UDP - Revision history

Inthar at 03:35, 26 July 2022

2022-07-26T03:35:11Z

← Older revision		Revision as of 03:35, 26 July 2022
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	#redirect [[Modal UDP notation]]		#redirect [[Modal UDP notation]]

			[[Category:Acronyms]]

Inthar: Redirected page to Modal UDP notation

2022-07-26T03:34:39Z

Redirected page to Modal UDP notation

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Fredg999: Layout/markup, misc. edits

2022-07-26T03:25:17Z

Layout/markup, misc. edits

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Inthar: /* Things to watch out for */

2022-07-26T00:36:12Z

Things to watch out for

← Older revision		Revision as of 00:36, 26 July 2022
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	* The major pentatonic scale is a subset of the major scale. The genchain is simply shortened on either end. Thus one would expect the major pentatonic scale contained within Meantone[7] 5\|1 to be Meantone[5] 4\|0. But instead it's Meantone[5] 0\|4. This is because changing the size of the MOS scale often changes the generator to its octave inverse. Meantone[5]'s bright generator is the 4th not the 5th.		* The major pentatonic scale is a subset of the major scale. The genchain is simply shortened on either end. Thus one would expect the major pentatonic scale contained within Meantone[7] 5\|1 to be Meantone[5] 4\|0. But instead it's Meantone[5] 0\|4. This is because changing the size of the MOS scale often changes the generator to its octave inverse. Meantone[5]'s bright generator is the 4th not the 5th.
	* It's impossible to determine the bright generator in a non-MOS scale like Meantone[8], thus Meantone[8] 5\|2 is ambiguous.		* It's impossible to determine the bright generator in a non-MOS scale like Meantone[8], thus Meantone[8] 5\|2 is ambiguous.
	* Because the mos type that a temperament's mos represents is tuning-dependent, the choice of bright generator can be tuning-dependent. For example, assume you are using approximately but not exactly 700¢ for dominant meantone. Then Dominant[12] is either 7L 5s (if generator < 700¢), in which case the bright generator is the fourth, or 5L 7s (if generator > 700¢), meaning that the bright generator is the fifth. As a result, Dominant[12] 7\|4 is ambiguous.		* Because the mos type that a temperament's mos represents is tuning-dependent, the choice of bright generator can be tuning-dependent. For example, assume you are using approximately but not exactly 700¢ for dominant meantone. Then Dominant[12] is either [[7L 5s]] (if generator < 700¢), in which case the bright generator is the fourth, or [[5L 7s]] (if generator > 700¢), meaning that the bright generator is the fifth. As a result, Dominant[12] 7\|4 is ambiguous.

	== Other Notations ==		== Other Notations ==

Inthar: /* Things to watch out for */

2022-07-26T00:35:05Z

Things to watch out for

← Older revision		Revision as of 00:35, 26 July 2022
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	* The major pentatonic scale is a subset of the major scale. The genchain is simply shortened on either end. Thus one would expect the major pentatonic scale contained within Meantone[7] 5\|1 to be Meantone[5] 4\|0. But instead it's Meantone[5] 0\|4. This is because changing the size of the MOS scale often changes the generator to its octave inverse. Meantone[5]'s bright generator is the 4th not the 5th.		* The major pentatonic scale is a subset of the major scale. The genchain is simply shortened on either end. Thus one would expect the major pentatonic scale contained within Meantone[7] 5\|1 to be Meantone[5] 4\|0. But instead it's Meantone[5] 0\|4. This is because changing the size of the MOS scale often changes the generator to its octave inverse. Meantone[5]'s bright generator is the 4th not the 5th.
	* It's impossible to determine the bright generator in a non-MOS scale like Meantone[8], thus Meantone[8] 5\|2 is ambiguous.		* It's impossible to determine the bright generator in a non-MOS scale like Meantone[8], thus Meantone[8] 5\|2 is ambiguous.
	* Because the mos type that a temperament's mos represents is tuning-dependent, the choice of bright generator can be tuning-dependent. For example, assume you are using approximately 700¢ for dominant meantone. Then Dominant[12] is 7L 5s (if generator < 700¢), in which case the bright generator is the fourth, or 5L 7s (if generator > 700¢), meaning that the bright generator is the fifth. As a result, Dominant[12] 7\|4 is ambiguous.		* Because the mos type that a temperament's mos represents is tuning-dependent, the choice of bright generator can be tuning-dependent. For example, assume you are using approximately but not exactly 700¢ for dominant meantone. Then Dominant[12] is either 7L 5s (if generator < 700¢), in which case the bright generator is the fourth, or 5L 7s (if generator > 700¢), meaning that the bright generator is the fifth. As a result, Dominant[12] 7\|4 is ambiguous.

	== Other Notations ==		== Other Notations ==

Inthar: /* Things to watch out for */

2022-07-26T00:34:00Z

Things to watch out for

← Older revision		Revision as of 00:34, 26 July 2022
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	* The major pentatonic scale is a subset of the major scale. The genchain is simply shortened on either end. Thus one would expect the major pentatonic scale contained within Meantone[7] 5\|1 to be Meantone[5] 4\|0. But instead it's Meantone[5] 0\|4. This is because changing the size of the MOS scale often changes the generator to its octave inverse. Meantone[5]'s bright generator is the 4th not the 5th.		* The major pentatonic scale is a subset of the major scale. The genchain is simply shortened on either end. Thus one would expect the major pentatonic scale contained within Meantone[7] 5\|1 to be Meantone[5] 4\|0. But instead it's Meantone[5] 0\|4. This is because changing the size of the MOS scale often changes the generator to its octave inverse. Meantone[5]'s bright generator is the 4th not the 5th.
	* It's impossible to determine the bright generator in a non-MOS scale like Meantone[8], thus Meantone[8] 5\|2 is ambiguous.		* It's impossible to determine the bright generator in a non-MOS scale like Meantone[8], thus Meantone[8] 5\|2 is ambiguous.
	* Because the mos type is tuning-dependent, the choice of bright generator can be tuning-dependent. For example, assume you are using approximately 700¢ for dominant meantone. Then Dominant[12] is 7L 5s (if generator < 700¢), in which case the bright generator is the fourth, or 5L 7s (if generator > 700¢), meaning that the bright generator is the fifth. As a result, Dominant[12] 7\|4 is ambiguous.		* Because the mos type that a temperament's mos represents is tuning-dependent, the choice of bright generator can be tuning-dependent. For example, assume you are using approximately 700¢ for dominant meantone. Then Dominant[12] is 7L 5s (if generator < 700¢), in which case the bright generator is the fourth, or 5L 7s (if generator > 700¢), meaning that the bright generator is the fifth. As a result, Dominant[12] 7\|4 is ambiguous.

	== Other Notations ==		== Other Notations ==

Inthar: /* Things to watch out for */

2022-07-26T00:33:26Z

Things to watch out for

← Older revision		Revision as of 00:33, 26 July 2022
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	== Things to watch out for ==		== Things to watch out for ==
	Requiring the generator to always be ~~chroma-positive~~ causes certain issues:		Requiring the generator to always be bright causes certain issues:
	* The major pentatonic scale is a subset of the major scale. The genchain is simply shortened on either end. Thus one would expect the major pentatonic scale contained within Meantone[7] 5\|1 to be Meantone[5] 4\|0. But instead it's Meantone[5] 0\|4. This is because changing the size of the MOS scale often changes the generator to its octave inverse. Meantone[5]'s bright generator is the 4th not the 5th.		* The major pentatonic scale is a subset of the major scale. The genchain is simply shortened on either end. Thus one would expect the major pentatonic scale contained within Meantone[7] 5\|1 to be Meantone[5] 4\|0. But instead it's Meantone[5] 0\|4. This is because changing the size of the MOS scale often changes the generator to its octave inverse. Meantone[5]'s bright generator is the 4th not the 5th.
	* It's impossible to determine the ~~chroma-positive~~ generator in a non-MOS scale like Meantone[8], thus Meantone[8] 5\|2 is ambiguous.		* It's impossible to determine the bright generator in a non-MOS scale like Meantone[8], thus Meantone[8] 5\|2 is ambiguous.
	* Because the mos type is tuning-dependent, the choice of ~~chroma-positive~~ generator can be tuning-dependent. For example, assume you are using approximately 700¢ for dominant meantone. Then Dominant[12] is 7L 5s (if generator < 700¢), in which case the ~~chroma-positive~~ generator is the fourth, or 5L 7s (if generator > 700¢), meaning that the ~~chroma-positive~~ generator is the fifth. As a result, Dominant[12] 7\|4 is ambiguous.		* Because the mos type is tuning-dependent, the choice of bright generator can be tuning-dependent. For example, assume you are using approximately 700¢ for dominant meantone. Then Dominant[12] is 7L 5s (if generator < 700¢), in which case the bright generator is the fourth, or 5L 7s (if generator > 700¢), meaning that the bright generator is the fifth. As a result, Dominant[12] 7\|4 is ambiguous.

	== Other Notations ==		== Other Notations ==

Inthar: /* Generalizing to Arbitrary MOS's: Bright and Dark Generators (Chroma-Positive and Chroma-Negative) */

2022-07-26T00:33:09Z

Generalizing to Arbitrary MOS's: Bright and Dark Generators (Chroma-Positive and Chroma-Negative)

← Older revision		Revision as of 00:33, 26 July 2022
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	So why did we pick the fifth for the diatonic scale? And for an arbitrary MOS, how do we choose the generator?		So why did we pick the fifth for the diatonic scale? And for an arbitrary MOS, how do we choose the generator?

	It so happens that there is a useful way to answer this question. Each MOS can be thought of as having a '''bright generator''' and a '''dark generator''':		It so happens that there is a useful way to answer this question. Each MOS can be thought of as having a '''bright generator''' (or '''chroma-positive generator''') and a '''dark generator''' (or '''chroma-negative generator'''):

	* The bright generator increases the number of "sharps", or "large-sized" intervals as you stack more of them going "up" from the tonic.		* The bright generator increases the number of "sharps", or "large-sized" intervals as you stack more of them going "up" from the tonic.

Inthar: /* Issues and Limitations */

2022-07-26T00:32:27Z

Issues and Limitations

← Older revision		Revision as of 00:32, 26 July 2022
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	* Paul Erlich's standard pentachordal major for Pajara[10] is 4\|4(2) #8, or alternatively 6\|2(2) b3.		* Paul Erlich's standard pentachordal major for Pajara[10] is 4\|4(2) #8, or alternatively 6\|2(2) b3.

	== ~~Issues and Limitations~~ ==		== Things to watch out for ==
	Requiring the generator to always be ~~bright~~ causes certain issues:		Requiring the generator to always be chroma-positive causes certain issues:
	* The major pentatonic scale is a subset of the major scale. The genchain is simply shortened on either end. Thus one would expect the major pentatonic scale contained within Meantone[7] 5\|1 to be Meantone[5] 4\|0. But instead it's Meantone[5] 0\|4. This is because changing the size of the MOS scale often changes the generator to its octave inverse. Meantone[5]'s bright generator is the 4th not the 5th.		* The major pentatonic scale is a subset of the major scale. The genchain is simply shortened on either end. Thus one would expect the major pentatonic scale contained within Meantone[7] 5\|1 to be Meantone[5] 4\|0. But instead it's Meantone[5] 0\|4. This is because changing the size of the MOS scale often changes the generator to its octave inverse. Meantone[5]'s bright generator is the 4th not the 5th.
	* It's impossible to determine the ~~bright~~ generator in a non-MOS scale like Meantone[8], thus Meantone[8] 5\|2 is ambiguous.		* It's impossible to determine the chroma-positive generator in a non-MOS scale like Meantone[8], thus Meantone[8] 5\|2 is ambiguous.
	* ~~The~~ choice of generator can be tuning-dependent. For example, ~~Dominant meantone's generator is~~ approximately 700¢. Dominant[12]~~'s bright~~ generator is ~~either~~ the ~~4th~~ or the ~~5th, depending on~~ the ~~exact tuning~~. As a result, Dominant[12] 7\|4 is ambiguous.		* Because the mos type is tuning-dependent, the choice of chroma-positive generator can be tuning-dependent. For example, assume you are using approximately 700¢ for dominant meantone. Then Dominant[12] is 7L 5s (if generator < 700¢), in which case the chroma-positive generator is the fourth, or 5L 7s (if generator > 700¢), meaning that the chroma-positive generator is the fifth. As a result, Dominant[12] 7\|4 is ambiguous.

	== Other Notations ==		== Other Notations ==

TallKite: /* Issues */

2022-07-26T00:09:39Z

Issues

← Older revision		Revision as of 00:09, 26 July 2022
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	* Porcupine[7] Lssssss: 6\|0		* Porcupine[7] Lssssss: 6\|0
	* Porcupine[7] Lssssss mode, but altered with 7/4 instead of 11/6: 6\|0 b7		* Porcupine[7] Lssssss mode, but altered with 7/4 instead of 11/6: 6\|0 b7
	* Porcupine[7] sssLsss: 3\|3~~</li>~~<li>Diminished[8] sLsLsLsL 0\|4(4)		* Porcupine[7] sssLsss: 3\|3<li>Diminished[8] sLsLsLsL 0\|4(4)
	* Diminished[8] LsLsLsLs 4\|0(4)</li><li>Triforce[9] LLsLLsLLs: 6\|0(3)		* Diminished[8] LsLsLsLs 4\|0(4)</li><li>Triforce[9] LLsLLsLLs: 6\|0(3)
	* Meantone[5] minor pentatonic, LssLs: 3\|1		* Meantone[5] minor pentatonic, LssLs: 3\|1
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	* Paul Erlich's standard pentachordal major for Pajara[10] is 4\|4(2) #8, or alternatively 6\|2(2) b3.		* Paul Erlich's standard pentachordal major for Pajara[10] is 4\|4(2) #8, or alternatively 6\|2(2) b3.

	== Issues ==		== Issues and Limitations ==
	Requiring the generator to always be bright causes certain issues:		Requiring the generator to always be bright causes certain issues:
	* The major pentatonic scale is a subset of the major scale. The genchain is simply shortened on either end. Thus one would expect the major pentatonic scale contained within Meantone[7] 5\|1 to be Meantone[5] 4\|0. But instead it's Meantone[5] 0\|4. This is because changing the size of the MOS scale often changes the generator to its octave inverse. Meantone[5]'s bright generator is the 4th not the 5th.		* The major pentatonic scale is a subset of the major scale. The genchain is simply shortened on either end. Thus one would expect the major pentatonic scale contained within Meantone[7] 5\|1 to be Meantone[5] 4\|0. But instead it's Meantone[5] 0\|4. This is because changing the size of the MOS scale often changes the generator to its octave inverse. Meantone[5]'s bright generator is the 4th not the 5th.

← Older revision		Revision as of 00:09, 26 July 2022
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	* Porcupine[7] Lssssss: 6\|0		* Porcupine[7] Lssssss: 6\|0
	* Porcupine[7] Lssssss mode, but altered with 7/4 instead of 11/6: 6\|0 b7		* Porcupine[7] Lssssss mode, but altered with 7/4 instead of 11/6: 6\|0 b7
	* Porcupine[7] sssLsss: 3\|3~~</li>~~<li>Diminished[8] sLsLsLsL 0\|4(4)		* Porcupine[7] sssLsss: 3\|3<li>Diminished[8] sLsLsLsL 0\|4(4)
	* Diminished[8] LsLsLsLs 4\|0(4)</li><li>Triforce[9] LLsLLsLLs: 6\|0(3)		* Diminished[8] LsLsLsLs 4\|0(4)</li><li>Triforce[9] LLsLLsLLs: 6\|0(3)
	* Meantone[5] minor pentatonic, LssLs: 3\|1		* Meantone[5] minor pentatonic, LssLs: 3\|1
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	* Paul Erlich's standard pentachordal major for Pajara[10] is 4\|4(2) #8, or alternatively 6\|2(2) b3.		* Paul Erlich's standard pentachordal major for Pajara[10] is 4\|4(2) #8, or alternatively 6\|2(2) b3.

	== Issues ==		== Issues and Limitations ==
	Requiring the generator to always be bright causes certain issues:		Requiring the generator to always be bright causes certain issues:
	* The major pentatonic scale is a subset of the major scale. The genchain is simply shortened on either end. Thus one would expect the major pentatonic scale contained within Meantone[7] 5\|1 to be Meantone[5] 4\|0. But instead it's Meantone[5] 0\|4. This is because changing the size of the MOS scale often changes the generator to its octave inverse. Meantone[5]'s bright generator is the 4th not the 5th.		* The major pentatonic scale is a subset of the major scale. The genchain is simply shortened on either end. Thus one would expect the major pentatonic scale contained within Meantone[7] 5\|1 to be Meantone[5] 4\|0. But instead it's Meantone[5] 0\|4. This is because changing the size of the MOS scale often changes the generator to its octave inverse. Meantone[5]'s bright generator is the 4th not the 5th.