Erv Wilson's Linear Notations: Difference between revisions

Line 6:

# 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.

[[File:Eikosany Keyboard.png|left|thumb|Picture of the Eikosany keyboard, pg. 7]]

[[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 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.

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|~~306x306px~~|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 ~~the size of~~ B# ~~compared to~~ 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.

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"

|etc

Line 24:

|

|5

|[[5edo|5]]

|12

|[[12edo|12]]

|19

|[[19edo|19]]

|Singulary

|-

|

|10

|[[10edo|10]]

|17

|[[17edo|17]]

|24

|[[24edo|24]]

|31

|[[31edo|31]]

|Binary

|-

|

|15

|[[15edo|15]]

|22

|[[22edo|22]]

|29

|[[29edo|29]]

|36

|[[36edo|36]]

|43

|[[43edo|43]]

|Ternary

|-

|

|27

|[[27edo|27]]

|34

|[[34edo|34]]

|41

|[[41edo|41]]

|48

|[[48edo|48]]

|55

|[[55edo|55]]

|Quaternary

|-

|

|39

|[[39edo|39]]

|46

|[[46edo|46]]

|53

|[[53edo|53]]

|60

|[[60edo|60]]

|67

|[[67edo|67]]

|Quinary

|-

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 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, & 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.

@@ Line 6: / Line 6: @@
 # 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.
-[[File:Eikosany Keyboard.png|left|thumb|Picture of the Eikosany keyboard, pg. 7]]
+[[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 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.
-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|306x306px|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 the size of B# compared to 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.
+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"
 |etc
@@ Line 24: / Line 24: @@
 |
 |
-|5
+|[[5edo|5]]
-|12
+|[[12edo|12]]
-|19
+|[[19edo|19]]
 |Singulary
 |-
 |
 |
-|10
+|[[10edo|10]]
-|17
+|[[17edo|17]]
-|24
+|[[24edo|24]]
-|31
+|[[31edo|31]]
 |Binary
 |-
 |
-|15
+|[[15edo|15]]
-|22
+|[[22edo|22]]
-|29
+|[[29edo|29]]
-|36
+|[[36edo|36]]
-|43
+|[[43edo|43]]
 |Ternary
 |-
 |
-|27
+|[[27edo|27]]
-|34
+|[[34edo|34]]
-|41
+|[[41edo|41]]
-|48
+|[[48edo|48]]
-|55
+|[[55edo|55]]
 |Quaternary
 |-
 |
-|39
+|[[39edo|39]]
-|46
+|[[46edo|46]]
-|53
+|[[53edo|53]]
-|60
+|[[60edo|60]]
-|67
+|[[67edo|67]]
 |Quinary
 |-
@@ 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 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, & 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.