Comparison of mode notation systems - Revision history

TallKite: updated the GMN names

2025-06-05T08:44:30Z

updated the GMN names

← Older revision		Revision as of 08:44, 5 June 2025
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	\|LLLsLLs		\|LLLsLLs
	\|5L 2s <nowiki>6\|0</nowiki>		\|5L 2s <nowiki>6\|0</nowiki>
	\|~~7th~~ 5L 2s		\|1st 5L 2s
	\|5L 2s mode 4		\|5L 2s mode 4
	\|-		\|-
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	\|LLsLLLs		\|LLsLLLs
	\|5L 2s <nowiki>5\|1</nowiki>		\|5L 2s <nowiki>5\|1</nowiki>
	\|~~6th~~ 5L 2s		\|2nd 5L 2s
	\|5L 2s mode 1		\|5L 2s mode 1
	\|-		\|-
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	\|LLsLLsL		\|LLsLLsL
	\|5L 2s <nowiki>4\|2</nowiki>		\|5L 2s <nowiki>4\|2</nowiki>
	\|~~5th~~ 5L 2s		\|3rd 5L 2s
	\|5L 2s mode 5		\|5L 2s mode 5
	\|-		\|-
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	\|LsLLsLL		\|LsLLsLL
	\|5L 2s <nowiki>2\|4</nowiki>		\|5L 2s <nowiki>2\|4</nowiki>
	\|~~3rd~~ 5L 2s		\|5th 5L 2s
	\|5L 2s mode 6		\|5L 2s mode 6
	\|-		\|-
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	\|sLLLsLL		\|sLLLsLL
	\|5L 2s <nowiki>1\|5</nowiki>		\|5L 2s <nowiki>1\|5</nowiki>
	\|~~2nd~~ 5L 2s		\|6th 5L 2s
	\|5L 2s mode 3		\|5L 2s mode 3
	\|-		\|-
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	\|sLLsLLL		\|sLLsLLL
	\|5L 2s <nowiki>0\|6</nowiki>		\|5L 2s <nowiki>0\|6</nowiki>
	\|~~1st~~ 5L 2s		\|7th 5L 2s
	\|5L 2s mode 7		\|5L 2s mode 7
	\|}		\|}

Fredg999: Remove emphasis on system creators, add missing scale names in table, added 5L 2s table, misc. edits

2022-07-27T03:33:38Z

Remove emphasis on system creators, add missing scale names in table, added 5L 2s table, misc. edits

← Older revision		Revision as of 03:33, 27 July 2022
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	Several ~~people~~ have ~~attempted~~ to generalize the [[mode]]s of the [[5L 2s\|diatonic]] scale ~~by designing a system~~ to ~~notate or number the modes of any~~ given scale, or at least any scale with certain properties such as [[MOS]]:		Several mode numbering or notation systems have been designed in an attempt to generalize the [[mode]]s of the [[5L 2s\|diatonic]] scale. These systems aim to work for given scale, or at least any scale with certain properties such as [[MOS]].

	* ~~[[Mike Battaglia]]'s system:~~ [[Modal UDP notation]];		Here are the most common systems used proposed by the xenharmonic community:
	* ~~[[Kite Giedraitis]]' system:~~ [[Genchain mode numbering]] or GMN;		* [[Modal UDP notation]];
	* ~~[[Jake Freivald]]'s system:~~ [[Jake Freivald's mode numbering system]].		* [[Genchain mode numbering]] (GMN);
			* [[Jake Freivald's mode numbering system]].

	== Comparison tables ==		== Comparison tables ==
	This section compares the different notations enumerated above. As an example, the seven diatonic modes (Ionian, Dorian, Phrygian, etc) will be used.		This section compares the different notations enumerated above. As an example, the seven diatonic modes (Ionian, Dorian, Phrygian, etc) will be used, first using the tempered meantone[7] scale and then using the abstract 5L 2s scale.
	{\| class="wikitable sortable"		{\| class="wikitable sortable center-all"
	\|+ Comparison for ~~diatonic (5L 2s)~~ modes		\|+ Comparison for meantone[7] modes
	!Mode name		!Mode name
	!Step pattern		!Step pattern
	!~~Battaglia's method~~		!Modal UDP notation
	~~(or~~ UDP notation)		!Genchain mode numbering
	!~~GMN~~
	!Freivald's method		!Freivald's method
	\|-		\|-
	\|Lydian		\|Lydian
	\|LLLsLLs		\|LLLsLLs
	\|<nowiki>6\|0</nowiki>		\|meantone[7] <nowiki>6\|0</nowiki>
	\|1st meantone[7]		\|1st meantone[7]
	\|~~Mode~~ 4		\|meantone[7] mode 4
	\|-		\|-
	\|Ionian		\|Ionian
	\|LLsLLLs		\|LLsLLLs
	\|<nowiki>5\|1</nowiki>		\|meantone[7] <nowiki>5\|1</nowiki>
	\|2nd meantone[7]		\|2nd meantone[7]
	\|~~Mode~~ 1		\|meantone[7] mode 1
	\|-		\|-
	\|Mixolydian		\|Mixolydian
	\|LLsLLsL		\|LLsLLsL
	\|<nowiki>4\|2</nowiki>		\|meantone[7] <nowiki>4\|2</nowiki>
	\|3rd meantone[7]		\|3rd meantone[7]
	\|~~Mode~~ 5		\|meantone[7] mode 5
	\|-		\|-
	\|Dorian		\|Dorian
	\|LsLLLsL		\|LsLLLsL
	\|<nowiki>3\|3</nowiki>		\|meantone[7] <nowiki>3\|3</nowiki>
	\|4th meantone[7]		\|4th meantone[7]
	\|~~Mode~~ 2		\|meantone[7] mode 2
	\|-		\|-
	\|Aeolian		\|Aeolian
	\|LsLLsLL		\|LsLLsLL
	\|<nowiki>2\|4</nowiki>		\|meantone[7] <nowiki>2\|4</nowiki>
	\|5th meantone[7]		\|5th meantone[7]
	\|~~Mode~~ 6		\|meantone[7] mode 6
	\|-		\|-
	\|Phrygian		\|Phrygian
	\|sLLLsLL		\|sLLLsLL
	\|<nowiki>1\|5</nowiki>		\|meantone[7] <nowiki>1\|5</nowiki>
	\|6th meantone[7]		\|6th meantone[7]
	\|~~Mode~~ 3		\|meantone[7] mode 3
	\|-		\|-
	\|Locrian		\|Locrian
	\|sLLsLLL		\|sLLsLLL
	\|<nowiki>0\|6</nowiki>		\|meantone[7] <nowiki>0\|6</nowiki>
	\|7th meantone[7]		\|7th meantone[7]
	\|Mode 7		\|meantone[7] mode 7
			\|}

			{\| class="wikitable sortable center-all"
			\|+ Comparison for 5L 2s modes
			!Mode name
			!Step pattern
			!Modal UDP notation
			!Genchain mode numbering
			!Freivald's method
			\|-
			\|Lydian
			\|LLLsLLs
			\|5L 2s <nowiki>6\|0</nowiki>
			\|7th 5L 2s
			\|5L 2s mode 4
			\|-
			\|Ionian
			\|LLsLLLs
			\|5L 2s <nowiki>5\|1</nowiki>
			\|6th 5L 2s
			\|5L 2s mode 1
			\|-
			\|Mixolydian
			\|LLsLLsL
			\|5L 2s <nowiki>4\|2</nowiki>
			\|5th 5L 2s
			\|5L 2s mode 5
			\|-
			\|Dorian
			\|LsLLLsL
			\|5L 2s <nowiki>3\|3</nowiki>
			\|4th 5L 2s
			\|5L 2s mode 2
			\|-
			\|Aeolian
			\|LsLLsLL
			\|5L 2s <nowiki>2\|4</nowiki>
			\|3rd 5L 2s
			\|5L 2s mode 6
			\|-
			\|Phrygian
			\|sLLLsLL
			\|5L 2s <nowiki>1\|5</nowiki>
			\|2nd 5L 2s
			\|5L 2s mode 3
			\|-
			\|Locrian
			\|sLLsLLL
			\|5L 2s <nowiki>0\|6</nowiki>
			\|1st 5L 2s
			\|5L 2s mode 7
	\|}		\|}

TallKite: /* Comparison tables */

2022-07-27T02:11:50Z

Comparison tables

← Older revision		Revision as of 02:11, 27 July 2022
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	* [[Mike Battaglia]]'s system: [[Modal UDP notation]];		* [[Mike Battaglia]]'s system: [[Modal UDP notation]];
	* [[Kite Giedraitis]]' system: [[Genchain mode numbering]];		* [[Kite Giedraitis]]' system: [[Genchain mode numbering]] or GMN;
	* [[Jake Freivald]]'s system: [[Jake Freivald's mode numbering system]].		* [[Jake Freivald]]'s system: [[Jake Freivald's mode numbering system]].

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	!Battaglia's method		!Battaglia's method
	(or UDP notation)		(or UDP notation)
	!~~Kite's method~~		!GMN
	!Freivald's method		!Freivald's method
	\|-		\|-

Fredg999: Update internal link

2022-07-27T01:44:13Z

Update internal link

← Older revision		Revision as of 01:44, 27 July 2022
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	* [[Mike Battaglia]]'s system: [[Modal UDP notation]];		* [[Mike Battaglia]]'s system: [[Modal UDP notation]];
	* [[Kite Giedraitis]]' system: [[~~Kite's Method of Naming Rank-2 Scales using Mode Numbers~~]];		* [[Kite Giedraitis]]' system: [[Genchain mode numbering]];
	* [[Jake Freivald]]'s system: [[Jake Freivald's mode numbering system]].		* [[Jake Freivald]]'s system: [[Jake Freivald's mode numbering system]].

Fredg999: Fredg999 moved page Naming Rank-2 Scales to Comparison of mode notation systems: Better description of the page's current contents

2022-07-26T11:41:05Z

Fredg999 moved page Naming Rank-2 Scales to Comparison of mode notation systems: Better description of the page's current contents

← Older revision	Revision as of 11:41, 26 July 2022
(No difference)

Fredg999: Moved 3rd section to Jake Freivald's mode numbering system, new intro, misc. edits

2022-07-26T11:40:05Z

Moved 3rd section to Jake Freivald's mode numbering system, new intro, misc. edits

Show changes

Ganaram inukshuk: Comparison of notations added. There's some gotchas here...

2022-07-26T03:49:36Z

Comparison of notations added. There's some gotchas here...

← Older revision		Revision as of 03:49, 26 July 2022
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	NOTE: NO collapsing genchains. NO generator knowledge needed. No mapping knowledge (or indeed mapping at all) required. Extensible to higher ranks without problems. It doesn't matter whether the scale is a temperament at all.		NOTE: NO collapsing genchains. NO generator knowledge needed. No mapping knowledge (or indeed mapping at all) required. Extensible to higher ranks without problems. It doesn't matter whether the scale is a temperament at all.

			== Comparison of notations ==
			This section compares the different notations described above. As an example, the seven church modes (ionian, dorian, phrygian, etc) will be used.
			{\| class="wikitable sortable"
			\|+
			!Mode name
			!Scalestring
			!Battaglia's method
			(or UDP notation)
			!Kite's method
			!Freivald's method
			\|-
			\|Lydian
			\|LLLsLLs
			\|<nowiki>6\|0</nowiki>
			\|1st meantone[7]
			\|Mode 4
			\|-
			\|Ionian
			\|LLsLLLs
			\|<nowiki>5\|1</nowiki>
			\|2nd meantone[7]
			\|Mode 1
			\|-
			\|Mixolydian
			\|LLsLLsL
			\|<nowiki>4\|2</nowiki>
			\|3rd meantone[7]
			\|Mode 5
			\|-
			\|Dorian
			\|LsLLLsL
			\|<nowiki>3\|3</nowiki>
			\|4th meantone[7]
			\|Mode 2
			\|-
			\|Aeolian
			\|LsLLsLL
			\|<nowiki>2\|4</nowiki>
			\|5th meantone[7]
			\|Mode 6
			\|-
			\|Phrygian
			\|sLLLsLL
			\|<nowiki>1\|5</nowiki>
			\|6th meantone[7]
			\|Mode 3
			\|-
			\|Locrian
			\|sLLsLLL
			\|<nowiki>0\|6</nowiki>
			\|7th meantone[7]
			\|Mode 7
			\|}
			It should be noted that the mos 5L 2s is supported by multiple temperaments, and as such, the name "meantone" is not meant to exclusively describe 5L 2s.
	[[category:rank 2]]		[[category:rank 2]]

TallKite at 18:47, 8 July 2019

2019-07-08T18:47:03Z

← Older revision		Revision as of 18:47, 8 July 2019
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	I also have built-in checks: I know that if I start and end with the same step size that I'm doing something wrong, and using the technique for meantone[7] gives me the diatonic major scale LLsLLLs, or CDEFGABC.		I also have built-in checks: I know that if I start and end with the same step size that I'm doing something wrong, and using the technique for meantone[7] gives me the diatonic major scale LLsLLLs, or CDEFGABC.

	==Extending to non-MOS==		===Extending to non-MOS===
	My suggestion is that (a) you still start with the step size that occurs the largest number of times, and (b) you still push the largest cluster of that as far out as possible		My suggestion is that (a) you still start with the step size that occurs the largest number of times, and (b) you still push the largest cluster of that as far out as possible

TallKite: Added a link to Mike's method

2019-07-08T18:46:29Z

Added a link to Mike's method

← Older revision		Revision as of 18:46, 8 July 2019
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	__FORCETOC__		__FORCETOC__
	~~=[[KiteGiedraitis\|Kite Giedraitis]] method=~~

	==~~Proposed~~ method ~~of naming all possible rank-2 scales~~==		== [[Mike Battaglia]] Method ==
			See [[Modal_UDP_Notation\|Modal UDP notation]].

			==[[KiteGiedraitis\|Kite Giedraitis]] method==

	'''Mode numbers''' provide a way to name MOS, MODMOS and even non-MOS rank-2 scales and modes systematically. Like [[Modal_UDP_Notation\|Modal UDP notation]], it starts with the convention of using ''some-temperament-name''[''some-number''] to create a generator-chain, and adds a way to number each mode uniquely.		'''Mode numbers''' provide a way to name MOS, MODMOS and even non-MOS rank-2 scales and modes systematically. Like [[Modal_UDP_Notation\|Modal UDP notation]], it starts with the convention of using ''some-temperament-name''[''some-number''] to create a generator-chain, and adds a way to number each mode uniquely.
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	See [[Naming Rank-2 Scales using Mode Numbers]].		See [[Naming Rank-2 Scales using Mode Numbers]].

	=[[Jake Freivald]] method=		==[[Jake Freivald]] method==
	My goals for numbering the modes are to make it as simple as possible for people to identify and use the modes they're talking about. As such, desired characteristics include		My goals for numbering the modes are to make it as simple as possible for people to identify and use the modes they're talking about. As such, desired characteristics include

Spt3125 at 22:26, 1 December 2018

2018-12-01T22:26:23Z

← Older revision		Revision as of 22:26, 1 December 2018
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	~~= =~~
	__FORCETOC__		__FORCETOC__
	=~~<u>'''~~Kite~~'''~~ Giedraitis method~~</u>~~=		=[[KiteGiedraitis\|Kite Giedraitis]] method=

	==~~<u><span style="font-size: 1.3em; line-height: 1.5;">~~Proposed method of naming all possible rank-2 scales~~</span></u>~~==		==Proposed method of naming all possible rank-2 scales==

	'''Mode numbers''' provide a way to name MOS, MODMOS and even non-MOS rank-2 scales and modes systematically. Like [[Modal_UDP_Notation\|Modal UDP notation]], it starts with the convention of using ''some-temperament-name''[''some-number''] to create a generator-chain, and adds a way to number each mode uniquely.		'''Mode numbers''' provide a way to name MOS, MODMOS and even non-MOS rank-2 scales and modes systematically. Like [[Modal_UDP_Notation\|Modal UDP notation]], it starts with the convention of using ''some-temperament-name''[''some-number''] to create a generator-chain, and adds a way to number each mode uniquely.

	See [[~~Naming_Rank-2_Scales_using_Mode_Numbers\|http://xenharmonic.wikispaces.com/~~Naming+Rank-2+Scales+using+Mode+Numbers]]		See [[Naming Rank-2 Scales using Mode Numbers]].

	=Jake Freivald method=		=[[Jake Freivald]] method=
	My goals for numbering the modes are to make it as simple as possible for people to identify and use the modes they're talking about. As such, desired characteristics include		My goals for numbering the modes are to make it as simple as possible for people to identify and use the modes they're talking about. As such, desired characteristics include

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	==Extending to non-MOS==		==Extending to non-MOS==
	~~<span style="line-height: 1.5;">~~My suggestion is that (a) you still start with the step size that occurs the largest number of times, and (b) you still push the largest cluster of that as far out as possible~~. </span>~~		My suggestion is that (a) you still start with the step size that occurs the largest number of times, and (b) you still push the largest cluster of that as far out as possible

	~~<span style="line-height: 1.5;">~~If the scale is made of xL+ys+zM, and any two of x, y, or z are the same, and they're larger than the third number, then the scale starts with the larger of the steps -- just like meantone major starts with larger steps. In other words, if it's 3L+3s+2M, we start with L. If it's 2L+3s+3M, we start with M.~~</span>~~		If the scale is made of xL+ys+zM, and any two of x, y, or z are the same, and they're larger than the third number, then the scale starts with the larger of the steps -- just like meantone major starts with larger steps. In other words, if it's 3L+3s+2M, we start with L. If it's 2L+3s+3M, we start with M.

	(Note that the word "scale" is ambiguous in some of what follows. I don't think we'll get away from that in real life, so I'm just pushing on, even where it sounds weird.)		(Note that the word "scale" is ambiguous in some of what follows. I don't think we'll get away from that in real life, so I'm just pushing on, even where it sounds weird.)
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	This also works for Kite's question about meantone[8], which is LMsMLLML. There are more L's than any other step size, so the scale has to start with L. The L's are in equal clusters of two, so there's no obvious way to pick which one goes first: mode 1 must start with LL. So let's again pick the mode that has the longest string of non-L's to go after that first LL: Mode 1 of meantone[8] is LLMsMLLM. (That's C - D - E - F - F# - G - A - B - C, or something like it.)		This also works for Kite's question about meantone[8], which is LMsMLLML. There are more L's than any other step size, so the scale has to start with L. The L's are in equal clusters of two, so there's no obvious way to pick which one goes first: mode 1 must start with LL. So let's again pick the mode that has the longest string of non-L's to go after that first LL: Mode 1 of meantone[8] is LLMsMLLM. (That's C - D - E - F - F# - G - A - B - C, or something like it.)

	Let's try something harder: the rank-3 scale [[http://x31eq.com/cgi-bin/scala.cgi?ets=12_31_22&limit=11&tuning=po ~~minerva[12],]] which I found through~~ Graham's temperament finder. Since there are four step sizes, I'm going to label them LMms, where the capital M is larger than the small m. With steps of 113, 113, 87, 113, 87, 99, 113, 87, 113, 87, 113, and 73, that's LLmLmMLmLmLs, 6L+1M+4m+1s. L has to go first. There's a cluster of two L's in the string, and I push that as close to the end as possible: LmMLmLmLsLLm. Graham is showing mode 10 of this scale in his temperament finder.		Let's try something harder: the rank-3 scale minerva[12], which I found through [http://x31eq.com/cgi-bin/scala.cgi?ets=12_31_22&limit=11&tuning=po Graham's temperament finder]. Since there are four step sizes, I'm going to label them LMms, where the capital M is larger than the small m. With steps of 113, 113, 87, 113, 87, 99, 113, 87, 113, 87, 113, and 73, that's LLmLmMLmLmLs, 6L+1M+4m+1s. L has to go first. There's a cluster of two L's in the string, and I push that as close to the end as possible: LmMLmLmLsLLm. Graham is showing mode 10 of this scale in his temperament finder.

	NOTE: NO collapsing genchains. NO generator knowledge needed. No mapping knowledge (or indeed mapping at all) required. Extensible to higher ranks without problems. It doesn't matter whether the scale is a temperament at all.		NOTE: NO collapsing genchains. NO generator knowledge needed. No mapping knowledge (or indeed mapping at all) required. Extensible to higher ranks without problems. It doesn't matter whether the scale is a temperament at all.

	~~=Request for admins=~~		[[category:rank 2]]

	~~Admins: Please delete the blank page at~~ [[~~Modal_Notation_by_Genchain_Position\|http~~:~~//xenharmonic.wikispaces.com/Modal+Notation+by+Genchain+Position~~]]

	<span style="display: block; height: 1px; left: 0px; overflow: hidden; position: absolute; top: 4019.5px; width: 1px;"><span style="background-color: #f6f7f8; color: #141823; font-family: helvetica,arial,sans-serif; font-size: 12px; line-height: 16.08px;">'''<span style="color: #3b5998;">[https://www.facebook.com/kite.giedraitis?fref=ufi Giedraitis]</span>''' <span style="">Been</span></span></span>