Armodue theory: Difference between revisions
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=Armodue Theory of 16EDO= | =Armodue Theory of 16EDO= | ||
''(summary translation from the | ''(summary translation from the Italian language site'' [http://www.armodue.com/ricerche.htm Armodue] '')'' | ||
Referring not only to the [[16edo|16- | Referring not only to the [[16edo|16-tone equal temperament]], but also to half-equal and [[Lou_Harrison|Lou Harrison]]'s [[JustIntonation|Just intonation]] 16 note scale, the natural octave division by [http://www.pertout.com/ Andrián Pertout] and the 16-to-31 [[OverToneSeries|overtone scale]], Armodue has been proposed as a new notation and theory system. | ||
Desiring to make the approach to Armodue as easy as possible, but conscious that they had to give new names to the notes that constitute the system, the Italian creators of the | Desiring to make the approach to Armodue as easy as possible, but conscious that they had to give new names to the notes that constitute the system, the Italian creators of the [http://armodue.com/ Armodue] system named them numbering from 1 to 9: | ||
1, 1#, 2, 2#, 3, 3#, 4, 5, 5#, 6, 6#, 7, 7#, 8, 8#, 9 | 1, 1#, 2, 2#, 3, 3#, 4, 5, 5#, 6, 6#, 7, 7#, 8, 8#, 9 | ||
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The basic semitone of Armodue, whatever concrete temperament is used, is always called ''eka'' (from Sanskrit eka: one, unit). In the chromatic Armodue scale, one eka always corresponds to the interval between any two consecutive notes. | The basic semitone of Armodue, whatever concrete temperament is used, is always called ''eka'' (from Sanskrit eka: one, unit). In the chromatic Armodue scale, one eka always corresponds to the interval between any two consecutive notes. | ||
For composing in Armodue it's useful to use a ''tetragram'' (staff with 4 lines) | For composing in Armodue it's useful to use a ''tetragram'' (staff with 4 lines): | ||
[[file:armodue-TETR-1.jpg|frame|none|© Armodue; used with permission.]] | |||
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The notes without accidentals form a [[Mavila|Mavila]] [[7L_2s|superdiatonic scale (7L 2s)]]. | The notes without accidentals form a [[Mavila|Mavila]] [[7L_2s|superdiatonic scale (7L 2s)]]. | ||
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In other words, the "1" note will be written immediately under the first line <u>in every tenth</u>. | In other words, the "1" note will be written immediately under the first line <u>in every tenth</u>. | ||
In Armodue we have only a numeric clef, that | In Armodue we have only a numeric clef, that shows us the tenth: | ||
[[file:armodue-Chiave.gif|frame|none|© Armodue; used with permission.]] | |||
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The clefs 1,2,3... refers to the tenths: first, second, third... | The clefs 1,2,3... refers to the tenths: first, second, third... | ||
So, in the illustrated example above, the first tetragram (from top) refers to the 3rd tenth (central tenth, corresponding to the octave C3-C4), | So, in the illustrated example above, the first tetragram (from top) refers to the 3rd tenth (central tenth, corresponding to the octave C3-C4), the second tetragram to the 5th tenth and the third to the 2nd. If we need to write simultaneously on several staves, we will draw normal braces. | ||
the | The keyboard conceived by the Armodue authors has the same disposition as Goldsmith's one (except the curvature): | ||
[[file:armodue-Tastiera.jpg|frame|none|© Armodue; used with permission.]] | |||
The white keys, corresponding to the notes without accidentals in the notation system, form again a [[Mavila|Mavila]] [[7L_2s|superdiatonic scale (7L 2s).]] | The white keys, corresponding to the notes without accidentals in the notation system, form again a [[Mavila|Mavila]] [[7L_2s|superdiatonic scale (7L 2s).]] | ||
[[file:Armodue_Neck.PNG|frame|none|Dot-Pattern inlays, by Armodue]] | |||
| | Dot-Pattern inlays, by Armodue | |||
=Armodue just intonation - connection to Lou Harrison and Andrián Pertout= | =Armodue just intonation - connection to Lou Harrison and Andrián Pertout= | ||
Armodue Just Intonation is nothing else than the 16-note scale by[[Lou_Harrison| Lou Harrison]] based on simple ratios and pure intervals. In this scale there are practically the same twelve intervals of the "natural" or "Zarlinian" scale (the semitone 16/15, the minor wholetone 10/9, the minor third 6/5, the major third 5/4, the pure forth and fifth 4/3 and 3/2, the minor sixth 8/5, the major sixth 5/3, the minor seventh that is the complement of the minor wholetone 9/5, the major seventh 15/8) in | Armodue Just Intonation is nothing else than the 16-note scale by[[Lou_Harrison| Lou Harrison]] based on simple ratios and pure intervals. In this scale there are practically the same twelve intervals of the "natural" or "Zarlinian" scale (the semitone 16/15, the minor wholetone 10/9, the minor third 6/5, the major third 5/4, the pure forth and fifth 4/3 and 3/2, the minor sixth 8/5, the major sixth 5/3, the minor seventh that is the complement of the minor wholetone 9/5, the major seventh 15/8) in addition to the tritone and four other intervals that are based on the harmonic seventh (the ratios 8/7, 7/6, 12/7, 7/4). | ||
The composer Andrián Pertout used a very similar scale in his composition "Sonus dulcis" ([http://web.archive.org/web/20040511172650/http://www.users.bigpond.com/apertout/Sonus.htm article on archive.org]), namely the following (according to [http://www.armodue.com/risorse.htm Armodue]): | The composer Andrián Pertout used a very similar scale in his composition "Sonus dulcis" ([http://web.archive.org/web/20040511172650/http://www.users.bigpond.com/apertout/Sonus.htm article on archive.org]), namely the following (according to [http://www.armodue.com/risorse.htm Armodue]): | ||