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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]] |
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| == Alternative Armodue tunings ==
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| As the standard intervals of Armodue may be too discordant for some composers and/or listeners, here are several alternative tunings:
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| === Armodue just intonation - connection to Lou Harrison and Andrián Pertout ===
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| 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).
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| 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]):
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| {| class="wikitable"
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| |-
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| ! | Armodue note
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| ! | Interval
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| ! | Ratio
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| ! | Cents
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| |-
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| | | 1
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| | | unison
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| | | 1/1
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| | | 0
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| |-
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| | | 1#
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| | | major half-tone
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| | | 16/15
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| | | 112
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| |-
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| | | 2
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| | | minor tone
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| | | 10/9
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| | | 182
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| |-
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| | | 2#
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| | | major tone
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| | | 9/8
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| | | 204
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| |-
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| | | 3
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| | | minor third
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| | | 6/5
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| | | 316
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| |-
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| | | 3#
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| | | major third
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| | | 5/4
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| | | 386
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| |-
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| | | 4
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| | | fourth
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| | | 4/3
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| | | 498
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| |-
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| | | 5
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| | | harmonic tritone
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| | | 45/32
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| | | 590
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| |-
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| | | 5#
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| | | cyclic tritone
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| | | 64/45
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| | | 610
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| |-
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| | | 6
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| | | fifth
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| | | 3/2
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| | | 702
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| |-
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| | | 6#
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| | | diminished sixth
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| | | 8/5
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| | | 814
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| |-
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| | | 7
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| | | harmonic sixth
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| | | 5/3
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| | | 884
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| |-
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| | | 7#
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| | | harmonic minor seventh
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| | | 7/4
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| | | 969
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| |-
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| | | 8
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| | | minor seventh
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| | | 16/9
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| | | 996
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| |-
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| | | 8#
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| | | minor seventh
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| | | 9/5
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| | | 1018
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| |-
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| | | 9
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| | | major seventh
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| | | 15/8
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| | | 1088
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| |}
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| === Semi-equalized Armodue ===
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| 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.
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| 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.
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| {| class="wikitable"
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| |-
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| ! | Armodue note
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| ! | cents (16edo)
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| ! | cents (semi-equalized Armodue based on [[31edo|31edo]])
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| |-
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| | | 1
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| | | 0
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| | | 0
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| |-
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| | | 1#
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| | | 75
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| | | 77.42
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| |-
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| | | 2
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| | | 150
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| | | 154.84
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| |-
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| | | 2#
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| | | 225
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| | | 232.26
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| |-
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| | | 3
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| | | 300
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| | | 309.68
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| |-
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| | | 3#
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| | | 375
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| | | 387.10
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| |-
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| | | 4
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| | | 450
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| | | 464.52
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| |-
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| | | 5
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| | | 525
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| | | 541.94
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| |-
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| | | 5#
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| | | 600
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| | | 619.35
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| |-
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| | | 6
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| | | 675
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| | | 696.77
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| |-
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| | | 6#
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| | | 750
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| | | 774.19
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| |-
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| | | 7
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| | | 825
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| | | 851.61
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| |-
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| | | 7#
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| | | 900
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| | | 929.03
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| |-
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| | | 8
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| | | 975
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| | | 967.74
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| |-
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| | | 8#
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| | | 1050
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| | | 1045.16
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| |-
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| | | 9
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| | | 1125
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| | | 1122.58
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| |}
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| [[Category:16edo]] | | [[Category:16edo]] |
| [[Category:Armodue]] | | [[Category:Armodue]] |