Otonality and utonality: Difference between revisions

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If a chord can be voiced as a "palindrome", it inverts to itself, and is ambitonal. Such a voicing makes the lowest interval the same as the highest, the next lowest the same as the next highest, etc. For example, the min7 chord can be voiced as 1-m3-P5-m7 = min 3rd, maj 3rd, min 3rd, therefore it must be ambitonal. Note that some ambitonal chords, such as the maj7no5, cannot be voiced as a palindrome.

By this definition all ~~monads, dyads~~ and ~~intervals~~ are ambitonal. (Dyads and intervals are not the same thing; 2:3:4 is a dyad but not an interval, and 2/1 is an interval but not a dyad.)

=== Dyads vs. intervals ===

By this definition all [[monad]]s and [[dyad]]s are ambitonal. (Dyads and intervals are not the same thing; 2:3:4 is a dyad but not an interval, and 2/1 is an interval but not a dyad.)

Therefore take note that while [[43/32]] may be the "prime harmonic fourth" (in that it is rooted/of the form ''k'' / 2''n''), it is only because we are seeing it as an ''interval'' that it is so, because seeing it as a ''dyad'' would mean seeing it as 32:43:64 so that it isn't clear whether it is otonal or utonal as [[64/43]] is the "prime subharmonic fifth", so interpreting it as a dyad means that whether it is harmonic or subharmonic (or neither) depends on the voicing and/or inversion used.

Note that a dyad (consisting of ''two'' [[pitch class]]es) thus has ''two'' possible ''inversions'' (which is a distinct concept to [[octave complement]]s!). For further clarity, see the section directly below.

=== Telling inversion of an ''n''-ad ===

To determine the inversion of an (''n''+''d'')-note chord consisting of ''n'' pitches up to [[octave equivalence]] (that is, given an ''n''-ad), go through all the pitches from lowest to highest until every pitch class is accounted for; that representation will then tell you which inversion the ''n''-ad has.

Example: going through the pitches of the 5-note chord 5:8:10:16:20 lowest to highest, we find that 5:8 accounts for all higher pitches (in that all higher pitches are a whole number of octaves above one of those harmonics); therefore this chord is a ''dyad'' (''n''=2); in this case, as one of the integers in the ''interval'' is a power of 2, we can classify this inversion of the dyad as ''subharmonic''.

== Properties of types of chords ==

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 If a chord can be voiced as a "palindrome", it inverts to itself, and is ambitonal. Such a voicing makes the lowest interval the same as the highest, the next lowest the same as the next highest, etc. For example, the min7 chord can be voiced as 1-m3-P5-m7 = min 3rd, maj 3rd, min 3rd, therefore it must be ambitonal. Note that some ambitonal chords, such as the maj7no5, cannot be voiced as a palindrome.
-By this definition all monads, dyads and intervals are ambitonal. (Dyads and intervals are <u>not</u> the same thing; 2:3:4 is a dyad but not an interval, and 2/1 is an interval but not a dyad.)
+=== Dyads vs. intervals ===
+By this definition all [[monad]]s and [[dyad]]s are ambitonal. (Dyads and intervals are <u>not</u> the same thing; 2:3:4 is a dyad but not an interval, and 2/1 is an interval but not a dyad.)
+Therefore take note that while [[43/32]] may be the "prime harmonic fourth" (in  that it is rooted/of the form ''k'' / 2<sup>''n''</sup>), it is only because we are seeing it as an ''interval'' that it is so, because seeing it as a ''dyad'' would mean seeing it as 32:43:64 so that it isn't clear whether it is otonal or utonal as [[64/43]] is the "prime subharmonic fifth", so interpreting it as a dyad means that whether it is harmonic or subharmonic (or neither) depends on the voicing and/or inversion used.
+Note that a dyad (consisting of ''two'' [[pitch class]]es) thus has ''two'' possible ''inversions'' (which is a distinct concept to [[octave complement]]s!). For further clarity, see the section directly below.
+=== Telling inversion of an ''n''-ad ===
+To determine the inversion of an (''n''+''d'')-note chord consisting of ''n'' pitches up to [[octave equivalence]] (that is, given an ''n''-ad), go through all the pitches from lowest to highest until every pitch class is accounted for; that representation will then tell you which inversion the ''n''-ad has.
+Example: going through the pitches of the 5-note chord 5:8:10:16:20 lowest to highest, we find that 5:8 accounts for all higher pitches (in that all higher pitches are a whole number of octaves above one of those harmonics); therefore this chord is a ''dyad'' (''n''=2); in this case, as one of the integers in the ''interval'' is a power of 2, we can classify this inversion of the dyad as ''subharmonic''.
 == Properties of types of chords ==