Talk:Tritone

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[edit] Alternatives

Where do we mention that the tritone is alo known as Diabolo in Musica, Diabolus in musica, or Diavolo in musica? Would improve findability. PS apologies for any newbie mistakes in editing Tacoekkel (talk) 16:35, 1 May 2008 (UTC)

[edit] Examples

Need to mention use of the tritone in Don Giovanni.

Feel free to do so by editing the article! (I can't add anything about this myself, because I didn't know the tritone was particularly significant in Don Giovanni.) --Camembert
tritone is used a lot in West Side Story too -- Tarquin 14:58 17 May 2003 (UTC)
Danse Macabre also uses the tritone, I believe that to achieve the correct opening effect (after the "clock" strikes thirteen) the soloist is required to detune his E string to E flat thus forming a tritone between the open A and E(flat) strings.

I think the opening notes of "The Simpsons" theme are a tritone (actually, something like C -> F#+G) and it is used heavily throughout the tune. njh 4 July 2005 00:09 (UTC)

I knos that the simpsons theme song is in the dorian key. I don't think there are any intervals of a tritone however.207.157.121.50 11:17, 14 October 2005 (UTC)mightyafrowhitey
Actually it's in the Lydian mode.
Note quite - it's in "Lydian dominant"! (lydian 7) Musical_mode#Other_types_of_modes

There were way too many examples, there are thousands and thousands of popular songs with this paticular interval in them and we don't need more than a handful. To point out some famous heavy metal songs or a single film soundtrack by a well known film composer use it is useful, that a paticular Primus or a Red Hot Chili Peppers song has it in is not. The Jimi Hendrix one is good though because that intro is nothing but the interval. 86.130.146.221 22:01, 9 January 2007 (UTC)

"The tritone is used very extensively throughout Beethoven's Piano Sonata No. 8 in C minor, "Pathétique"." Is this use more extensive than in other minor key works of the composer/period? Any references to published studies? Apus 11:38, 19 April 2007 (UTC)

Unfortunately little study has been done, to my knowledge, on the tritone. The AS Cambridge music course focuses on this interval quite significantly which may lead to students doing research in this area for their a2 investigation and report. I conducted my report on the Diminished 7th chord which is really a close relative of the tritone, but not solely on the tritone. Beethoven used it profusely in the Pathetique sonata. Every few bars you experience a tritone. Especially at the beginning and end.

What I find interesting about the tritone is how people were afraid of using it in the past due to its connections with satan. Does anyone have any examples of the tritone being used in baroque or earlier works? Many church hymns include tritones (For those in peril on the sea and such) but other than that, I have been unable to find many tritones being used deliberately in older music. An interesting field to look into.

Jake381 10:41, 30 May 2007 (UTC)

Hi Jake! Are you sure that people were afraid of using it in the past on account of its connections with Satan? This seems to be a recent myth, as the article discusses, and not something supportable based on the documents of the time. It was not an often used interval because it was both large and dissonant (you won't find many melodic sevenths either), but I've never seen a demonic or Satanic connection before the 18th c. (when it's already in common use). There's a fourteenth century work about avoiding the tritone, but it's couched entirely in musical reasons, not religious or moral. -- Myke Cuthbert (talk) 16:24, 30 May 2007 (UTC)
Greetings Mscuthbert! Though I would not place my life upon my statements as above, from my searchings I have come to my personal conclusion that it was used for this reason. I cannot see any reason otherwise why they would avoid this interval so determinedly. Dissonance creates interest in music. Before say Mozarts time I would hazrad to say that people were much more afraid of the powers that be. Though there will most likely be no written evidence that people avoided this interval, it did inherit the name "diabolus in musica". Surely nobody would wish to put the devil in their music without worrying about public reaction? Pre Classical composers still had patrons didn't they? Nice to converse with other musically aware! I don't get to much anymore :( Jake381 07:10, 7 June 2007 (UTC)
Except that they didn't actually avoid it all that markedly. It's present even in Renaissance church music—in passing, like all dissonances (and this was a time when even major and minor thirds were considered dissonant). The term "diabolus in musica" doesn't appear in a religious context anywhere. It probably comes from the fact that they're really difficult to sing and stay in tune. — Gwalla | Talk 04:07, 29 February 2008 (UTC)

[edit] Abbreviation for Tritone

All the other articles about intervals mention an abbreviation, such as P5 or M2. i can't seem to recall what the abbreviation is for augmented and diminished intervals, and I was displeased not to find the answer here... Luqui 19:55, 31 December 2005 (UTC)

a4 (or A4) or d5 are in common use. Frequently you will see them notated as x4 for the augmented 4th and ο5 for the dim 5th

[edit] Pi

Is it true that "a common symbol for tritone is π"? We used "TT" in school. Hyacinth 11:28, 23 February 2006 (UTC)

I have never seen pi used, so I'm removing it until someone provides a source. —Keenan Pepper 13:59, 23 February 2006 (UTC)
For goodness sake that's T.T (Tri Tone), which is commonly used, only someone wrote the two Ts too close together once and someone else interpreted it as a pi symbol.--JamesTheNumberless 15:52, 19 January 2007 (UTC)

[edit] April 08 edit

The tritone wasn't exploited after equal temperament (which doesn't really have a good date to speak of, anyway, if you leave it unqualified. 1600? 1920?). It really began to be exploited as a modulation in the Romantic period by composers like Chopin, Liszt, and Schumann (there are of course earlier examples, but they are less extensive). By the 20th century is was a natural part of the tonal language of composers like Holst, Vaughan Williams, and Rachmaninov. The reason it was used is for that "unexpected" quality of modulating to a key drastically unrelated to the previous. (How much of this should go in the article?)

Inverted at the octave, no interval except the tritone retains its identity. Why qualify it as the only one within the octave, when none without the octave do?

To say it has no "harmonic relationship" is false unless your definition of harmonic interval dictates that every equal tempered interval has no harmonic relationship. The ET-tritone has justifications; they are just more ambiguous than any other interval.

I've put the later points into a bulleted list, because they are more or less a random collection of facts about the tritone. Rainwarrior 19:30, 8 April 2006 (UTC)

By "no harmonic relationship" I mean that because the ratio of 1 to the square root of 2 is mathematically irrational, two vibrating bodies tuned to a tritone that start in unision will NEVER return to unison, whereas when they are tuned to, say, an octave they will be passing the zero point in the same direction simultaneously (which is what I mean by "move in unison" in this context) after the slower has gone through one cycle and the faster through two. This follows from the mathematical nature of the root of 2. --Hugh7 08:20, 8 June 2006 (UTC)
I don't quite understand what process you are describing. Two pitches at a tritone, which "start" in unison? Then they return to unison, while constantly moving in the same direction? Is the speed in this direction geometric or arithmetic in this case? I can't picture what you mean; I'm sorry. What is the "zero point" you are referring to? I'll respond though:
The perfect fifth in equal temperament has the ratio of 1 to the twelfth root of 128, which is no less irrational than the square root of two. Irrationality is not the issue with regard to harmonic relationships; the harmonic relationship is defined more by the whole number ratio it approximates. For instance, the twelfth root of 128 is very close to 3/2. Similarly, in most tonal usage, the (equal tempered) tritone is more or less a stand in for 7/4. The difference is that it is not as closely aligned to this simpler ratio as, say, a fifth to 3/2, or even a major third to 5/4.
It would not be used so extensively in dominant chords if it did not have a harmonic relationship to the rest of the chord. As a place to modulate it is definitely more "distant" than modulation by a fifth or third. My opinion is that it's actually more strongly numerically related to the original key than the semitone relationship (though most harmony books use the circle of fifths as a metric of distance, and will state otherwise; In modulation, however, the most important factor seems to be how many tones are held common, and how many or not). - Rainwarrior 15:35, 8 June 2006 (UTC)
I was using "start in unision" in the lay sense, not the musical sense, or the micro (within one vibration) not macro (measured over many vibrations) sense. If two vibrating bodies start moving from their neutral (unstressed) position (easiest to think of two strips of steel clamped in the same vice being twanged together, or reeds of a reed organ); If they are equal length etc, they will sound in unison and continue to move together. If one is twice as long as the other, it will vibrate half as fast (they will sound an octave) and they will move together past the neutral point after one vibration of the longer one, two of the shorter. However, if they are tuned in the ratio of 1: root 2 because the ratio is mathematically irrational, they will never move simultaneously through their neutral points again. Rainwarrior said "the harmonic relationship is defined more by the whole number ratio it approximates." but the ratio of 1: root 2 does not approximate to any other. I think we are at cross purposes here because I am looking at it from a mathematical/acoustic point of view, not a musical/harmonic one. But isn't "the perfect fifth in equal temperament" a contradiction, because a fifth in equal temperatment is not perfect? --Hugh7 23:08, 24 April 2007 (UTC)

[edit] Degree of dissonance of the tritone

I don't think this should be exaggerated, which I think the article did. Persichetti in Twentieth-Century Harmony has what I think is a more usual view:

It is difficult to classify the tritone or the perfect fourth out of musical context. The tritone divides the octave at its halfway point and is the least stable of intervals. It sounds primarily neutral in chromatic passages and restless in diatonic passages. The perfect fourth sounds consonant in dissonant surroundings, and dissonant in consonant surroundings.

That's more like it, I think. Gene Ward Smith 03:01, 11 June 2006 (UTC)


I just added a sentence in the article based on that book.--Roivas 21:50, 16 November 2006 (UTC)

[edit] The Tritone's usage in history

The tritone is a restless interval, classed as a dissonance in common practice music; even more dissonant than the minor second or seventh[citation needed], and given the name diabolus in musica ("the Devil in music") by some from the early music era to the baroque period, likely because of its unwanted occurrence as F against B when two voices were singing a fifth apart[citation needed]. It was exploited heavily in the Romantic period as an interval of modulation for its ability to evoke a strong reaction by entering the key least related (retaining only two common tones, the least possible) to what occurs previously[citation needed].

I'll try to provide some better information on this. Anyway, this paragraph needs to be improved.

Anyway, you'd think the "key least related" would have no common tones.

The secondary dominant and diminished seventh relations are what facilitates modulation in tonal music. Both of which contain tritones. Not sure what the paragraph above is trying to get at and I think it would just confuse someone who is trying to learn the basics of music theory.--Roivas 22:02, 16 November 2006 (UTC)

When taking 7 of 12 tones to build your scale, you only have 5 tones left over. So, if you want to pick the most unrelated scale of 7 tones, you have to reuse at least 2 (7-5 = 2). (Though the minor-second modulation also has only 2 common tones.) - Rainwarrior 22:55, 16 November 2006 (UTC)

Okay, two keys with roots a tritone apart have two common notes between them. I get what you mean now. I would make the paragraph a little more clear, that's all.--Roivas 23:54, 16 November 2006 (UTC)

As for the diabolus in musica stuff, a citation should be really easy to find. If my books weren't packed up in boxes right now I'd put one down for you, but if anyone else out there has, say, the Richard Hoppin Medieval Music, or even the Grout history, check the index for it. You'll find something. - Rainwarrior 23:01, 16 November 2006 (UTC)
I put in some clarification there--the Diabolus in Musica is not a medieval term (search for it in the Thesaurus musicarum latinum and you won't find anything). I also tried to start a little section on its use in the classical and baroque eras. I think that after the initial definitions, dividing the article by usage historically is important. (I also think that the list of pieces with tritones in them needs to be pruned carefully--naming works without prominent tritones is harder than naming works with them). --Myke Cuthbert 00:32, 28 November 2006 (UTC)

Yeah, I've never been too clear on this. I saw the term mentioned in Walter Piston's "Harmony" when I was flipping through it, but only as a passing comment. Agree on your other points as well.

An answer might be found in this great little collection of papers: Music in the Western World, a History in Documents. I can get it from a local library in the next couple of weeks.

Funny that Black Sabbath's "Symptom of the Universe" wasn't mentioned! That's a great tritone riff. Just kidding.--Roivas 07:05, 28 November 2006 (UTC)

I have the Weiss-Taruskin Music in the Western World sitting here, but I didn't see anything on the tritone (it avoids music notation for the most part, so discussion of elements such as tritones is sparse). The Strunk volume of documents might have something on this topic, but I also doubt it. --Myke Cuthbert 22:41, 28 November 2006 (UTC)
Btw -- Nice job on so many edits, Roivas. I want to move the part about the TT in "first inversion" chords from Jeppesen to between the Medieval and Baroque sections, since it's really dealing with 16th century music which played by different rules. We don't yet have a subsection on the tritone's use in Renaissance music. --Myke Cuthbert 03:23, 1 December 2006 (UTC)

Sounds good. Thanks!--Roivas 05:08, 1 December 2006 (UTC)

My suspicion is that people use it because it "sounds cool."--Roivas 22:50, 28 November 2006 (UTC)

"even more dissonant than the minor second or seventh[citation needed]"

This statement bothers me as dissonant and consonant are fairly subjective terms and the definitions for both tend to change drastically within short periods of time. I know that Hindemith qualifies what you are saying (for his own reasons), but I'm sure I can find sources that say otherwise. Can we make this statement less definite or, at least, qualify it with a source?--Roivas 19:30, 27 November 2006 (UTC)

[edit] Occurrences

If folks would please refrain from adding more and more "tritone occurences" in popular culture, that would be great. It's one of the most ubiquitous musical devices in Western Music. Nothing special about it. Suprised no one has mentioned the English police siren! At least that's sort of interesting.--Roivas 22:08, 3 December 2006 (UTC)

Agreed. The newest Ravel example seems absolutely silly. A list of Ravel works without tritones would be more interesting. Or a discussion of how Ravel uses it would help someone who comes to this article expecting to learn something. The European siren usage would be a good mention though. --Myke Cuthbert 04:32, 31 January 2007 (UTC)

[edit] Can someone...

Can someone translate the German regarding the tritone in the history section? Not all of us (including me) understand German. bibliomaniac15 05:26, 27 January 2007 (UTC)

I'm not so fluent, but since I did add the texts, I guess I have some responsibility.  :) I am surprised by the "angenehme" and really hope I didn't mistranscribe "unangenehme," but given other things Mattheson has written, it is entirely possible. Also, I added a little section explaining how mi-fa can be a tritone. --Myke Cuthbert 05:11, 29 January 2007 (UTC)

[edit] Tritone Substitutes

With respects to Jazz music, shouldn't someone mention tritone substitutions? (unsigned message)

An important element not mentioned in the article, but I have little expertise on the issue, so I can't add this section.--Myke Cuthbert 16:40, 24 March 2007 (UTC)

[edit] Mi contra Fa

Historically, the interval of the tritone was Mi-contra-fa, not Si contra fa; Si against Fa implies solfeggio thinking, while Mi against fa is hexachordal thinking. Please read the 18th century theoretical examples before changing this again. --Myke Cuthbert 02:15, 20 February 2007 (UTC)

[edit] most dissonant interval?

isn't the tritone the most dissonant musical interval? 67.172.61.222 22:48, 9 March 2007 (UTC)

No. Aside from dissonance being difficult to define in a quantitative way, it shows up in every dominant seventh chord. If anything is "most dissonant", it's probably the minor second. - Rainwarrior 17:33, 10 March 2007 (UTC)
I'll see your "no" and raise you a "yes for the following reasons"-
  • since a tritone divides the octave in half symmetrically, there is no tonal center between the two notes, and it is always unstable regardless of context (from a purely clinical viewpoint, a lack of tonal center is a pretty concrete definition of dissonance, imo).
  • a dominant seventh chord is relatively dissonant, but it doesn't always sound out of place, given certain contexts (i.e. building tension to resolve to the tonic or elsewhere or harmonizing with a scale).
  • when you play the two intervals as one note after another, there is a pretty obvious difference. going from E to F sounds much different than going from E to A#.
  • like all other imperfectly consonant intervals, a semitone can sound perfectly fine in certain contexts. listen to "From the Morning" by nick drake for example. A tritone never sounds melodic.
  • finally, since an interval is roughly as consonant as it's inverse (i.e. a fourth and a fifth), a major seventh would have to be similarly dissonant. it is, of course, not especially consonant, but when you play a maj7 chord it's certainly not comparable to what a b5 chord (or a diminished chord) sounds like.67.172.61.222 00:23, 16 March 2007 (UTC)
Dissonance and consonance are culturally defined terms and don't obey particular universal rules. You could correctly say that an interval was "treated as the most dissonant interval by composer X" or "in period Y" or "in Noh theater" but your ear is not a good judge of universal dissonance. For instance, C->B# is considered a dissonance by most tonal theorists (augmented 7th). Similarly, a bare perfect 4th is definitely treated as a dissonance in nearly all common-practice harmony--it does not have roughly the same degree of consonance as the P5.
Your point about harmonic and melodic dissonances being different beasts is a quite good one. --Myke Cuthbert 01:03, 16 March 2007 (UTC)
What do you mean by "sounds melodic"? And what is melodic dissonance? Do you have a definition or is this an entirely subjective measurement? And as for "harmonic" dissonance, consider any chord with exactly two semitones and no tritones (either C D♭ D♯ E, or C D♭ E F) and and compare to any chord with two tritones but no semitones (C D F♯ G♯, or C E♭ G♭ B♭♭); which is more "dissonant" subjectively? Or similarly with three semitones (C D♭ E F G♯ A) vs three tritones (C D E F♯ G♯ A♯)? - Rainwarrior 06:53, 16 March 2007 (UTC)
Rainwarrior, how do you do the sharp and flat symbols? --63.25.21.154 (talk) 11:10, 7 March 2008 (UTC)
The easy way is to use the {{music}} template. For a sharp use # as the parameter, for flat use b, for double sharp ##, for double flat bb. It can do a lot of other things too. It's pretty handy. — Gwalla | Talk 17:48, 27 May 2008 (UTC)

Myke and Rainwarrior are right. There is no fixed definition of "most dissonant interval" in equal temperament. It's completely subjective. Maybe if User:67.172.61.222 took beats into consideration he/she may have something going for his/her argument. Even then it wouldn't matter.--Roivas 22:07, 18 April 2007 (UTC)


I'm inclined to agree with 67.172.61.222. In twelve-tone music, this is roughly how consonance and dissonance play out:


INTERVAL AND INVERSION:
Most consonant
0 (perfect unison) and 12 (perfect octave)
5 (perfect fourth) and 7 (perfect fifth)
4 (major third) and 8 (minor sixth)
3 (minor third) and 9 (major sixth)
2 (major second) and 10 (minor seventh)
1 (minor second) and 11 (major seventh)
6 (augmented fourth) and 6 (diminished fifth)
Most dissonant


I imagine the only thing that changes culturally is exactly how strict the definition of "consonant" is (in medieval times only 0/12 was consonant, gradually growing to include 5/7, 4/8, and 3/9)--but that still gives you a pretty clear indication of where every interval falls regarding sonance. Joe routt (talk) 04:40, 27 May 2008 (UTC)
Can you cite a source for this information per Wikipedia:Citing sources? Hyacinth (talk) 06:09, 27 May 2008 (UTC)
I'm afraid not, it's original research. I was making a point, not an edit.Joe routt (talk) 08:10, 27 May 2008 (UTC)
Huh? 4/8 is 1/2, aka an octave, which is consonant no matter what culture or time period you're looking at. 3/9 is 1/3, octave-equivalent to a perfect fifth. 0/12 isn't even possible (I guess it could mean a single string with no harmony at all). Not sure what you intended. — Gwalla | Talk 17:48, 27 May 2008 (UTC)
You misunderstand me. When I refer to 0/12, 5/7, etc, I am not referring to fractions. In this case 0/12 would be an interval of 0 semitones (unison), paired with its inverse, an interval of 12 semitones (octave). Likewise, I used 5/7 to mean a perfect fourth and fifth. Allow me to rephrase myself: In medieval times, only unisons and octaves were consonant, gradually growing to include perfect fourths and fifths, and major and minor thirds and sixths. I hope that clarifies things. Joe routt (talk) 00:06, 28 May 2008 (UTC)
Oh, I see what you mean. — Gwalla | Talk 19:43, 28 May 2008 (UTC)

[edit] Historical uses

Wouldn't it be helpful to make it clearer that the equal tempered tritone familiar today is not the same as most older tritones? Close, perhaps, but I wonder how easy it is for people today to hear an equal tempered tritone and think that is the sound that was supposedly the devil in music and something to be avoided. I know I had that misconception for a long time. As I understand it, there are multiple types of tritones found in early temperaments and in just intonation, none of them quite the same as that familiar today. If so, it strikes me as potentially misleading to talk about the tritone's history as if it is a single thing. Does this make sense? Also, I have the impression that the "devil in music" thing was less about how dissonant it was and more about how the tritone's existence made it clear that a "perfect" system of harmony and tuning was impossible. Pfly 06:53, 12 March 2007 (UTC)

There is no historical evidence for the Devil in Music idea going before the middle Baroque era, so it's hard to say how temperament would have affected this idea. The tritone's unacceptability in certain contexts comes from the way it substitutes for a perfect fifth (or, more rarely, P4) and not from the way one tritone differs from another. Discussions of the size of the semitone, tone, major and minor thirds, etc, are common. Discussions of the size of the tritone are rare. --Myke Cuthbert 16:12, 12 March 2007 (UTC)
I just looked up what I could find on the topic in W.A. Mathieu's "Harmonic Experience" book, checking pitch names at the Scala site [1]. Again, I am still too unsure about this to edit the actual page but thought I'd put some thoughts here. Interestingly, Mathieu makes almost no mention of the word "tritone" in his book. His main theme seems to be showing out equal tempered intervals (ET) "stand in" for the more consonant justly tuned ones (JI) described with ratios; and that one ET pitch can "stand for" more than one JI pitch, depending on the harmonic context; and that the context can set up an ET pitch to stand for one JI pitch but then continue as if it was a different JI pitch. He makes a good case for this being one of the major strengths of ET and something composers have exploited, knowingly or not, for the way it can "trick the ear" (ie, sound cool). So in this framework, the term "tritone" is not very useful since it does not indicate what JI pitch is involved. So instead he almost always refers to tritones as "augmented fourths" or "diminished fifths", or less frequently, other terms. In ET an augmented fourth is the same pitch as a diminished fifth; the tritone. But in harmonic progressions, the two have different functions. Anyway, I made a list of the various JI pitches for which the ET tritone could "stand for" harmonically. Some are purely theoretical (too hard to set up a harmonic progression that would bring it out), but at least 4 are heard as different, maybe 5:
The augmented fourth F# 45:32 (590 cents) (aka "diatonic tritone"); the "diminished fifth Gb 64:45 (610 cents) (aka "2nd tritone"); the eleventh partial "undecimal semi-augmented fourth" F# 11:8 (551 cents); and the "grave fifth" or "wretched pa" 40:27 (680 cents), this last being more a "bad fifth" than a "tritone". Other intervals in the tritone range that are more theoretical than useful include "acute fourth" 27:20 (520 cents, more a bad fourth than tritone); the 555 cent quarter-tone; "classic augmented fourth" 25:18 (568 cents); "septimal tritone" 7:5 (583 cents); and the "Pythagorean tritone/augmented fourth" 729:512 (612 cents).
Anyway, I was just curious enough to look up stuff this far, but must attend to other things. Unsure whether this stuff is useful for this page (though its been very useful to me personally in understanding harmony), but thought it worth posting here. And yea, the "devil in music" comment was something dredged up from memory and probably just a theory I randomly speculated about once rather than something real. I'll keep my eye out for references on the topic though! Pfly 19:46, 12 March 2007 (UTC)
Sorry I jumped too much on the "devil in music" aspects of your first post. I think there is a lot of important information in your second comment which should be added to the article. A couple of thoughts though. Many of the names of pitches on the Scala site are not conventionally used, and are in fact historically inaccurate ways of attributing a name to an interval. The one that jumps out at me immediately is "wretched pa" -- "pa" is an Indian note name (from Sa to Pa is basically from Do to Sol), so no pre-ET European composer would have been thinking of their interval as any form of "pa". The terms I recognize are "septimal tritone" and "Pythagorean tritone". In many tuning systems, there would be all sorts of different A4s and d5s in use which don't have conventional names. I don't know which parts of the article would need to be modified to take account of these subtleties, but I suspect not all of it.
The part of the article which I think needs the most work is the use of the tritone from about 1650-1800, and as this is the period where ET thinking became dominant, it may be the best place to add your information. --Myke Cuthbert 19:22, 14 March 2007 (UTC)
Hmm, having research a bit more, I've gotten the impression that of the JI pitches I mentioned only the 45:32, the augmented fourth, is what the word tritone has mostly meant, historically. Maybe the diminished fifth as well, but I'm not so sure anymore. Today in ET I'm sure both are often called tritones due to enharmonic equivalence. The 11:8 pitch is supposedly a possible "blue note" rather than a "tritone", if it is harmonically used at all. The 729:512 Pythagorean tritone might count as a historically significant tritone, if it is not merely a theoretical construct. The rest of the pitches I mentioned seem better called fourths or fifths rather than tritones, except perhaps the 7:5, which as I understand is probably a modern theoretical invention anyway.
So I take it back! Except perhaps something about the difference between an aug4 and a dim5 and how they relate to the term tritone historically, and how once upon a time, the pitch of the tritone was different from that in common use today (the "wretched pa" term comes from Mathieu's book -- he uses Indian sagram terms for prime factors, "pa" being equivalent to "Pythagorean", but a lot easier to say and write!) Pfly 23:51, 14 March 2007 (UTC)
7/5 is far from modern. Offhand, I remember that Giuseppe Tartini wrote about them and a notation for them, but I'm reasonably certain there are earlier references to it. The tuning of a dominant seventh as 4:5:6:7 is really quite natural, and can be frequently heard in vocal quartets, string quartets, and small brass ensembles. It would be strange to think that this extremely stable chord was not used before modern times. - Rainwarrior 05:41, 15 March 2007 (UTC)

[edit] Sympathy for the Devil's Interval

I've always thought that the lowest note in the repeated bass line of the Rolling Stone's "Sympathy for the Devil" sounds like "the wrong note". Someone suggested to me recently that maybe they were using "the Devil's interval". Does someone know if this is true? If so, it seems like that fact would be a worthy addition to that article (and maybe this one). - dcljr (talk) 03:13, 21 March 2007 (UTC)

No, the wrong note is an 'A' beneath an E major chord. Usually a bassist should play a 'B' in this context, but here he plays an 'A'. The interval is a perfect-fourth which sounds wrong because it's not part of the harmony (producing other dissonant intervals, like a major second/ninth and a major seventh, but no tritones). - Rainwarrior 05:37, 21 March 2007 (UTC)

[edit] Hugh7 trivia

It seems to say more about Lillian Hellman or Dorothy Parker than about the tritone. Consensus to remove? --Myke Cuthbert 19:39, 23 April 2007 (UTC)

Yes, it's amusing and characteristic of Parker's wit but obviously pretty irrelevant here. Rigadoun (talk) 19:04, 24 April 2007 (UTC)

Isn't trivia always more or less irrelevant? Rather than delete, if you must, please move it to Dorothy Parker or Lillian Hellman --Hugh7 23:15, 24 April 2007 (UTC)

I might be more against trivia sections in articles than others, but I think this piece of trivia might not have a good place in Wikipedia. There are many great jokes about diminished fifths, but I don't know where they should go. Though I think an article on humorous statements made about music theory would be a fine addition to WP, and I'd definitely want to contribute. --Myke Cuthbert 01:06, 25 April 2007 (UTC)

[edit] Tritone as irrational ratio

That the equal-tempered tritone stems from an irrational number ratio does not explain it as a dissonance. Except for the octave, all intervals in ET are irrational numbers. The perfect fifth, for instance is 1.4983070768766..., yet it is treated as a consonance. --Myke Cuthbert 01:06, 25 April 2007 (UTC)

We almost need another name for the frequency exactly half way up or down the octave whose frequency is the square root of two times the tonic. "tritone" doesn't quite cover it because it depends which kinds of tone it's three of. ET is an approximation to Pythagorean perfect intervals. The "perfect" fifth sounds consonant in ET and so "is treated as a consonance" because for most ears it is near enough to 1.5. Using the figure above, the ET "perfect" fifth from A440 is 659.2551138257 Hz, the true perfect fifth is 660, so they would beat together at 0.745 Hz, a slow throb that would not be perceived as "out of tune" by most people (two slow even for a vox humana effect). The true root-2 interval is not near to anything. That's the point I've been trying to get across. --Hugh7 08:18, 25 April 2007 (UTC)

It's near to several just intervals, like 7/5. Furthermore irrationality is certainly not the cause of dissonance, and equal temperament is not the cause of the tritone's dissonance. The tritone is still dissonant in just intonation (and it was known to be dissonant long before temperament began). - Rainwarrior 16:05, 25 April 2007 (UTC)
7/5 is pretty remote for a just interval, being the ratio of two non-trivial prime numbers. Two vibrating bodies tuned to 7:5 will pass through their rest-points in the same direction only every 35 cycles, which is rather too many for the ear to "count". Do people hear that as "more harmonious" than an accurate 2^½:1? --Hugh7 07:49, 1 May 2007 (UTC)
And 6/5 only once every 30, but that one's long been catalogued as a consonance, and what about 7/4, shouldn't that be by your logic more consonant than 6/5? The lowest common multiple isn't really a measure of consonance. Dissonance and consonance are largely contrapuntal functions, for instance, 4/3 is "dissonant" in much theory. 7/5 is dissonant in tonal use in general. This has nothing to do with the fact that 7/5 is an audibly pure and stable interval and 2^1/2 is not. If you put it in the context of a justified dominant seventh chord 4:5:6:7, compared to the ET version it is profoundly stable. - Rainwarrior 17:37, 7 July 2007 (UTC)

[edit] Musical examples (getting out of hand again...)

I think that the musical examples section is getting a little out of hand again. My suggestion: can we make the section "Music which explicitly mentions the tritone" which would include "Slayer" or call the section "Unusual uses of the tritone," which would include the retuned timpani in Fidelio (extremely unusual for its time). And move the rest either to a new article "Prominent uses of the tritone" or more generally, "Prominent uses of particular musical intervals." Thoughts? --Myke Cuthbert 01:06, 25 April 2007 (UTC)

I cut the list down to pieces in which the tritone appears unusually or self-referentially. Yes, there are lots of Metal pieces which feature tritones, but also lots of country songs, Lawrence Welk ballads, etc. The Slayer reference could be returned, but does it use a tritone prominently anywhere except in its name? The "Charmed" example seemed the only one from popular culture which explicitly linked a tritone to specific "evil" effect. I think that if we had a musical example of Purple Haze or the opening chords of Elfman's "Simpsons," then they'd be worth mentioning in section on how the tritone is commonly used, but they're no more unusual than hundreds of other examples. --Myke Cuthbert 21:02, 12 May 2007 (UTC)
Actually (having just tried to give the article some sense of order), I think the best thing would be to incorporate these in the main text, noting why they are historical. In particular, this would be useful for the heavy metal examples (about which I know nothing)...which songs were the "first" to use the tritone that was "practically endemic" to black metal (I deleted that phrase, as the wealth of examples from other kinds of music make it clear there is no endemism here) and how did it become so associated with the genre? In general, instead of a list, putting in text gives you more context about why they are notable (e.g. first of its kind in such-and-such genre, or widely familiar, etc.). Maybe I'll get around to it someday. Rigadoun (talk) 05:14, 12 November 2007 (UTC)

The musical examples should at the very least say whether the tritone is used harmonically or melodically, so readers will know what to listen for. — Gwalla | Talk 04:39, 29 February 2008 (UTC)

[edit] function of chord

can someone please add a section to explain its function? Jackzhp 20:53, 7 May 2007 (UTC)

Function of what chord? Hyacinth 20:56, 7 May 2007 (UTC)