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Adaptive diatonic interval names: Difference between revisions

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The fundamental premise of ADIN goes like this.
The fundamental premise of ADIN goes like this.


For an EDO (let's say, 58edo), identify the "central intervals" for each category. These are the diatonic neutral intervals, which may be between edosteps, with the exception of the fifth and fourth, which use their perfect varieties, and the tritone, which is always the semioctave.
For an EDO (let's say, 58edo), identify the "central intervals" for each category. These are the diatonic neutral intervals, which may be between edosteps, and the tritone, which is always the semioctave.


What interval qualities will label is distances from these "central intervals". For the most complex case (intervals with major and minor quality), follow the following procedure.
What interval qualities will label is distances from these "central intervals". For the most complex case (intervals with major and minor quality), follow the following procedure.
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For the minor side of any interval class, swap "major" and "minor", "sub" and "super/supra" (super applies only to major and unqualified intervals, other types use supra), "ultra" and "infra", and "arto" and "tendo" (in all senses).  
For the minor side of any interval class, swap "major" and "minor", "sub" and "super/supra" (super applies only to major and unqualified intervals, other types use supra), "ultra" and "infra", and "arto" and "tendo" (in all senses).  


Fourths and fifths have the special exception that the closest fourth and fifth to 4/3 and 3/2 respectively receive the label "perfect". If the interval that was relabeled "perfect" was major, novamajor, neomajor, pentamajor, trimajor, shrubmajor, or magimajor, all "major" intervals of that class have the word "major" removed; same goes for "minor".


Fourths/fifths and tritones utilize the exact same interval qualities, except that the "neutral" is removed from the neutral qualities. Note that the terms "penta-" and "tri-" now no longer directly correspond to 5- or 3-limit JI intervals in the case of intervals in this region.
For tritones, start at the semi-octave. If the semioctave exists in the scale, label it "neutral tritone", otherwise label the two closest intervals "artoneutral tritone" for the smaller and "tendoneutral tritone" for the larger. Label the sharpest tritone interval flatter than the neutral or artoneutral tritone "narrow tritone" (and label its complement "wide tritone"). If the interval closest to 565 cents has not already been labelled as a tritone, label it a "subtritone". If there are intervals between the subtritone and narrow tritone, label "grave tritone" if only 1 interval and "grave tritone" (for the smaller) and "small tritone" (for the larger) if there are two. Label the tritone interval one step smaller than the subtritone the infratritone.
 
Note that here, "infra" is preferred in lieu of "supraminor", and likewise "ultra" in place of "submajor" (unless "sub-" and "super-" are not already taken, in which case, those are used).  


For unisons, the term "diesis" is used in place of "major unison" and "counterdiesis" in place of "minor octave"; "comma" is "submajor unison" and "countercomma" is "supraminor octave".  
For unisons, the term "diesis" is used in place of "major unison" and "counterdiesis" in place of "minor octave"; "comma" is "submajor unison" and "countercomma" is "supraminor octave".  


Priority: "fourth", "fifth", "tritone", "unison", and "octave" have the same priority as a "novamajor third", "neomajor third", or "major third", whichever is the first one listed that exists in the labeling; priority decreases by one as you go further from the central interval, and increases by one as you go closer to it. Where the central interval is halfway between an edostep, the two closest intervals have a priority of -0.5. The interval name with the highest priority is used.
Priority: "perfect fourth", "perfect fifth", "tritone", "unison", and "octave" have the same priority as a "novamajor third", "neomajor third", or "major third", whichever is the first one listed that exists in the labeling; priority decreases by one as you go further from the central interval (or perfect interval in the case of fourths and fifths), and increases by one as you go closer to it. Where the central interval is halfway between an edostep, the two closest intervals have a priority of -0.5. The interval name with the highest priority is used.


An unqualified fourth or fifth is labelled "perfect"; an unqualified tritone is labelled "neutral" (importantly, subtritone and supratritone remain unchanged).
If "narrow tritone", "subtritone", or "small tritone" (in decreasing order of precedence) do not appear in the list of highest-priority names, and "artoneutral tritone" exists, then relabel artoneutral to whichever is available.  


If there is only one type of major or minor (not including submajor or supraminor), the qualifier on major or minor (i.e. penta- or magi-) is removed.
If there is only one type of major or minor (not including submajor or supraminor), the qualifier on major or minor (i.e. penta- or magi-) is removed.
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| -1
| -1
|26
|26
|minor fourth
|infrafourth
| -5
| -5
|-
|-
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| -4
| -4
|29
|29
|superfourth
|novafourth
| -4
| -4
|-
|-
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| -5
| -5
|30
|30
|pentamajor fourth
|pentafourth
| -5
| -5
|-
|-
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| -6
| -6
|31
|31
|novaminor tritone, novamajor fourth
|superfourth
| -6
| -6
|-
|-
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| -5
| -5
|32
|32
|pentaminor tritone
|subtritone
| -5
| -5
|-
|-
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| -4
| -4
|33
|33
|subtritone
|narrow tritone
| -4
| -4
|-
|-
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| -3
| -3
|34
|34
|tritone
|neutral tritone
| -3
| -3
|}
|}
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|-
|-
|10
|10
|subfourth
|neutral fourth
| -2
| -2
|-
|-
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|-
|-
|12
|12
|subtritone
|narrow tritone
| -1.5
| -1.5
|}
|}
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|-
|-
|13
|13
|minor tritone, major fourth
|narrow tritone, major fourth
| -2
| -2
|-
|-
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|-
|-
|7
|7
|minor tritone
|narrow tritone
| -0.5
| -0.5
|}
|}
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|-
|-
|8
|8
|major fourth, minor tritone
|subminor fourth, narrow tritone
| -1.5
| -1.5
|-
|-
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