Interseptimal interval: Difference between revisions

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 === Within a pentatonic framework ===
-A pentatonic framework, as elucidated in Kite Giedraitis's [http://www.tallkite.com/AlternativeTunings.html Alternative Tuning guide], is far more amenable to interseptimal intervals than the traditional Western heptatonic framework. In a pentatonic framework, there are 5 categories of intervals in the octave rather than 7, into which interseptimals fit much more cleanly:
+A pentatonic framework, as elucidated in Kite Giedraitis's [http://www.tallkite.com/AlternativeTunings.html Alternative Tuning guide], is far more amenable to interseptimal intervals than the traditional Western heptatonic framework.
+{| class="wikitable"
+|+The pentatonic framework
+! colspan="2" |names
+!quality
+!boundaries
+! colspan="2" |heptatonic equivalent
+|-
+| rowspan="3" |1sn
+| rowspan="3" |unison
+|perfect
+|1/1 to 64/63
+|perfect
+|1sn
+|-
+|half-augmented
+|(interseptimal)
+! colspan="2" |
+|-
+|augmented
+|28/27 to 16/15
+|minor
+| rowspan="3" |2nd
+|-
+! colspan="3" |
+|(interpental)
+|neutral
+|-
+| rowspan="3" |penta-2nd
+| rowspan="3" |subthird
+|minor
+|10/9 to 8/7
+|major
+|-
+|neutral
+|(interseptimal)
+! colspan="2" |
+|-
+|major
+|7/6 to 6/5
+|minor
+| rowspan="3" |3rd
+|-
+! colspan="3" |
+|(interpental)
+|neutral
+|-
+| rowspan="5" |penta-3rd
+| rowspan="5" |fourthoid
+|diminished
+|5/4 to 9/7
+|major
+|-
+|half-diminished
+|(interseptimal)
+! colspan="2" |
+|-
+|perfect
+|21/16 to 27/20
+|perfect
+| rowspan="3" |4th
+|-
+|half-augmented
+|(interpental)
+|half-augmented
+|-
+|augmented
+| rowspan="2" |7/5 to 10/7
+|augmented
+|-
+| rowspan="5" |penta-4th
+| rowspan="5" |fifthoid
+|diminished
+|diminished
+| rowspan="3" |5th
+|-
+|half-diminished
+|(interpental)
+|half-diminished
+|-
+|perfect
+|40/27 to 32/21
+|perfect
+|-
+|half-augmented
+|(interseptimal)
+! colspan="2" |
+|-
+|augmented
+|14/9 to 8/5
+|minor
+| rowspan="3" |6th
+|-
+! colspan="3" |
+|(interpental)
+|neutral
+|-
+| rowspan="3" |penta-5th
+| rowspan="3" |subseventh
+|minor
+|5/3 to 12/7
+|major
+|-
+|neutral
+|(interseptimal)
+! colspan="2" |
+|-
+|major
+|7/4 to 9/5
+|minor
+| rowspan="3" |7th
+|-
+! colspan="3" |
+|(interpental)
+|neutral
+|-
+| rowspan="3" |hexave
+| rowspan="3" |octoid
+|diminished
+|15/8 to 27/14
+|major
+|-
+|half-diminished
+|(interseptimal)
+! colspan="2" |
+|-
+|perfect
+|63/32 to 2/1
+|perfect
+|8ve
+|}
+Note the two additional interseptimal regions. The boundary ratios are mostly either 81/80 or 64/63 away from a 3-limit interval. The exceptions are 7/5 and 10/7, which are only a [[5120/5103|Saruyo]] comma away from the 3-limit diminished 5th and augmented 4th respectively.
-* the subthird or penta-2nd (imperfect)
+Interseptimal intervals are now easily named. However there are now hard-to-name "interpental" intervals which would be neutral intervals in the heptatonic framework, containing such ratios as 12/11, 11/9, etc. This is because interseptimal intervals are the neutral intervals with respect to the parent [[mos]] [[2L 3s]] of the diatonic mos [[5L 2s]]. See [[Neutral and interordinal k-mossteps]] for a partial generalization of this behavior to other mosses.
-** <- semifourth/chthonic region
-* the fourthoid or penta-3rd (perfect)
-** <- semisixth/naiadic region
-* the fifthoid or penta-4th (perfect)
-** <- semitenth/cocytic region
-* the subseventh or penta-5th (imperfect)
-** <- semitwelfth/ouranic region
-* the octoid or hexave (perfect, reducing to a unison)
-Of especial interest are the chthonic and ouranic regions, being very close to intervals of [[5edo|5EDO]], and in central positions within the two imperfect interval categories. In this framework, they can easily function as "neutral/middle" intervals to which other intervals in their pentatonic category are compared. So composing in a pentatonic framework may allow interseptimal intervals to play much more pivotal roles than usual.
+So composing in a pentatonic framework may allow interseptimal intervals to play much more pivotal roles than usual.
-This is because interseptimal intervals are the neutral intervals with respect to the parent [[mos]] [[2L 3s]] of the diatonic mos [[5L 2s]]. See [[Neutral and interordinal k-mossteps]] for a partial generalization of this behavior to other mosses.
 == Examples ==