[7] 4M as an example - the Meantone melodic scale - We start with the [[Meantone]][7] generator chain F-C-G-D-A-E-B. Replacing C with C# (moving it up 7 generators) leads to the chain F-.-G-D-A-E-B-.-C#, which is the notes of the D melodic scale D E F G A B C# D. Alternatively, replacing E with Eb (moving it down 7 generators) leads to the chain Eb-.-F-C-G-D-A-.-B, which we can see is the same scale on a different pitch, i.e., C D Eb F G A B C. The generator chain of the 4M of MOS with one period per equave always takes this shape, with a generator span length 2 generators longer than the number of notes in the scale. Like MOS, 4Ms of MOS with equave period are [[Chirality\|achiral]], or mirror-symmetric.

	The 4M of a multi-MOS is found by raising the first note or lowering the last note of one generator chain by a chroma. For example, the pentachordal decatonic, 4M of [[Pajara]][10]: In [[22edo]], Pajara[10] has gen chroma-positive gen chains 0-9-7-5-3 and 11-20-18-16-14. Raising '11' by a chroma to '12' leads to the scale 0-3-5-7-9-12-14-16-18-20, or 3222322222, which is the pentachord decatonic, which has chroma-positive gen chains 0-9-7-5-3 and 20-18-16-14-12.		The 4M of a multi-MOS is found by raising the first note or lowering the last note of one generator chain by a chroma. For example, the pentachordal decatonic, 4M of [[Pajara]][10]: In [[22edo]], Pajara[10] has gen chroma-positive gen chains 0-9-7-5-3 and 11-20-18-16-14. Raising '11' by a chroma to '12' leads to the scale 0-3-5-7-9-12-14-16-18-20, or 3222322222, which is the pentachord decatonic, which has chroma-positive gen chains 0-9-7-5-3 and 20-18-16-14-12.

	'''Conjecture:''' Abstract 4Ms are the abstract MODMOS with the lowest variety.		'''Conjecture:''' Abstract 4Ms are the abstract MODMOS with the lowest variety.

Lhearne at 07:21, 13 March 2024

2024-03-13T07:21:45Z

← Older revision		Revision as of 07:21, 13 March 2024
Line 3:		Line 3:
	For MOS with equave period the 4M is the [[MOS scale\|MOS]] with the second note in the [[chroma-positive]] generator chain raised by a chroma, or the second last note in the generator chain lowered by a chroma. Using Meantone[7] 4M as an example - the Meantone melodic scale - We start with the [[Meantone]][7] generator chain F-C-G-D-A-E-B. Replacing C with C# (moving it up 7 generators) leads to the chain F-.-G-D-A-E-B-.-C#, which is the notes of the D melodic scale D E F G A B C# D. Alternatively, replacing E with Eb (moving it down 7 generators) leads to the chain Eb-.-F-C-G-D-A-.-B, which we can see is the same scale on a different pitch, i.e., C D Eb F G A B C. The generator chain of the 4M of MOS with one period per equave always takes this shape, with a generator span length 2 generators longer than the number of notes in the scale. Like MOS, 4Ms of MOS with equave period are [[Chirality\|achiral]], or mirror-symmetric.		For MOS with equave period the 4M is the [[MOS scale\|MOS]] with the second note in the [[chroma-positive]] generator chain raised by a chroma, or the second last note in the generator chain lowered by a chroma. Using Meantone[7] 4M as an example - the Meantone melodic scale - We start with the [[Meantone]][7] generator chain F-C-G-D-A-E-B. Replacing C with C# (moving it up 7 generators) leads to the chain F-.-G-D-A-E-B-.-C#, which is the notes of the D melodic scale D E F G A B C# D. Alternatively, replacing E with Eb (moving it down 7 generators) leads to the chain Eb-.-F-C-G-D-A-.-B, which we can see is the same scale on a different pitch, i.e., C D Eb F G A B C. The generator chain of the 4M of MOS with one period per equave always takes this shape, with a generator span length 2 generators longer than the number of notes in the scale. Like MOS, 4Ms of MOS with equave period are [[Chirality\|achiral]], or mirror-symmetric.

	The 4M of a multi-MOS is found by raising the first note or lowering the last note of one generator chain by a chroma. For example, ~~take~~ the pentachordal decatonic, 4M of [[Pajara]][10]. In [[22edo]], Pajara[10] has gen chroma-positive gen chains 0-9-7-5-3 and 11-20-18-16-14. Raising '11' by a chroma to '12' leads to the scale 0-3-5-7-9-12-14-16-18-20, or 3222322222, which is the pentachord decatonic, which has chroma-positive gen chains 0-9-7-5-3 and 20-18-16-14-12.		The 4M of a multi-MOS is found by raising the first note or lowering the last note of one generator chain by a chroma. For example, the pentachordal decatonic, 4M of [[Pajara]][10]: In [[22edo]], Pajara[10] has gen chroma-positive gen chains 0-9-7-5-3 and 11-20-18-16-14. Raising '11' by a chroma to '12' leads to the scale 0-3-5-7-9-12-14-16-18-20, or 3222322222, which is the pentachord decatonic, which has chroma-positive gen chains 0-9-7-5-3 and 20-18-16-14-12.

	'''Conjecture:''' Abstract 4Ms are the abstract MODMOS with the lowest variety.		'''Conjecture:''' Abstract 4Ms are the abstract MODMOS with the lowest variety.

Lhearne: created page

2024-03-13T07:20:50Z

created page

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Minimally Modified [[MODMOS scale|MODMOS]]: '4M' because the initialism would be 4Ms, i.e., MMMM.

For MOS with equave period the 4M is the [[MOS scale|MOS]] with the second note in the [[chroma-positive]] generator chain raised by a chroma, or the second last note in the generator chain lowered by a chroma. Using Meantone[7] 4M as an example - the Meantone melodic scale - We start with the [[Meantone]][7] generator chain F-C-G-D-A-E-B. Replacing C with C# (moving it up 7 generators) leads to the chain F-.-G-D-A-E-B-.-C#, which is the notes of the D melodic scale D E F G A B C# D. Alternatively, replacing E with Eb (moving it down 7 generators) leads to the chain Eb-.-F-C-G-D-A-.-B, which we can see is the same scale on a different pitch, i.e., C D Eb F G A B C. The generator chain of the 4M of MOS with one period per equave always takes this shape, with a generator span length 2 generators longer than the number of notes in the scale. Like MOS, 4Ms of MOS with equave period are [[Chirality|achiral]], or mirror-symmetric.

The 4M of a multi-MOS is found by raising the first note or lowering the last note of one generator chain by a chroma. For example, take the pentachordal decatonic, 4M of [[Pajara]][10]. In [[22edo]], Pajara[10] has gen chroma-positive gen chains 0-9-7-5-3 and 11-20-18-16-14. Raising '11' by a chroma to '12' leads to the scale 0-3-5-7-9-12-14-16-18-20, or 3222322222, which is the pentachord decatonic, which has chroma-positive gen chains 0-9-7-5-3 and 20-18-16-14-12.

'''Conjecture:''' Abstract 4Ms are the abstract MODMOS with the lowest variety.

← Older revision		Revision as of 22:20, 14 March 2024
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	'''Conjecture:''' Abstract 4Ms are the abstract MODMOS with the lowest variety.		'''Conjecture:''' Abstract 4Ms are the abstract MODMOS with the lowest variety.

			[[Category:MODMOS]]