Kite's Genchain mode numbering - Revision history

TallKite: TallKite moved page Genchain mode numbering to Kite's Genchain mode numbering: Editor VectorGraphics has repeatedly edited pages I've written about my own research and inserted misinformation. On discord he is openly hostile to me. This move is necessary to avoid a toxic work environment for me.

2025-08-20T00:49:28Z

TallKite moved page Genchain mode numbering to Kite's Genchain mode numbering: Editor VectorGraphics has repeatedly edited pages I've written about my own research and inserted misinformation. On discord he is openly hostile to me. This move is necessary to avoid a toxic work environment for me.

← Older revision	Revision as of 00:49, 20 August 2025
(No difference)

TallKite: /* Generalization to temperament-agnostic MOS scales */ changed the rules for temperament-agnostic scales

2025-06-05T08:38:27Z

Generalization to temperament-agnostic MOS scales: changed the rules for temperament-agnostic scales

← Older revision		Revision as of 08:38, 5 June 2025
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	* etc.		* etc.

	~~In this context~~, ~~when no specific temperament~~ is ~~named, the choice of generator follows slightly different rules. Prioritizing 3/2~~ over ~~4/3 doesn't make any sense, because~~ the ~~generator doesn't have an actual ratio~~. So the generator is ~~always chosen to be as small as possible, i.e. less than half of a period. Thus while Meantone[7]'s generator is 3/2, i.e. a 5th, 5L 2s's generator is in~~ the ~~480-514¢ range, i.e. a 4th~~.		For a MOS pattern with a fifth-sized generator, the fifth is still prioritized over the fourth. Otherwise the generator is the mingen.

	== Rationale ==		== Rationale ==

TallKite: updated EI to EU

2024-12-29T00:27:51Z

updated EI to EU

← Older revision		Revision as of 00:27, 29 December 2024
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	[[Porcupine]] aka Triyo has a [[pergen]] of (P8, P4/3) and a generator of ~10/9, notated as a vM2 or a ^^m2 using [[ups and downs notation]]. The enharmonic ~~interval~~ is v<sup>3</sup>A1. Because the generator is a 2nd, the genchain resembles the scale.		[[Porcupine]] aka Triyo has a [[pergen]] of (P8, P4/3) and a generator of ~10/9, notated as a vM2 or a ^^m2 using [[ups and downs notation]]. The [[Enharmonic unisons in ups and downs notation\|enharmonic unison]] is v<sup>3</sup>A1. Because the generator is a 2nd, the genchain resembles the scale.

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	[[Sensi]] aka Sepgu has pergen (P8, ccP5/7). The ~9/7 generator is both a ^<sup>3</sup>d4 and a v<sup>4</sup>A3, and the enharmonic ~~interval~~ is ^<sup>7</sup>dd2.		[[Sensi]] aka Sepgu has pergen (P8, ccP5/7). The ~9/7 generator is both a ^<sup>3</sup>d4 and a v<sup>4</sup>A3, and the [[Enharmonic unisons in ups and downs notation\|enharmonic unison]] is ^<sup>7</sup>dd2.
	{\| class="wikitable"		{\| class="wikitable"
	\|+ Sensi[8]/Sepgu[8] modes		\|+ Sensi[8]/Sepgu[8] modes

TallKite: added clarifications, fixed typos

2022-07-30T22:52:26Z

added clarifications, fixed typos

← Older revision		Revision as of 22:52, 30 July 2022
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	== Temperaments with split octaves ==		== Temperaments with split octaves ==
	If a rank-2 temperament's [[pergen]] has a split octave, the temperament has multiple genchains running in parallel~~, using~~ ups and downs. In order to be a MOS scale, the parallel genchains must not only be the right length, and without any gaps, but also must line up exactly, so that each note has a neighbor immediately above and/or below. In other words, every column of the lattice must be complete. The number in the brackets becomes two numbers, and the Ls pattern is ~~broken up into periods with~~ hyphens.		If a rank-2 temperament's [[pergen]] has a split octave, the temperament has multiple genchains running in parallel. Using ups and downs notation, each genchain has its own height. There is a plain one, an up one, perhaps a down one, etc. In order to be a MOS scale, the parallel genchains must not only be the right length, and without any gaps, but also must line up exactly, so that each note has a neighbor immediately above and/or below. In other words, every column of the lattice generated by the 5th and the up must be complete. The number in the brackets becomes two numbers, and the Ls pattern as written here is grouped by period, using hyphens.

	[[Srutal]] aka Diaschismatic aka Sagugu has a half-8ve period of ~45/32. All five Srutal[2x5] modes. Every other scale note has a down.		[[Srutal]] aka Diaschismatic aka Sagugu has a half-8ve period of ~45/32. All five Srutal[2x5] modes. Every other scale note has a down.
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	Using ~25/24 as the generator yields the same scales and mode numbers. 1st Diminished[4x2] would have genchains C – ^^C#, vEb – ^E, ^^F# – G and ^A – vBb, just like the scale.		Using ~25/24 as the generator yields the same scales and mode numbers. 1st Diminished[4x2] would have genchains C – ^^C#, vEb – ^E, ^^F# – G and ^A – vBb, just like the scale.

	[[Blackwood\|'''Blackwood''']] '''aka ~~5edo~~+ya''' has a fifth-octave period of 240¢. The generator is a just 5/4 = 386¢. There are only two [[Blackwood]][5x2] modes. Ups and downs indicate the generator, not the period.		[[Blackwood\|'''Blackwood''']] '''aka Sawa+ya''' has a fifth-octave period of 240¢. The generator is a just 5/4 = 386¢. There are only two [[Blackwood]][5x2] modes. Ups and downs indicate the generator, not the period.

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	The modes of the sister MOS 3L 5s are the same, just exchange L and s:		The modes of the sister MOS 3L 5s are the same, just exchange L and s:

	* 1st ~~3s 5L~~ = ssLssLsL		* 1st 3L 5s = ssLssLsL
	* 2nd ~~3s 5L~~ = ssLsLssL		* 2nd 3L 5s = ssLsLssL
	* 3rd ~~3s 5L~~ = sLssLssL		* 3rd 3L 5s = sLssLssL
	* etc.		* etc.

	In this context, when no specific temperament is named, the choice of generator follows slightly different rules. Prioritizing 3/2 over 4/3 doesn't make any sense, because the generator doesn't have an actual ratio. Thus while Meantone[7]'s generator is 3/2, i.e. a 5th, 5L 2s's generator is in the 480-514¢ range, i.e. a 4th.		In this context, when no specific temperament is named, the choice of generator follows slightly different rules. Prioritizing 3/2 over 4/3 doesn't make any sense, because the generator doesn't have an actual ratio. So the generator is always chosen to be as small as possible, i.e. less than half of a period. Thus while Meantone[7]'s generator is 3/2, i.e. a 5th, 5L 2s's generator is in the 480-514¢ range, i.e. a 4th.

	== Rationale ==		== Rationale ==

Fredg999: Internal link format, misc. edit

2022-07-27T03:14:29Z

Internal link format, misc. edit

← Older revision		Revision as of 03:14, 27 July 2022
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	== Generalization to temperament-agnostic MOS scales ==		== Generalization to temperament-agnostic MOS scales ==
	[~~https~~:~~//en.xen.wiki/w/~~Category:~~Abstract_MOS_patterns~~ Abstract MOS patterns] like 5L 3s are not specific temperaments in which specific commas vanish. Thus there are no ratios other than the octave 2/1 (or more generally the equave 3/1 or whatever). Genchain mode numbers can be applied to these patterns. For example, 5L 3s has a generator in the 450-480¢ range. The "[8]" is redundant, so we drop it to get		[[:Category:Abstract MOS patterns\|Abstract MOS patterns]] like 5L 3s are not specific temperaments in which specific commas vanish. Thus there are no ratios other than the octave 2/1 (or more generally the equave 3/1 or whatever). Genchain mode numbers can be applied to these patterns. For example, 5L 3s has a generator in the 450-480¢ range. The "[8]" is redundant, so we drop it to get

	* 1st 5L 3s = LLsLLsLs		* 1st 5L 3s = LLsLLsLs
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	* etc.		* etc.

	in this context, when no specific temperament is named, the choice of generator follows slightly different rules. Prioritizing 3/2 over 4/3 doesn't make any sense, because the generator doesn't have an actual ratio. Thus while Meantone[7]'s generator is 3/2, i.e. a 5th, 5L 2s's generator is in the 480-514¢ range, i.e. a 4th.		In this context, when no specific temperament is named, the choice of generator follows slightly different rules. Prioritizing 3/2 over 4/3 doesn't make any sense, because the generator doesn't have an actual ratio. Thus while Meantone[7]'s generator is 3/2, i.e. a 5th, 5L 2s's generator is in the 480-514¢ range, i.e. a 4th.

	== Rationale ==		== Rationale ==

TallKite: GMN as a term for a specific mode's number

2022-07-27T02:09:18Z

GMN as a term for a specific mode's number

← Older revision		Revision as of 02:09, 27 July 2022
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	'''Genchain mode numbering''' (GMN for short) provides a way to name MOS, MODMOS and even non-MOS rank-2 scales and modes systematically. Like [[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. It also applies to abstract MOS patterns like 5L 3s.		'''Genchain mode numbering''' ('''GMN''' for short) provides a way to name MOS, MODMOS and even non-MOS rank-2 scales and modes systematically. Like [[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. It also applies to abstract MOS patterns like 5L 3s.

	This mode notation system was designed by [[Kite Giedraitis]].		This mode notation system was designed by [[Kite Giedraitis]].
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	[[MOS scale]]s are formed from a segment of the [[periods_and_generators\|generator-chain]], or genchain. The first note in the genchain is the tonic of the 1st mode, the 2nd note is the tonic of the 2nd mode, etc., somewhat analogous to harmonica positions.		[[MOS scale]]s are formed from a segment of the [[periods_and_generators\|generator-chain]], or genchain. The first note in the genchain is the tonic of the 1st mode, the 2nd note is the tonic of the 2nd mode, etc., somewhat analogous to harmonica positions.

	For example, here are all the modes of [[Meantone]][7], using ~3/2 as the generator. ~~The~~ Ls pattern is divided into two halves, for readability. The first half runs from the tonic to the 5th. and the second half runs from the 5th to the 8ve.		For example, here are all the modes of [[Meantone]][7], using ~3/2 as the generator. On this page, the Ls pattern is divided into two halves, for readability. The first half runs from the tonic to the 5th. and the second half runs from the 5th to the 8ve.

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	4th Meantone[7] is spoken as "fourth meantone heptatonic", or possibly "fourth meantone seven". If in D, as above, it would be "D fourth meantone heptatonic".		4th Meantone[7] is spoken as "fourth meantone heptatonic", or possibly "fourth meantone seven". If in D, as above, it would be "D fourth meantone heptatonic". The term GMN can also be read as genchain mode <u>number</u>, and can refer to the numbers 1st, 2nd, 3rd etc., as in "Dorian's GMN is 4".

	The same seven modes, all with C as the tonic, to illustrate the difference between modes. Adjacent modes differ by only one note. The modes proceed from sharper (Lydian) to flatter (Locrian).		The same seven modes, all with C as the tonic, to illustrate the difference between modes. Adjacent modes differ by only one note. The modes proceed from sharper (Lydian) to flatter (Locrian).

TallKite: intro paragraph

2022-07-27T02:00:30Z

intro paragraph

← Older revision		Revision as of 02:00, 27 July 2022
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	'''Genchain mode numbering''' provides a way to name MOS, MODMOS and even non-MOS rank-2 scales and modes systematically. Like [[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.		'''Genchain mode numbering''' (GMN for short) provides a way to name MOS, MODMOS and even non-MOS rank-2 scales and modes systematically. Like [[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. It also applies to abstract MOS patterns like 5L 3s.

	This mode notation system was designed by [[Kite Giedraitis]].		This mode notation system was designed by [[Kite Giedraitis]].

TallKite: added a section, "Generalization to temperament-agnostic MOS scales"

2022-07-27T01:52:31Z

added a section, "Generalization to temperament-agnostic MOS scales"

@@ Line 844: / Line 844: @@
 |vF# * vG# vD# vA# * vB#
 |}
 == Rationale ==

Fredg999: Fredg999 moved page Kite's Method of Naming Rank-2 Scales using Mode Numbers to Genchain mode numbering: The system was renamed (see latest edit summary)

2022-07-27T01:43:44Z

Fredg999 moved page Kite's Method of Naming Rank-2 Scales using Mode Numbers to Genchain mode numbering: The system was renamed (see latest edit summary)

← Older revision	Revision as of 01:43, 27 July 2022
(No difference)

Fredg999: Brought back the original name for this system from an old version of Naming Rank-2 Scales, after discussing with Kite on Discord

2022-07-27T01:43:12Z

Brought back the original name for this system from an old version of Naming Rank-2 Scales, after discussing with Kite on Discord

← Older revision		Revision as of 01:43, 27 July 2022
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	'''~~Kite's~~ mode ~~numbers~~''' ~~provide~~ a way to name MOS, MODMOS and even non-MOS rank-2 scales and modes systematically. Like [[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.		'''Genchain mode numbering''' provides a way to name MOS, MODMOS and even non-MOS rank-2 scales and modes systematically. Like [[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.

	This mode notation system was designed by [[Kite Giedraitis]].		This mode notation system was designed by [[Kite Giedraitis]].