Erv Wilson's Linear Notations: Difference between revisions

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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.

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.

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 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.
+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.