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dissonance requiring a resolution to a major or minor 10th, chords that expand to the 11th or beyond typically raise the 11th a semitone (thus giving us an augmented or sharp 11th, or an octave plus a tritone from the root of the chord) and present it in conjunction with the perfect 5th of the chord. Also in jazz harmony, the tritone is both part of the dominant chord and its substitute dominant (also known as the sub V chord). Because they share the same tritone, they are possible substitutes for one another. This is known as a
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1842:. In that system (which is the fundamental musical grammar of Baroque and Classical music), the tritone is one of the defining intervals of the dominant-seventh chord and two tritones separated by a minor third give the fully diminished seventh chord its characteristic sound. In minor, the diminished triad (comprising two minor thirds, which together add up to a tritone) appears on the second scale degree—and thus features prominently in the progression ii–V–i. Often, the
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diminished fifth of 588.270 cents, and that both intervals lie below the middle of the octave of 600.000 cents. It is no wonder that, following the ear, we want to resolve both downwards. The ear only desires the tritone to be resolved upwards when it is bigger than the middle of the octave. Therefore the opposite is the case with the just diminished fifth of 609.776 cents.
2100:: "The idea that the chorus and orchestra are confident in their wrong-headed piety is repeatedly disputed by the music. From the instability of the opening tritone—that unsettling interval between C and F sharp—accompanied by the tolling of warning bells ... eventually resolves into a major chord for the arrival of the boys singing 'Te decet hymnus'."
1438:). The melodic minor scale, having two forms, presents a tritone in different locations when ascending and descending (when the scale ascends, the tritone appears between the third and sixth scale degrees and the fourth and seventh scale degrees, and when the scale descends, the tritone appears between the second and sixth scale degrees).
522:, and according to a rule explained elsewhere, the composition of three seconds is always a fourth (for instance, an A4). To obtain a fifth (for instance, a d5), it is necessary to add another second. For instance, using the notes of the C major scale, the diminished fifth B–F can be decomposed into the four adjacent intervals
1287:
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1194:) and 10:7 for the d5 (about 617.5 cents, also known as Euler's tritone). These ratios are more consonant than 17:12 (about 603.0 cents) and 24:17 (about 597.0 cents), which can be obtained in 17-limit tuning, yet the latter are also fairly common, as they are closer to the equal-tempered value of 600 cents.
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Although this ratio 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
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tertian harmony, where triads and seventh chords are often expanded to become 9th, 11th, or 13th chords, and the tritone often occurs as a substitute for the naturally occurring interval of the perfect 11th. Since the perfect 11th (i.e. an octave plus perfect fourth) is typically perceived as a
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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
2230:
These apparently contradictory aural experiences become understandable when the cents of both types of just tritones are compared with those of the true tritones and then read 'crossed-over'. One then notices that the just augmented fourth of 590.224 cents is only 2 cents bigger than the true
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2668:. "...septimal tritone, 10:7; smaller septimal tritone, 7:5;...This list is not exhaustive, even when limited to the first sixteen partials. Consider the very narrow augmented fourth, 13:9....just intonation is not an attempt to generate necessarily consonant intervals."
1846:
ii is used to move the tritone to the inner voices as this allows for stepwise motion in the bass to the dominant root. In three-part counterpoint, free use of the diminished triad in first inversion is permitted, as this eliminates the tritone relation to the bass.
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According to this definition, with the twelve notes of a chromatic scale it is possible to define twelve different tritones, each starting from a different note and ending six notes above it. Although all of them span six semitones, six of them are classified as
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The augmented fourth resolves outward to a minor or major sixth (the first measure below). The inversion of this, a diminished fifth, resolves inward to a major or minor third (the second measure below). The diminished fifth is often called a tritone in modern
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According to this interpretation, the d5 is not a tritone. Indeed, in a diatonic scale, there is only one d5, and this interval does not meet the strict definition of tritone, as it is formed by one semitone, two whole tones, and another semitone:
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2138:". According to Dave Moskowitz (2010, p. 12), Hendrix "ripped into 'Purple Haze' by beginning the song with the sinister sounding tritone interval creating an opening dissonance, long described as 'The Devil in Music'." The opening riff of "
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2028:(1972, p19) says that "the bare fourths, the wide spacing, the tremolos, all depict the words—'the light thrilled towards her'—with sudden, overwhelming power." Debussy's String Quartet also features passages that emphasize the tritone.
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2070:, and other 20th century compositional idioms, composers considered it a neutral interval. In some analyses of the works of 20th century composers, the tritone plays an important structural role; perhaps the most cited is the
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1834:. For instance, in the tritone B–F, B would be "mi", that is the third scale degree in the "hard" hexachord beginning on G, while F would be "fa", that is the fourth scale degree in the "natural" hexachord beginning on C.
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or 'the devil in music'." Although the latter two of these authors cite the association with the devil as from the past, there are no known citations of this term from the Middle Ages, as is commonly asserted. However
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in music') has been applied to the interval from at least the early 18th century, or the late Middle Ages, though its use is not restricted to the tritone, being that the original found example of the term
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diminished fifth that is perfectly in tune, for example, there is no wish to resolve it to a major third. Just the opposite—aurally one wants to enlarge it to a minor sixth. The opposite holds true for the
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is formed by 12 pitches (each a semitone apart from its neighbors), it contains 12 distinct tritones, each starting from a different pitch and spanning six semitones. According to a complex but widely used
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Later, with the rise of the
Baroque and Classical music era, composers accepted the tritone, but used it in a specific, controlled way—notably through the principle of the tension-release mechanism of the
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1961:
216:. According to this definition, a diatonic scale contains two tritones for each octave. For instance, the above-mentioned C major scale contains the tritones F–B (from F to the B above it, also called
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theory, but functionally and notationally it can only resolve inwards as a diminished fifth and is therefore not reckoned a tritone—that is, an interval composed of three adjacent whole tones—in mid-
1812:
or otherwise punished by the Church for invoking this interval are likely fanciful. At any rate, avoidance of the interval for musical reasons has a long history, stretching back to the parallel
515:
Any augmented fourth can be decomposed into three whole tones. For instance, the interval F–B is an augmented fourth and can be decomposed into the three adjacent whole tones F–G, G–A, and A–B.
419:
2897:... mi contra fa ... welches die alten den Satan in der Music nenneten ... alten Solmisatores dieses angenehme Intervall mi contra fa oder den Teufel in der Music genannt haben.
802:. In other words, they cannot be divided into smaller intervals. Consequently, in this context the above-mentioned "decomposition" of the tritone into six semitones is typically not allowed.
1632:
period. This interval was frequently avoided in medieval ecclesiastical singing because of its dissonant quality. The first explicit prohibition of it seems to occur with the development of
1320:. 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.
1808:
That original symbolic association with the devil and its avoidance led to
Western cultural convention seeing the tritone as suggesting "evil" in music. However, stories that singers were
232:); the latter is decomposed as a semitone B–C, a whole tone C–D, a whole tone D–E, and a semitone E–F, for a total width of three whole tones, but composed as four steps in the scale. In
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that composers started to use it totally freely, without functional limitations notably in an expressive way to exploit the "evil" connotations culturally associated with it, such as
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features a tritone between C and F♯ as a recurring motif. John
Bridcut (2010, p. 271) describes the power of the interval in creating the sombre and ambiguous opening of the
766:, which in a chromatic scale lies between C and D. This means that, when a chromatic scale is used, a tritone can be also defined as any musical interval spanning six semitones:
418:
917:
2387:, in D. Raffaello Baralli and Luigi Torri, "Il Trattato di Prosdocimo de' Beldomandi contro il Lucidario di Marchetto da Padova per la prima volta trascritto e illustrato",
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In the theory of harmony it is known that a diminished interval needs to be resolved inwards, and an augmented interval outwards. ... and with the correct resolution of the
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189:). For instance, the interval from F up to the B above it (in short, F–B) is a tritone as it can be decomposed into the three adjacent whole tones F–G, G–A, and A–B.
608:, these notes are produced by the same key. However, in the above-mentioned naming convention, they are considered different notes, as they are written on different
263:
can also drive the piece of music towards resolution with its tonic. These various uses exhibit the flexibility, ubiquity, and distinctness of the tritone in music.
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The dominant seventh chord in root position contains a diminished fifth (tritone) within its pitch construction: it occurs between the third and seventh above the
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tuning systems, besides 12-tone equal temperament, A4 and d5 are distinct intervals because neither is exactly half an octave. In any meantone tuning near to
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tuning allows for the justest possible ratios (ratios with the smallest numerator and denominator), namely 7:5 for the A4 (about 582.5 cents, also known as
738:, the interval between any note and the previous or next is a semitone. Using the notes of a chromatic scale, each tone can be divided into two semitones:
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diatonic scale (C–D–E–F–G–A–B–...), the only tritone is from F to B. It is a tritone because F–G, G–A, and A–B are three adjacent whole tones. It is a
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2130:", creating a prolonged sense of suspended resolution. Perhaps the most striking use of the interval in rock music of the late 1960s can be found in
1462:, some of which are enharmonic to dominant seventh chords, contain tritones spelled as augmented fourths (for example, the German sixth, from A to D
1300:
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1100:, for example, the A4 is 580.65 cents, whereas the d5 is 619.35 cents. This is perceptually indistinguishable from septimal meantone temperament.
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In all of the sonorities mentioned above, used in functional harmonic analysis, the tritone pushes towards resolution, generally resolving by
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developed his system of hexachords and with the introduction of B flat as a diatonic note, at much the same time acquiring its nickname of
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chords using the notes from the natural minor mode thus contain a tritone, regardless of inversion. Containing tritones, these scales are
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to emerge may be avoided by introducing a note three whole tones distant from the key note of that tonality." The tritone found in the
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2146:'s eponymous debut album, is an inversion of a tritone; the album, and this song in particular, are considered to mark the birth of
2556:, translated from the German by Bevis Stevens, with additional editing by Anna R. Meuss (Forest Row: Temple Lodge): p. 15–16.
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The unstable character of the tritone sets it apart, as discussed in . It can be expressed as a ratio by compounding suitable
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as being used by "the old authorities" for both the tritone and for the clash between chromatically related tones such as F
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1092:-comma meantone the A4 is near to the ratio 7:5 (582.51) and the d5 to 10:7 (617.49), which is what these intervals are in
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The half-octave or equal tempered A4 and d5 are unique in being equal to their own inverse (each to the other). In other
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It is not possible to decompose a diminished fifth into three adjacent whole tones. The reason is that a whole tone is a
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also contains a tritone in its construction, deriving its name from the diminished-fifth interval (i.e. a tritone). The
1175:, the A4 is either 45:32 or 25:18, and the d5 is either 64:45 or 36:25. The 64:45 just diminished fifth arises in the C
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On the other hand, two A4 add up to six whole tones. In equal temperament, this is equal to exactly one perfect octave:
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scale. More broadly, a tritone is also commonly defined as any interval with a width of three whole tones (spanning six
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If a diatonic scale is used, with its 7 notes it is possible to form only one sequence of three adjacent whole tones (
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a diatonic note, the hexachord be moved and based on C to avoid the F–B tritone altogether. Later theorists such as
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Haluska (2003). p. xxiii. "7:5 septimal or
Huygens' tritone, Bohlen-Pierce fourth", "10:7 Euler's tritone".
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Full ascending and descending chromatic scale on C, with tritone above each pitch. Pairs of tritones that are
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may reach the twelfth harmonic and transcriptions of their music usually show the eleventh harmonic sharp (F
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512:. In most other tuning systems, they are not equivalent, and neither is exactly equal to half an octave.
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in just intonation or
Pythagorean tunings, but the pure eleventh harmonic was used in pieces including
798:, whole tones are always formed by adjacent notes (such as C and D) and therefore they are regarded as
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2887:. Neue Heidelberger Studien zur Musikwissenschaft (in German). Vol. 6. Bern: Francke. p. 7.
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1230:
1071:. The inverse of 600 cents is 600 cents. Thus, in this tuning system, the A4 and its inverse (d5) are
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https://pearl-hifi.com/06_Lit_Archive/02_PEARL_Arch/Vol_16/Sec_51/4555_Genesis_of_a_Music_2nd_Edn.pdf
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thumbs, which could have been reached simply and directly and non-"diabolically" via the number 7....
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2606:, Pure and Applied Mathematics Series 262 (New York: Marcel Dekker; London: Momenta), p. xxiv.
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Using the notes of a chromatic scale, B–F may be also decomposed into the four adjacent intervals
204:. For instance, the above-mentioned interval F–B is the only tritone formed from the notes of the
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the tritone was regarded as an unstable interval and rejected as a consonance by most theorists.
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1472:); the French sixth chord can be viewed as a superposition of two tritones a major second apart.
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The augmented fourth (A4) occurs naturally between the fourth and seventh scale degrees of the
1336:-perverted ear could possibly prefer 45/32 to a small-number interval of about the same width.
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1103:
Since they are the inverse of each other, by definition A4 and d5 always add up to exactly one
748:
For instance, the tone from C to D (in short, C–D) can be decomposed into the two semitones C–C
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2210:. The tritone substitution is one of the most common chord and improvisation devices in jazz.
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as the interval formed between the second and sixth scale degrees (for example, from D to A
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848:(i.e. narrowed) because it is smaller than most of the fifths found in the scale (they are
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24:
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821:(i.e., widened) because it is wider than most of the fourths found in the scale (they are
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The half-octave tritone interval is used in the musical/auditory illusion known as the
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236:, the tritone divides the octave exactly in half as 6 of 12 semitones or 600 of 1,200
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1945:
1790:, suggests that the nickname was already applied early in the medieval music itself:
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A manual of harmony for use in music-schools and seminaries and for self-instruction
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several different sizes can be chosen both for the A4 and the d5. For instance, in
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2051:(1846) consists of a transition between "huge B and F chords" as Faust arrives in
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2379:, London: British Library, Lansdowne MS 763, ff.89v-94v, citations on f.92r,2–3;
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between B and F, consequently the 45:32 augmented fourth arises between F and B.
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For instance, in the C major diatonic scale, the only d5 is from B to F. It is a
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1773:, writes that the "older singers with solmization called this pleasant interval
1243:, is found in some just tunings and on many instruments. For example, very long
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This definition, however, has two different interpretations (broad and strict).
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2909:
Smith, F. J. (1979). "Some aspects of the tritone and the semitritone in the
2479:(1991). "Ben Johnston's Extended Just Intonation: A Guide for Interpreters".
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Only if the three tones are of the same size (which is not the case for many
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279:
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255:. The tritone can be used to avoid traditional tonality: "Any tendency for a
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to convey a brooding atmosphere at the start of the second act of the opera
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describes, "mi against fa", which the ancients called "Satan in music"—and
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3256:"'Sleeping (In the Fire)': Listening Room fearless leader faces down fear"
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2738:
Bent, Margaret (1994). "Accidentals, Counterpoint and
Notation in Aaron's
2575:
On the
Sensations of Tone as a Physiological Basis for the Theory of Music
1909:
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The ratio of the eleventh harmonic, 11:8 (551.318 cents; approximated as F
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500:(A4 + d5 = P8). In twelve-tone equal temperament, the most commonly used
3201:"Why did Bernstein build West Side Story around 'The Devil's Interval'?"
2363:, 1961): 128–31, citations on 192–96, 200, and 229; Jacobus Leodiensis,
2031:
The tritone was also exploited heavily in that period as an interval of
960:
931:
4272:
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Harmonologia musica, oder kurze
Anleitung zur musicalischen Composition
2261:
2153:
1439:
1383: in this section. Unsourced material may be challenged and removed.
1072:
650: in this section. Unsourced material may be challenged and removed.
589:
505:
481:
404:
328: in this section. Unsourced material may be challenged and removed.
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Satan's all-time greatest hit: Will
Hodgkinson on the devil's interval
2767:
2589:, Number to an Octave: 2.0. Cents in interval: 612, Name of Interval:
2502:
2407:...its symmetry with respect to the octave gives it a special role in
1794:
It seems first to have been designated as a "dangerous" interval when
4172:
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3094:
2885:
Diabolus in musica: Studien zur
Ikonographie der Musik im Mittelalter
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tritones this desire is totally satisfied. However, if one plays a
1839:
1735:, respectively) because these notes represent the juxtaposition of
694:) is traditionally defined as a musical interval composed of three
256:
209:
186:
75:
530:), C–D (major second), D–E (major second), and E–F (minor second).
192:
Narrowly defined, each of these whole tones must be a step in the
57:
augmented fourth, diminished fifth, the Devil’s interval (obscure)
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3259:
2974:
Counterpoint: the polyphonic vocal style of the sixteenth century
1990:
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for its ability to evoke a strong reaction by moving quickly to
1531:. This determines the resolution of chords containing tritones.
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case where, because of the largeness of the numbers, none but a
23:"Devil's Chord" redirects here. For the Doctor Who episode, see
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4146:
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Musicalische Paradoxal-Discourse, oder allgemeine Vorstellungen
2526:: An Account of a Creative Work, Its Roots and Its Fulfillments
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may substitute for C, and vice versa, because they both share E
1934:
1143:
1134:
1104:
1055:
509:
201:
2623:
Haluska (2003), p. xxv. "36/25 classic diminished fifth".
2371:, edited by Roger Bragard, Corpus Scriptorum de Musica 3/6 (:
2359:, edited by Roger Bragard, Corpus Scriptorum de Musica 3/2 (:
844:
because the notes from B to F are five (B, C, D, E, F). It is
496:
of each other, meaning that their sum is exactly equal to one
3640:
1681:
3341:
1054:
In twelve-tone equal temperament, the A4 is exactly half an
3162:
Essential Britten, a pocket guide for the Britten Centenary
2850:(Frankfurt and Leipzig: Theodor Philipp Calvisius 1702): 6.
2698:
Fauvel, John; Flood, Raymond; and Wilson, Robin J. (2006).
2375:, 1973): 1–161, citations on 52 and 68; Johannes Torkesey,
2202:
1487:
is made up of two superposed tritones a minor third apart.
1031:
Comparison of intervals near or enharmonic with the tritone
817:
because the notes from F to B are four (F, G, A, B). It is
612:
and have different diatonic functions within music theory.
1290:
Use of the eleventh harmonic in the prologue to Britten's
360:
Chromatic scale on C: full octave ascending and descending
2114:
uses tritones on the downbeats of the opening phrases of
2078:, in his analysis of the use of tonality in the music of
1824:. In all these expressions, including the commonly cited
1586:
Audio playback is not supported in your browser. You can
1510:
Audio playback is not supported in your browser. You can
789:
729:
3176:"The Unsettling Sound Of Tritones, The Devil's Interval"
3053:
Twentieth-century Harmony: Creative Aspects and Practice
2658:
The contemporary violin: Extended performance techniques
1551:
The tritone is also one of the defining features of the
588:
Notice that the last diminished second is formed by two
293:
2082:. Tritone relations are also important in the music of
2870:(Quedlinburg: Theodor Philipp Calvisius, 1707): 75–76.
2554:
Intervals, Scales, Tones and the Concert Pitch C=128Hz
2458:, seventh edition (Boston: McGraw-Hill), p. 54.
2201:
Tritones also became important in the development of
1830:, the "mi" and "fa" refer to notes from two adjacent
1186:
but they are the justest possible in 5-limit tuning.
855:
3050:
2971:
1993:uses a tritone to convey the words of the poem by
702:, this definition may also be written as follows:
508:to a d5, as both have the size of exactly half an
3311:, Amazon Digital Services, Inc., ASIN: B008FRWNIW
2528:, 2nd ed. (New York: Da Capo Press): p. 69.
2454:Bruce Benward & Marilyn Nadine Saker (2003).
1620:The tritone is a restless interval, classed as a
1494:, often include tritones (as diminished fifths).
1411:
1182:These ratios are not in all contexts regarded as
492:. They both span six semitones, and they are the
220:) and B–F (from B to the F above it, also called
4313:
2104:uses the tritone harmony as a basis for much of
1307:
809:). This interval is an A4. For instance, in the
3286:Black Sabbath and Philosophy: Mastering Reality
1283:a good approximation of the eleventh harmonic.
108: 25:18, 36:25; 45:32, 64:45
2780:
2679:The Musical Topic: Hunt, Military And Pastoral
2656:Strange, Patricia and Patricia, Allen (2001).
3357:
3097:. London: Kahn & Averill. pp. 1–16.
2638:, p. 165. Theodore Baker, trans. G. Schirmer.
2585:. "Cents in interval: 590, Name of Interval:
2420:
1862:'s use of the tritone to suggest Hell in his
1640:system, who suggested that rather than make B
1261:. This note is often corrected to 4:3 on the
3309:DOG EAR Tritone Substitution for Jazz Guitar
2982:. foreword by Alfred Mann. New York: Dover.
2864:
2844:
2044:
1982:
1971:
1889:
1602:
908:Pythagorean augmented fourth between C and F
3332:BBC News Magazine article about the tritone
3045:
1895:
1825:
1817:
1799:
1774:
1750:
1736:
1723:the opposition of "square" and "round" B (B
1718:
1692:
1686:
1671:
1483:contains the same tritone, while the fully
472:) are defined as the intervals produced by
266:The condition of having tritones is called
4298:
3364:
3350:
3020:. Cambridge University Press. p. 254.
2950:, Volume 1: A–J, Oxford University Press.
2722:
2641:
2617:
2596:
2059:calls this "a tonal wrench by a tritone".
1399:Learn how and when to remove this message
666:Learn how and when to remove this message
464:for more details). The augmented fourth (
344:Learn how and when to remove this message
251:and is important in the study of musical
2966:
2879:
2567:
2548:
2546:
2514:
2512:
2475:
2272:Consecutive fifths § Unequal fifths
2152:
1449:
1420:(for example, from F to B in the key of
1285:
1203:
1152:
1039:
966:Classic diminished fifth between C and G
937:Classic augmented fourth between C and F
677:
397:and the diminished fifth between C and G
386:
374:
361:
355:
247:, the tritone is a harmonic and melodic
3085:
3030:
3015:
2650:
2604:The Mathematical Theory of Tone Systems
2469:
2391:20 (1913): 731–62, citations on 732–34.
2318:10.1093/gmo/9781561592630.article.28403
2299:
1697:(Mi against Fa is the devil in music).
995:Lesser septimal tritone between C and G
212:in the chromatic scale), regardless of
4314:
3722:
3253:
3225:The Songwriting Secrets of the Beatles
2018:Debussy, String Quartet, 2nd movement,
1717:, and five years later likewise calls
1137:(128:125) less than a perfect octave:
790:Strict interpretation (diatonic scale)
730:Broad interpretation (chromatic scale)
460:encompasses five staff positions (see
3345:
3198:
3173:
3127:"Musical Analysis of the War Requiem"
3091:Béla Bartók: An Analysis of his Music
2908:
2543:
2509:
2456:Music: In Theory and Practice, Vol. I
1827:"mi contra fa est diabolus in musica"
1694:"Mi Contra Fa est diabolus en musica"
1490:Other chords built on these, such as
1424:). It is also present in the natural
716:) can this formula be simplified to:
294:Augmented fourth and diminished fifth
2737:
2300:Drabkin, William (20 January 2001).
2267:Hexatonic scale § Tritone scale
2055:, the capital of Hell. Musicologist
1381:adding citations to reliable sources
1352:
1292:Serenade for Tenor, Horn and Strings
1272:Serenade for tenor, horn and strings
1197:
648:adding citations to reliable sources
619:
326:adding citations to reliable sources
297:
3242:The Words and Music of Jimi Hendrix
2795:
2614:. "25:18 classic augmented fourth".
1543:(early 16th-century) music theory.
200:there is only one tritone for each
13:
3301:
3288:(Hoboken: Wiley-Blackwell, 2012),
3254:Chesna, James (26 February 2010).
3167:
2369:Jacobi Leodiensis Speculum musicae
2357:Jacobi Leodiensis Speculum musicae
1937:'s use of timpani tuned to C and F
1573:
698:. As the symbol for whole tone is
196:, so by this definition, within a
14:
4343:
3322:Tritone paradox and Shepard Tones
3315:
2948:The New Oxford Companion to Music
2919:Journal of Musicological Research
1605:Prélude à l'après-midi d'un faune
1208:Eleventh harmonic between C and F
452:is an interval encompassing four
4297:
2373:American Institute of Musicology
2361:American Institute of Musicology
2189:
2007:
2002:
1959:
1954:
1913:
1908:
1876:
1745:cites the phrase in his seminal
1624:in Western music from the early
1557:
1357:
1295:
1229:
1213:
1024:
1009:
997:
988:
973:
959:
944:
930:
915:
901:
886:
869:
856:Size in different tuning systems
624:
437:, six of them are classified as
416:
391:Augmented fourth between C and F
302:
270:; that of having no tritones is
3328: (archived January 6, 2008)
3278:
3247:
3234:
3217:
3192:
3154:
3140:
3119:
3079:
3039:
3024:
3018:The Musical Language of Berlioz
3009:
2996:
2960:
2937:
2902:
2873:
2853:
2833:
2821:
2789:
2774:
2731:
2713:
2692:
2671:
2626:
2573:Helmholtz, Hermann von (2005).
1663:From then until the end of the
1368:needs additional citations for
1241:undecimal semi-augmented fourth
635:needs additional citations for
383:of each other are marked below.
313:needs additional citations for
2448:
2414:
2403:. "A prominent element in the
2394:
2341:
2293:
1609:outlines the tritone between C
1412:Occurrences in diatonic scales
1348:
615:
282:containing tritones is called
1:
3371:
2287:
2039:. For example, the climax of
1787:New Oxford Companion to Music
1555:, being featured between the
1546:
1497:
1481:half-diminished seventh chord
1308:Dissonance and expressiveness
1253:above C, for example), as in
1094:septimal meantone temperament
4332:The Devil in classical music
3174:Kogan, Judith (2017-10-31).
2719:Haluska (2003), p. 286.
2593:, Number to an Octave: 2.0."
2385:Tractatus musice speculative
1924:Wagner, Prelude to Act 2 of
1891:"Après une lecture du Dante"
1654:advocated the inclusion of B
1583:
1507:
7:
3919:septimal chromatic semitone
3199:Rizzi, Sofia (2019-03-04).
2913:: the non‐emergence of the
2728:Partch (1974), p. 115.
2235:
914:++ – 729:512 (611.73 cents)
10:
4348:
3925:septimal diatonic semitone
3713:(Numbers in brackets refer
3231:. London, 2010 pp. 522–523
3057:. New York: W. W. Norton.
3035:. Oxford University Press.
3006:. Oxford University Press.
2381:Prosdocimus de Beldemandis
2242:List of meantone intervals
1628:through to the end of the
1235:4 above C1), known as the
1161:Just diminished fifth on C
286:; one without tritones is
22:
15:
4295:
4253:
4220:
4109:
4079:
4049:
4006:
3997:
3970:
3897:
3880:
3715:to fractional semitones.)
3708:24-tone equal temperament
3705:
3694:
3631:
3576:
3521:
3484:
3447:
3412:
3379:
2931:10.1080/01411897908574507
2677:Monelle, Raymond (2006).
2540:. Retrieved July 22, 2021
2482:Perspectives of New Music
2389:Rivista Musicale Italiana
2247:List of musical intervals
1890:
1800:
1775:
1563:and fifth scale degrees.
690:A tritone (abbreviation:
590:enharmonically equivalent
448:Under that convention, a
405:enharmonically equivalent
369:Play in equal temperament
139:
131:12-Tone equal temperament
129:
122:
94:
84:
74:
69:
61:
53:
48:
38:
3031:Rushton, Julian (2001).
3016:Rushton, Julian (1983).
2783:Epistola de ignoto cantu
1485:diminished seventh chord
1237:lesser undecimal tritone
885:+ – 45:32 (590.22 cents)
782:s, and the other six as
771:TT = T+T+T = S+S+S+S+S+S
468:) and diminished fifth (
407:intervals. Both are 600
234:twelve-equal temperament
181:spanning three adjacent
18:Tritone (disambiguation)
4303:List of pitch intervals
4041:Subminor and supermajor
3980:minor diatonic semitone
3890:refer to pitch ratios.)
2432:Oxford University Press
2422:Smith Brindle, Reginald
2377:Declaratio et expositio
2252:List of pitch intervals
1804:("the devil in music").
1588:download the audio file
1512:download the audio file
1133:temperament, this is a
972:– 36:25 (631.28 cents)
441:, and the other six as
4101:Undecimal quarter tone
3240:Moskowitz, D. (2010).
3148:"Britten: War Requiem"
2946:(1983). "Tritone". in
2865:
2845:
2552:Renold, Maria (2004).
2233:
2227:augmented fourth. ...
2198:
2128:Within You Without You
2045:
2037:distantly related keys
1995:Dante Gabriel Rossetti
1983:
1972:
1896:
1856:modern classical music
1826:
1818:
1806:
1759:Georg Philipp Telemann
1751:
1737:
1719:
1693:
1687:
1672:
1603:
1460:augmented sixth chords
1346:
1322:
1318:superparticular ratios
1304:
1222:
1162:
1131:quarter-comma meantone
1049:
943:– 25:18 (568.72 cents)
760:–D by using the note C
687:
425:
384:
372:
370:
261:dominant seventh chord
4096:Septimal quarter tone
3907:septimal quarter tone
2881:Reinhold, Hammerstein
2805:(subscription access)
2748:Journal of Musicology
2700:Music And Mathematics
2602:Haluska, Ján (2003),
2401:Randel (2003), p. 911
2355:, Liber secundus, in
2212:
2156:
2142:", the first song on
2047:La damnation de Faust
1981:In his early cantata
1792:
1597:The theme that opens
1450:Occurrences in chords
1329:
1314:
1289:
1212:– 11:8 (551.32 cents)
1207:
1160:
1047:
877:just augmented fourth
800:incomposite intervals
682:Tritone drawn in the
681:
568:(major second), and E
390:
378:
368:
359:
4283:Incomposite interval
4036:Pythagorean interval
3888:(Numbers in brackets
3396:(Numbers in brackets
3160:Bridcut, J. (2010),
3047:Persichetti, Vincent
3033:The Music of Berlioz
3002:Nichols, R. (1972).
2860:Andreas Werckmeister
2840:Andreas Werckmeister
2828:Randel (2003), p.239
2744:Toscanello in Musica
2632:Paul, Oscar (1885).
2208:tritone substitution
2158:Tritone substitution
1897:Années de Pèlerinage
1850:It is only with the
1801:"Diabolus in Musica"
1720:"diabolus in musica"
1699:Andreas Werckmeister
1688:"diabolus en musica"
1377:improve this article
1098:31 equal temperament
1008:– 7:5 (582.51 cents)
644:improve this article
322:improve this article
16:For other uses, see
4066:Pythagorean apotome
3913:septimal third tone
3227:. Music Sales Ltd.
2809:Oxford Music Online
2367:, Liber sextus, in
2309:Oxford Music Online
2020:bars 140–147.
1753:Gradus ad Parnassum
1701:cites this term in
1312:Ján Haluska wrote:
1277:Ivan Wyschnegradsky
35:
4179:Septimal semicomma
2915:diabolus in musica
2803:Grove Music Online
2796:Drabkin, William.
2524:Genesis of a Music
2427:Serial Composition
2349:Jacobus Leodiensis
2199:
1985:La Damoiselle élue
1973:La Damoiselle élue
1820:Musica Enchiriadis
1673:diabolus in musica
1305:
1223:
1163:
1058:(i.e., a ratio of
1050:
688:
490:chromatic semitone
426:
385:
373:
371:
153:569, 631; 590, 610
33:
4327:Diminished fifths
4322:Augmented fourths
4309:
4308:
4291:
4290:
4121:Pythagorean comma
4061:Pythagorean limma
3993:
3992:
3989:
3988:
3955:supermajor fourth
3931:supermajor second
3876:
3875:
3690:
3689:
3686:
3685:
3398:are the number of
2464:978-0-07-294262-0
2409:twelve-tone music
2327:978-1-56159-263-0
2195:
2148:heavy metal music
2102:Leonard Bernstein
2064:twelve-tone music
2013:
1965:
1919:
1882:
1743:Johann Joseph Fux
1648:Ugolino d'Orvieto
1592:
1516:
1409:
1408:
1401:
1341:Pythagorean ratio
1301:
1219:
1198:Eleventh harmonic
1158:
1045:
1015:
979:
950:
921:
892:
784:diminished fifths
676:
675:
668:
582:diminished second
556:(major second), D
544:(major second), C
443:diminished fifths
439:augmented fourths
435:naming convention
422:
366:
354:
353:
346:
167:
166:
103:729:512, 1024:729
25:The Devil's Chord
4339:
4301:
4300:
4191:Septimal kleisma
4004:
4003:
3961:subminor seventh
3943:supermajor third
3895:
3894:
3883:Just intonations
3868:
3867:
3863:
3860:
3848:
3847:
3843:
3840:
3828:
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3808:
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3409:
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3359:
3352:
3343:
3342:
3307:R., Ken (2012).
3296:
3282:
3276:
3275:
3273:
3271:
3262:. Archived from
3251:
3245:
3238:
3232:
3223:Dominic Pedler.
3221:
3215:
3214:
3212:
3211:
3196:
3190:
3189:
3187:
3186:
3171:
3165:
3164:. London, Faber.
3158:
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3083:
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3013:
3007:
3000:
2994:
2993:
2978:. Translated by
2977:
2964:
2958:
2941:
2935:
2934:
2911:Speculum Musicae
2906:
2900:
2899:
2877:
2871:
2868:
2857:
2851:
2848:
2837:
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2825:
2819:
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2793:
2787:
2786:
2781:Guido d'Arezzo,
2778:
2772:
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2735:
2729:
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2717:
2711:
2696:
2690:
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2541:
2516:
2507:
2506:
2473:
2467:
2452:
2446:
2445:
2418:
2412:
2405:whole-tone scale
2398:
2392:
2365:Speculum musicae
2353:Speculum musicae
2345:
2339:
2338:
2336:
2334:
2305:
2297:
2197:
2196:
2183:
2182:
2177:
2176:
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2165:
2164:
2088:Benjamin Britten
2050:
2015:
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2006:
1988:
1975:
1967:
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1802:
1778:
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1767:Johann Mattheson
1756:
1740:
1734:
1733:
1728:
1727:
1722:
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1710:
1709:
1696:
1690:
1675:
1659:
1658:
1645:
1644:
1614:
1613:
1608:
1562:
1561:
1477:diminished triad
1467:
1466:
1433:
1432:
1404:
1397:
1393:
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1384:
1361:
1353:
1303:
1302:
1252:
1251:
1234:
1233:
1221:
1220:
1211:
1192:septimal tritone
1159:
1091:
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1065:
1064:
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905:
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780:augmented fourth
765:
764:
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684:chromatic circle
671:
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396:
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367:
349:
342:
338:
335:
329:
306:
298:
222:diminished fifth
218:augmented fourth
179:musical interval
177:is defined as a
36:
32:
30:Musical interval
4347:
4346:
4342:
4341:
4340:
4338:
4337:
4336:
4312:
4311:
4310:
4305:
4287:
4249:
4216:
4159:Septimal diesis
4105:
4075:
4045:
3999:
3985:
3966:
3889:
3886:
3872:
3865:
3861:
3858:
3856:
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3517:
3480:
3443:
3404:
3399:
3397:
3387:
3385:
3382:
3375:
3370:
3326:Wayback Machine
3318:
3304:
3302:Further reading
3299:
3284:William Irwin,
3283:
3279:
3269:
3267:
3266:on 29 June 2011
3252:
3248:
3239:
3235:
3222:
3218:
3209:
3207:
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3184:
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3159:
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3120:
3105:
3084:
3080:
3065:
3044:
3040:
3029:
3025:
3014:
3010:
3001:
2997:
2990:
2965:
2961:
2942:
2938:
2925:(1–2): 63–74 .
2907:
2903:
2878:
2874:
2858:
2854:
2838:
2834:
2826:
2822:
2813:
2811:
2794:
2790:
2785:, lines 309–322
2779:
2775:
2754:(3): 306–344 .
2736:
2732:
2727:
2723:
2718:
2714:
2697:
2693:
2676:
2672:
2660:, p. 147.
2655:
2651:
2646:
2642:
2631:
2627:
2622:
2618:
2601:
2597:
2577:, p. 457.
2572:
2568:
2551:
2544:
2517:
2510:
2474:
2470:
2453:
2449:
2442:
2419:
2415:
2399:
2395:
2346:
2342:
2332:
2330:
2328:
2298:
2294:
2290:
2277:Petrushka chord
2238:
2190:
2188:considerations.
2180:
2179:
2174:
2173:
2168:
2167:
2162:
2161:
2120:The Inner Light
2112:George Harrison
2107:West Side Story
2023:
2022:
2021:
2019:
2016:
2008:
1979:
1978:
1977:
1968:
1960:
1939:
1938:
1931:
1930:
1929:
1922:
1914:
1904:
1903:
1902:
1901:
1886:
1885:
1877:
1796:Guido of Arezzo
1731:
1730:
1725:
1724:
1713:
1712:
1707:
1706:
1656:
1655:
1642:
1641:
1634:Guido of Arezzo
1630:common practice
1618:
1617:
1616:
1611:
1610:
1595:
1594:
1593:
1591:
1576:
1574:Historical uses
1568:tritone paradox
1556:
1549:
1529:contrary motion
1521:
1520:
1519:
1518:
1517:
1515:
1500:
1464:
1463:
1458:. In addition,
1452:
1430:
1429:
1414:
1405:
1394:
1388:
1385:
1374:
1362:
1351:
1310:
1296:
1279:considered the
1249:
1248:
1228:
1225:
1224:
1214:
1209:
1200:
1169:just intonation
1165:
1164:
1153:
1142:A4 + A4 = P8 −
1088:
1084:
1083:
1062:
1060:
1052:
1051:
1040:
1036:
1035:
1034:
1033:
1032:
1029:
1020:
1019:
1018:
1010:
1004:
1003:
996:
993:
984:
983:
982:
974:
968:
967:
964:
955:
954:
953:
945:
939:
938:
935:
926:
925:
924:
916:
910:
909:
906:
897:
896:
895:
887:
881:
880:
879:between C and F
874:
865:
864:
858:
823:perfect fourths
792:
762:
761:
756:
755:
750:
749:
736:chromatic scale
732:
672:
661:
655:
652:
641:
629:
618:
610:staff positions
600:
599:
594:
593:
576:
575:
570:
569:
564:
563:
558:
557:
552:
551:
546:
545:
540:
539:
462:interval number
454:staff positions
430:chromatic scale
417:
399:
398:
393:
392:
362:
350:
339:
333:
330:
319:
307:
296:
245:classical music
159:
154:
149:
141:Just intonation
114:
109:
104:
31:
28:
21:
12:
11:
5:
4345:
4335:
4334:
4329:
4324:
4307:
4306:
4296:
4293:
4292:
4289:
4288:
4286:
4285:
4280:
4275:
4270:
4265:
4259:
4257:
4251:
4250:
4248:
4247:
4242:
4237:
4232:
4226:
4224:
4218:
4217:
4215:
4214:
4208:
4202:
4195:
4194:
4188:
4182:
4176:
4170:
4163:
4162:
4156:
4153:Greater diesis
4150:
4143:
4142:
4139:Septimal comma
4136:
4133:Holdrian comma
4130:
4127:Syntonic comma
4124:
4117:
4115:
4107:
4106:
4104:
4103:
4098:
4093:
4087:
4085:
4077:
4076:
4074:
4073:
4068:
4063:
4057:
4055:
4047:
4046:
4044:
4043:
4038:
4033:
4028:
4023:
4018:
4012:
4010:
4001:
3995:
3994:
3991:
3990:
3987:
3986:
3984:
3983:
3976:
3974:
3968:
3967:
3965:
3964:
3958:
3952:
3949:subminor fifth
3946:
3940:
3937:subminor third
3934:
3928:
3922:
3916:
3910:
3903:
3901:
3892:
3878:
3877:
3874:
3873:
3871:
3870:
3850:
3830:
3810:
3790:
3770:
3750:
3733:
3731:
3723:
3717:
3700:
3692:
3691:
3688:
3687:
3684:
3683:
3681:
3680:
3674:
3668:
3662:
3656:
3650:
3644:
3637:
3635:
3629:
3628:
3626:
3625:
3619:
3613:
3607:
3601:
3595:
3589:
3582:
3580:
3574:
3573:
3571:
3570:
3564:
3558:
3552:
3546:
3540:
3534:
3527:
3525:
3519:
3518:
3516:
3515:
3509:
3503:
3497:
3490:
3488:
3482:
3481:
3479:
3478:
3472:
3466:
3460:
3453:
3451:
3445:
3444:
3442:
3441:
3435:
3429:
3423:
3416:
3414:
3407:
3389:
3377:
3376:
3369:
3368:
3361:
3354:
3346:
3340:
3339:
3334:
3329:
3317:
3316:External links
3314:
3313:
3312:
3303:
3300:
3298:
3297:
3294:978-1118397596
3277:
3246:
3233:
3216:
3191:
3166:
3153:
3139:
3118:
3103:
3078:
3063:
3038:
3023:
3008:
2995:
2988:
2968:Jeppesen, Knud
2959:
2936:
2901:
2872:
2852:
2832:
2820:
2788:
2773:
2760:10.2307/764089
2730:
2721:
2712:
2691:
2670:
2649:
2640:
2625:
2616:
2595:
2566:
2542:
2508:
2495:10.2307/833435
2489:(2): 106–137.
2477:Fonville, John
2468:
2447:
2440:
2434:. p. 66.
2413:
2393:
2340:
2326:
2291:
2289:
2286:
2285:
2284:
2282:Tritonic scale
2279:
2274:
2269:
2264:
2259:
2254:
2249:
2244:
2237:
2234:
2074:, proposed by
2057:Julian Rushton
2041:Hector Berlioz
2017:
2001:
2000:
1999:
1969:
1953:
1952:
1951:
1923:
1907:
1906:
1905:
1887:
1873:
1872:
1871:
1870:
1852:Romantic music
1810:excommunicated
1776:'mi contra fa'
1738:"mi contra fa"
1599:Claude Debussy
1596:
1585:
1582:
1579:
1578:
1577:
1575:
1572:
1548:
1545:
1509:
1506:
1503:
1502:
1501:
1499:
1496:
1468:in the key of
1451:
1448:
1434:in the key of
1413:
1410:
1407:
1406:
1365:
1363:
1356:
1350:
1347:
1309:
1306:
1259:First Symphony
1202:
1201:
1199:
1196:
1173:5-limit tuning
1151:
1150:
1149:
1148:
1127:
1126:
1116:
1115:
1105:perfect octave
1038:
1037:
1030:
1023:
1022:
1021:
994:
987:
986:
985:
965:
958:
957:
956:
936:
929:
928:
927:
907:
900:
899:
898:
875:
868:
867:
866:
862:
861:
860:
859:
857:
854:
850:perfect fifths
838:
837:
796:diatonic scale
791:
788:
775:
774:
746:
745:
731:
728:
724:
723:
714:tuning systems
710:
709:
674:
673:
632:
630:
623:
617:
614:
606:piano keyboard
586:
585:
532:
531:
498:perfect octave
478:perfect fourth
352:
351:
310:
308:
301:
295:
292:
198:diatonic scale
165:
164:
143:
137:
136:
133:
127:
126:
120:
119:
98:
92:
91:
88:
86:Interval class
82:
81:
78:
72:
71:
67:
66:
63:
59:
58:
55:
51:
50:
46:
45:
42:
29:
9:
6:
4:
3:
2:
4344:
4333:
4330:
4328:
4325:
4323:
4320:
4319:
4317:
4304:
4294:
4284:
4281:
4279:
4276:
4274:
4271:
4269:
4266:
4264:
4261:
4260:
4258:
4256:
4252:
4246:
4243:
4241:
4238:
4236:
4233:
4231:
4228:
4227:
4225:
4223:
4219:
4212:
4209:
4206:
4203:
4200:
4197:
4196:
4192:
4189:
4186:
4183:
4180:
4177:
4174:
4171:
4168:
4165:
4164:
4160:
4157:
4154:
4151:
4148:
4147:Lesser diesis
4145:
4144:
4140:
4137:
4134:
4131:
4128:
4125:
4122:
4119:
4118:
4116:
4114:
4113:
4108:
4102:
4099:
4097:
4094:
4092:
4089:
4088:
4086:
4084:
4083:
4082:Quarter tones
4078:
4072:
4069:
4067:
4064:
4062:
4059:
4058:
4056:
4054:
4053:
4048:
4042:
4039:
4037:
4034:
4032:
4031:Pseudo-octave
4029:
4027:
4024:
4022:
4019:
4017:
4014:
4013:
4011:
4009:
4005:
4002:
3996:
3981:
3978:
3977:
3975:
3973:
3969:
3962:
3959:
3956:
3953:
3950:
3947:
3944:
3941:
3938:
3935:
3932:
3929:
3926:
3923:
3920:
3917:
3914:
3911:
3908:
3905:
3904:
3902:
3900:
3896:
3893:
3891:
3885:
3884:
3879:
3854:
3851:
3834:
3831:
3814:
3811:
3794:
3791:
3774:
3771:
3754:
3751:
3738:
3735:
3734:
3732:
3727:
3721:
3718:
3716:
3710:
3709:
3704:
3701:
3693:
3678:
3675:
3672:
3669:
3666:
3663:
3660:
3657:
3654:
3651:
3648:
3645:
3642:
3639:
3638:
3636:
3634:
3630:
3623:
3620:
3617:
3614:
3611:
3608:
3605:
3602:
3599:
3596:
3593:
3590:
3587:
3584:
3583:
3581:
3579:
3575:
3568:
3565:
3562:
3559:
3556:
3553:
3550:
3547:
3544:
3541:
3538:
3535:
3532:
3529:
3528:
3526:
3524:
3520:
3513:
3510:
3507:
3504:
3501:
3498:
3495:
3492:
3491:
3489:
3487:
3483:
3476:
3473:
3470:
3467:
3464:
3461:
3458:
3455:
3454:
3452:
3450:
3446:
3439:
3436:
3433:
3430:
3427:
3424:
3421:
3418:
3417:
3415:
3411:
3408:
3406:
3402:
3393:
3390:
3384:
3378:
3374:
3367:
3362:
3360:
3355:
3353:
3348:
3347:
3344:
3338:
3335:
3333:
3330:
3327:
3323:
3320:
3319:
3310:
3306:
3305:
3295:
3291:
3287:
3281:
3265:
3261:
3257:
3250:
3243:
3237:
3230:
3229:Omnibus Press
3226:
3220:
3206:
3202:
3195:
3181:
3177:
3170:
3163:
3157:
3149:
3143:
3128:
3122:
3114:
3110:
3106:
3104:0-900707-04-6
3100:
3096:
3093:. introd. by
3092:
3088:
3087:Lendvai, Ernő
3082:
3074:
3070:
3066:
3064:0-393-09539-8
3060:
3055:
3054:
3048:
3042:
3034:
3027:
3019:
3012:
3005:
2999:
2991:
2989:0-486-27036-X
2985:
2981:
2976:
2975:
2969:
2963:
2957:
2956:0-19-311316-3
2953:
2949:
2945:
2944:Arnold, Denis
2940:
2932:
2928:
2924:
2920:
2916:
2912:
2905:
2898:
2894:
2890:
2886:
2882:
2876:
2869:
2867:
2861:
2856:
2849:
2847:
2841:
2836:
2829:
2824:
2810:
2806:
2804:
2799:
2792:
2784:
2777:
2769:
2765:
2761:
2757:
2753:
2749:
2745:
2741:
2734:
2725:
2716:
2709:
2708:9780199298938
2705:
2702:, pp. 21–22.
2701:
2695:
2688:
2687:9780253347664
2684:
2680:
2674:
2667:
2666:0-520-22409-4
2663:
2659:
2653:
2644:
2637:
2636:
2629:
2620:
2613:
2612:0-8247-4714-3
2609:
2605:
2599:
2592:
2591:Pyth. Tritone
2588:
2584:
2583:1-4191-7893-8
2580:
2576:
2570:
2563:
2562:1-902636-46-5
2559:
2555:
2549:
2547:
2539:
2535:
2534:0-306-80106-X
2531:
2527:
2525:
2520:
2519:Partch, Harry
2515:
2513:
2504:
2500:
2496:
2492:
2488:
2484:
2483:
2478:
2472:
2465:
2461:
2457:
2451:
2443:
2441:0-19-311906-4
2437:
2433:
2429:
2428:
2423:
2417:
2410:
2406:
2402:
2397:
2390:
2386:
2382:
2378:
2374:
2370:
2366:
2362:
2358:
2354:
2350:
2344:
2329:
2323:
2319:
2315:
2311:
2310:
2304:
2296:
2292:
2283:
2280:
2278:
2275:
2273:
2270:
2268:
2265:
2263:
2260:
2258:
2255:
2253:
2250:
2248:
2245:
2243:
2240:
2239:
2232:
2228:
2226:
2221:
2217:
2211:
2209:
2204:
2187:
2186:voice leading
2159:
2155:
2151:
2149:
2145:
2144:Black Sabbath
2141:
2140:Black Sabbath
2137:
2133:
2129:
2125:
2121:
2117:
2113:
2109:
2108:
2103:
2099:
2095:
2094:
2089:
2085:
2081:
2077:
2073:
2069:
2065:
2060:
2058:
2054:
2049:
2048:
2042:
2038:
2034:
2029:
2027:
2026:Roger Nichols
2005:
1998:
1996:
1992:
1987:
1986:
1974:
1957:
1950:
1948:
1947:
1936:
1927:
1911:
1898:
1869:
1867:
1866:
1861:
1857:
1853:
1848:
1845:
1841:
1835:
1833:
1828:
1822:
1821:
1815:
1811:
1805:
1797:
1791:
1789:
1788:
1783:
1772:
1768:
1764:
1760:
1755:
1754:
1748:
1744:
1739:
1721:
1704:
1700:
1695:
1689:
1683:
1680:for 'the
1679:
1674:
1668:
1666:
1661:
1653:
1649:
1639:
1635:
1631:
1627:
1623:
1607:
1606:
1600:
1589:
1571:
1569:
1564:
1560:
1554:
1544:
1542:
1538:
1532:
1530:
1526:
1513:
1495:
1493:
1488:
1486:
1482:
1478:
1473:
1471:
1461:
1457:
1447:
1445:
1441:
1437:
1427:
1423:
1419:
1403:
1400:
1392:
1382:
1378:
1372:
1371:
1366:This section
1364:
1360:
1355:
1354:
1345:
1342:
1337:
1335:
1328:
1327:has written:
1326:
1321:
1319:
1313:
1293:
1288:
1284:
1282:
1278:
1274:
1273:
1268:
1264:
1260:
1256:
1246:
1242:
1238:
1232:
1206:
1195:
1193:
1189:
1185:
1184:strictly just
1180:
1178:
1174:
1170:
1146:
1145:
1140:
1139:
1138:
1136:
1132:
1124:
1121:
1120:
1119:
1113:
1110:
1109:
1108:
1106:
1101:
1099:
1095:
1081:
1076:
1074:
1070:
1066:
1057:
1027:
1000:
991:
962:
933:
904:
878:
872:
853:
851:
847:
843:
835:
832:
831:
830:
826:
824:
820:
816:
812:
808:
803:
801:
797:
787:
785:
781:
772:
769:
768:
767:
744:
741:
740:
739:
737:
727:
722:
719:
718:
717:
715:
708:
705:
704:
703:
701:
697:
693:
685:
680:
670:
667:
659:
649:
645:
639:
638:
633:This section
631:
627:
622:
621:
613:
611:
607:
591:
583:
537:
536:
535:
529:
525:
524:
523:
521:
516:
513:
511:
507:
503:
502:tuning system
499:
495:
491:
487:
486:perfect fifth
483:
479:
475:
471:
467:
463:
459:
455:
451:
446:
444:
440:
436:
431:
414:
410:
406:
389:
382:
377:
358:
348:
345:
337:
327:
323:
317:
316:
311:This section
309:
305:
300:
299:
291:
289:
285:
281:
277:
276:musical scale
273:
269:
264:
262:
258:
254:
250:
246:
241:
239:
235:
231:
227:
223:
219:
215:
214:scale degrees
211:
207:
203:
199:
195:
190:
188:
184:
180:
176:
172:
162:
157:
152:
147:
144:
142:
138:
134:
132:
128:
125:
121:
117:
112:
107:
102:
99:
97:
96:Just interval
93:
89:
87:
83:
79:
77:
73:
68:
64:
60:
56:
52:
47:
43:
41:
37:
26:
19:
4254:
4221:
4207:(0.72 cents)
4201:(1.95 cents)
4181:(13.8 cents)
4175:(10.1 cents)
4169:(19.5 cents)
4161:(35.7 cents)
4155:(62.6 cents)
4149:(41.1 cents)
4141:(27.3 cents)
4135:(22.6 cents)
4129:(21.5 cents)
4123:(23.5 cents)
4110:
4091:Quarter tone
4081:
4080:
4051:
4050:
4007:
3972:Higher-limit
3887:
3881:
3793:major fourth
3737:quarter tone
3712:
3706:
3603:
3548:
3395:
3308:
3285:
3280:
3268:. Retrieved
3264:the original
3249:
3241:
3236:
3224:
3219:
3208:. Retrieved
3204:
3194:
3183:. Retrieved
3179:
3169:
3161:
3156:
3142:
3130:. Retrieved
3121:
3090:
3081:
3052:
3041:
3032:
3026:
3017:
3011:
3003:
2998:
2980:Haydon, Glen
2973:
2962:
2947:
2939:
2922:
2918:
2914:
2910:
2904:
2896:
2884:
2875:
2855:
2835:
2823:
2812:. Retrieved
2801:
2791:
2782:
2776:
2751:
2747:
2743:
2739:
2733:
2724:
2715:
2699:
2694:
2678:
2673:
2657:
2652:
2643:
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2628:
2619:
2603:
2598:
2590:
2587:Just Tritone
2586:
2574:
2569:
2553:
2522:
2486:
2480:
2471:
2455:
2450:
2426:
2416:
2396:
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2376:
2368:
2364:
2356:
2352:
2343:
2331:. Retrieved
2307:
2295:
2229:
2224:
2219:
2215:
2213:
2200:
2132:Jimi Hendrix
2124:Blue Jay Way
2105:
2097:
2091:
2084:George Crumb
2076:Ernő Lendvai
2061:
2053:Pandaemonium
2030:
2024:
1980:
1976:, Figure 30.
1944:
1932:
1925:
1865:Dante Sonata
1863:
1849:
1840:tonal system
1836:
1807:
1795:
1793:
1785:
1782:Denis Arnold
1669:
1662:
1619:
1565:
1553:Locrian mode
1550:
1533:
1522:
1492:ninth chords
1489:
1474:
1453:
1415:
1395:
1389:January 2017
1386:
1375:Please help
1370:verification
1367:
1338:
1330:
1325:Harry Partch
1323:
1315:
1311:
1281:major fourth
1270:
1263:natural horn
1240:
1236:
1226:
1181:
1166:
1141:
1128:
1123:A4 + A4 = P8
1122:
1117:
1112:A4 + d5 = P8
1111:
1102:
1077:
1053:
845:
841:
839:
834:d5 = S+T+T+S
833:
827:
818:
814:
806:
804:
793:
783:
779:
776:
770:
747:
742:
733:
725:
720:
711:
706:
699:
691:
689:
662:
656:January 2017
653:
642:Please help
637:verification
634:
587:
533:
528:minor second
520:major second
517:
514:
504:, the A4 is
469:
465:
457:
449:
447:
442:
438:
427:
340:
334:January 2017
331:
320:Please help
315:verification
312:
265:
242:
230:semitritonus
229:
226:semidiapente
225:
221:
217:
191:
174:
171:music theory
168:
160:
155:
150:
146:Pythagorean:
145:
115:
110:
105:
101:Pythagorean:
100:
62:Abbreviation
4240:Millioctave
4222:Measurement
4213:(0.4 cents)
4193:(7.7 cents)
4187:(8.1 cents)
4071:Major limma
3813:minor fifth
3270:28 February
2521:. (1979 ).
2184:and due to
2136:Purple Haze
2116:the Beatles
2098:War Requiem
2093:War Requiem
2080:Béla Bartók
2072:axis system
1860:Franz Liszt
1665:Renaissance
1638:hexachordal
1626:Middle Ages
1541:renaissance
1426:minor scale
1418:major scale
1349:Common uses
1334:temperament
1177:major scale
696:whole tones
616:Definitions
183:whole tones
118:13:9, 18:13
54:Other names
4316:Categories
4273:Semiditone
4167:Diaschisma
3982:(17-limit)
3673:(22 or 23)
3671:fourteenth
3667:(20 or 21)
3665:thirteenth
3661:(18 or 19)
3655:(17 or 18)
3649:(15 or 16)
3643:(13 or 14)
3578:Diminished
3405:interval.)
3386:(post-Bach
3260:WJRT-TV/DT
3244:. Praeger.
3210:2021-11-11
3205:Classic FM
3185:2021-11-11
3150:. YouTube.
2814:2008-07-21
2681:, p. 102.
2333:August 31,
2288:References
2062:Later, in
2033:modulation
1832:hexachords
1622:dissonance
1547:Other uses
1498:Resolution
1440:Supertonic
1073:equivalent
1067::1 or 600
846:diminished
707:TT = T+T+T
506:equivalent
456:, while a
381:inversions
249:dissonance
65:TT, A4, d5
4235:Centitone
4173:Semicomma
4052:Semitones
4016:Microtone
4000:intervals
3677:fifteenth
3523:Augmented
3401:semitones
3373:Intervals
3095:Alan Bush
2970:(1992) .
2798:"Tritone"
2411:as well."
2303:"Tritone"
2134:'s song "
2068:serialism
1970:Debussy,
1946:Siegfried
1926:Siegfried
1844:inversion
1784:, in the
1670:The name
1652:Tinctoris
819:augmented
794:Within a
482:narrowing
288:atritonic
272:atritonia
210:semitones
187:semitones
161:13-limit:
158:583, 617
116:13-limit:
113:7:5, 10:7
76:Semitones
4205:Breedsma
3653:eleventh
3633:Compound
3388:Western)
3383:semitone
3132:16 March
3089:(1971).
3049:(1961).
2883:(1974).
2740:Aggiunta
2424:(1966).
2236:See also
2181:♯
2175:♭
2169:♮
2163:♯
2126:", and "
2090:, whose
1940:♯
1732:♭
1726:♮
1714:♯
1708:♮
1657:♭
1643:♭
1612:♯
1465:♯
1444:tritonic
1431:♭
1250:♯
1245:alphorns
1080:meantone
1005:♭
969:♭
940:♯
911:♯
882:♯
863:Tritones
763:♯
757:♯
751:♯
604:). On a
601:♮
595:♯
592:notes (E
577:♮
571:♯
565:♯
559:♯
553:♯
547:♯
541:♯
474:widening
428:Since a
411:wide in
400:♭
394:♯
284:tritonic
268:tritonia
257:tonality
163:563, 637
156:7-limit:
151:5-limit:
148:612, 588
111:7-limit:
106:5-limit:
4211:Ragisma
4199:Schisma
4185:Kleisma
4021:5-limit
3927:(15:14)
3921:(21:20)
3915:(28:27)
3909:(36:35)
3899:7-limit
3864:⁄
3853:seventh
3844:⁄
3824:⁄
3804:⁄
3784:⁄
3764:⁄
3744:⁄
3726:Neutral
3699:systems
3659:twelfth
3616:seventh
3567:seventh
3512:seventh
3475:seventh
3413:Perfect
3381:Twelve-
3324:at the
3004:Debussy
2893:1390982
2742:to the
2536:(pbk).
2118:songs "
1991:Debussy
1888:Liszt,
1816:of the
1814:organum
1470:A minor
1436:C minor
1422:C major
1339:In the
1267:Britten
1188:7-limit
1087:⁄
1061:√
1048:Tritone
811:C major
743:T = S+S
721:TT = 3T
494:inverse
488:by one
253:harmony
206:C major
175:tritone
44:tritone
40:Inverse
34:tritone
4268:Ditone
4255:Others
4245:Savart
4112:Commas
4008:Groups
3957:(10:7)
3753:second
3697:tuning
3622:octave
3598:fourth
3586:second
3549:fourth
3537:second
3531:unison
3494:second
3457:second
3438:octave
3426:fourth
3420:unison
3403:in the
3292:
3113:240301
3111:
3101:
3073:398434
3071:
3061:
2986:
2954:
2891:
2768:764089
2766:
2706:
2685:
2664:
2610:
2581:
2560:
2532:
2503:833435
2501:
2462:
2438:
2347:E.g.,
2324:
2257:Ditone
1935:Wagner
1615:and G.
1255:Brahms
1144:diesis
1135:diesis
1056:octave
815:fourth
510:octave
450:fourth
413:12-TET
202:octave
173:, the
4278:Secor
4026:Comma
3998:Other
3963:(7:4)
3951:(7:5)
3945:(9:7)
3939:(7:6)
3933:(8:7)
3833:sixth
3773:third
3695:Other
3647:tenth
3641:ninth
3610:sixth
3604:fifth
3592:third
3561:sixth
3555:fifth
3543:third
3506:sixth
3500:third
3486:Minor
3469:sixth
3463:third
3449:Major
3432:fifth
2764:JSTOR
2499:JSTOR
2172:and B
1894:from
1769:, in
1749:work
1729:and B
1711:and F
1682:Devil
1678:Latin
1537:tonal
1096:. In
1069:cents
842:fifth
807:T+T+T
754:and C
734:In a
598:and F
526:B–C (
458:fifth
409:cents
280:chord
238:cents
228:, or
194:scale
185:(six
124:Cents
4263:Wolf
4230:Cent
3679:(24)
3624:(11)
3569:(12)
3563:(10)
3514:(10)
3477:(11)
3440:(12)
3290:ISBN
3272:2010
3134:2016
3109:OCLC
3099:ISBN
3069:OCLC
3059:ISBN
2984:ISBN
2952:ISBN
2889:OCLC
2704:ISBN
2683:ISBN
2662:ISBN
2608:ISBN
2579:ISBN
2558:ISBN
2530:ISBN
2460:ISBN
2436:ISBN
2335:2020
2322:ISBN
2262:Tone
2225:just
2220:just
2216:true
2203:jazz
2122:", "
2086:and
1933:—or
1854:and
1771:1739
1763:1733
1747:1725
1703:1702
1650:and
1525:step
1475:The
1456:root
484:the
480:and
476:the
403:are
274:. A
70:Size
49:Name
3618:(9)
3612:(7)
3606:(6)
3600:(4)
3594:(2)
3588:(0)
3557:(8)
3551:(6)
3545:(5)
3539:(3)
3533:(1)
3508:(8)
3502:(3)
3496:(1)
3471:(9)
3465:(4)
3459:(2)
3434:(7)
3428:(5)
3422:(0)
3180:NPR
2927:doi
2917:".
2756:doi
2746:".
2491:doi
2314:doi
2160:: F
2043:'s
1761:in
1691:is
1636:'s
1601:'s
1527:in
1379:by
1269:'s
1257:'s
1239:or
1167:In
1129:In
852:).
825:).
646:by
538:B–C
324:by
278:or
243:In
169:In
135:600
4318::
3857:10
3258:.
3203:.
3178:.
3107:.
3067:.
2921:.
2895:.
2862:,
2842:.
2807:.
2800:.
2762:.
2752:12
2750:.
2545:^
2511:^
2497:.
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2430:.
2383:,
2351:,
2320:.
2312:.
2306:.
2178:/A
2150:.
2110:.
2066:,
1997:.
1989:,
1949:.
1868::
1757:,
1741:.
1660:.
1570:.
1446:.
1275:.
1107::
1075:.
786:.
692:TT
584:).
574:–F
562:–E
550:–D
470:d5
466:A4
445:.
290:.
240:.
224:,
3869:)
3866:2
3862:1
3859:+
3855:(
3849:)
3846:2
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3837:8
3835:(
3829:)
3826:2
3822:1
3819:+
3817:6
3815:(
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3806:2
3802:1
3799:+
3797:5
3795:(
3789:)
3786:2
3782:1
3779:+
3777:3
3775:(
3769:)
3766:2
3762:1
3759:+
3757:1
3755:(
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2923:3
2830:.
2817:.
2770:.
2758::
2710:.
2689:.
2564:.
2505:.
2493::
2466:.
2444:.
2337:.
2316::
1928:.
1900:.
1676:(
1590:.
1514:.
1402:)
1396:(
1391:)
1387:(
1373:.
1294:.
1210:↑
1147:.
1125:.
1114:.
1089:9
1085:2
1063:2
836:.
773:.
700:T
686:.
669:)
663:(
658:)
654:(
640:.
580:(
415:.
347:)
341:(
336:)
332:(
318:.
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80:6
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