View source for Tritone

== Dissonance and expressiveness ==
{{Image frame|content=<div style="zoom: 80%;"><score sound="1"> {
\relative c' {
  \clef treble \time 9/8 \key e \major
  \set Score.tempoHideNote = ##t \tempo "Très modéré" 4. = 36
   \override Score.SpacingSpanner #'common-shortest-duration = #(ly:make-moment 1 8)
  \set Staff.midiInstrument = "flute"
  \stemDown cis'4.~(^"Flute"\p cis8~_\markup \italic "doux et expressif" cis16 \set stemRightBeamCount = #1 b \times 2/3 { \set stemLeftBeamCount = #1 ais16 a gis } g8. a16 b bis)
  cis4.~( cis8~ cis16 \set stemRightBeamCount = #1 b \times 2/3 { \set stemLeftBeamCount = #1 ais16 a gis } g8. a16 b bis) \override DynamicLineSpanner.staff-padding = #3
}
}
</score></div>|width=430|caption=The [[theme (music)|theme]] that opens [[Claude Debussy]]'s {{lang|fr|[[Prélude à l'après-midi d'un faune]]}} outlines the tritone between C{{music|#}} and G.}}Ján Haluska wrote:

{{Blockquote|The unstable character of the tritone sets it apart, as discussed in <!--original text "[28]"--><nowiki>[</nowiki>[[Paul Hindemith]]. ''The Craft of Musical Composition'', Book I. Associated Music Publishers, New York, 1945]. It can be expressed as a ratio by compounding suitable [[superparticular ratio]]s. Whether it is assigned the ratio 64/45 or 45/32, depending on the musical context, or indeed some other ratio, it is not superparticular, which is in keeping with its unique role in music.<ref>Haluska (2003), p.&nbsp;286.</ref>}}

[[Harry Partch]] has written:

{{blockquote|
Although this ratio [45/32] is composed of numbers which are multiples of 5 or under, they are excessively large for a 5-limit scale, and are sufficient justification, either in this form or as the tempered "tritone", for the epithet "diabolic", which has been used to characterize the interval. This is a case where, because of the largeness of the numbers, none but a [[musical temperament|temperament]]-perverted ear could possibly prefer 45/32 to a small-number interval of about the same width.

In the [[Pythagorean interval|Pythagorean ratio]] 81/64 both numbers are multiples of 3 or under, yet because of their excessive largeness the ear certainly prefers 5/4 for this approximate degree, even though it involves a prime number higher than 3. In the case of the 45/32 "tritone" our theorists have gone around their elbows to reach their thumbs, which could have been reached simply and directly and non-"diabolically" via the number 7....<ref name="Partch 115">Partch (1974), p.&nbsp;115.</ref>}}