Minor dominant in minor mode?

Jonathan Dunsby · August 2014

Here’s a thing which has intrigued me long‑term. I regularly challenge theory students to identify a tonal composition in minor that does not “somewhere use the dominant minor”. There’s one Schumann song which might just demonstrate it, but it uses III a lot, and the flat 7 could well be emblematic of v, rather than V. Otherwise, zilch, which is also my own experience of the tonal repertoire.

I know (=I know, I know, I know) Schenker says chromatics are a foreground feature. Obviously there is something intuitively grammatical about any v in i.

Anyway, never mind Schenker. (1) Why is there always a dominant minor in minor mode music—is it some kind of “obligatory” feature? (2) Where in the history of theory has this been discussed before?

Jonathan

Nicolas Meeùs · September 2014

Jonathan, when you write that "Schenker says chromatics are a foreground feature", do you have in mind a chromaticism that may change V in v or (as Schenker would have it), a chromaticism that change v in V? In other words, what do you consider the "normal" dominant in minor, V or v?

Jonathan Dunsby · September 2014

Nicolas, I meant chromatics changing v into V. I hope that makes sense.

Nicolas Meeùs · September 2014

Jonathan, your question kept me puzzled. You ask

1) "Why is there always a dominant minor in minor mode music—is it some kind of “obligatory” feature?" Shouldn't the question turned the other way around, "Why is there always a dominant major in minor mode music?". Schenker and Riemann share the idea that the minor mode 'naturally' has a minor dominant. Riemann, in Harmony simplified, first discusses the progressions °T–°S and °T–°D, then turns (p. 44 ss.) to T–°S and °T–⁺D, in which, like Schenker, he sees a kind of mixture between major and minor. But he does not view this as a matter of chromaticism (nor does Schenker, really), because he does not (yet) discuss the progression from °D to ⁺D.

2) "Where in the history of theory has this been discussed before?". This may not have been discussed in these terms. The question discussed is rather which is the 'true' dominant. Schoenberg, as you know, considers that the function of dominant implies a major chord and that the minor v can be just that, a minor v. Riemann and Schenker, on the contrary, view the minor dominant as the 'normal' one in minor. Simon Sechter (p. 62) discusses the matter in terms of how one should proceed after either 5th degree: for him, in minor, only the major dominant (der wahre Dominanten-Dreiklang) can lead back to I and the minor dominant should be followed by I⁷ going to IV, and possibly returning through ii° to V (major) for the cadence. This is because for Sechter (melodic) degree 7 in minor should be sharp if going to 8, flat if going to 6.

But does any of this answer your question?

Jonathan Dunsby · September 2014

Nicolas, thank you for some valuable clarification there. Yes, the question should be the other way round, but it sounds almost provocative that way because it is so counterintuitive to think of a minor chord functioning as a dominant, in common practice music at least; though as you rightly say it's what Riemann and Schenker would have us assume, and their reasons for that assumption are anything but counterintuitive. Sechter's voice-leading explanation is reassuringly practical, but I'm not sure it goes to the heart of the question why there should be the kind of disconnect between harmony and voice-leading that you correctly identify as theorized differently by Schoenberg on the one hand, and Schenker on the other. So I like and am grateful for your responses, while remaining intrigued.

Jonathan

Adam Shanley · September 2014

Not sure if this would fit the parameters that you are looking for, but whenever I think of a song that makes use of a minor dominant, in a minor key, I think of Radiohead's "Knives Out." The two distinct sections project Cm and then Am and are connected through an Em chord with an added C# (muddying the waters a bit, but I think it still sounds like a minor dominant despite this). In the Cm section there is also use of a Gm7 in first inversion to aid in a stepwise descending bass. Basically the song is a whole lot of minor and works well for a listening example in Sophmore aural skills and written theory when discussing mixture and chromatic mediants. It also works for a really easy way into teaching students about reductive analysis because of all the clear descending lines connecting the work.

I hope this helps and is fitting.

Here is a link to the song on youtube.

Jonathan Dunsby · September 2014

Great catch Adam! I guess everyone pretty much knows this old song. Not ever having looked at a transcription, truly just as a listener I had always assumed that what you are calling v was in fact the focal i (i.e. the song beginning, and each verse beginning, on iv). Yet looking at some transcriptions I see that they all want the opening chord of the basic six-chord progression in 'Knives Out' to be its tonic, in which case you're so right, there is no single drop of a V anywhere. There are two clear 2ndary dominants (lines 5 + 6 etc.), and I even think the guys who made this song were maybe hearing your verse-ending Ems with C#s as a 2ndary dominant, including at the end (i.e. II# of your v--a stretch, I know, theroetically, but I'm still betting that's what they thought they were hearing, even with its sharp 9 = B natural...). [BTW my "i" does have its V, initially at "mouse", and maybe that's what a tonal ear can take in subliminally as structure-determinng, wrong-headedly you might think....] So then the only thing left is that I did say "tonal composition", but here you've got Chopin 2nd Ballade syndrome; maybe tonalish pieces which don't seem to end in their tonic shouldn't be expected to do regular things with their dominants either?

Dimitar Ninov · September 2014

Dear Colleagues,

Very nice comments. Of course, I did not expect an open statement that a minor V does not possess a dominant potential per se (something that one regrettably keeps overhearing here and there). Those who claim things like that that and preach the fable that only the leading tone produces a real dominant function will have to go back to the overtone series and realize that the D-T relationship is dormant between the third harmonic and the fundamental, and this clear acoustic connection does not need a leading tone to express dominant-tonic activities, even between minor chords. It is another matter that, in the common practice period, Vm does not typically behave as an actual dominant, because it participates in specific harmonizations where it departs from the tonic and, being a sixth chord, connects either VI or IVm6. But in other styles (Take Five by Dave Brubeck, for instance) it is a dominant which goes back to its tonic (although the harmonic dominant with the leading tone appears at a certain point in the culmination). It is regrettable that some instructors advise students "not to use minor V". In fact, both VII and V from natural minor are excellent common chords for modulation - the role of the common chord is not to be a strong function in either key, but to offer a convenient link in terms of a collection of tones. The modulating chord which comes after the common chord will shift the motion more definitely into the new key. But...again, if your hear statements like "minor V and major VII do not make good common chords in a modualtion", you would at least know that some musicians confuse the role of the common chord with that of the modulating chord. And such fables are written in modern, thick, and representative books, with colorful pages and a lot of nice pictures and diagrams. The time is ripe to turn the pages of the old books of harmony and see how they match more naturally musical phenomena in tonal harmony. Also, in jazz and popular music, take the example of bVII7 (in some instances bVII9+11) which is such a characteristic dominant in a major key that they call it "a backdoor dominant". For instance, many tunes contain a resolution bVII7 - I, and this is a good instance of the application of melodic major in both harmonization and melodic improvisation. If you play C mel. major over the cadence Bb7 - C (in C major), that is an excellent expression of a modified D - T relationship with no leading tone present. Literally hundreds of tunes contained that connection, including Stella by Starlight. Jazz musicians have a more practical sense of harmony and their intuition in expanding tonality through substitutes literally expands the boundaries of functional thinking. Needles to say, in the best books of jazz theory three main functions are present - T, S, and D, wtih their families of substitutes. A friend of mine has published an article some of you may know. It is entitled "Bill Evans and the Limitations of Schenkerian Theory". He presented that here et Texas State in 2011.

Andrew Aziz · October 2014

Hi Jonathan, et al.,

I believe this kind of thing has popped up in Java's or any other round table in my myriad advising sessions at Eastman, where I was lucky enough to be Jonathan's advisee. So as I understand the question (correct me if I'm wrong!): noting the statistical prominence of major V in minor-mode music (e.g., implying "harmonic" minor)--whether it be the dualistic arguments or Riemann or the voice-leading explanations of Sechter--GIVEN the statistical prominence of major V, HOW is it still that minor v is lurking behind the scenes, perhaps secretly even calling the shots?

And assuming we're thinking the common practice zone, since it's not the most productive question in music in which the b7 is more vernacular, such as jazz / pop. So, my short answer would probably be hidding in some kind reductio ad absurdum of work such as Kurth; if the raised leading tone is in some way an "energetic" tone, then the b7 seems to be lacking that quality. In addition, is it necessary that the dominant scale degree 5 be "wed" to the raised 7? Well, yes, if it's a "dominant" in the Rameau sense; yet Rameau does seem to acknowledge that "fifth progressions" are never truly resolved until they get to tonic, creating the strange paradox of a not very ultimate v - i (other than mimicking the not very ultimate descending "i - iv"!)

So, I can only conclude that this is used in a context where the dominant *scale degree* is divorced from the thing that makes it polar, which seem *completely* plausible. In this sense, it would not be correct to view v as a substitute chord for V, as both functioning and voice leading wise, this would lead to an implausible result (start with the lament bass, and work outwardly from there...although by no means should this be a "melodic minor" thing). If all we're doing is trying to solve the conditions that allows so easily for the dominant minor, we should think about what it is, not what it isn't; then, what allows it to be what it is.

As a purely statistical phenomenon, I would call on Dmitri Tymoczko's Markov-chain type model from EuroMAC this year; I'd be personally be interested to see how, and if, the "minor v" was able to serviceably break free from its origins in the descending tetrachord and become liberated as a consistent new "function" in the common practice.

Regards,

Andrew Aziz

VAP in Music Theory, Florida State

Jonathan Dunsby · October 2014

Dimitar and Andrew, all well understood and appreciated. (Charles Smith's textbook has a lucid tabular vademecum for common [pivot] chords between keys of which he theorizes that since the 19thC there are 12 keys, not 24, defined by their dominants whether major or minor; and my impression, and I've read Mark McFarland's stimulating work, was anyway that Bill Evans is about the same with V/v as other tonal greats.)

It's really the "statistical prominence" of v in common-or-garden minor mode 'classical' music, and all tonal masterpieces if I may be forgiven my Schenkerian inclinatiions for a moment, which intrigues me. By statistical I mean that although v in minor is rarely prolonged or even prominent, nevertheless just find me an example where it's not there somehow, often only for a moment (which durational or proportional quality I know, with my orthodox Schenkerian hat on, would be considered structurally irrelevant).

Nobody ever taught me about this phenomenon of the obligatory v in minor, if that's what it is, and I wouldn't know where to recommend a student to read about it in HoT or current textbooks.

I'm not saying this is necessarily any kind of Hilbert problem. But when I know what composers did, and look at what textbooks of old and currently say, and they don't seem to match up...well that's my thread.

Nicolas Meeùs · October 2014

Schenker rather convicingly writes, in § 23 of Harmonielehre (especially p. 65, p. 50 of the translation), that the use of v (and of iv) in the minor mode may result from the requirements of motivic parallelism. He comes back on this point in his analysis of BWV 940, in MWM I. This analysis has formed the object of some discussion in French circles, by Célestin Deliège and Serge Gut, both criticizing the licences taken by Schenker with respect to Bach's text. Serge Gut, in particular, argued that Schenker read a minor v where there was none.

The case seems to me interesting because it compelled Gut (may God have mercy on his soul) to produce an alternative analysis that makes very little sense. You may know all this, and I know some of us here loose temper at reading the name Schenker. I will therefore only refer you to my comments on Deliège and Gut, http://nicolas.meeus.free.fr/JSBach/Deliege_Gut.pdf, and my own reading of the case, http://nicolas.meeus.free.fr/JSBach/Meeus12N.pdf. (Both in French.)

Nicolas

Jason Yust · October 2014

Jonathan,

My explanation would be that, though this may seem too easy at first, that minor v is diatonically close to the home key tonic. This notion of “diatonically close” can be precisely measure by circle-of-fifths balances. The relates to the Lewin/Quinn DFT procedure, which I have been working with recently. Basically, any music that is concerned about controlling the diatonicity of its materials (their circle-of-fifths balances)—that would be essentially all tonal music—will tend to use these diatonically close chords. This is directly related to Nicolas' Riemannian explanation, if you add in another factor which is that v is “triadically close” to the dominant (and also the relative major). The Schenkerian angle is a red herring, I think, because if you are looking at all the chords that are used in a piece, regardless of how or where, the specific voice-leading concerns will become statistical noise. Basically, given the range of voice-leading concerns that could possibly govern any particular moment in the piece, one could come up with a voice leading reason to use almost any chord (given the proper context—that is, if we are allowed to choose contexts arbitrarily).

Jonathan Dunsby · October 2014

Yes Jason, and thank you. Although I can agree with every point that's been made in all this thread so far (except for agreeing with Serge Gut's Bach reading and theory comments), which is converging on Andrew's explicit and telling observation that v is not a kind of V, this would lead me back nevertheless to my question. Wouldn't you think--given that all tonal masterpieces in minor must use V, and that because of diatonic closeness (asserted e.g. in Schoenberg's chart of regions for minor) v is strongly associated with i--all such factors surely don't mean that v has to be present and explicit; that it is an obligatory feature of minor-mode masterpieces, or tonal music in minor if you prefer? I could compose any number of plausible tonal pieces in minor which don't touch v at all, yet the empirical evidence seems to indicate that these would have seemed defective to the ears of real composers in the tonal past. Tending to use close chords to control diatonicity (to adopt Jason's well chosen words) is a preference rule or we might say is sufficient, but v of i seems to have been an unspoken requirement, necessary.

The encyclopedists in 18thC France teach us to learn from exceptions--if you want to know about vision, listen closely to the blind, etc.. So I'm stamping my foot here in frustration. I don't want to comb through endless examples of v in i, obviously, since I know that's what I've always encountered. This is a repertoire challenge (with I suspect significant theoretical implications): is there maybe just one credible tonal piece out there in minor with no hint of v? I won't harp on about this, after this contribution, but further to years of advocating for evidence-based music analysis (I got such spurs as I have in reaction to the endless indulgences of 'new musicology' which I think we are still experiencing although it's not fashionable to say so) I don't feel too bad about asking that question again.

Nicolas Meeùs · October 2014

Jonathan,

Would you read an explicit v in a piece like Chopin's Mazurka op. 17 n. 2? Would you count i-iv-VII-III (m. 1-4, etc.) as a hint to v (even if the progression involves several ♭7)? It seems obvious that diatonic proximity justifies the presence of v in i – and of diatonic progressions that strongly mark the minor, with or without v. On the other hand cadences require V, i.e. a marked dominant function, one that v could not fulfill.

The requirement of diatonic proximity obviously creates a common feature, but an obligatory one? I trust that there are tonal pieces that hardly hint to v. See Handel's famous Passacaglia in G minor, going i-iv-VII-III-VI-ii°-V-i, i.e. abandoning diatonicity, because of the requirement of the cadence, at the point where it would reach v. Or some of Brahms' Waltzes op. 39, n. 7, 9, 14, 16, or Mendelssohn's Song without words op. 30 n. 6, etc.

Nicolas

Jonathan Dunsby · October 2014

Nice collection of suggestions Nicolas. I could do some special pleading (e.g. in general these pieces are short-winded and one might say—indefensibly probably to some—over-simplified; the Chopin is in major a lot [as is a Schubert song that I think someone else is about to post about]; the 9^th Brahms waltz is one of those Schumannian ‘imperfect’ pieces ending on V [2ndary V to No. 10 of course]; and the Handel HWV 432 is presumably a special case, as would be any number of non-v-using ‘lament’ bass compositions by his predecessors and contemporaries—cf. Dreyfus’s ‘The Hermeneutics of Lament’ in MusA, 10/3, 1991 and I guess I should mention that his topic Mozart K. 594 is yet another demonstration of v in minor [bars 25-8]) but thank you for thinking about these examples.

In the 14^th waltz, what’s that chord at beat 4³before the end?! And don’t you love it that Chopin passes through the flat 7 over the dominant right before the a tempo, so nearly a touch of v but, I fully admit, definitely not?

Poundie Burstein · October 2014

In a personal message to Jonathan, I mentioned Schubert’s "Der Müller und der Bach" as another piece in a minor key that does not use minor v. Jonathan agreed that this song is a rare exception, though he (correctly) pointed out that though this song is in a minor key, a large portion of it is in major.

Perhaps the ultimate answer to Jonathan’s question is that chances are that any piece that stays in a key long enough will eventually use every chord available to it. Minor v has standard uses (such as part of a modulation; or as part of a descending scale in the bass). If we stay in a minor key long enough, shouldn't’t we expect to find all of its available chords (even the less common ones) crop up within it eventually?

To make an analogy: The letter “z” (that is, the letter known outside of the US as “zed”) is not absolutely needed in order to write an intelligible sentence in English. No doubt we could all could easily construct many a sentence in English that does not use the letter “z.” Indeed, even those who are not masters of the Oulipo school of writing could probably compose a short story in which the letter “z” is deliberately avoided. But my guess is that in most short stories you can find at least one letter “z”—and the longer the story is, the greater the odds that a “z” will appear. This does not suggest that using "z" is obligatory, but rather simply that it is possible.

Likewise, we all could easily write a short harmonic progression that does not use a minor v, or a short minor-key piece in which we deliberately avoid the use of minor v. But the longer the minor-key piece is, the better is the chance that it will include a minor v at least once.

Jonathan Dunsby · October 2014

There must be something in the 'statistical likelihood' argument, but it's not as if distributional analysis has made much headway in linguistics, Poundie. In music theory it's the kind of argument I've heard used also to throw doubt on the idea of significant aggregate formation ('chromatic completion') in Haydn and Mozart, which I've also observed in Schumann and Brahms. I'd prefer to think that there is a syntagmatic system of values at work, something which marks tonality as tonal, but I guess we're in danger of re-opening debates from long ago...

Meanwhile, not much missing v in minor is being suggested, so maybe the question is on firm ground at least empirically.

Nicolas Meeùs · October 2014

Indeed, statistical distribution cannot explain everything. In major, even in pieces of extended dimensions, iii may be missing completely. Syntactic considerations must be at work.

Let's consider 'diatonicity' within the following series:

... B g♯ E c♯ A f♯ D b G e C a F d B♭ g E♭ c ...

in which each step is separated from the preceding (or the following) one by a single neo-Riemannian relation, from left to right either R (from major to minor) or L (from minor to major). This neo-Riemannian 'omnibus' can also be described as formed of two intertwined cycles of fifth, one consisting of major chords, the other of minor ones.

Tonal phrases normally go flatwards (i.e.. from left to right), but something must happen if the phrase is to come back to its starting point, let's call it the tonic. In C major, the diatonicity extends from b (more precisely bº) to d. What allows closing the tonal circle is something that usually happens as the progression reaches d (or F), a neo-Riemannian P relation (of the order of Rameau's double emploi) in which d is implicitly transformed in D, seven steps further on the left.

A parsimonious voice leading could in theory justify e between G and C (i.e. iii between V and I), but more often the RL progression from V to I is direct because the resolution of the leading tone cannot be delayed, which may be explained either by an 'attraction', a will of the leading tone, or by the will of the composer to convey the effect of this attraction. (I don't believe in attractions, I believe in composers.) A similar situation exists with bº between (D) and G, again because the leading tone movement hardly could be delayed.

The case of the minor is highly more complex because all sorts of substitutions are at play. In a minor, within the series above, E and a (V–i) are separated by as many as nine parsimonious steps. And while some of the intervening steps usually are found in minor, e.g.. VII–III–VI (G–C–F) or v (e), others are so to say never present, ♯vi (f♯), I (A) or ♯iii (c♯). If some sort or statistical distribution were at work here, it certainly could be justified neither by diatony nor by parsimonious voice leading.

Nicolas

Carson Farley · December 2014

This is interesting and in going to the piano and playing through some progressions using the minor dominant and major dominant I agree that the minor dominant migrates smoothly through the natural minor tonality (say of a D minor tonality). For instance: Dm - Am/C - Gm/Bb - F - Gm - Dm - C or i - v6 - iv6 - bIII - iv - i - bVII (cadence on C bVII seems to suggest a model quality?)

Jonathan Dunsby · December 2014

It makes sense to me Carson. How harmonic progression feels in the musical foreground is bound to be a somewhat individual matter, given all our variation in taste and experience. Then there's the question of how much that 'feel' is in play when we're considering long-range tonal relationships (cf. Bill Benjamin's point that, in my words, I-V-IV-I is a ubiquitous tonal progression but a virtually invalid [= never used] harmonic paradigm at the musical surface). I've found that students can be quite surprised, given what they learn in theory class, when I ask them to find me any Bach suite item in major which fails to touch flat 7 (therefore, some kind of IV) long after V has been established, tonicized, stood-on or however one wishes to describe it. Musicians being surprised that, in the topic under discussion, v (almost?) invariably appears in a tonal piece in i may be an item in a category of differences between modern theoretical assumption and historical actual practice...

Carson Farley · December 2014

Thank you for your comments Jonathan. In his Theory of Harmony, Schoenberg states rather early on (it's been a while since I read the exact quote and I will trace it down) that root movements from bass note to bass note are of primal importance to the character of a progression. The movement of a whole step has a forceful effect for example and root movements of thirds migrate through the progression in a more subtle manner (with exceptions of course). The dominant and subdominant being pillars of the tonality so to speak are the strongest of root movements, even if one uses a domiant root with a substitute harmony (say for example in the key of C - a V root with an F or Fm chord or F/G or Fm/G, the effect of the dominant is still noticable. So it would seem natural (without being too simple minded) that a dominant root for either a major dominant or minor dominant would still have one of the strongest root movement harmonic functions according to Schoenberg's idea. It's interesting to me that the D natural minor scale identical to the Aeolian mode has both minor iv and v chords and the strongest cadential chord (with exceptions) seems to be G - Am or bVII - i, which lacks a leading tone, but the B does move to the C in a kind of secondary leading tone function. I will review what Schoenberg said about this and see if I can provide some more clarity on the subject. Now I'm intersted in going back and reading the entire thread more carefully as I am very interested in understanding the various viewpoints and your perspective. Thank you.

Carson Farley · December 2014

Hi Jonathan,

I found the discussions by Schoenberg [Theory of Harmony] mentioned in my previous post. Of interest is page 56 in the chapter Major Mode: Diatonic Chords in the last two paragraphs - "Thus the treatment of the harmonic events is referred back to root relationships, even if in the notation it does rest on the bass note. That the bass voice is accorderd unusual signifigance nevertheless reflects a correct intuition." I hope I haven't taken this out of context. Continuing . . .

"In the tone, too, which is indeed composite, the lowest tone is recognized as the one that produces the whole complex, the one for which the total phenomenon is named. The following is to be regarded, however, as the most important reason for the special importance of the bass: . . . "

And Chapter VII beginning on page 115 details Schoenberg's ideas about the various gravity of certain progressions/root movement/bass movement. I hope this is related to the thread and I have not gone off on a tangent. When I first read the initial post this came to mind at least.

Hello!

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