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Hi: I know everyone has an answer to this question: What is your preferred definition of tonality? I'm curious to see whether trends or consensus emerge, if enough people post short responses.
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Thanks, Jason. I suppose I was being a little glib. Let’s start with Fétis:
One sign, I think, that Fétis is thinking about this very differently is that he is willing to—indeed, wants to—talk about tonalités (in the plural). For Riemann, in contrast, to speak of Tonalitäten would be almost a contradiction in terms.
Nicholas Meeùs has already alluded above to the basic distinction, which Fétis takes over from Choron, between tonalité ancienne and tonalité moderne. In later writings, Fétis also seems to believe that various world musics all have their own proper tonalités. (Unfortunately, by this point Fétis has also discovered, and gotten very excited about, Arthur de Gobineau’s writings and nineteenth-century “scientific” racism more generally; so what might have been a salutary recognition of the potential cultural relativity of musical systems instead comes out as a very ugly hierarchization of the world’s musics based on nineteenth-century European conceptions of race.)
So what does Fétis think a tonalité is? To a first approximation, I think you could say that a tonalité for Fétis is a scale plus a selection of that scale’s affordances. Consider, for instance the “Ionian” mode (that should be Glarean’s mode 11; subsequently renumbered as mode 1 by Zarlino, if memory serves).
This mode, of course, looks like a C-major scale. But crucially, for Fétis, it’s not. A C-major scale evinces tonalité moderne, whereas the Ionian scale is an artifact of tonalité ancienne. What’s the difference? Essentially, it has to do with the tritone (consonance appellative) between ^7 and ^4. Although this property is latent in the Ionian scale, it’s not exploited there—that only happens once Monteverdi introduces chord sevenths. And for Fétis that’s the difference. This is what I meant in saying “a selection of the scale’s affordances.”
So a tonalité isn’t the same as a scale, but it is tied to scales in the sense that different scales, having different affordances, necessarily represent different tonalités. (A slight correction here—probably, I should say “a scale-system together with a selection of its affordances”: I don’t think Fétis wants to say that the major and minor scales represent different tonalités as my first approximation would imply; rather they are both part of a single tonalité moderne. Hence “scale systems.”)
I should say that I’m offering this as something more like a “rational reconstruction” (Lakatos) of Fétis position than a full exegesis of his writings. But the full version with chapter and verse is going to have to wait for an article. I do think, though, that what I’ve said is consistent with Fétis’ general position: pentatonic scales in Chinese scale-systems, the elaborate maqam system in Arabic music, etc. all lead, in the Histoire, to different tonalités. (And again: this gets tied, in a very ugly way to repugnant ideas about race; Fétis ends up basically suggesting that differences in tonalité are biologically determined—and no prize for guessing which tonalité comes out on top.)
Hopefully that’s a fair stab at your first query. I think I can also defend what I said about Riemann, but that’s going to have to wait for a few more days.
Many thanks to Nathan Martin for the information on modalité. Choron obviously was less successful with it than with tonalité.
Thank you also for your comments on Fétis. I think it extremely important to discuss these matters – this is, after all, the reason of the existence of SMT Discuss.
The Histoire générale de la musique indeed was Fétis' project since a long time, already announced in the Preface to his Biographie universelle in 1835 (he was then 51 years old, if I am not mistaken) and perhaps earlier. Gobineau did not begin developing his racist theories before 1847 at the earliest, 12 years later. And the first volume of the Histoire générale was published in 1869, Fétis then aged 85. He died two years later; some volumes were published posthumously, and the whole project remained unfinished. The difference between the Esquisse, where Fétis describes Indian, Chinese, Arabic, African, and other musics, and the Histoire générale is in a way striking, but at the same one finds in both works similar descriptions of non Western musics.
We may discuss that further and compare these texts at length, but that is not my point now. To say that music theory today is racist because of Fétis (or Schenker) in a way provides an excuse for present-day racism, and what I'd like to stress is that such an excuse would be utterly invalid. As the matter was presented in the US, the real problem is circumvented: why, and how, should one be racist today?
I say "how", and I'd very much like to discuss this, because I'd myself want to understand how to get out. Universities are inherently discriminatory, because even here in Europe where university studies often are supposedly as cheap as possible, it is clear that for the students to be unproductive for several years has a high cost. And this is even clearer in a domain like music theory, which is not particularly productive in terms of future income.
This will not be solved by "reframing" music theory. Studying the theory of other musics will change nothing: university studies will remain as expensive, and music theory studies as unproductive. That is to say that music theory as a discipline inherently is elitist, whatever the theory and whatever the music. It is not the music or its theories that need reframing, but the elitism.
A force field of musical tones with varying felt relationships directed to a central tone.
Tonality is an inclusion relation between two or more perceptual frames--namely, at least the frame of a pitch or pitch-class collection and the frame of one or more "tonic" pitches or pitch classes.
It is analogous to meter, which is an inclusion relation between two or more pulses (Cohn).
My own go-to for a definition has been Tymoczko's (2011) 5 features, but since you're looking for original definitions, here's my personal attempt, probably too lengthy to be correct:
An emergent aspect of (pitched) music through which pitch-classes are perceived as relating to one another in a systematic, hierarchically arranged manner, especially with respect to stability/tension and implication/realization relations. Enables, but does not necessarily entail, a single or literally sounding tonal "center." Arises in specific pieces/performances/styles through the coordination of melody, harmony, meter, & counterpoint according to broadly understood cultural and stylistic norms.
Tonality is a harmonic system of functional relationships in which all chords have a measurable distance from a central pitch (the tonic).
In general, tonality is a perception of the preeminence of one tone and its force acting upon other
Tonality has to do with choice of consonant and dissonant frequencies organized as referential melodic/harmonic identity recognizable and comprehensible by various world cultures.
History of theory perspective: "tonality" is also a discourse developed and promulgated in nineteenth-century Europe to aid and abet historiographical narratives of progress and decline and to promote the supremacy of some musics over others.
Here is a simple definition from my Harmony book:
Tonality is a hierarchical organization of musical elements which gravitate around a central triad. This triad, built on the first scale degree of a major or minor scale, is known as tonal center or tonic.
We should also be aware that a vertical mode represents tonality, but it is a tonlaity with limited parameters as determined by the mode type (natural, harmonic, melodic, double-harmonic, etc.). On the other hand, tonality (as term) may have a broader menaning than mode, because it may ancompass various modes subordinated to the same center.
[etc.], as August Sheehy does, appears to me excessively ideologic. Joseph Kerman wrote about this, and I would have hoped that this debate was settled. Yet, it may indicate one reason why it seems extremely difficult to answer Jason's initial question.
The English word "tonality" is quite ambiguous, because "tone" may mean "sound", "note", "pitch", "pitch class", etc., while none of these words are really synonymous. The situation may have been less confused for the 19th-century French authors (Choron, Fétis) who devised the name tonalité. The fact that they spoke of a tonalité moderne, opposing it among others to a tonalité des Grecs or to a tonalité ecclesiastique, evidences that they realized that the term was both precise and general.
In a general meaning, "tonality" refers to a centripetal organization of the music concerned, which includes not only tonal music properly speaking, but also modal musics of various kinds. Pentatonic music of the far East may not be concerned. In a more precise meaning, it obviously concerns an organization of Western music between, say, the late 17th and the early 20th centuries. This organization is characterized not only by centricity, but also by directionality: this is what may distinguish it from tonality in the general meaning.
Directionality remains one of the most puzzling aspects of common practice tonality. It probably has to do with the resolution of dissonances, which drastically reduces the possibility of chord progressions – and which also restrict tonality itself to a music based on the opposition between vertical consonances and dissonances. One might therefore argue that there is, on the one hand, a kind of "melodic tonality" and, on the other hand, a "polyphonic" or "harmonic" one.
I won't be longer about this, because it would need volumes. Let me however mention the problem of what Schenker named Tonraum, "the space of the horizontal fulfillment of the fundamental line" (Free Composition, § 13). Oster translated Tonraum as "tone-space", which would seem to refer to a space between different tones (pitches? sounds?). But Schenker obviously meant the space between notes of a tonal entity, a "tonal space", between the notes of a Naturklang. Once again, I won't be long about this, but I invite you to ponder about the possible meaning of these two expressions, "tone space", and "tonal space". It indicates, I think, the compexity of the problem in English. (In French, the difference would be obvious: "tone space" may translate as espace sonore ("sound space"), "tonal space" as espace tonal.)
One of two major systems in the human brain that regulates the intrepretation of sound patterns. Tonality regulates the interpretation of pitched sounds; the other system, "meter," regulates the interpretation of sound patterns in time. The tonal system classifies pitched sounds into categories, places them into asymmetric stability relations, and assigns semantic predicates to those relations. Like natural language, tonaliity is rooted in neuro-biological affordance, but conditioned by culture and shaped by experience.
This is my definition: "Tonality is the organization of pitches, both simultaneously and across time, so that certain pitches or chords are heard as attracted, in varying degrees, to other pitches and chords" (Milne, 2013, p. 3)
Milne, A. J. (2013). A Computational Model of the Cognition of Tonality. PhD thesis, The Open University.
When I was teaching gen-ed students, I defined tonality as "the way we talk about and understand musical phenomena in reference to the tonic"
I would then describe it as the battle between tension and release that creates the musical grammar and syntax known as tonality.
I think of “tonality” more as a discourse space surrounding (a) pitch relations (b) within a chosen body of repertoire (c) for a specific creative, analytical, or pedagogical purpose.
For instance, let's examine the undergraduate theory discourse space. Its repetoire usually includes everything from Bach to Brahms. Lately, it often reaches back to the Renaissance and forward to jazz, rock, and film scores, but still with a 18th/19th-century bias. Common pedagogical goals for this repertoire include teaching aural skills and part writing. In turn, the need to teach these things within the span of four semesters privileges concepts that are easy to teach in abstract, highly applicable to those specific musical tasks, and hence create easily measureable learning benchmarks. Because of these repertoire and pedagogical choices, the undergraduate discourse of tonality often focuses on pitch centers, chord function theories, hierachical relationships among scale degrees, and local voice leading.
My own thinking about pitch relations has been greatly influenced by Harrison (2016), Huron (2016), Struas (2009, ironically about 12-tone music), and Tymoczko (2011), but perhaps most by Gjerdingen (2007).
I single out Gjerdingen, because I am primarily a composer. It feels the most natural to me to think about pitch relations in terms of characteristic gestures, their methods of elaboration, and their rhetorical purposes, because these conceptions more directly addresses the question of "how do I work in music?" rather than having first to address the question "how does music work?" That latter question, while often useful and insight-producing, may never lead to the former in more than cursory ways. It further begs the questions "Which music?" and "Why this music, but not that music?"
Thus, because initial assumptions about purpose and repertoire can lead to a variety of different ends, I find it more useful to locate my discussions about tonality within the discourse space rather than settling on a definitive definition.
I wrestled with Nicolas's question (is tonality merely centricity?) in my 2011 Theory and Practice article:
In this taxonomy, then, pitch centricity is a necessary but insufficient component of CP tonality, and a potential component of other types of tonality. Your mileage may vary. :-)
In a spirit of improvisation rather than recitation, how about: "Tonality is
or learned, participatory expectation;
or learned, participatory expectation for certain [tuning system] pitch/class orders and relationships."
*I do not intend to be held accountable for this definition and its various expansions. I'm riffing to see what comes out.
I'm totally impressed by the range and thoughtfulness of all of the different responses to this question. I shouldn't be -- this is something almost every theorist gives a lot of thought to -- but still I got a lot of perspectives I had not thought of before. You could almost assign this thread as a seminar reading!
I doubt it, at least in the very general sense of "referential pitch." But if centricity is meant to refer to something more specific, involving notions relative stability, resolution, and/or implication, things that can only be conferred by a shared musical syntax, then I think it is possible.
I'm also impressed by the thoughtfulness of each of the responses to your query. Though I'm also struck by how so far, the posts are coming from a mostly rather homogeneous subset of music theorists. Given the absolute centrality of the concept of tonality to our discipline, I would hope to get as many perspectives as possible.
Messageboards, even open and well-moderated ones like SMT-discuss, aren't always the most welcoming online spaces; perhaps an alternative means of gathering definitions could give you a more representative & diverse sample of voices on the matter?
Jason Yust considers that
then tonality may reduce to centricity. The problem to me, however, is not about that but about what I meant by "directionality", the fact that centripetal forces in tonality exert themselves in one direction only (what is sometimes described as "asymmetry").
Definitions of tonality that do not take in account that kind of directionality may IMO be said "static". Schenker is a case in point: for him, the Stufengang, the progression of the degrees, mainly works along the "spirit of the fifths", either in ascending or in descending. His descriptions may evidence a slight preference for the descending direction, but that remains quite implicit (i.e. unsaid).
Schoenberg's description is more "dynamic" in that he describes a strong preference for "ascending" progressions, those where the root of a chord "ascends" in the series of partials, becoming an upper partial of the following chord. (As such, Schoenberg's "ascending" progressions often are the same as Schenker's "descending" ones.)
In the most active period of Common Practice Tonality, Schoenberg's ascending progressions (or even more those that I describe as "dominant" progression in my own theory of harmonic vectors) attain 90 to 100% of all progressions. This, to me, describes tonality perhaps better than ideas of instability or implication, which often have no privileged direction.
Frank Lehman rightly stresses that we should widen our perspective. In this respect, let me stress that as soon as counterpoint results in some sort of triadic harmony (say, from Josquin Desprez), some directionality is evident, even at a time where there is no question of "common practice tonality". Modal directionality is probably less affirmed than that of tonality, but it is there, at least from the 16th century.
And if one widens the perspective to include monodic Christian modality, or the maqam, the directionality already is there: a majority of the melodies seek the tonic (or the final, or whatever you want to call it) in melodically descending direction (which, in a way, may have been one cause of the triadic directionality).
Tonality, to me, is an oriented (or directional) centricity.
That's true: I didn't actually have a specific goal in mind with this (as in, something I would analyze statistically) but I thought one way or another it would be an enlightening exercise, and maybe could inform some work in the future. Certainly I wouldn't treat it as a representative sample. You're right, though, it would be possible to get a statistically usable representative sample by other means, and it could be really useful.
To play devil's advocate to Nicholas Meeùs:
Directionality can possibly be accounted for including in the notion of centricity some kind of distinction of stability. There is an assymmetry between stable->unstable and unstable->stable, but it is necessarily style/"language" dependent. The trick is, our idea of prograde/retrograde distinctions is very much based on "common practice" tonality. But there appears to be no such preference for prograde motions in, e.g., rock music, and it would seem arbitrary to exclude rock music from tonality. Or, for example, raga music.
Jason Yust wrote
My colleague Philippe Cathé, of Sorbonne University, wrote several papers about asymmetry in rock music, among which this one, "La nostalgie chez les Beatles", in French (nobody is perfect) but available online. It shows that, indeed, the amount of "prograde" motions tends to reduce in the music of the Beatles or, more generally, in what may be generally dubbed "rock" music, however never completely.
As to raga music, the case certainly cannot be evaluated in the same manner. Yet, I trust that a majority of raga melodies reach their "tonic" in descending – which must be considered a form of asymmetric directionality. That is to say that, even in "modality" (if we agree that raga is a form of modality), directionality was there from the start, as in maqam.
As a matter of fact, I hardly could imagine a centricity, a centripetal force in music, that wouldn't be somehow asymmetric, i.e. directional.
Yes, I notice that that is the most consistent thing (some element of centricity). But it is at the same time the case that everyone (I think) believes that tonality is a more specific concept than centricity, meaning that they would not reduce one to the other. The sticking point is that there are so many ways, often with radical differences in methodological and disciplinary context, of getting from one to the other.
How about: a purely ideological construct introduced by Hugo Riemann in the late nineteenth century, and which has subsequently enjoyed a curious ascendency. (And yes, I'm aware that the term was popularized earlier by François-Joseph Fétis; he meant something rather different by it, though.)
I think this is worth explaining a little bit more!
(1) What is the difference between how Fétis meant the word and how we do, or how Riemann did? (Is it the “tonality” vs. “tonalities” distinction?)
(2) Can you defend the idea that Riemann’s concept of tonality is purely ideological? Emphasizing “purely” because the fact that it is ideological is easy to see, but “purely” seems to mean that when you strip away the ideology there is nothing left, no real musical substance to the idea. That seems pretty radical.
Nathan: This is very interesting. On one hand, there seems to be something perceptive in how Fétis distinguishes the older tonalities from the modern (something perhaps lost in Riemann's reformulation). On the other hand, the idea that at the historical origin of the concept of tonality it is tied up with a racist agenda, is also something to chew on.
In my opinion, one main difference between Fetis' and Riemann's conceptions of "tonality" is that while Riemann is speaking of Western harmonic tonality exclusively, Fetis half a century before had considered all "tonalities" in the world and through the ages.
(Let's leave aside Fetis' ramblings as an elderely man. I would not put too much confidence in Riemann's openness to non Western tonalities, and Fetis' original concept of tonalities certainly was not "tied up with a racist agenda".)
Fetis and Riemann obviously were speaking of different things, and the many definitions proposed above demonstrate that we do not clearly distinguish between them.
Riemann's description of Western common practice harmonic functional tonality probably would not have been possible without Fetis' concept of (world) tonalities of half a century before, and ours without theirs – nor without those of some other theorists, among whom Schenker. We cannot deny our own history.
We should consider the relation between the concept of tonality, which is almost two centuries old, and that of modality. Modality apparently is a very recent concept: the New Grove online does not even devote it a separate entry. It has an important entry on "Mode", but which does not really endorse the concept of modality. "Modality" probably was coined on the model of "tonality" – I have no idea when, I'd really be interested. Yet, modality, for Fétis, merely would have been one aspect of tonalité ancienne.
Most of the definitions proposed above (not all of them, though) could apply to modality as well. If we want to push further the discussion initiated by Jason Yust, we should clarify this. And by "modality", I don't mean medieval Church modality exclusively, but all modal musics of the world.
At a time when SMT apparently discovers that it should open to other musics (as Fétis had done two centuries ago), this becomes an important discussion.
Well, it's taking me longer than I expected to get back to this, and this message will also be something of a place-holder. But I can answer Nicolas Meeùs' query about the term "modality."
It turns out that Choron uses that term in the very same passage where he coins(?) the term "tonality":
On conçoit comme possibles, un très-grand nombre de modes différens, dont on peut former divers systèmes. Chacun de ces systèmes de modes constituera essentiellement autant d'idiômes ou langages de musique, qui appartiendront à des races d'hommes différentes. C'est ainsi que les peuples du levant paraissent avoir une modalité tout à fait différente de la nôtre, et qui, pour le remarquer en passant, ne nous est point encore bien connue jusqu'à ce jour.
This is from the "Sommaire de l'histoire de la musique" (on p. xxxvii) prefaced to his and Fayotte's Dictionnaire historique des musiciens (1810).
So "modality" is at least coeval with "tonality." And the implication in Powers' work ("Is mode real?" and elsewhere) that the word was formed much later and by analogy turns out to be clearly wrong.
I also don't think that Fétis' hard committment to de Gobineau can be dismissed as his "ramblings as an elderly man." The Histoire is, in a sense, his magnum opus, the culmination towards which the historiographical writings from the "Résumé philosophique" on tend.
"Tonality" is whatever one's axioms say it is.