page_title: Semitone
section_title: Just 5-limit intonation
hierarchical_section_title: Semitone / Semitones in different tunings / Just 5-limit intonation
caption_attribution_description: English: Just diatonic semitone on C&#160;= D&#x266d;-&#160;(Ben Johnston's notation). Just: 16:15&#160;= 111.73 cents. Limit: 5-limit. Created by Hyacinth (talk) in Sibelius 5.
context_page_description: A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically.
  It is defined as the interval between two adjacent notes in a 12-tone scale. For example, C is adjacent to C♯; the interval between them is a semitone.
  In a 12-note approximately equally divided scale, any interval can be defined in terms of an appropriate number of semitones
context_section_description: A minor second in just intonation typically corresponds to a pitch ratio of 16:15 (play ) or 1.0666... (approximately 111.7 cents), called the just diatonic semitone. This is a practical just semitone, since it is the difference between a perfect fourth and major third ().
  The 16:15 just minor second arises in the C major scale between B & C and E & F, and is, "the sharpest dissonance found in the scale."
  An augmented unison in just intonation is another semitone of 25:24 (play ) or 1.0416... (approximately 70.7 cents). It is the difference between a 5:4 major third and a 6:5 minor third. Composer Ben Johnston uses a sharp (♯) to indicate a note is raised 70.7 cents, or a flat (♭) to indicate a note is lowered 70.7 cents.
  Two other kinds of semitones are produced by 5-limit tuning. A chromatic scale defines 12 semitones as the 12 intervals between the 13 adjacent notes forming a full octave (e.g. from C4 to C5). The 12 semitones produced by a commonly used version of 5-limit tuning have four different sizes, and can be classified as follows:
  Just, or smaller, or minor, chromatic semitone, e.g. between E♭ and E:
  Larger, or major, chromatic semitone, or larger limma, or major chroma, e.g. between C and C♯:
  Just, or smaller, or minor, diatonic semitone, e.g. between C and D♭:
  Larger, or major, diatonic semitone, e.g. between A and B♭:
  The most frequently occurring semitones are the just ones (S₃ and S₁): S₃ occurs six times out of 12, S₁ three times, S₂ twice, and S₄ only once.
  The smaller chromatic and diatonic semitones differ from the larger by the syntonic comma (81:80 or 21.5 cents). The smaller and larger chromatic semitones differ from the respective diatonic semitones by the same 128:125 diesis as the above meantone semitones. Finally, while the inner semitones differ by the diaschisma (2048:2025 or 19.6 cents), the outer differ by the greater diesis (648:625 or 62.6 cents).
caption: 16:15 diatonic semitone About this soundPlay (help·info).
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