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Is there any definition of tonality which generalizes beyond a diatonic scale? For instance, can you have resolution from a dominant to a tonic if you're only using a pentatonic scale? Clearly you can't just say a dominant is the chord rooted on the 5th scale degree for every scale, when in each scale "5" will mean something else. I have read that even using a whole tone scale in Voiles Debussy was able to maintain a distinction between dominant and tonic, but I'm not sure exactly what that means.

Thanks!

  • Of the five pentatonic modes, only one doesn't have the interval of a (diatonic) fifth between its first and fourth scale degrees, so a typical dominant-tonic relationship is usually available when using a pentatonic scale. – Todd Wilcox Jun 15 '18 at 18:00
  • right, but then what is the definition of a dominant-tonic relationship if it can be between the first and fourth (and not fifth) scale degrees of a scale? – lightning Jun 15 '18 at 18:59
  • I don't think you can define it by interval, because there are scales where a tritone serves as dominant and others where tritone serves as subdominant – lightning Jun 15 '18 at 19:00
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    Why this fixation on the dominant? IV-I is just as good a cadence to fix the key as V-I. Even ii-I will do the job pretty well. Or a bit more extreme, Ab7 Bb9 C is a perfectly satisfactory cadence in C major. – user19146 Jun 15 '18 at 19:00
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Tonality doesn't really need any particular scale or harmonies. It mostly needs one thing: one note that feels like home. In many genres around the world, such a “home” is simply established with an all-underlying drone note, and all melody/harmony is developed around the overtones of that drone. In e.g. Indian music, this involves lots of notes that don't even exist in Western scales. Still there can be no doubt what would be the tonic, if you called it thus.

Pentatonic scales are in fact very often used in drone-based folk music. The most obvious examples are bagpipe or hurdy-gurdy tunes.

And (as alephzero already commented) if you do use harmonies, then there are lots of ways that clearly point to a tonic without using any dominant in the classical sense. The most common alternative is the plagal cadence -, which is quite common across pop/rock/country, again indeed often in connection with pentatonic scales.

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    It is certainly true that it is very possible to establish a tonic without relying on functional harmony; although I don't think that that's the complete answer to this question, it's definitely an important thing to recognize. – Fugu Jun 15 '18 at 20:33
  • Pentatonic scales on bagpipes? I hear Mixolydian! And plagal cadence would miss the fairly important root of the IV. – Tim Jun 16 '18 at 7:41
  • @Tim sure you can play full diatonic scales on bagpipes, just, many of the traditional tunes don't. — About the you're right; I said in connection with pentatonic scale: those pieces generally don't restrict themselves to only notes from the pentatonic, but instead lay a pentatonic melody over an accompaniment with extra diatonic or even chromatic notes. – leftaroundabout Jun 16 '18 at 9:15
  • Maybe I hear the drones as representing the root note, which then means there's no leading note, but b7 instead? – Tim Jun 16 '18 at 10:40
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I offer not a complete answer, but rather counter assertion: that key (tonality) is cultural. By way of argument i offer this just-so story told by one of my composition teachers:

During WWII René Leibowitz befriended a Moroccan living in the Free French territories. After the war, he invited this Moroccan friend to attend a concert in Paris where he was conducting. Knowing that this friend had limited art music experience, the performance that Leibowitz invited his friend to was of Beethoven 5. After the performance Leibowitz asked his friend what he thought of this example of European Art Music. "It was wonderful!" came the reply, "but why did it end on the wrong note?"

What this story demonstrates (along with Western, colonialist chauvinism) is that not even 8 perfect cadences in C in a row followed by 30-odd bars of C major chords will guarantee that your audience will hear C as the home key if their musical vocabulary is sufficiently different!

Additionally, i would posit that equally important as root movement to the feeling of harmonic motion, & by extension key, is the melodic movement of tendency tones. The motion 7→8, 2→1, 4→3, 6→5 all tend to reinforce the primacy of the tonic (or the tonic harmony) in the Western tradition. So your non-diatonic scale can leverage these tendency tones — in fact it could set up its own tendency tones (e.g. Poulenc & Bartok were fond of ♭2→1) — to build its own sense of key regardless of the chordal structures availed by the scale. In an example like Debussy's works exploiting modes of limited transposition like the whole-tone scale, this melodic movement, as well as the semi-tone offset relationship of the whole-tone scales (which is also an offset of a perfect 5th), can be exploited by a skilled composer in the Western tradition to give the impression of "tonic" & "dominant" harmonic regions despite the lack of harmonic motion in the whole-tone scale itself.

  • That is an interesting anecdote, but as it stands, there is plenty reason to be skeptical IMO. What did the Moroccan really mean? That the end note was the wrong note, or that the way the end note was played was wrong? You don't need to come from a different musical culture to find those over-the-top endings by Beethoven or Tchaikovsky ridiculous. – leftaroundabout Jun 17 '18 at 10:32
  • I doubt that Leibovitz would have got Beethoven 5 “wrong” with a major Parisian orchestra, even in the years soon after WWII. Oh, by the way, i don’t maintain that the story is anything other than a tall tale that can be used to illustrate a point. Your cynicism is noted. – Dean Ransevycz Jun 20 '18 at 6:13
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The general term for this is non-functional harmony. The term's meaning is fairly obvious if you understand the antonym: It means that the harmony does not readily (or usefully, if you prefer) match with functional harmonic descriptors, like "dominant", that are based more or less on the roles that chords play in diatonic scales or those that highly resemble diatonic scales, like the harmonic and melodic minor.

Truthfully, you are going to have a hard time finding a satisfying answer to your question as stated, because tonality outside of diatonic systems (non-functional harmony) is much more difficult to define than tonality within it, and oftentimes you're going to have to look into the theory of the idiom you're analyzing to find a sufficient answer to this question. The major pentatonic scale is a great example of this, and you touched on the problem: What use is there calling the fifth the dominant interval when you can't even form a dominant chord on it? The fact is that you can't really create a strong cadence out of the major pentatonic scale because there's no tritone and no leading tone to the root, so you have to come up with different ways to describe the relationship between notes and chords formed out of the pentatonic scale than T-S-D. What functional tonality does tell you about the pentatonic scale is, as I mentioned above, that with those combination of notes you'll be unable to reproduce a perfect cadence and that therefore you can't create any strong tension-resolve contrasts like you can in the major scale (and other scales that can replicate the V7-I relationship). It is more complicated to do this kind of analysis with the whole tone scale because its relationship to diatonic harmony is considerably more complex, but it is possible. For example, using the whole tone scale built a semitone away from the root gives a collection of notes that strongly suggest the dominant (since you can form V7#5 with them, as well as its tritone sub if you're a jazz person).

To say that this is a deep rabbit hole is an understatement. For example, you can look at twelve-tone as being a total rejection of functional harmony specifically because it is impossible to ascertain any tonality from twelve pitches given roughly equal emphasis. There's also the diminished scale, which reveals a number of connections between chords that are otherwise very difficult to explain within the bounds of functional harmony.

  • hmm... your comment makes me think that maybe we can loosen {S,D,T} to {resolves to something like a tonic, resolves to something unlike a tonic, is something like a tonic}, and see to what extent those categories hold. Does that at all make sense to you? – lightning Jun 15 '18 at 21:50
  • @lightning I get what you're driving at, but I think it's more logical to simply acknowledge that the divisions in functional harmony don't really apply to non-functional harmony. There's some value in recognizing that something sounds like a perfect cadence (for example), but some information is invariably lost in the comparison when it's not actually a perfect cadence. Besides, as I've said, for many truly non-diatonic systems (see the other answer's reference to drones) there are already analytic frameworks in place. – Fugu Jun 15 '18 at 22:57

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