Erv Wilson's Linear Notations: Difference between revisions

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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]].

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.<ref name="wilson1974bosanquet"/><ref name="wilson1975linear"/> 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'' ==

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# 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]]

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, & 3*9 keys are two [[~~Schisma|schismas~~]] off from the 5*7*11, 3*5*7*11, and 5*7*9*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 [[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, & 3*9 keys are two [[schisma]]s off from the 5*7*11, 3*5*7*11, and 5*7*9*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 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 ''shrutis'' 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"

|etc

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== 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.

Wilson's linear notations can be defined purely in terms of the keyboard positions of the fifth, the octave, and the comma corresponding to the accidental (e.g. C to C/).<ref name="ratan2026another"/>

From this point of view, the notations can be applied to any scale mapped to a two-dimensional keyboard, and in particular to rank-2 regular temperaments.

== References ==

Erv Wilson, [https://anaphoria.com/xen2.pdf Bosanquet - A Bridge - A Doorway to Dialog], Xenharmonikon 2 (1974)

</ref>

Erv Wilson, [https://anaphoria.com/xen3a.pdf On Linear Notations and the Bosanquet Keyboard], Xenharmonikon 3 (1975)

</ref>

Naren Ratan, [https://www.xenharmonikon.org/2026/05/19/another-look-at-wilsons-keyboard-mapping-system/ Another look at Wilson's keyboard mapping system], Xenharmonikon Online (2026)

</ref>

</references>

@@ 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] & [[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]].
+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.<ref name="wilson1974bosanquet"/><ref name="wilson1975linear"/> 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'' ==
@@ Line 7: / Line 7: @@
 # 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]]
-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, & 3*9 keys are two [[Schisma|schismas]] off from the 5*7*11, 3*5*7*11, and 5*7*9*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 [[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, & 3*9 keys are two [[schisma]]s off from the 5*7*11, 3*5*7*11, and 5*7*9*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 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 ''shrutis'' 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"
 |etc
@@ Line 88: / Line 88: @@
 == 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.
+Wilson's linear notations can be defined purely in terms of the keyboard positions of the fifth, the octave, and the comma corresponding to the accidental (e.g. C to C/).<ref name="ratan2026another"/>
+From this point of view, the notations can be applied to any scale mapped to a two-dimensional keyboard, and in particular to rank-2 regular temperaments.
+== References ==
+<references>
+<ref name="wilson1974bosanquet">
+Erv Wilson, [https://anaphoria.com/xen2.pdf Bosanquet - A Bridge - A Doorway to Dialog], Xenharmonikon 2 (1974)
+</ref>
+<ref name="wilson1975linear">
+Erv Wilson, [https://anaphoria.com/xen3a.pdf On Linear Notations and the Bosanquet Keyboard], Xenharmonikon 3 (1975)
+</ref>
+<ref name="ratan2026another">
+Naren Ratan, [https://www.xenharmonikon.org/2026/05/19/another-look-at-wilsons-keyboard-mapping-system/ Another look at Wilson's keyboard mapping system], Xenharmonikon Online (2026)
+</ref>
+</references>
 {{Navbox notation}}