Erv Wilson's Linear Notations - Revision history

ArrowHead294 at 18:28, 11 February 2025

2025-02-11T18:28:27Z

← Older revision		Revision as of 18:28, 11 February 2025
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	In the document for Wilson's ''On Linear Notations and The Bosanquet Keyboard'' from the [http://anaphoria.com/wilson.html Wilson Archives], [[Kraig Grady]] has been working on an appendix from [[Praveen Venkataramana]], showing not only two more systems of fifths (octal [5/[[8edo\|8]]] & novenal) but also demonstrating the various ways you can notate EDOs with these systems up to [[72edo\|72EDO]]. At the time of writing, there appears to be work showing that this can be applied to [[MOS\|MOS scales]] and constant structures, though Grady has not added these yet.		In the document for Wilson's ''On Linear Notations and The Bosanquet Keyboard'' from the [http://anaphoria.com/wilson.html Wilson Archives], [[Kraig Grady]] has been working on an appendix from [[Praveen Venkataramana]], showing not only two more systems of fifths (octal [5/[[8edo\|8]]] & novenal) but also demonstrating the various ways you can notate EDOs with these systems up to [[72edo\|72EDO]]. At the time of writing, there appears to be work showing that this can be applied to [[MOS\|MOS scales]] and constant structures, though Grady has not added these yet.

			{{Navbox notation}}
	{{~~Notation navbox~~}}


	[[Category:Notation]]		[[Category:Notation]]
	[[Category:Erv Wilson]]		[[Category:Erv Wilson]]

BudjarnLambeth: Add links

2024-12-24T09:21:24Z

Add links

BudjarnLambeth: {{Notation navbox}}

2024-12-02T23:50:04Z

← Older revision		Revision as of 23:50, 2 December 2024
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	== Updates After Wilson ==		== Updates After Wilson ==
	In the document for Wilson's ''On Linear Notations and The Bosanquet Keyboard'' from the [http://anaphoria.com/wilson.html Wilson Archives], [[Kraig Grady]] has been working on an appendix from Praveen Venkataramana, showing not only two more systems of fifths (octal [5/[[8edo\|8]]] & novenal) but also demonstrating the various ways you can notate EDOs with these systems up to [[72edo\|72EDO]]. At the time of writing, there appears to be work showing that this can be applied to [[MOS\|MOS scales]] and constant structures, though Grady has not added these yet.		In the document for Wilson's ''On Linear Notations and The Bosanquet Keyboard'' from the [http://anaphoria.com/wilson.html Wilson Archives], [[Kraig Grady]] has been working on an appendix from Praveen Venkataramana, showing not only two more systems of fifths (octal [5/[[8edo\|8]]] & novenal) but also demonstrating the various ways you can notate EDOs with these systems up to [[72edo\|72EDO]]. At the time of writing, there appears to be work showing that this can be applied to [[MOS\|MOS scales]] and constant structures, though Grady has not added these yet.


			{{Notation navbox}}


	[[Category:Notation]]		[[Category:Notation]]
	[[Category:Erv Wilson]]		[[Category:Erv Wilson]]

Jolohaga: Adding Erv Wilson category

2022-12-29T15:24:23Z

Adding Erv Wilson category

← Older revision		Revision as of 15:24, 29 December 2022
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	[[Category:Notation]]		[[Category:Notation]]
			[[Category:Erv Wilson]]

Xenllium at 13:33, 25 June 2022

2022-06-25T13:33:29Z

← Older revision		Revision as of 13:33, 25 June 2022
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	In this paper, Wilson elaborates more on the notation he first brought up in 1974. First, he brings up three families of fifths and their direction on the Bosanquet keyboard:		In this paper, Wilson elaborates more on the notation he first brought up in 1974. First, he brings up three families of fifths and their direction on the Bosanquet keyboard:
	* (Vertical) doudecimally ''positive'' (>7\[[12edo\|12]]): [[17edo\|17]], [[29edo\|29]], [[41edo\|41]], [[53edo\|53]], etc \| ''negative'' (<7\12): [[19edo\|19]], [[31edo\|31]], [[43edo\|43]], [[50edo\|50]], etc		* (Vertical) doudecimally ''positive'' (>7\[[12edo\|12]]): [[17edo\|17]], [[29edo\|29]], [[41edo\|41]], [[53edo\|53]], etc \| ''negative'' (<7\12): [[19edo\|19]], [[31edo\|31]], [[43edo\|43]], [[50edo\|50]], etc
	* (Right-leaning) septimally ''positive'' (>5\[[7edo\|7]]): 12, 19, [[26edo\|26]], 31, etc \| ''negative'' (<5\7): [[9edo\|9]], [[16edo\|16]], [[23edo\|23]], [[25edo\|25]], etc		* (Right-leaning) septimally ''positive'' (>4\[[7edo\|7]]): 12, 19, [[26edo\|26]], 31, etc \| ''negative'' (<4\7): [[9edo\|9]], [[16edo\|16]], [[23edo\|23]], [[25edo\|25]], etc
	* (Left-leaning) quintally ''positive'' (>3\[[5edo\|5]]): [[8edo\|8]], [[13edo\|13]], [[18edo\|18]], [[23edo\|23]], etc \| ''negative'' (<3\5): 7, 12, 17, 22, etc		* (Left-leaning) quintally ''positive'' (>3\[[5edo\|5]]): [[8edo\|8]], [[13edo\|13]], [[18edo\|18]], [[23edo\|23]], etc \| ''negative'' (<3\5): 7, 12, 17, 22, etc
	Although the positive & negative notations of each family are part of the same system, they require different treatments in order to stay melodically consistent. Thus, there are different nominal systems for each kind of system. He gives four examples:		Although the positive & negative notations of each family are part of the same system, they require different treatments in order to stay melodically consistent. Thus, there are different nominal systems for each kind of system. He gives four examples:
	[[File:Quintally positive.png\|thumb\|407x407px\|Quintally positive]][[File:Positive Septimal Notation.png\|none\|thumb\|347x347px\|Septimally positive]]		[[File:Quintally positive.png\|thumb\|407x407px\|Quintally positive]][[File:Positive Septimal Notation.png\|none\|thumb\|347x347px\|Septimally positive]]
	[[File:Septimally negative.png\|thumb\|351x351px\|Septimally negative\|left]][[File:Doudecimally positive notation.png\|thumb\|424x424px\|Duodecimally positive]]Wilson mentions that its possible to use a traditional staff with seven nominals for duodecimally negative systems due to tradition, though he mentions that it would be better to use the duodecimal system for more complex works.		[[File:Septimally negative.png\|thumb\|351x351px\|Septimally negative\|left]][[File:Doudecimally positive notation.png\|thumb\|424x424px\|Duodecimally positive]]
			Wilson mentions that its possible to use a traditional staff with seven nominals for duodecimally negative systems due to tradition, though he mentions that it would be better to use the duodecimal system for more complex works.
	~~''.''~~

	[[File:Erv Wilson's Linear Accidentals.png\|left\|222x222px\|The linear accidentals\|thumb]]For accidentals, he suggests two pairs; one for positive systems, one for negative. Since there is three systems mentioned here, there are twelve total accidentals.[[File:A System of Fluctuating Nominal Systems.png\|thumb\|A graph to show the evolution of nominals in different systems\|242x242px]]		[[File:Erv Wilson's Linear Accidentals.png\|left\|222x222px\|The linear accidentals\|thumb]]For accidentals, he suggests two pairs; one for positive systems, one for negative. Since there is three systems mentioned here, there are twelve total accidentals.[[File:A System of Fluctuating Nominal Systems.png\|thumb\|A graph to show the evolution of nominals in different systems\|242x242px]]

AthiTrydhen: /* Updates After Wilson */

2022-01-30T08:24:50Z

Updates After Wilson

← Older revision		Revision as of 08:24, 30 January 2022
Line 88:		Line 88:

	== Updates After Wilson ==		== Updates After Wilson ==
	In the document for Wilson's ''On Linear Notations and The Bosanquet Keyboard'' from the [http://anaphoria.com/wilson.html Wilson Archives], [[Kraig Grady]] has been working on an appendix from Praveen Venkataramana, showing not only two more systems of fifths (~~octonal~~ [5/[[8edo\|8]]] & novenal) but also demonstrating the various ways you can notate EDOs with these systems up to [[72edo\|72EDO]]. At the time of writing, there appears to be work showing that this can be applied to [[MOS\|MOS scales]] and constant structures, though Grady has not added these yet.		In the document for Wilson's ''On Linear Notations and The Bosanquet Keyboard'' from the [http://anaphoria.com/wilson.html Wilson Archives], [[Kraig Grady]] has been working on an appendix from Praveen Venkataramana, showing not only two more systems of fifths (octal [5/[[8edo\|8]]] & novenal) but also demonstrating the various ways you can notate EDOs with these systems up to [[72edo\|72EDO]]. At the time of writing, there appears to be work showing that this can be applied to [[MOS\|MOS scales]] and constant structures, though Grady has not added these yet.

	[[Category:Notation]]		[[Category:Notation]]

Keenan Pepper: Category:Notation

2021-04-17T17:28:36Z

Category:Notation

← Older revision		Revision as of 17:28, 17 April 2021
Line 89:		Line 89:
	== Updates After Wilson ==		== Updates After Wilson ==
	In the document for Wilson's ''On Linear Notations and The Bosanquet Keyboard'' from the [http://anaphoria.com/wilson.html Wilson Archives], [[Kraig Grady]] has been working on an appendix from Praveen Venkataramana, showing not only two more systems of fifths (octonal [5/[[8edo\|8]]] & novenal) but also demonstrating the various ways you can notate EDOs with these systems up to [[72edo\|72EDO]]. At the time of writing, there appears to be work showing that this can be applied to [[MOS\|MOS scales]] and constant structures, though Grady has not added these yet.		In the document for Wilson's ''On Linear Notations and The Bosanquet Keyboard'' from the [http://anaphoria.com/wilson.html Wilson Archives], [[Kraig Grady]] has been working on an appendix from Praveen Venkataramana, showing not only two more systems of fifths (octonal [5/[[8edo\|8]]] & novenal) but also demonstrating the various ways you can notate EDOs with these systems up to [[72edo\|72EDO]]. At the time of writing, there appears to be work showing that this can be applied to [[MOS\|MOS scales]] and constant structures, though Grady has not added these yet.

			[[Category:Notation]]

CritDeathX: /* A Doorway to Dialog */

2020-07-21T06:29:55Z

A Doorway to Dialog

← Older revision		Revision as of 06:29, 21 July 2020
Line 9:		Line 9:
	Wilson makes an example of a scale that could be made into a linear temperament by presenting his [[Combination product sets\|Eikosany]] scale on a keyboard inspired by one for 41 notes. With the layout he chose, D'''\''' and β<big>ł</big> fall onto a homogeneous position from C (two keys down for D\, two keys up for β<big>ł</big>). Another detail shows that the 3, 9, & 39 keys are two [[Schisma\|schismas]] off from the 5711, 35711, and 579*11 keys. With these two oddities, he suggests that a [[41edo\|41EDO]] keyboard would be proper in hosting the Eikosany.		Wilson makes an example of a scale that could be made into a linear temperament by presenting his [[Combination product sets\|Eikosany]] scale on a keyboard inspired by one for 41 notes. With the layout he chose, D'''\''' and β<big>ł</big> fall onto a homogeneous position from C (two keys down for D\, two keys up for β<big>ł</big>). Another detail shows that the 3, 9, & 39 keys are two [[Schisma\|schismas]] off from the 5711, 35711, and 579*11 keys. With these two oddities, he suggests that a [[41edo\|41EDO]] keyboard would be proper in hosting the Eikosany.

	Wilson says that he's "''emphatically biased towards the positive systems''", where the fifth is greater than Pythagorean. He mentions that unlike systems like [[meantone]], where the fifth is damaged to make the third pure, a positive system would be the first time in Western history where a tuning had pure thirds and pure fifths. If the third was damaged, it would only be to help the [[7/4\|harmonic seventh]] and [[11/8\|eleventh]] pure, which Wilson calls "''far lesser apostles''". He also brings up that [[wikipedia:Raga\|the ragas of India]] could be hosted in these positive systems as well.		Wilson says that he's "''emphatically biased towards the positive systems''", where the fifth is greater than Pythagorean. He mentions that unlike systems like [[meantone]], where the fifth is damaged to make the third pure, a positive system would be the first time in Western history where a tuning had pure thirds and pure fifths. If the third was damaged, it would only be to help turn the [[7/4\|harmonic seventh]] and [[11/8\|eleventh]] pure, which Wilson calls "''far lesser apostles''". He also brings up that [[wikipedia:Raga\|the ragas of India]] could be hosted in these positive systems as well.

	On the next page, he gives a section of his thoughts on the original Bosanquet layout, noting things like key shape and the width of intervals. In the current & future papers, he suggests & uses smaller hexagonal keys, saying that it eliminates dead space & suits more scales, like meantone & [[just intonation]]. Along with the Eikosany keyboard, he demonstrates two other keyboards with this variation of the layout, those being the [[wikipedia:Shruti_(music)\|22 ''shruitis'' of India]] and a traditional [[Arabic, Turkish, Persian\|Arabic]] system of 17 notes.[[File:A Handy Guide For The Notation Of 12-, 22-, 31-, And 41-Tone Systems.png\|thumb\|366x366px\|An example of Wilson's notation system]]On the last two pages of the document, Wilson makes mention of a system of notation he issued in 1965. In these pages, he makes two categories based on how many steps C is from C#, and how many steps B# is from C. If C-C# is one step, its singular, two steps is binary, three steps is ternary, etc etc; if B# is less than C, its negative, neutral if they're the same, positive if B# is greater by one step, 2bly positive if B# is greater by two steps, etc etc. He also gives examples for accidentals up to the quaternary system; by this point, he hasn't made accidentals for a quinary system.		On the next page, he gives a section of his thoughts on the original Bosanquet layout, noting things like key shape and the width of intervals. In the current & future papers, he suggests & uses smaller hexagonal keys, saying that it eliminates dead space & suits more scales, like meantone & [[just intonation]]. Along with the Eikosany keyboard, he demonstrates two other keyboards with this variation of the layout, those being the [[wikipedia:Shruti_(music)\|22 ''shruitis'' of India]] and a traditional [[Arabic, Turkish, Persian\|Arabic]] system of 17 notes.[[File:A Handy Guide For The Notation Of 12-, 22-, 31-, And 41-Tone Systems.png\|thumb\|366x366px\|An example of Wilson's notation system]]On the last two pages of the document, Wilson makes mention of a system of notation he issued in 1965. In these pages, he makes two categories based on how many steps C is from C#, and how many steps B# is from C. If C-C# is one step, its singular, two steps is binary, three steps is ternary, etc etc; if B# is less than C, its negative, neutral if they're the same, positive if B# is greater by one step, 2bly positive if B# is greater by two steps, etc etc. He also gives examples for accidentals up to the quaternary system; by this point, he hasn't made accidentals for a quinary system.

CritDeathX: /* Updates After Wilson */

2020-07-12T20:10:34Z

Updates After Wilson

← Older revision		Revision as of 20:10, 12 July 2020
Line 88:		Line 88:

	== Updates After Wilson ==		== Updates After Wilson ==
	In the document for Wilson's ''On Linear Notations and The Bosanquet Keyboard'' from the [http://anaphoria.com/wilson.html Wilson Archives], [[Kraig Grady]] has been working on an appendix from Praveen Venkataramana, showing not only ~~three~~ more systems of fifths (octonal [5/[[8edo\|8]]], novenal~~, & tridecimal~~) but also demonstrating the various ways you can notate EDOs with these systems up to [[72edo\|72EDO]]. At the time of writing, there appears to be work showing that this can be applied to [[MOS\|MOS scales]] and constant structures, though Grady has not added these yet.		In the document for Wilson's ''On Linear Notations and The Bosanquet Keyboard'' from the [http://anaphoria.com/wilson.html Wilson Archives], [[Kraig Grady]] has been working on an appendix from Praveen Venkataramana, showing not only two more systems of fifths (octonal [5/[[8edo\|8]]] & novenal) but also demonstrating the various ways you can notate EDOs with these systems up to [[72edo\|72EDO]]. At the time of writing, there appears to be work showing that this can be applied to [[MOS\|MOS scales]] and constant structures, though Grady has not added these yet.

CritDeathX: /* Updates After Wilson */

2020-07-12T20:09:27Z

Updates After Wilson

← Older revision		Revision as of 20:09, 12 July 2020
Line 88:		Line 88:

	== Updates After Wilson ==		== Updates After Wilson ==
	In the document for Wilson's ''On Linear Notations and The Bosanquet Keyboard'' from the [http://anaphoria.com/wilson.html Wilson Archives], [[Kraig Grady]] has been working on an appendix from Praveen Venkataramana, showing not only ~~two~~ more systems of fifths (octonal [5/[[8edo\|8]]], novenal, & tridecimal) but also demonstrating the various ways you can notate EDOs with these systems up to [[72edo\|72EDO]]. At the time of writing, there appears to be work showing that this can be applied to [[MOS\|MOS scales]] and constant structures, though Grady has not added these yet.		In the document for Wilson's ''On Linear Notations and The Bosanquet Keyboard'' from the [http://anaphoria.com/wilson.html Wilson Archives], [[Kraig Grady]] has been working on an appendix from Praveen Venkataramana, showing not only three more systems of fifths (octonal [5/[[8edo\|8]]], novenal, & tridecimal) but also demonstrating the various ways you can notate EDOs with these systems up to [[72edo\|72EDO]]. At the time of writing, there appears to be work showing that this can be applied to [[MOS\|MOS scales]] and constant structures, though Grady has not added these yet.

← Older revision		Revision as of 13:33, 25 June 2022
Line 73:		Line 73:
	In this paper, Wilson elaborates more on the notation he first brought up in 1974. First, he brings up three families of fifths and their direction on the Bosanquet keyboard:		In this paper, Wilson elaborates more on the notation he first brought up in 1974. First, he brings up three families of fifths and their direction on the Bosanquet keyboard:
	* (Vertical) doudecimally ''positive'' (>7\[[12edo\|12]]): [[17edo\|17]], [[29edo\|29]], [[41edo\|41]], [[53edo\|53]], etc \| ''negative'' (<7\12): [[19edo\|19]], [[31edo\|31]], [[43edo\|43]], [[50edo\|50]], etc		* (Vertical) doudecimally ''positive'' (>7\[[12edo\|12]]): [[17edo\|17]], [[29edo\|29]], [[41edo\|41]], [[53edo\|53]], etc \| ''negative'' (<7\12): [[19edo\|19]], [[31edo\|31]], [[43edo\|43]], [[50edo\|50]], etc
	* (Right-leaning) septimally ''positive'' (>5\[[7edo\|7]]): 12, 19, [[26edo\|26]], 31, etc \| ''negative'' (<5\7): [[9edo\|9]], [[16edo\|16]], [[23edo\|23]], [[25edo\|25]], etc		* (Right-leaning) septimally ''positive'' (>4\[[7edo\|7]]): 12, 19, [[26edo\|26]], 31, etc \| ''negative'' (<4\7): [[9edo\|9]], [[16edo\|16]], [[23edo\|23]], [[25edo\|25]], etc
	* (Left-leaning) quintally ''positive'' (>3\[[5edo\|5]]): [[8edo\|8]], [[13edo\|13]], [[18edo\|18]], [[23edo\|23]], etc \| ''negative'' (<3\5): 7, 12, 17, 22, etc		* (Left-leaning) quintally ''positive'' (>3\[[5edo\|5]]): [[8edo\|8]], [[13edo\|13]], [[18edo\|18]], [[23edo\|23]], etc \| ''negative'' (<3\5): 7, 12, 17, 22, etc
	Although the positive & negative notations of each family are part of the same system, they require different treatments in order to stay melodically consistent. Thus, there are different nominal systems for each kind of system. He gives four examples:		Although the positive & negative notations of each family are part of the same system, they require different treatments in order to stay melodically consistent. Thus, there are different nominal systems for each kind of system. He gives four examples:
	[[File:Quintally positive.png\|thumb\|407x407px\|Quintally positive]][[File:Positive Septimal Notation.png\|none\|thumb\|347x347px\|Septimally positive]]		[[File:Quintally positive.png\|thumb\|407x407px\|Quintally positive]][[File:Positive Septimal Notation.png\|none\|thumb\|347x347px\|Septimally positive]]
	[[File:Septimally negative.png\|thumb\|351x351px\|Septimally negative\|left]][[File:Doudecimally positive notation.png\|thumb\|424x424px\|Duodecimally positive]]Wilson mentions that its possible to use a traditional staff with seven nominals for duodecimally negative systems due to tradition, though he mentions that it would be better to use the duodecimal system for more complex works.		[[File:Septimally negative.png\|thumb\|351x351px\|Septimally negative\|left]][[File:Doudecimally positive notation.png\|thumb\|424x424px\|Duodecimally positive]]
			Wilson mentions that its possible to use a traditional staff with seven nominals for duodecimally negative systems due to tradition, though he mentions that it would be better to use the duodecimal system for more complex works.
	~~''.''~~

	[[File:Erv Wilson's Linear Accidentals.png\|left\|222x222px\|The linear accidentals\|thumb]]For accidentals, he suggests two pairs; one for positive systems, one for negative. Since there is three systems mentioned here, there are twelve total accidentals.[[File:A System of Fluctuating Nominal Systems.png\|thumb\|A graph to show the evolution of nominals in different systems\|242x242px]]		[[File:Erv Wilson's Linear Accidentals.png\|left\|222x222px\|The linear accidentals\|thumb]]For accidentals, he suggests two pairs; one for positive systems, one for negative. Since there is three systems mentioned here, there are twelve total accidentals.[[File:A System of Fluctuating Nominal Systems.png\|thumb\|A graph to show the evolution of nominals in different systems\|242x242px]]

← Older revision		Revision as of 06:29, 21 July 2020
Line 9:		Line 9:
	Wilson makes an example of a scale that could be made into a linear temperament by presenting his [[Combination product sets\|Eikosany]] scale on a keyboard inspired by one for 41 notes. With the layout he chose, D'''\''' and β<big>ł</big> fall onto a homogeneous position from C (two keys down for D\, two keys up for β<big>ł</big>). Another detail shows that the 3, 9, & 39 keys are two [[Schisma\|schismas]] off from the 5711, 35711, and 579*11 keys. With these two oddities, he suggests that a [[41edo\|41EDO]] keyboard would be proper in hosting the Eikosany.		Wilson makes an example of a scale that could be made into a linear temperament by presenting his [[Combination product sets\|Eikosany]] scale on a keyboard inspired by one for 41 notes. With the layout he chose, D'''\''' and β<big>ł</big> fall onto a homogeneous position from C (two keys down for D\, two keys up for β<big>ł</big>). Another detail shows that the 3, 9, & 39 keys are two [[Schisma\|schismas]] off from the 5711, 35711, and 579*11 keys. With these two oddities, he suggests that a [[41edo\|41EDO]] keyboard would be proper in hosting the Eikosany.

	Wilson says that he's "''emphatically biased towards the positive systems''", where the fifth is greater than Pythagorean. He mentions that unlike systems like [[meantone]], where the fifth is damaged to make the third pure, a positive system would be the first time in Western history where a tuning had pure thirds and pure fifths. If the third was damaged, it would only be to help the [[7/4\|harmonic seventh]] and [[11/8\|eleventh]] pure, which Wilson calls "''far lesser apostles''". He also brings up that [[wikipedia:Raga\|the ragas of India]] could be hosted in these positive systems as well.		Wilson says that he's "''emphatically biased towards the positive systems''", where the fifth is greater than Pythagorean. He mentions that unlike systems like [[meantone]], where the fifth is damaged to make the third pure, a positive system would be the first time in Western history where a tuning had pure thirds and pure fifths. If the third was damaged, it would only be to help turn the [[7/4\|harmonic seventh]] and [[11/8\|eleventh]] pure, which Wilson calls "''far lesser apostles''". He also brings up that [[wikipedia:Raga\|the ragas of India]] could be hosted in these positive systems as well.

	On the next page, he gives a section of his thoughts on the original Bosanquet layout, noting things like key shape and the width of intervals. In the current & future papers, he suggests & uses smaller hexagonal keys, saying that it eliminates dead space & suits more scales, like meantone & [[just intonation]]. Along with the Eikosany keyboard, he demonstrates two other keyboards with this variation of the layout, those being the [[wikipedia:Shruti_(music)\|22 ''shruitis'' of India]] and a traditional [[Arabic, Turkish, Persian\|Arabic]] system of 17 notes.[[File:A Handy Guide For The Notation Of 12-, 22-, 31-, And 41-Tone Systems.png\|thumb\|366x366px\|An example of Wilson's notation system]]On the last two pages of the document, Wilson makes mention of a system of notation he issued in 1965. In these pages, he makes two categories based on how many steps C is from C#, and how many steps B# is from C. If C-C# is one step, its singular, two steps is binary, three steps is ternary, etc etc; if B# is less than C, its negative, neutral if they're the same, positive if B# is greater by one step, 2bly positive if B# is greater by two steps, etc etc. He also gives examples for accidentals up to the quaternary system; by this point, he hasn't made accidentals for a quinary system.		On the next page, he gives a section of his thoughts on the original Bosanquet layout, noting things like key shape and the width of intervals. In the current & future papers, he suggests & uses smaller hexagonal keys, saying that it eliminates dead space & suits more scales, like meantone & [[just intonation]]. Along with the Eikosany keyboard, he demonstrates two other keyboards with this variation of the layout, those being the [[wikipedia:Shruti_(music)\|22 ''shruitis'' of India]] and a traditional [[Arabic, Turkish, Persian\|Arabic]] system of 17 notes.[[File:A Handy Guide For The Notation Of 12-, 22-, 31-, And 41-Tone Systems.png\|thumb\|366x366px\|An example of Wilson's notation system]]On the last two pages of the document, Wilson makes mention of a system of notation he issued in 1965. In these pages, he makes two categories based on how many steps C is from C#, and how many steps B# is from C. If C-C# is one step, its singular, two steps is binary, three steps is ternary, etc etc; if B# is less than C, its negative, neutral if they're the same, positive if B# is greater by one step, 2bly positive if B# is greater by two steps, etc etc. He also gives examples for accidentals up to the quaternary system; by this point, he hasn't made accidentals for a quinary system.

← Older revision		Revision as of 09:21, 24 December 2024
Line 1:		Line 1:
	The linear notations from [[Erv Wilson]] is a system of [[notation]] created to fit [https://en.xen.wiki/w/Tour_of_Regular_Temperaments linear temperaments] & [[~~EDO~~\|equal scales]] on a [[wikipedia:Robert_Holford_Macdowall_Bosanquet\|Bosanquet keyboard]]. They were first mentioned in the [http://anaphoria.com/xen2.pdf second volume] of the ''Xenharmonikôn'' in 1974, but discussed more in-depth in the [http://anaphoria.com/xen3a.pdf third volume], published in the spring of 1975. The system describes notations to be used for ~~EDOs~~ with different versions depending on ~~the~~ the size of the [[perfect fifth]].		The linear notations from [[Erv Wilson]] is a system of [[notation]] created to fit [https://en.xen.wiki/w/Tour_of_Regular_Temperaments linear temperaments] & [[equal-step tuning\|equal scales]] on a [[wikipedia:Robert_Holford_Macdowall_Bosanquet\|Bosanquet keyboard]]. They were first mentioned in the [http://anaphoria.com/xen2.pdf second volume] of the ''[[Xenharmonikôn]]'' in 1974, but discussed more in-depth in the [http://anaphoria.com/xen3a.pdf third volume], published in the spring of 1975. The system describes notations to be used for [[EDO]]s with different versions depending on the size of the [[perfect fifth]].

	== ''A Doorway to Dialog'' ==		== ''A Doorway to Dialog'' ==
	The earliest paper first mentions that the keyboard in question seems to imply linear temperaments over equal scales, due to the issues with fingering. Because of this, he gives three reasons as to why to equalize a scale:		The earliest paper first mentions that the keyboard in question seems to imply linear temperaments over equal scales, due to the issues with fingering. Because of this, he gives three reasons as to why to equalize a scale:
	# In equal scales, there is less math required.		# In equal scales, there is less math required.
	# It simplifies the actual process of tuning instruments.		# It simplifies the actual process of tuning [[instruments]].
	# Some equal scales have ~~generators~~ close to the original temperament, so a case could be made that it would make sense to use that instead of an unequal scale.		# Some equal scales have [[generator]]s close to the original temperament, so a case could be made that it would make sense to use that instead of an unequal scale.
	[[File:Eikosany Keyboard.png\|left\|thumb\|Picture of the Eikosany keyboard, pg. 7\|371x371px]]		[[File:Eikosany Keyboard.png\|left\|thumb\|Picture of the Eikosany keyboard, pg. 7\|371x371px]]
	Wilson makes an example of a scale that could be made into a linear temperament by presenting his [[Combination product sets\|Eikosany]] scale on a keyboard inspired by one for 41 notes. With the layout he chose, D'''\''' and β<big>ł</big> fall onto a homogeneous position from C (two keys down for D\, two keys up for β<big>ł</big>). Another detail shows that the 3, 9, & 39 keys are two [[Schisma\|schismas]] off from the 5711, 35711, and 579*11 keys. With these two oddities, he suggests that a [[41edo\|41EDO]] keyboard would be proper in hosting the Eikosany.		Wilson makes an example of a scale that could be made into a linear temperament by presenting his [[Combination product sets\|Eikosany]] scale on a keyboard inspired by one for 41 notes. With the layout he chose, D'''\''' and β<big>ł</big> fall onto a homogeneous position from C (two keys down for D\, two keys up for β<big>ł</big>). Another detail shows that the 3, 9, & 39 keys are two [[Schisma\|schismas]] off from the 5711, 35711, and 579*11 keys. With these two oddities, he suggests that a [[41edo\|41EDO]] keyboard would be proper in hosting the Eikosany.
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	Wilson says that he's "''emphatically biased towards the positive systems''", where the fifth is greater than Pythagorean. He mentions that unlike systems like [[meantone]], where the fifth is damaged to make the third pure, a positive system would be the first time in Western history where a tuning had pure thirds and pure fifths. If the third was damaged, it would only be to help turn the [[7/4\|harmonic seventh]] and [[11/8\|eleventh]] pure, which Wilson calls "''far lesser apostles''". He also brings up that [[wikipedia:Raga\|the ragas of India]] could be hosted in these positive systems as well.		Wilson says that he's "''emphatically biased towards the positive systems''", where the fifth is greater than Pythagorean. He mentions that unlike systems like [[meantone]], where the fifth is damaged to make the third pure, a positive system would be the first time in Western history where a tuning had pure thirds and pure fifths. If the third was damaged, it would only be to help turn the [[7/4\|harmonic seventh]] and [[11/8\|eleventh]] pure, which Wilson calls "''far lesser apostles''". He also brings up that [[wikipedia:Raga\|the ragas of India]] could be hosted in these positive systems as well.

	On the next page, he gives a section of his thoughts on the original Bosanquet layout, noting things like key shape and the width of intervals. In the current & future papers, he suggests & uses smaller hexagonal keys, saying that it eliminates dead space & suits more scales, like meantone & [[just intonation]]. Along with the Eikosany keyboard, he demonstrates two other keyboards with this variation of the layout, those being the [[wikipedia:Shruti_(music)\|22 ''shruitis'' of India]] and a traditional [[Arabic, Turkish, Persian\|Arabic]] system of 17 notes.[[File:A Handy Guide For The Notation Of 12-, 22-, 31-, And 41-Tone Systems.png\|thumb\|366x366px\|An example of Wilson's notation system]]On the last two pages of the document, Wilson makes mention of a system of notation he issued in 1965. In these pages, he makes two categories based on how many steps C is from C#, and how many steps B# is from C. If C-C# is one step, its singular, two steps is binary, three steps is ternary, etc etc; if B# is less than C, its negative, neutral if they're the same, positive if B# is greater by one step, 2bly positive if B# is greater by two steps, etc etc. He also gives examples for accidentals up to the quaternary system; by this point, he hasn't made accidentals for a quinary system.		On the next page, he gives a section of his thoughts on the original Bosanquet layout, noting things like key shape and the width of intervals. In the current & future papers, he suggests & uses smaller hexagonal keys, saying that it eliminates dead space & suits more scales, like meantone & [[just intonation]]. Along with the Eikosany keyboard, he demonstrates two other keyboards with this variation of the layout, those being the [[wikipedia:Shruti_(music)\|22 ''shruitis'' of India]] and a traditional [[Arabic, Turkish, Persian\|Arabic]] system of 17 notes.[[File:A Handy Guide For The Notation Of 12-, 22-, 31-, And 41-Tone Systems.png\|thumb\|366x366px\|An example of Wilson's notation system]]On the last two pages of the document, Wilson makes mention of a system of [[notation]] he issued in 1965. In these pages, he makes two categories based on how many steps C is from C#, and how many steps B# is from C. If C-C# is one step, its singular, two steps is binary, three steps is ternary, etc etc; if B# is less than C, its negative, neutral if they're the same, positive if B# is greater by one step, 2bly positive if B# is greater by two steps, etc etc. He also gives examples for accidentals up to the quaternary system; by this point, he hasn't made accidentals for a quinary system.
	{\| class="wikitable"		{\| class="wikitable"
	\|etc		\|etc
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	Wilson made the accidentals mirror each other so that there would be no confusion in the sheet music, assuming one won't use positive & negative accidentals in the same piece. At this time, Wilson hadn't explored novenal (5\[[9edo\|9]]) or tridecimal (8\[[13edo\|13]]) accidentals, saying "''I need to experiment more with the septimally negative and quintally positive systems before expressing a view on this.''"		Wilson made the accidentals mirror each other so that there would be no confusion in the sheet music, assuming one won't use positive & negative accidentals in the same piece. At this time, Wilson hadn't explored novenal (5\[[9edo\|9]]) or tridecimal (8\[[13edo\|13]]) accidentals, saying "''I need to experiment more with the septimally negative and quintally positive systems before expressing a view on this.''"

	For the last few pages of the paper, he demonstrates six keyboards to demonstrate each unique system mentioned in the paper. Along with this, he also includes the notation for each system. In order of appearance, the EDOs used for the notation section are 41, 31, 23, 26, and ~~22EDO~~.		For the last few pages of the paper, he demonstrates six keyboards to demonstrate each unique system mentioned in the paper. Along with this, he also includes the notation for each system. In order of appearance, the EDOs used for the notation section are {{EDOs\|41, 31, 23, 26, and 22}} EDO.

	== Updates After Wilson ==		== Updates After Wilson ==
	In the document for Wilson's ''On Linear Notations and The Bosanquet Keyboard'' from the [http://anaphoria.com/wilson.html Wilson Archives], [[Kraig Grady]] has been working on an appendix from Praveen Venkataramana, showing not only two more systems of fifths (octal [5/[[8edo\|8]]] & novenal) but also demonstrating the various ways you can notate EDOs with these systems up to [[72edo\|72EDO]]. At the time of writing, there appears to be work showing that this can be applied to [[MOS\|MOS scales]] and constant structures, though Grady has not added these yet.		In the document for Wilson's ''On Linear Notations and The Bosanquet Keyboard'' from the [http://anaphoria.com/wilson.html Wilson Archives], [[Kraig Grady]] has been working on an appendix from [[Praveen Venkataramana]], showing not only two more systems of fifths (octal [5/[[8edo\|8]]] & novenal) but also demonstrating the various ways you can notate EDOs with these systems up to [[72edo\|72EDO]]. At the time of writing, there appears to be work showing that this can be applied to [[MOS\|MOS scales]] and constant structures, though Grady has not added these yet.