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Armodue theory: Difference between revisions

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[[file:Armodue_Neck.PNG|frame|none|Dot-Pattern inlays, by Armodue]]
[[file:Armodue_Neck.PNG|frame|none|Dot-Pattern inlays, by Armodue]]
== Alternative Armodue tunings ==
As the standard intervals of Armodue may be too discordant for some composers and/or listeners, here are several alternative tunings:
=== 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 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]):
{| class="wikitable"
|-
! | Armodue note
! | Interval
! | Ratio
! | Cents
|-
| | 1
| | unison
| | 1/1
| | 0
|-
| | 1#
| | major half-tone
| | 16/15
| | 112
|-
| | 2
| | minor tone
| | 10/9
| | 182
|-
| | 2#
| | major tone
| | 9/8
| | 204
|-
| | 3
| | minor third
| | 6/5
| | 316
|-
| | 3#
| | major third
| | 5/4
| | 386
|-
| | 4
| | fourth
| | 4/3
| | 498
|-
| | 5
| | harmonic tritone
| | 45/32
| | 590
|-
| | 5#
| | cyclic tritone
| | 64/45
| | 610
|-
| | 6
| | fifth
| | 3/2
| | 702
|-
| | 6#
| | diminished sixth
| | 8/5
| | 814
|-
| | 7
| | harmonic sixth
| | 5/3
| | 884
|-
| | 7#
| | harmonic minor seventh
| | 7/4
| | 969
|-
| | 8
| | minor seventh
| | 16/9
| | 996
|-
| | 8#
| | minor seventh
| | 9/5
| | 1018
|-
| | 9
| | major seventh
| | 15/8
| | 1088
|}
=== Semi-equalized Armodue ===
One step of 16edo (75 cents) is nearly equal to two steps (2\31) of [[31edo|31edo]] (77.42 cents). If we take the latter as a base, we get semi-equalized Armodue. In this temperament there is inevitably a smaller microtone (eka between the notes '7#' and '8'). leading to the 16 note MOS Valentine[16] of [[Starling_temperaments#Valentine temperament|valentine temperament]]. Similarly we might use three steps of [[46edo|46edo]], 3\46, 78.26 cents, or five steps of [[77edo|77edo]], 77.92 cents.
Semi-equalized Armodue provides a balance between the symmetry of the equalized system and the purity of natural intervals: intervals of semi-equalized Armodue are very pure, and at the same time it preserves the symmetry of the equalized system and its interval sizes almost unchanged.
{| class="wikitable"
|-
! | Armodue note
! | cents (16edo)
! | cents (semi-equalized Armodue based on [[31edo|31edo]])
|-
| | 1
| | 0
| | 0
|-
| | 1#
| | 75
| | 77.42
|-
| | 2
| | 150
| | 154.84
|-
| | 2#
| | 225
| | 232.26
|-
| | 3
| | 300
| | 309.68
|-
| | 3#
| | 375
| | 387.10
|-
| | 4
| | 450
| | 464.52
|-
| | 5
| | 525
| | 541.94
|-
| | 5#
| | 600
| | 619.35
|-
| | 6
| | 675
| | 696.77
|-
| | 6#
| | 750
| | 774.19
|-
| | 7
| | 825
| | 851.61
|-
| | 7#
| | 900
| | 929.03
|-
| | 8
| | 975
| | 967.74
|-
| | 8#
| | 1050
| | 1045.16
|-
| | 9
| | 1125
| | 1122.58
|}
[[Category:16edo]]
[[Category:16edo]]
[[Category:Armodue]]
[[Category:Armodue]]
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