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Armodue harmony: Difference between revisions

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1 eka - 15 eka (eka, major seventh)
1 eka - 15 eka (eka, major seventh)


2 eka - 14 eka (neutral tone, dominant seventh)
2 eka - 14 eka (neutral tone, neutral seventh)


3 eka - 13 eka (whole tone, harmonic seventh)
3 eka - 13 eka (whole tone, minor seventh)


4 eka - 12 eka (minor third, major sixth)
4 eka - 12 eka (minor third, major sixth)
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8 eka (tritone)
8 eka (tritone)
The intervals are categorized into categories from consonance to dissonance, progressing from the center of the chromatic scale outwards to the unison and octave, except for the median which is an unstable dissonance. These befit a more melodic perception of dissonance and consonance, ignoring just targets, likely similar to the perception of intervals that people drawn to 16edo have in the first place. Note that these additionally coincide with perceived harmonic dissonance on a timbre with only octaves of sine waves.
Notably, the harmonic seventh is a "sweet dissonance" (a kind of ambisonance, essentially), and the flat fifth is an open consonance.
{| class="wikitable"
|+
!Eka
!Name
!Category
|-
|1
|Eka, semitone
|Harsh dissonance
|-
|2
|Neutral tone
|Neutral dissonance
|-
|3
|Whole tone
|Sweet dissonance
|-
|4
|Minor third
| rowspan="2" |Sweet consonance
|-
|5
|Major third
|-
|6
|Subfourth
|Neutral consonance
|-
|7
|Perfect fourth
|Open consonance
|-
|8
|Tritone
|Unstable dissonance
|-
|9
|Perfect fifth
|Open consonance
|-
|10
|Superfifth
|Neutral consonance
|-
|11
|Minor sixth
| rowspan="2" |Sweet consonance
|-
|12
|Major sixth
|-
|13
|Minor seventh
|Sweet dissonance
|-
|14
|Neutral seventh
|Neutral dissonance
|-
|15
|Major seventh
|Harsh dissonance
|}


==1 eka and 15 eka==
==1 eka and 15 eka==
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Because of this, the eka sounds particularly euphonious and familiar to the ear: the eka is perceived as a natural interval not less than a semitone of the dodecatonic scale. In a free melodic improvisation, chromatic successions of consecutive ekas sound much like chromatic successions of semitones. Therefore, all the harmonic techniques inherent in chromaticism can be applied in Armodue considering the eka as equivalent to a tempered semitone. The complement of one eka is the interval of 15 eka, the "major 8-step", comparable to a slightly enlarged major seventh of the dodecatonic system. The small intervals of 1 eka, 2 eka and 3 eka in Armodue lend themselves magnificiently to the design of melodies and scales of exquisite modal flavour.
Because of this, the eka sounds particularly euphonious and familiar to the ear: the eka is perceived as a natural interval not less than a semitone of the dodecatonic scale. In a free melodic improvisation, chromatic successions of consecutive ekas sound much like chromatic successions of semitones. Therefore, all the harmonic techniques inherent in chromaticism can be applied in Armodue considering the eka as equivalent to a tempered semitone. The complement of one eka is the interval of 15 eka, the "major 8-step", comparable to a slightly enlarged major seventh of the dodecatonic system. The small intervals of 1 eka, 2 eka and 3 eka in Armodue lend themselves magnificiently to the design of melodies and scales of exquisite modal flavour.


In Armodue the intervals of 1 and 15 eka eka are considered harsh dissonances and as such should be used with caution in chords. However, all rules may be applied that already govern the treatment of harsh dissonances in the dodecatonic system.
In Armodue the intervals of 1 and 15 eka are considered harsh dissonances and as such should be used with caution in chords. However, all rules may be applied that already govern the treatment of harsh dissonances in the dodecatonic system.


==2 eka and 14 eka==
==2 eka and 14 eka==
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A very particular sound in the Armodue environment is achieved by the symmetrical scale with the structure 1 + 3 + 1 + 3 + 1 + 3 + 1 + 3 eka or its variant 3 + 1 + 3 + 1 + 3 + 1 + 3 + 1 eka.
A very particular sound in the Armodue environment is achieved by the symmetrical scale with the structure 1 + 3 + 1 + 3 + 1 + 3 + 1 + 3 eka or its variant 3 + 1 + 3 + 1 + 3 + 1 + 3 + 1 eka.


These two scales strongly evoke the sound of the "diminished" scales of the dodecatonic tempered system with their alternating tone-semitone pattern (widely used in jazz and blues): c - c# - d# - e - f# g - a - a#- - c (symmetrical scale of type semitone-tone) or c - d - eb - f - gb - g# - a - h - c (symmetrical scale of type tone-semitone). In Armodue, these scales are named for their special quality "neo-diminished" scales. (Actually, they are scales of [[Diminished|diminished temperament]], in 12edo as well as in 16edo!)
These two scales strongly evoke the sound of the "diminished" scales of the dodecatonic tempered system with their alternating tone-semitone pattern (widely used in jazz and blues): c - c# - d# - e - f# g - a - a#- - c (symmetrical scale of type semitone-tone) or c - d - eb - f - gb - g# - a - h - c (symmetrical scale of type tone-semitone). In Armodue, these scales are named for their special quality "neo-diminished" scales. (Actually, they are scales of [[diminished (temperament)|diminished]] temperament, in 12edo as well as in 16edo!)


{| class="wikitable"
{| class="wikitable"
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