page_title: Anhemitonic scale
section_title: Example: hemitonia and tritonia of the perfect-fifth projection
hierarchical_section_title: Anhemitonic scale / Example: hemitonia and tritonia of the perfect-fifth projection
caption_attribution_description: English: Ionian mode C
context_page_description: Musicology commonly classifies scales as either hemitonic or anhemitonic. Hemitonic scales contain one or more semitones, while anhemitonic scales do not contain semitones. For example, in traditional Japanese music, the anhemitonic yo scale is contrasted with the hemitonic in scale. The simplest and most commonly used scale in the world is the atritonic anhemitonic "major" pentatonic scale. The whole tone scale is also anhemitonic.
  A special subclass of the hemitonic scales is the cohemitonic scales. Cohemitonic scales contain two or more semitones such that two or more of the semitones appear consecutively in scale order. For example, the Hungarian minor scale in C includes F♯, G, and A♭ in that order, with a semitone between F♯ and G, and then a semitone between G and A♭.
  Ancohemitonic scales, in contrast, either contain no semitones, or contain semitones where none of the semitones appear consecutively in scale order.‹See TfM› Some authors, however, do not include anhemitonic scales in their definition of ancohemitonic scales.
context_section_description: The interrelationship of semitones, tritones, and increasing note count can be demonstrated by taking five consecutive pitches from the circle of fifths; starting on C, these are C, G, D, A, and E. Transposing the pitches to fit into one octave rearranges the pitches into the major pentatonic scale: C, D, E, G, A.  This scale is anhemitonic, having no semitones; it is atritonic, having no tritones.
  In addition, this is the maximal number of notes taken consecutively from the circle of fifths for which is it still possible to avoid a semitone.
  Adding another note from the circle of fifths gives the major hexatonic scale: C D E G A B.  This scale is hemitonic, having a semitone between B and C; it is atritonic, having no tritones.  In addition, this is the maximal number of notes taken consecutively from the circle of fifths for which is it still possible to avoid a tritone.‹See TfM›
  Adding still another note from the circle of fifths gives the major heptatonic scale: C D E F G A B (when the fifth is added from below the tonic).  This scale is strictly ancohemitonic, having 2 semitones but not consecutively; it is tritonic, having a tritone between F and B.  Past this point in the projection series, no new intervals are added to the Interval vector analysis of the scale, but cohemitonia results.
  Adding still another note from the circle of fifths gives the major octatonic scale: C D E F F♯ G A B (when the fifth is added from above the top note in the series--B in this case).  This scale is cohemitonic, having 3 semitones together at E F F♯ G, and tritonic as well.‹See TfM›
  Similar behavior is seen across all scales generally, that more notes in a scale tend cumulatively to add dissonant intervals (specifically: hemitonia and tritonia in no particular order) and cohemitonia not already present.  While also true that more notes in a scale tend to allow more and varied intervals in the interval vector, there might be said to be a point of diminishing returns, when qualified against the also increasing dissonance, hemitonia, tritonia and cohemitonia.  It is near these points where most popular scales lie.
caption: P7 projection/major heptatonic on C About this soundPlay (help·info).
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