Discussion document concerning the
1. Tonality and form
Philip Tagg, 1 November, 2013

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Formal conventions

• All source references are listed in a single ‘References’ appendix. • This text follows the Cambridge University Press house style, e.g. synthesise rather than synthesize, single rather than double quotes. • The following typeface conventions are used: 1. Sans-serif bold lower case for note names, e.g. b$ b@, c, c#; 2. Tahoma for lead-sheet chord names, e.g. E7>Am; 3. roman numerals in IMPRINT font for non-key-specific tertial chords based on scale degree e.g. $VII> IV> I. 4. arabic numerals for non-key-specific scale degrees, e.g. 1 2 $3 4 5 $6 #7 1 (ascending harmonic minor scale). 5. Chord loops are delimited by arrows turning 180° horizontally, e.g. {C Am Dm G7} (I-vi-ii-V7 vamp in C major); Chord shuttles are denoted by a double-headed arrow, e.g. B$ u G$ at the start of Chopin’s March funèbre. Scope of this text This text is part of efforts to reform, democratise and de-ethnocentrify the study of music. It addresses some fundamental problems of logic and cultural equity in the denotation of musical structure. It focuses on the ‘troubles with tonal terminology’ (p. 7, ff.) and on the restrictive notion of ‘form’ in music (p. 24, ff.). It does not address issues of timbre, vocalisation, sound design, aural staging, rhythm, periodicity, phrasing, etc. in any detail.


My own awareness of problems denoting musical structures is the result of forty years of work as a ‘musicologist of the popular’. Back in the 1970s I was certainly aware of incongruities when trying to apply the terminology of conventional music theory to popular music, but it was not until the 1990s that I came to realise the general extent to which that terminology can be both inadequate and deceptive. It was a gradual process of awakening that, summarised in the following six stages, will hopefully make for instructive historical reading for anyone interested in music theory or the epistemology of music. Six stages [1] When I was very young, my mother used to sing the minor hexatonic tune The Tailor and the Mouse. I also remember her humming ionian mini-chromatic music-hall numbers like If You Were The Only Girl/Boy In The World. My father, a self-taught amateur pianist, could muddle through piano arrangements of minuets from Mozart symphonies and accompany traditional tunes like the dorian What Shall We Do With The Drunken Sailor?, as well as ionian nursery rhymes like Hickory Dickory Dock. He could also occasionally be heard ‘doodle-doo-ing’ a Glenn Miller or Jack Hylton horn riff. Then, as a teenager, my piano and organ teacher, Ken Naylor, not only introduced me to bebop and Bartók but also taught me to play jazz standards and to do close-harmony arrangements. With that musical background, which I later discovered was considered ‘unusually eclectic’ by others, I became a music student at Cambridge University in the early 1960s and was confronted by an almost exclusively euroclassical world. During my three years at that institution (1962-65) I had to actively seek out musical opportunities outside the academy, not so much for prosaïc financial reasons as to preserve my own psycho-socio-musical sanity. I joined a a Scottish country dance band and a soul/R&B combo while trying to find the time, even if I rarely found the inclination, to ‘complete this motet in the style of Palestrina’. Before studying at Cambridge I had not met many who heard one sort of music as intrinsically superior to another, but during my time in that privileged Disneyland of the English Renaissance I found myself repeatedly trying to convince those who held such narrow views of aesthetic excellence that they were missing something. Therein, I suppose, lie the origins of my subsequent career as musicologist of the popular. The first really substantial writing I produced on the subject was my doctoral thesis (Tagg 1979). [2] One of the main points in the explanation of popular music analysis method presented in my PhD was that the hierarchy of ‘primary’ (scribal) and ‘secondary’ (non-scribal) parameters of expression was inapplicable to music whose mediation rarely relied on notation and whose expressive dynamic resided in bouts of the extended present (intensional aesthetic) rather than in long-term harmonic and melodic narrative (extensional). Another critical point was insistence on a semiotic approach to music analysis and on the notion that thoughts about musical structuration should include discussion of its meanings. [3] Invited in 1984 by Coriún Aharonián to run popular music analysis seminars at the Cursos latino-americanos de música contemporânea in Tatuí, Brazil, I had to confront my Euro-North-American cultural limitations and to listen with open ears to previously unfamiliar types of music. With help from other course participants, I gained insights into how the actual sounds of popular musics in Latin America, like those of many popular styles from my own part of the world, could not be adequately described using the terminology of conventional music theory. Coriún also brought to my attention the work of Carlos Vega whose writings on popular music I later found useful in explaining the functions of harmony in chord shuttles and loops. [4] Later, when questioning reductionist and ethnocentric assumptions about the structural traits of ‘black’ and ‘white’ in music (Tagg 1989), I stumbled on strange contradictions in terminology descriptive of rhythm and metre. Firstly, the 1958 Harvard Dictionary of Music entry on ‘Dotted Notes’ refers to the ‘Scotch snap’ as ‘the reverse of the ordinary dotted rhythm’, noting that ‘[i]nverted dotting is… very frequent in Oriental and in primitive [sic] music, where the normal dotted rhythm is rather rare.’ Whoops! If ordinary and normal are ‘rare’ and if the reverse or inverse is ‘very frequent’, linguistic logic has broken down, unless the oxymoron is intended as a humorous rhetorical device. Secondly, if syncopation is, according to the same Harvard Dictionary, ‘any deliberate upsetting of the normal pulse of metre, accent and rhythm’, and if ‘[o]ur system of musical rhythm rests upon the grouping of equal beats into groups of two and three, with a regularly recurring accent on the first beat of each group’, then ‘[a]ny deviation from this scheme is felt as a disturbance or contradiction between the underlying (normal) pulse and the actual (abnormal) rhythm’. This definition means that syncopation can only occur in monometric music because, as soon as two metres co-occur, ‘disturbance’ in one beat pattern (the ‘abnormal rhythm’) is normally the norm in the other, and because together those two patterns produce a composite norm of cross-rhythm, a single metric unit in a permanent state of contradiction. It’s simply wrong to qualify as syncopated whatever those of us from a monometric background happen to hear as abnormal in terms of shifting up- and downbeats. [5] During the 1990s an increasing number of students in my film music and popular music analysis seminars came from disciplines other than music[ology]. I soon discovered that these students were competent members of the music culture[s] to which they belonged. They could identify significant aspects of musical structure in terms like ‘the chord at 1 minute 40 [seconds]’ (unequivocal timecode designation), or ‘what the drummer does just before the final chorus’ (designation by paramusical synchrony). They were also often better than music students at identifying the expressive qualities of the structures they identified in this sort of way —‘the Celtic folk virgin voice’, ‘the detective chord’, ‘the sexophone’, ‘the tiptoe bass’, for example. It became clear that there was a sharp divide between structural descriptors deriving chiefly from the production of music —poïetic descriptors like ‘head voice tessitura’ and ‘minor major nine chord’— and those based on perception —aesthesic descriptors like the ‘princess voice’ and the ‘detective chord’. It became increasingly obvious that music theory’s structural descriptors, unlike those used in, say, the visual arts, were almost exclusively poïetic and gobbledygook to those with no formal training in music theory. The most disturbing symptoms of this contradiction are of course: [i] that musical analysis is more often than not absent in media education; [ii] that film directors and film composers often have difficulties understanding each other; and [iii] that vernacular musical competence —as in references to, say, the ‘sexy sax’ or ‘tiptoe bass’— is trivialised and academically disqualified. We musicologists have, I fear, largely failed to recognise, let alone systematise, this ubiquitous type of cultural competence. The need for a democratic reform of structural terminology in music is critical in this age of digital media, smartphones, gaming, satellite TV, audio and video streaming or downloading, etc. [6] The final stage in the process of awareness under review started in the late 1990s when I had to write substantial entries on melody, harmony, polyphony and modes for volume 2 of EPMOW (2003), the Continuum Encyclopedia of Popular Music of the World. This task forced me to directly confront the sort of problems I had experienced earlier. It became impossible to even pretend thinking that the terminology of conventional music theory might somehow sort itself out. I felt obliged to raise some sort of alarm. My subsequent efforts to bring at least some semblance of logic to very basic terms of structural denotation started with a small but significant anomaly —what to call chords based on stacked thirds if those based on stacked fourths are called ‘quartal’. I agonised for weeks when writing the article on harmony before realising that I had no alternative but to propose a neologism, as explained in the next section. Then, when asked by Franco Fabbri in 2006 to use those encyclopaedia articles as the basis for a handbook in music theory (Tagg 2009a, 2011b) and by Coriún to contribute to the conference Muscologia y colonialismo (Tagg 2009b), I finally managed to connect the dots. It was not only a matter of scholarly logic but also, as both Franco and Coriún were well aware, of coming up with alternatives to an ethnocentric and class-centric terminology that is also colonialist (Aharonián 1992).

Tonal terminology

Triads and tertial harmony

Ex. 1. Four tertial and five quartal chords

Example 1 shows nine chords, the first four based on stacked thirds ([1] c e g, [2] c e g inverted as e g c, [3] c e g b$ and [4] f a c inverted), the last five on stacked fourths ([5] g c f inverted as c f g, [6] b$ e$ a$ as e$ a$ b$, [7] f b$ e$ as e$ f b$, [8] g c f b$ as c f g b$, and [9] d g c f b$ arranged c d f g b$. Chord numbers 1, 2, 4, 5, 6 and 7 are triads because each contains three differently named tones, chord numbers 3 and 8 are tetrads (four differently named tones) and number 9 is a pentad (five). So far, so good: chords 5, 6 and 7 are quartal triads, chord 8 a quartal tetrad and chord 9 a quartal pentad. The trouble starts when you try to be equally precise about chords 1-4 because many music theorists insist on calling them ‘triadic’ even though chords 5-7 are no less triadic than chords 1, 2 and 4. It is, I suppose, understandable that the stacking of thirds seemed to need no qualification as long as it was considered the single norm from which all other types of tonality were assumed to diverge, but that assumption is clearly untenable as soon as a variety of tonal idioms needs to be described. Therefore, if harmony based on stacked fourths is called quartal, harmony characterised by the stacking of thirds has to be called tertial. The supposed binary triadic/quartal is false because it confuses two distinct criteria for chord denotation —the number of notes in a chord (triadic, tetradic) and the principle of interval stacking in a chord (tertial for thirds, quartal for fourths). It’s worth noting that whereas quartal harmony, the ‘abnormal’ idiom in euroclassical ears, was assigned an adequate qualifier (quartal) the ‘normal’ idiom (tertial) seems to have been considered so normal as to require no qualification. Euroclassical tertial harmony is also sometimes referred to as functional as if other types of tonal polyphony had no function. The fact that the chord loops, shuttles, matrices and turnarounds of popular music styles function either as ongoing tonal-motoric gesture (part of ‘groove’), or as episodic markers, and that change from one ongoing tonal pattern to another can be instrumental in establishing a sense of narrative (diataxis or episodic ‘form’) seems to escape disciples of Riemann or Schenker. I’ve even heard ‘diatonic’ used as a label for tertial harmony as if no quartal polyphony ever visited all notes in a diatonic heptatonic mode: it’s as if the music of Hindemith, Bartók, Freddie Hubbard, Miles Davis, McCoy Tyner, Clarence Ashley and Sokratis Malamas had never existed. Euroclassical tertial harmony is simply one particular (and in terms of narrative construction particularly interesting) variant of tonal polyphony. There are many others but their denotation can, like that of euroclassical tertiality, often be problematic, sometimes to the point of absurdity. Particularly muddle-headed in this context are the two binaries tonal v. atonal and tonal v. modal.

Underlying problem concepts

Basic tonal terms

Before disentangling the contradictory binaries just mentioned I need to posit six axiomatic working definitions. [1] Note: [i] any single, discrete sound of finite duration in a piece of music (midi definition); [ii] any such sound with audible fundamental pitch (for example c1, a low e$3, a 440 Hz, a high f#5); [iii] the duration, relative to the music’s underlying pulse, of any note according to definition [i] or [ii] (e.g. quarter-note, Viertel). The first definition of note will be used in this text: any single, discrete sound of finite duration in a piece of music (the ‘midi definition’). [2] Tone: note with audible fundamental pitch (definition [ii] of note). Tonal means having the characteristics of a tone or of tones. [3] Tonic (n.): reference tone, keynote or tone of central importance in a piece or extract of music. [4] Tonality: system, explicitly codified or not, according to which tones are configured in a musical culture or subculture. [5] Mode: tonal vocabulary, often abstracted and arranged in scalar form for theoretical purposes, of a piece or extract of music. [6] Polyphony: [i] music in which at least two sounds of clearly differing pitch, rhythm, timbre or type of articulation occur at the same time (midi definition); [ii] music in which at least two sounds of audible fundamental pitch occur simultaneously (tonal polyphony); [iii] a particular type of contrapuntal tonal polyphony used by certain European composers between c. 1400 and c. 1650 (restrictive euroclassical meaning). In this article polyphony will refer to music in which at least two sounds of clearly differing pitch, rhythm, timbre or type of articulation occur at the same time and polyphonic will qualify music exhibiting those traits. Drumkit patterns (non-tonal polyphony), melodies with drone or any other form of tonal or non-tonal accompaniment, four-part homophony, rock recordings, etc., as well as a Byrd Kyrie or Bach fugue (all tonal polyphony), are in other words (unlike, say, an accompanied monophonic melody or clave pattern sounding on its own) all polyphonic according to this commonsense definition used, for example, by the music industry to distinguish a polyphonic from a monophonic synthesiser.

Tonal and tonical

The most glaring terminological anomaly in conventional music theory is perhaps that between tonal and atonal music. Schönberg, for one, objected to the label ‘atonal’ because his compositional norms were defined by tonal rules, by twelve tone techniques. Besides, neither he, nor Berg, nor Webern were famous for their use of atonal sounds (atonal in the logical sense of non-tonal): you won’t find much hi-hat, snare drum, maracas or sampled traffic in their œuvre. It is indeed bizarre that euroclassical music theorists managed to confuse the notion of music with no intended tonic, as in the work of twelve-tone composers or in Herrmann’s music for the shower scene in Psycho (1960), with music containing no tones, as in, say, taiko drumming (e.g. Kodō 1985) or Herrmann’s score for The Birds (1963). Using appropriate linguistic derivatives, there are two conceivable solutions to this embarrassing problem: the ‘-al, -ality, -alist’ and the ‘-ic, -ical’ patterns set out in Table 1 (p. 11). Table 1. Linguistically conceivable solutions to the terminological confusion between tone and tonic Pattern 1: —, —al, —ality, —alist[ic] root noun adjective 1 abstract noun adjective 2 centre central centrality centralist form formal formality formalist crime criminal criminality criminalistic sense sensual sensuality sensualist tone tonal tonality ¿tonalist[ic]? Pattern 2: —ic, —ical noun adjective noun adjective comic comical clinic clinical ethic[s] ethical magic magical music musical rhetoric rhetorical polemic polemical tropic[s] tropical statistic[s] statistical tonic tonical Tone, tonal and tonality follow the linguistic logic of centre - central - centrality and form - formal - formality but, unlike those examples of that pattern, tone has no adjective deriving from the abstract noun tonality. Unlike centralist or formalist, tonalist (or tonalistic) just doesn’t exist. If it did, it might be used to qualify tonal music with a tonic, while ‘non-tonalist’ might be used to denote tonal music with none. However, apart from sounding like the name of a political movement —’we tonalists will introduce free mobile ringtones after the next election’— non-tonalist would erroneously imply that tonal music without a keynote had no tonality in the sense defined earlier, no system according to which tones were configured. Since that is patently untrue, the only logical solution is to use the second pattern of derivation to create an adjective ending in -al on the basis of a noun ending in -ic. Pattern 2 in Table 1 suggests that just as clinical things happen in clinics, just as the weather is tropical in the tropics, and just as rhetorical devices (like the ‘just as’ anaphora of this sentence) are used in rhetoric, tonal music that uses a tonic ought to be tonical and tonal music that does not should be called either atonical or non-tonical. That would at least rid us of the illogical uses of ‘atonal’ and ‘atonality’. The next item of widespread terminological disorder is less obviously absurd but it is, I believe, just as questionable. It is also more insidious.

‘Tonal’ and ‘modal’

Let me start with an analogy. I once overheard a French student on exchange at the Université de Montréal saying to one of her québécois classmates ‘Mais vous avez tous un accent ici’. I was struck by the chauvinism of her observation, not least because she was attending the oldest francophone university in the francophone world’s second largest city. It is probably less of a surprise to learn that, here in the UK, it was only a few decades ago that ‘talking with an accent’ (i.e. in any other way than that considered correct at ‘public’ (i.e. private) schools or at Oxbridge) was considered acceptable for BBC announcers and newsreaders. The analogy between the notion of ‘speaking with an accent’ and ‘making modal music’ should be clear. According to such chauvinist thinking it matters not, so to speak, if more people ‘speak with an accent’ than use ‘received pronunciation’, or if they make music using tonal vocabularies (modes) differing from those of the euroclassical canon. In both cases the former, usually practised by a majority, is given a label implying divergence or deviation from an assumed norm usually established by a minority. Indeed, ‘modal music’ in conventional music theory came to mean music in any other mode than the two used in the euroclassical repertoire of the eighteenth and nineteenth centuries. Those two modes are of course the heptatonic major scale (ionian — 1 2 #3 4 5 #6 #7) and the heptatonic minor scale which has three variants. 1. Melodic minor (ascending): 1 2 $3 4 5 #6 #7 (ionianised) 2. Melodic minor (descending): 8 $7 $6 5 4 $3 2 [1] (æolian) 3. Harmonic minor: 1 2 $3 4 5 $6 #7 (ionianised) Only the descending melodic minor corresponds to any of the other European heptatonic modes. The point is that in conventional music theory, tonal vocabularies using the euroclassical major and ionianised minor modes are often qualified as ‘tonal’, as if all other modes were not also tonal, as if their distinctive tonal traits were not also defined by the way their constituent tones are configured in relation to a tonic. That is clearly nonsense because all modes are by definition tonal in that they consist of tones. They are also tonical because they are defined by the way in which their constituent tones are configured in relation to a tonic. Conversely, the ionian mode, the most common tonal vocabulary in the euroclassical repertoire, is rarely, if ever, considered a mode ‘because’, I’ve heard people tautologically say, ‘it’s tonal, not modal’! This terminological travesty not only ethnocentrically relegates ‘modality’ to a state of alterity divergent from a unilaterally hijacked ‘tonal’ norm; also, by excluding the ionian from the realm of modality, it prevents us from investigating which particular characteristics of that mode may have led to its general adoption and popularity in Europe in the seventeenth through nineteenth centuries. It is in this context worth remembering that only two of the seven European heptatonic ‘church’ modes (ionian and lydian) contain raised subtonics (‘leading notes’, #7) and, in terms of harmony, that only the ionian mode features tertial major triads on the prime, the perfect fourth and the perfect fifth. Did the semitonal pull towards the tonic triad of notes inside the other two tertial major triads, one descending (4-3 in IV-I) and the other ascending (#7-8 in V-I), make for a stronger type of tonal directionality than those found in other European heptatonic modes? Did the popularity of the ionian mode, with its #7, lead to alteration of the subtonic in two of the euroclassical tradition’s three minor-mode variants? Did the ionian mode’s two leading notes, one rising and the other falling, make it more conducive to modulation than other available modes? Could any of those other modes have ever led to the development of extensional harmonic narrative, as in the sonata form of the first movement in a Beethoven symphony? I cannot answer any of these questions but I also fail to see how any light can be shed on such matters if the ionian is not considered as one mode among several. The terminological appropriation of ‘tonal’ to refer to just one set of tonal practices during a brief period in the history of the world’s smallest continent is, to say the least, problematic. The false dichotomy ‘tonal v. modal’ is one example of the confusion, the terms ‘pre-tonal’ and ‘post-tonal’ another, since they both patently imply that medieval and early Renaissance music (‘pre-’) is as devoid of tones as twelve-tone music (‘post-tonal’, ‘atonal’, etc.). And what about, for example, the anhemitonic pentatonicism in widespread use all over this planet before, during and after the so-called ‘tonal’ period, or of the widespread use of tertial ionian harmony in today’s supposedly ‘post-tonal’ era? This unilateral confiscation of ‘tonal’ has obvious repercussions on the notion of tonality.

Tonality, Grammaticality, Tonart, Tonalité

‘Tonality’ is still used by some scholars of music to denote the practices they consider tonal in the restrictive sense just criticised. Used in that way, ‘tonality’ refers to one system, and one only, according to which tones are configured. Just imagine if grammaticality could only refer to the grammatical rules of just one language or group of languages, for example to English or to Neo-Latin and Germanic languages, in which correct use of definite and indefinite articles is a central element of grammaticality. Such restrictive use of the term would mean that Chinese, Farsi, Hindi, Indonesian, Japanese, Russian and hundreds of other widely spoken languages which use no definite articles would not be considered grammatical. Such an implication would cause considerable uproar among comparative linguists but I have yet to come across uproar among musicologists against an equally restrictive use of the word tonality. That’s why I propose that tonality should mean the system or set of norms according to which tones are configured in any musical culture. However, even if that much less ethnocentric definition solves one important problem, it raises another. The broader definition just presented works well in English and in Germanic languages where tonality/Tonalität is distinguished from the concept of key/Tonart. In Neo-Latin languages, however, tonalité, tonalità, tonalitate, tonalidad and tonalidade tend to mean key/Tonart rather than tonality/Tonalität which, consequently, requires another expression to clarify the distinction. As a native anglophone I am hardly in a position to advise speakers of Catalan, French, Italian, Spanish, Portuguese or Romanian how tonality/Tonalität should be translated but I would have suggested to students at the francophone Université de Montréal who were uncomfortable using tonalité in both senses that they might consider, at least as a stop-gap solution, an expression like idiome tonal or système tonal to cover the concept tonality/Tonalität and stick to the more common use of tonalité as equivalent to the Anglo-Germanic concept of key/Tonart. I fully realise how unsatisfactory this suggestion may be and would be grateful to hear suggestions from colleagues in Iberia, Italy, Latin America, Romania and the francophone world as to how this conceptual problem might be resolved.

More ‘norms’

The confusion and culturally restrictive character of central concepts referring to tonality in conventional music theory runs deep in the details of structural description. I’ve already mentioned the problems of tonal, atonal and tonical, as well of tertial and quartal. I will end this part of my text with a very brief account of two interrelated problems: harmonic cadence nomenclature and monomodality.

Harmonic cadence nomenclature

There are four main harmonic cadence types in the conventional theory of euroclassical music. Two of those cadence types take one step flatwards, the other two one step sharpwards round the circle of fifths. The centrality of the flatwards V>I perfect or final cadence in euroclassical tonality needs no introduction but the three others warrant some discussion that can shed light on conceptual problems with the nomenclature of all four types. The two cadences which proceed clockwise round the circle of fifths are the half or imperfect cadence and the plagal cadence. The second anticlockwise type is usually called an interrupted cadence. The half cadence is so called because it marks the harmonic change from I to V in extremely common harmonic schemes like I V V I over a period of, say, four, eight or sixteen bars in which V is the obvious halfway house (ex. 2). A typical half cadence, like that in bars 3-4 of example 2, which proceeds from I to V, is a cadence because it marks a resting point on a different chord to the preceding one; and it is ‘half’ because it marks that change halfway through a longer harmonic scheme, such as the eight-bar period of ex. 2. It is an imperfect cadence because, in this context of ionian tertial tonality, it has no finality. By marking the end of a phrase or smaller part of a larger unit, of which half is still to come, it has the opposite effect of the perfect cadence V>I. Put simply, half or imperfect cadences (I>V) in ionian-tertial tonality serve rather to open up harmonic processes and perfect cadences (V>I) to close them. Ex. 2. Half/imperfect cadence : E viva España (Vrethammar, 1973). Ex. 3. Mila moja (‘A’ section; Serbian trad., quoted from memory) However, the notion that I>V cadences are intrinsically imperfect, incomplete or suspended obviously makes no sense in example 3, with its fermata and Fine on the final A. Of course, it’s doubtful if A is actually a V chord at all. It certainly can’t be a ‘dominant’ if it’s the piece’s final harmonic resting place. That in turn begs the question as to whether the tune is actually ‘in’ D. It’s more likely conceived according to quite different tonal norms. Like their ‘imperfect’ cousins, plagal cadences also run clockwise round the circle of fifths, but not from I to V. Instead they take the single sharpwards step IV>I. Since they end on the tonic, plagal cadences involve harmonic closure, as is evident from their use as the Amen chord formula par excellence. That said, it’s significant that medieval music theorists chose the Latin word for ‘oblique’ (plagius, from pl‹gioû meaning sideways, slanting, askance, misleading —the same etymological connotations as in plagiarism) to distinguish certain modes, not chords, from their ‘authentic’ variants. It’s also interesting to note how the same adjective connoting falsity came to qualify the chordal ‘Amen ending’ IV>I. Plagal cadences may in other words be endings but conventional music theory does not qualify them as true, authentic, direct, complete, full, final or perfect. Those adjectives are of course reserved for the perfect cadence V>I. Interrupted cadences in euroclassical tonality do exactly what their name suggests: they interrupt a V>I cadence by substituting I with a closely related chord, usually the common triad on degree 6 of the relevant key, V>vi, or sometimes V>VI, or, less commonly, V> $VI. Proceeding from V to vi (or VI) is of course an efficient way of interrupting euroclassical finality because, in that tonal tradition, vi or VI leads anticlockwise round the circle of fifths, via ii or II back to V again and the final/full/perfect cadence V>I. It’s also significant how the interrupted cadence (V>vi) is referred to in other European languages as ‘deceptive’ (cadence trompeuse, Trugschluss, cadenza d’inganno), ‘broken’ (cadence rompue) and ‘avoided’ (évitée). If anything demonstrates the ‘normality’ of V>I closure in conventional notions of euroclassical harmony it must surely be the distinction between qualifiers like, on the one hand, half, incomplete, plagal/oblique, interrupted, deceptive and false; and, on the other, perfect/final/full (V>I). However,… Ex. 4. Uninterrupted final cadence on vi: Um Um Um Um Um (Wayne Fontana and the Mindbenders, 1964): final refrain and ending. I’ve included example 4 as evidence that there need be nothing interrupted, oblique, deceptive, false, unauthentic, incomplete, or imperfect about a final cadence landing on vi (F#m), the relative minor triad of the song’s previous tonal centre (I in A major). There’s even a ritenuto and change of rhythmic articulation to underline finality —zl. |h | instead of the usual zl z;h . In short, euroclassical cadence categories and assumptions about harmonic direction may be fine for the musical-cultural practices on which such conceptualisation is based but it is absurd to assume that those categories and concepts apply to any other body of music To make this point quite clear, example 5 presents an unambiguously uninterrupted final melodic cadence from ‘pre-tonal’(!) times. That’s followed by two equally uninterrupted ‘interrupted’ cadences from ‘post-tonal’ (!) times (examples 5 and 7). Ex. 5. Psalm tone 2 (end of final Gloria Patri simplified) Ex. 6. Beatles: Not A Second Time (1963c: uninterrupted æolian cadence and I-vi/$III-i shuttle in fade-out) Ex. 7. Los Calchakis: ‘Quiquenita’ (Argentinian trad.); La flûte indienne, 1968) ― bimodal loop: $VII $III V i or IV I III vi?


While examples 4 and 5 illustrate final ‘uninterrupted’ cadences, examples 5 and 7 do not: they are simply ‘uninterrupted’ and carry no definite sense of finality. The Beatles tune (ex. 5) fades out over a shuttle between G major and E minor and although the actual Flûte indienne recording (ex. 7) ends on E minor it could go on repeating the loop [ C G B Em ] in aeternam. Now, students of conventional music theory are expected to identify the key of any tonical music they are asked to analyse. One obvious clue in euroclassical music is of course the final chord of the piece but in example 4 that clue would be quite misleading because the recording spends more time in A major than F# minor even if it cadences each verse and the whole performance on the latter. With the fade-out over a G«Em shuttle in example 5 and with the constant loop of example 7 the notion of a single tonic becomes even more untenable. As Carlos Vega noted (1944: 160) with reference to criollo song: ‘No hay melodias en mayor y melodias en minor: hay simplemente melodias bimodales’. Bimodality is common in many popular styles from Latin America and the British Isles. Apart from the I«vi or $III«i shuttle of examples 5 and 7, another variant of harmonic bimodality in Latin America is the familiar harmonic minor loop [ i iv V V ] (e.g. F#m Bm C# in ex. 8, b. 1-12) which, when the poles are reversed from ascending to descending (e.g. F#m E D C#, ex. 7, b. 13-16) becomes a phrygian sequence in C# (iv $III $II I). Ex. 8. Carlos Puebla: Comandante Che Guevara: æolian and phrygian. The next example (no. 9, p. 21) is closer to my home (Yorkshire) and provides a different slant on the issue of bimodality. What is the tonality of this tune? What key or mode is it in? Well, if the start and ending plus the recurrence of open-fifth C dyads (C5) in the guitar part (bars 1, 3, 7, 11, 15, 16) are anything to go by, it’s ‘in C’. Ex. 9. Steeleye Span: The Female Drummer (Eng. trad., rec. 1971) Some of my music students have on first listening heard the tune as C dorian, but I have to point out that no third, neither e@ nor e$, occurs anywhere in the recording: it might just as well be mixo-lydian with no major third. In short, no-one in the classroom, including myself, is really sure how the piece’s tonality should be denoted. Apparently hexatonic (c d f g a b$) and neither ‘major’ nor ‘minor’, it defies description using the sort of euroclassical music theory most of us have learnt. One way out of this conceptual impasse is to consider the tune as having two modes, each based on its own tonal centre: [1] as an anhemitonic pentatonic scale based on the tonic (c) and including heptatonic scale degrees 1, 2, 4, 5 and $7 (c d f g b$); [2] as a pentatonic major mode based on the first mode’s subtonic (b$) and including the same five notes (b$ c d f g) in relation to that b$ as (heptatonic) scale degrees 1, 2, #3, 5 and #6, plus the additional hexatonic #7 (a@). Table 2. Configuration of tonal poles in The Female Drummer (ex. 9) bar > 1 2 3 4 5 6 7 8 c y y g y g b$ y y y ­ tonal pole ¯ 9 10 11 13 13 14 15 16 c f y g y y b$ y y y As shown in Table 2, the first mode, based on c, occupies bars 1, 3, 7, 11, 15 and 16, while the second mode, with its tonal centre b$, is heard in bars 2, 4 (including the final a@ in bar 3), 5, 10, 12 (including the a@ upbeat) and 13. That leaves bars 6, 8, 9 and 14 which the guitarist marks with either the fifth above c (g in bars 6, 8 and 14) or the fifth above b$ (f in bar 9). This sort of fluctuation between two tonal poles that I call the (main) tonic and the counterpoise (c and b$ in example 9) is typical for many tunes from pre-industrial Britain and Ireland. It can be configured in a large variety of ways to generate interesting patterns of tonal movement and of periodicity —regular or irregular, equal or unequal—that, judging from the obvious difficulty I’m having in describing the phenomenon, seems to have no ready structural descriptors. Moreover, while the b$ mode (b$ c d f g without the additional a@) has two relatively familiar names —anhemitonic major pentatonic or, to use Kodály’s terminology, doh-pentatonic—, the pentatonic mode on c in example 9 —c d f g b$— is virtually unknown in tonal traditions where the presence of heptatonic scale degree 3 is essential. Containing scale degrees 1, 2, 4, 5 and $7, it’s neither major nor minor but, as shown in Table 3 and continuing with Kodály’s naming system, ré-pentatonic (ré mi sol la doh). It covers a$ to a$ on the black notes of a piano keyboard (a$ b$ d$ e$ g$) or d to d (d e g a c) on the white notes. And what about the melody in bars 6, 8, 9 and 14, none of which can be unequivocally assigned to either ré-pentatonic mode 1 or to hexatonically extended doh-pentatonic mode 2 even if the tune in those bars theoretically fits both? Are we perhaps hearing part of a G minor pentatonic mode (la-pentatonic on g) in bars 6, 8 and 14, and an F major pentatonic mode (do-pentatonic on f) in bar 9? The guitarist clearly seems to be hearing things that way in those bars. The question is how these variants of the two underlying pentatonic modes and the shifts in tonal nuance they produce should be denoted. I don’t know. Does anybody? Table 3. The five anhemitonic pentatonic modes Mode name Black notes only Heptatonic scale degrees White notes doh-pentatonic g$ a$ b$ d$ e$ [g$] 1 2 #3 5 #6 [8] c d e g a [c] ré-pentatonic a$ b$ d$ e$ g$ [a$] 1 2 4 5 $7 [8] d e g a c [d] mi-pentatonic b$ d$ e$ g$ a$ [b$] 1 $3 4 $6 $7 [8] e g a c d [e] sol-pentatonic d$ e$ g$ a$ b$ [d$] 1 2 4 5 #6 [8] g a c d e [g] la- pentatonic e$ g$ a$ b$ d$ [a$] 1 $3 4 5 $7 [8] a c d e g [a] Numerous other questions of structural designation arise from the problems just discussed. For example: • How do the two thirdless anhemitonic pentatonic modes on sol and ré (d$-d$ and a$-a$ respectively on the piano’s black notes) relate to principles of quartal harmony? • How can different quartal chords be denoted, also in abbreviated form, instead of being mistakenly identified in tertial terms like sus4 when harmonic suspension is neither intended nor heard? Are indications like C5 (open fifth dyad c-g), or C4,5 (triad c-f-g), C2,5 (triad c-d-g), C4,5,$7 (tetrad c-f-g-b$) of any use, or can such chords be labelled more efficiently? • Why do hexatonic modes seem to lack labels when each of the seven diatonic heptatonic modes has its own name? • Could the Guidonian hexachord be of any use in the systematisation of hexatonic modes and, if so, how? Or should we be thinking in terms of Arabic, Persian or European medieval tetrachords, or of hand shapes on stringed instruments? • How useful might Glarean’s hypomodes be in understanding the different types of bimodality of examples 4-9? • Could the concepts of vadi and samvadi in the theory of classical music from Northern India be applied in any useful way to the dynamic between what I call main tonic and counterpoise? • What do we call tertial ionian tonality in the euroclassical tradition and how do we conceptually distinguish it from the tertial ionian tonality of tunes like La Bamba or Guantanamera? I don’t have answers to any of these questions and look forward to suggestions from others struggling with similar problems.


Syntax and diataxis

According to the Oxford Concise English Dictionary (1995), Form means the shape or pattern into which different parts or elements are arranged, ordered, or otherwise combined into a whole. For example, the three words in the two sentences Tim hit Tom and Tom hit Tim have the same form ―subject - verb - object― but different meanings. In this instance form is a matter of English-language syntax created by presenting the constituent elements in a particular order. Syntax also exists in music in that, for example, melodic phrases consist of at least two motifs (Tagg, 2000a: 289-295). Ex. 10. Mozart: Symphony no. 40 in G minor (K550), I: (a) start of first theme; (b) commutation using same syntax; (c) different syntax Examples 10a and 10b are, as meaningful statements, as different as Tim hit Tom is from Tom hit Tim. At the same time, just like Tim hit Tom and Tom hit Tim, examples 10a and 10b share a common syntax consisting of a repeated initial motif followed by a different terminal motif highlighted by the preceding repetition. Example 10c, on the other hand, uses another syntax featuring initial and terminal motifs of equal duration without repetition. It’s a different musical statement not just in terms of the ordering but also of the relative importance of its constituent elements. Now, despite the dictionary definition of form, conventional Western music theory rarely considers such aspects of syntax in terms of form. Instead it uses form almost exclusively to designate the way in which episodes or sections rather than motifs are ordered along the unidirectional axis of passing time to create extensional patterns of musical change and recurrence like ‘sonata form’ or ‘rondo form’. This long-term, linear, episodic, ‘horizontal’ or ´diachronic’ sort of form needs to be distinguished from the ‘short-term horizontal’ type of form (syntax) operative in the construction of musical phrases. Diataxis was the least ambiguous word I could find to mark that distinction between those two types of form. But that is neither the only nor most important reason for having to come up with a new term. Contemplating a bush may help explain why the neologism was necessary…


The bush on the left is shaped like a mushroom. Its constituent elements —branches, twigs, leaves, etc.— have been purposely cut, pruned and trimmed (arranged) into a particular form. It may have taken years to produce that form but its perception as a ‘mushroom form’ is pretty immediate. Form in conventional painting, sculpture and photography has no diachronic aspect because perception of its constituent elements does not unfold over time, as in music, dance or film. Form in the visual arts is usually called ‘composition’ and refers to the synchronic arrangement of a work’s constituent elements which are, so to speak, fixed on the canvas, or in the sculpture or photo. Neither those elements nor the form in which they are presented change once you start viewing the work, even if you interpret them differently the longer or more attentively you look, or if you view the work in a different context or under different circumstances. Among the parameters defining form (‘composition’) in the visual arts are size, proportion, perspective, positioning and orientation of constituent elements, the viewer’s point and angle of entry, colour, negative space, contrast, symmetry and lighting. Several of the parameters just enumerated are relevant to music, not least the synchronic placement and relative importance of constituent elements. As I’ve suggested elsewhere (Tagg, 2013: 235), explanations of musical semiosis need to consider several individually meaningful layers that sound simultaneously. These composite layers of simultaneously sounding musemes —museme stacks— constitute form within the limits of the extended present. The museme stack shown as example 11 lasts four seconds (8 beats at l=120, well within the limits of the extended present. It’s heard 16 times, with a few variations, in the recording before it’s replaced by a slightly different groove. It has by definition a form because it contains several constituent elements —the jil L on guitar and bass, jjjl on violins and flute, zl il_z on trombones plus hi-hat and kick drum patterns (not shown)— all arranged into an identifiable whole (Gestalt) that repeats as a single unit. This sort of form is neither short-term syntax nor diataxis. Since it’s perceptible within the limits of the extended present ―typically as a composite of aurally staged, simultaneously sounding motifs, riffs, chords, instruments, voices, timbres, pitches, rhythms, etc. in a particular metre at a particular speed and dB level― it can be considered synchronic. Ex. 11. Museme stack (excl. drumkit) at in Shaft (Isaac Hayes, 1971) Moreover, since stacking (as in ‘museme stack’) implies height rather than length (‘museme string’), this synchronic type of musical form can also be thought of as more vertical than horizontal, more intensional than extensional. It takes the form of a state more than of a process or narrative, even though it can contain elements of short-term syntax. If this sort of form, a composite of ‘now sounds’, is neither syntax nor diataxis, what can we call it? I’ve opted for the word syncrisis.

Summary (‘form’)

To summarise, it’s essential to consider at least three types of musical form. I distinguish between them as follows. 1. Syntax denotes aspects of form and signification bearing on the temporal relationship of constituent elements. It usually covers the short-term ordering of elements inside the extended present. 2. Diataxis is the long-term, diachronic, processual and episodic aspect of syntax covering the extensional ordering of events over durations exceeding that of the extended present. It can be thought of in terms of overall narrative form, and as horizontal rather than vertical. In conventional Western music theory diataxis is usually called ‘form’, as if no other type of musical form existed. 3. Syncrisis denotes aspects of form and signification bearing on the synchronic, intensional, arrangement of structural elements inside the extended present. It can contain elements of short-term syntax and be thought of as vertical stacking rather than as a horizontal array. Conventional music theory’s conceptual monopolisation of ‘form’ is similar to its hijacking of ‘tonality’. The main difference is that while the conceptual falsification of tonality gives rise, as I explained earlier, to a seriously flawed terminology —’tonal’ versus ‘atonal’, ‘modal’, ‘pretonal’, ‘post-tonal’, etc.—, its inability or reluctance to deal with types of form other than diataxis constitutes an error of conceptual omission. Particularly serious is its neglect of syncrisis, more precisely the theoretical tradition’s failure to conceptualise form as an important dynamic, kinetic, synchronic, intensional, textural, tactile, spatial or ‘vertical’ state contained within the extended present (syncrisis). There is in other words no good reason why narrative processes in music (diataxis) should be prioritised at the expense of music’s dynamic states (syncrisis), especially in relation to musics where the latter, rather than the former, is of primary interest.

So what?

Although I’ve tried to suggest solutions to some of the problems discussed above, much of this text consists of questions and ‘don’t knows’. I’ve been unable here to discuss the description of timbre, vocal persona, or periodicity and I’ve done no more than skim issues of tonality and form. There are clearly many more issues of structural conceptualisation left to confront I hope nevertheless to at least have clarified how unreasonable and misleading it is to use terms like dominant, subdominant, perfect cadence, half cadence and interrupted cadence when describing tonality in the countless pieces of widely heard music in mixolydian, dorian, æolian or phrygian modes, where ‘half cadences’ and ‘interrupted cadences’ are often final, and where major tertial triads on scale degree 5 (V) are either altered from mode-specific minor triads or non-existent? In mixolydian, dorian and æolian rock harmony, for example, a ‘dominant’ tertial triad is most likely based on the fourth (IV, the ‘subdominant’ in euroclassical music theory) and a ‘subdominant’ chord on the unaltered subtonic ($VII) which, according to the music theory I was taught, apparently either has ‘no function’ or is a ‘subdominant to the subdominant’ which cannot exist because there is no dominant to which it can reasonably be ‘sub-’. In short, difficulties in the structural designation of non-euroclassical tonality can be crippling. It ought also to be clear that notions of form are extremely problematic because, as we just saw, only one of three main categories —diataxis— qualifies as ‘form’ in conventional ‘music theory’, while the other two —syntax and syncrisis— are at best sidelined, more often simply ignored as if they did not exist. ‘But do these problems really matter?’, objects my populist muso alter ego. ‘After all’, he argues, ‘we’re talking about music that is played, heard and felt. And besides,’ he says, ‘if you start to codify it you’ll just end up with another set of fixed rules that can be taught year after year in the academy. That’ll be no better than the system you’re currently criticising’. My musician devil’s advocate is both right and wrong. He’s right to point out the dangers of institutionalised codification but wrong to single out codification rather than its institutionalisation as the problem. Obviously, codified ‘rules’ extrapolated from existing practices easily become ‘fixed’ and normative if they are used to maintain a status quo of power established after their introduction into the institution. Among mechanisms conducive to such entrenchment are: [1] managerial inertia and short-term cost-cutting (the same courses with the same teacher is cheaper and less hassle); [2] not giving teachers enough time for research and innovation (it’s more profitable to teach more students with fewer teachers); [3] discouraging or marginalising teachers who might upset the apple cart; [4] preoccupation with league-table scams that force institutions to conform to a relatively homogenous set of activities so as to facilitate comparison on a scale of quantifiable ‘excellence’ (a conservative mechanism intrinsic to the magic market’s credo of ‘free’ competition). In addition to those four points it should also be remembered that teachers and researchers have to earn a living by working in such institutions, that they need to pay their rent or mortgage, send their children to school, etc., and that a few colleagues may have personal problems relating to careerism, self-aggrandisement, financial gain, positions of power, etc. All these factors mean that the risk of epistemic entrenchment and inertia is high. Indeed, my muso alter ego is right to the extent that such mechanisms of institutionalisation are prerequisites for the terminological chaos criticised in this article. However, as I try to explain by way of conclusion, none of this means that necessary terminological reform is either dangerous or pointless. On the contrary. If the tonal and formal practices of music other than the euroclassical and its offshoots remain uncodified, the terminology of conventional euroclassical music theory will stay unchallenged and continue to marginalise, trivialise and falsify all types of music exhibiting important traits for which it has either flawed concepts or no concepts at all. Not only would that prolong the undemocratic disrespect and embarrassingly ethnocentric ignorance it seems to show towards so many musics used by a majority of the world’s population; it would also, as I argued earlier, obstruct efforts to understand what made the musical tradition on which it based that same terminology both interesting and influential. Moreover, even though no-one can ever possibly understand every musical tradition existing at any time anywhere in the world, less inadequate concepts of musical structuration can at least give us a better chance of understanding how different types of music actually work. For example, insight into the workings of phrygian tertial harmony, as used by master flamenquistas like Sabicas (n.d.), or by Carlos Puebla and his son musicians (ex. 8), or by Chilean ‘good-time’ band Los Trukeros (2007), could have prevented at least one otherwise gifted young guitarist from attaching an extra ‘perfect cadence’ (E>Am) to the end of a malagueña performance that he had already ended with a resoundingly final $II>I phrygian cadence (F>E), complete with its three simultaneously descending leading semitones (c>b, a>g#, f@>e).

Final reflexions

This article has dealt with only a very small number of conceptual problems in conventional euroclassical music theory. Despite difficulty in presenting some structural points because I could find no vocabulary with which to designate them, I chose to limit the discussion to a few aspects of tonality and form for two interrelated reasons. The first is purely logistic in the sense that tonal and formal parameters are easier to put into the scribal form intrinsic to the medium of this text than are parameters of, say, timbre or aural mise-en-scène. The other reason is that conventional music theory has developed numerous terms to denote tonal and formal features specific to the euroclassical repertoire, fewer to denote those relating to time, speed, rhythm, metre, periodicity, etc., and far, far fewer to denote aspects of timbre and spatiality. Tonality and form are in other words areas of study in which music theorists are supposed to excel. I ought in other words to be able to assume that they will fully understand what I write or say on the topic. But will they? Having, in October 2011, given the first live presentation of ideas contained in this text, I can report that reactions were in general encouraging on fourteen of sixteen occasions. On one of the other two occasions (a depressingly conservative international music analysis conference) I was met with compact silence. After my talk, a helpful research student told me in the corridor that most participants thought I was causing unnecessary trouble and that they just wanted to regress into the ‘business as usual’ of their ivory towers. The other negative experience was at a postgraduate seminar in a university music school where I spoke to an audience of three. On that occasion I learnt from one of the three that my ideas were likely to be interpreted as an attack on the authoritarian intellectual agenda promoted by influential members of staff at the institution. In both instances I was clearly living on an epistemic planet radically different to that inhabited by the intellectually or literally absent audience. The other fourteen occasions were decidedly less alienating. That does not mean I met no critical comments in discussions following my presentation. For example, one student feared that cleaning up the terminology would just create another set of useless rules that students would have to follow. On another occasion, a senior professor of composition expressed a different kind of scepsis. ‘Of course you’re right and what you say is perfectly logical’, he said, ‘but there’s not a hope in hell that anything will come of it!’ That comment seemed quite realistic in the light of what I’d experienced on the two occasions sketched on the previous page. I was, however, able to assure him that I would not be dissuaded from efforts to bring some semblance of reason and socio-ethnic justice into the terminology of music theory. I’ve drawn considerable encouragement in this quest from the sort of reactions summarised below. At one seminar an experienced teacher recounted his embarrassment at having to use, as he put it, the ‘stupid word atonal’ when teaching composition and the history of twentieth-century music. ‘Tonical’, he agreed, might solve that problem. Elsewhere, those with experience in music outside the euroclassical and avant-garde spheres tended to go straight to the heart of the matter, several of them raising specific questions about designating particular structural features of non-euroclassical tonality. In fact the discussion of tonality in The Female Drummer (example 9 in this text) is largely the result of a question asked in the seminar at Glasgow University and of subsequent email correspondence with the member of staff who asked it. At Glasgow, with its strengths in composition and performance, at the Aarhus music department with its attachment to the university’s School of Media, as well as on all the other twelve occasions, several teachers and students wanted to discuss other ways in which music theory might be reformed. Of particular importance, they thought, was the development of concepts denoting aspects of timbre, kinetics, tactility and spatiality, a vocabulary acknowledging the vernacular competence of the listening majority who are exposed to an average daily dose of music lasting more than two hours. I agree with them and have elsewhere suggested ways in which musicology can contribute to that sort of development. Nevertheless, there can be little doubt that music theory, as it is still widely taught, is in need of terminological reform that opens up to all sorts of music and that such reform goes hand in hand with the interdisciplinary and democratic process requested by many of those I met when speaking about this topic. Most recently (July, 2013), I sent a short statement about the need for terminological reform to the IASPM email list. Here are just a few of the comments I received, from 34 individuals in 14 nations, in answer to that statement. ‘I've taught analysis in my [Latin-American] university for 25 years and I've met the same problems as you… We even tried to set up a musical terminology commission ten years ago but’... ‘I'm interested in developing appropriate discourse for subtle variations of intonation in... traditional music and trying to break free of a general analytical hierarchy. Popular music should never have been tackled as it were 18th-century western art music.’ ‘I'd like to see... a radical movement in multimodal semiotic analysis which… sweeps away the… terminology of Euro-American musicological theory and starts from the work [some authors] have already done in pointing out an… egalitarian terminology for a social semiotics of music.’ ‘I think “music theory” itself needs rethinking… I’m interested in how the musical vocabulary of other languages addresses these areas.’ ‘I was raised in a wide range of musical traditions. Then I recently studied musicology, so had to confront all those [strange terms]… Well, with the [local/regional/national] musical traditions I know... Wow! A lot of those terms just don't work at all.’ ‘I’m a teacher… interested in the reform of music teaching in secondary schools… The concepts/elements of music are becoming more central to music education and teachers here don’t know what they really are nor how to teach them. I’m keen to help build clarity on this!’ I still find myself emitting sighs of despair and disbelief each time I read or hear tonal opposed to modal, triadic instead of tertial, etc. I also find it depressing to read or hear form used to designate the order of the music’s episodes and nothing else. That said, I have to admit that I’m probably more frustrated with myself than with those who still perpetuate such conceptual falsehoods because, with my ‘unusually eclectic’ musical background, I was better placed much earlier in life than those with a more exclusively euroclassical upbringing to register the problems and to try and solve them. The fact that it took me nearly thirty years to do so to any significant extent is shameful and I can offer no valid excuse for such sluggishness. However, now that some of the basic problems are out in the open, I would urge everyone in music education and research to think at least twice before applying any concept of structural designation to any type of music if those concepts derive from conventional euroclassical music theory. After all, whereas I may have been ‘unusually eclectic’ in 1971, I am, if the students I’ve met since the late 1980s are anything to go by, no longer the exception but the rule. It would simply be embarrassing, if nothing else, for music studies to persist with its illogical, undemocratic, outdated, ethnocentric and muddle-headed ‘business as usual’. I think it’s high time for ‘music theory’ to grow up and to embrace social and musical realities in the real lives of real people.



This appendix contains all types of reference. To save space, the following symbols are used: b bibliographical source (written word). t audiovisual source; D dvd; 0 audio source; E YouTube file. Please also note that: ― The http://www prefix is removed from internet references. ― E replaces the string <http://www.youtube.com/watch?v=>― Dates of access to materials on the internet, including YouTube files, are expressed in the format yymmdd so that, for example, [111111] means 11 November 2011, [100521] 21 May 2010, etc.


b Aharonián, Coriún (1992) ‘Identidad, colonialismo y educación musical’. Conversaciones sobre música, cultura e identidad. Montevideo. b—(2002) Introducción a la música. Montevideo: Tacuabé. 0 Alexiou, Haris [Χάρις Αλεξίου] (1976) ‘Τρεις η ώρα νύχτα’ and ‘ Απ΄ τον περασμένο Μάρτη’. Σταύρος Κουγιουμτζής: Λαϊκές Κυριακές. Minos EMI Labelsound 72434 8013927 (2000) b Apel, Willi (ed., 1958). The Harvard Dictionary of Music. Cambridge, MA: Harvard U.P. 0 Beatles, The (1963) ‘Not A Second Time’. With The Beatles. 0 Parlophone PCS 3045/PMC 1206. The Birds (1963) F Universal f Hitchcock c Bernard Herrmann. 0 Calchakis, Los (1968) ‘Quinquenita’. La flûte indienne. 0 Barclay Panache 920014. 0 Como, Perry (1946) If You Were The Only Girl (In The World) c Nat D Ayer (1916) 0 hmv bd 1165. b Davis, Bob (2005) Who Got da Funk? An Etymphony of Funk from the 1950s to 1979. PhD, Faculté de musique, Université de Montréal G tagg.org/bookxtrax/DavisFunkPhDv1.pdf [2012-11-15]. b EPMOW (2003) The Continuum Encyclopedia of Popular Music of the World, Volume 2, ed. John Shepherd, David Horn, Dave Laing, Paul Oliver and Peter Wicke. London & New York: Continuum. 0 Er Malyk/Eр Mалък (1992) ‘Скоропоговорка’ (Skoropogorvka = tongue-twister) Eр Mалък 1 L KTM (Sofia). 0 Fontana, Wayne [and the Mindbenders] (1964) Um Um Um Um Um. Fontana H 497; cover of > Major Lance (1963). b Hall, Anne C (1992). Review of Meyer (1989 q.v.). Music Theory Spectrum, 14/2: 209-213; Univ. California Press/Society for Music Theory |www.jstor.org/stable/746108| [111111]. b The Harvard Dictionary of Music (ed. W. Apel et al., 1958) Cambridge, MA: Harvard U.P. 0 Herrmann, Bernard (1960) Psycho (Colonna sonora originale). 0 RCA Cinematre NL 33224 (1975). F — The Birds (c 1963) F Universal f Hitchcock. t Hickory Dickory Dock (n.d.) E A7xYz5P_rCw [111205]. b Hindemith, Paul (1961) A Composer's World. New York: Anchor/Doubleday. 0 Kodō (1985) ‘Miyake’. Kodō – Heartbeat Drummers Of Japan 0 Sheffield Lab – cd-kodo E juT0drDIcvw [111128]. b Kristeva, Julia (1988) Étrangers à nous-mêmes. Paris: Fayard. b Lacasse, Serge (2000) Listen to My Voice: The Evocative Power of Vocal Staging in Recorded Rock Music and Other Forms of Vocal Expression. PhD diss., Institute of Popular Music, University of Liverpool. www.mus.ulaval.ca/lacasse/texts/THESIS.pdf| [101021]. b Ladzekpo, C K (1995) Foundation Course in African Dance-Drumming Berkeley: University of California. https://home.comcast.net/~dzinyaladzekpo/Foundation.html [120725]. b Ling, Jan (1989) ‘Musik som klassisk konst. En 1700-talsidé som blev klassisk’. Frihetens former - en vänbok till Sven-Eric Liedman. Lund: Arkiv: 171-187 [=Music as classical art. An 18th-century idea that became classical]. 0 Major Lance (1963) Um Um Um Um Um (cj Curtis Mayfield), Okeh 4-7187; also on Major Lance — Swingin'est Hits, CBS P 17702 (1984). D Málamas, Sokrátes (2006) ‘Πριγκηπέσα’ (= Princess). Αλεξίου/Μάλαμας/Ιωαννίδης Live στο Λυκαβηττό, Σεπτέμβριο του 2006. minos-emi 094639249121. R0 Ο φύλακας και ο βασιλιάς (=The Guard and the King), Lyra CD 0798 (2000). b Mattelart, Armand; Neveu, Érik (1996) Cultural Studies’ Stories. La domestication d’une pensée sauvage? Paris: Réseaux no. 80 www.cnet. enssib.fr/autres-sites/reseaux-cnet/80/01-matte.pdf [110717]. b Meyer, Leonard B (1989) Style and Music: Theory, History and Ideology. Philadelphia: University of Pennsylvania Press. b Peñalosa, David (2009) The Clave Matrix: Afro-Cuban Rhythm, its Principles and African Origins. Redway, CA: Bembe Inc. 0 Puebla, Carlos (1965) ‘Hasta siempre’; ‘Che Guevara’. Marchas y canciones revolucionarias. Arito 3310 (n.d., c. 1970); also on Cantarte Comandante, egrem CD-0259 (1997). 0 Norman, Monty (1962) Theme from Dr No (a.k.a. James Bond Theme); on The Best of Bond, United Artists UAS 29021 (1975); tagg.org/audio/DrNoBondVinyl.mp3; see also E mF_6cSads0E and www.itunes.apple.com/us/artist/john-barry-orchestra/id133904310 [both 100923]; also dvd Dr No (ntsc) mgm 0-7298-4528-5 (n.d.) at 0:00:00. t Sabicas (Agustín Castellón Campos, n.d.) Malagueña (with Maria Alba and Company) E A3Iq0Qs0GAI [080609]. 0 Steeleye Span (1971) ‘Female Drummer’ (c Yorkshire Trad., via The Watersons and Bert Lloyd). Please to See the King. Crest 8. b Tagg, Philip (1979) Kojak: 50 Seconds of Television Music. Towards the Analysis of Affect in Popular Music. Göteborg: Musikvetenskapliga institutionen, Göteborgs universitet (out of print); 2nd ed. (2000): New York: MMMSP. tagg.org/mmmsp/kojak.html [111111]. b—(1989) ‘Open Letter about “Black” and “White” Music’. Popular Music, 8/3: 285-298; original version (1987) at www.tagg.org/articles/xpdfs/opelet.pdf [110717]. b—(1996) ‘Popular Music Studies versus the “Other”’. Paper delivered at conference Music and Life-world. Otherness and Transgression in the Culture of the 20th Century. In memoriam Fernando Lopes-Graça (Cascais, Dec. 1995). http://tagg.org/articles/xpdfs/cascais.pdf. b—(2009a) Everyday Tonality. New York & Montréal: Mass Media Music Scholarsʹ Press. www.tagg.org/mmmsp/EverydayTonalityInfo.htm [110717]. t—(2009b) Dominants and Dominance E rWlt9Is1nms [110723]. t—(2009c) Droned Fifths for The Tailor and the Mouse E Vvll55Pmyyg [111126]. t—(2011a) Scotch Snaps: The Big Picture E 3BQAD5uZsLY [110723]. b—(2011b) La tonalità di tutti i giorni — Armonia, modalità, tonalità nella popular music: un manuale. (ed. F Fabbri., transl. J Conti). Milano: Il Saggiatore. b—(2013) Music’s Meanings: a modern musicology for non-musos. New York & Huddersfield: Mass Media Music Scholars Press; www.tagg.org/mmmsp/NonMusoInfo.htm [130216]. b Tagg, Philip and Clarida, Bob (2003) Ten Little Title Tunes. New York & Montréal: Mass Media Music Scholarsʹ Press; www.tagg.org/mmmsp/10Titles.html [110722]. b Tamlyn, Garry (1998) The Big Beat — Origins and Development of Snare Backbeat and other Accompanimental Rhythms in Rock’n’Roll. PhD Thesis, 2 volumes, Instiute of Popular Music, University of Liverpool. www.tagg.org/others/TamlynPhD.html [110723]. 0 Trukeros, Los (2007) ‘La negrita con su llanto’ (cueca). De chilena; 0 Autoedición, Santiago de Chile; uploaded to tagg.org/Audio/LatAm/LosTrukerosLaNegritaYSuLlanto(DeChilena2007).mp3 [111205]; different live version at E v92yIsJbecY [110820]. b Vega, Carlos (1944) Panorama de la música popular argentina. Buenos Aires: Losada. 0 Vrethammar, Sylvia (1973) E viva España. Off-air Svensktoppen, Sveriges Radio, P3. t What Shall We Do With The Drunken Sailor (n.d.) m Irish Rovers E qGyPuey-1Jw [111205]. Fig. 1. The mushroom bush Terminology1309.fm. 2013-11-01, 18:12

Footnote texts

1. Substantial parts of this text were originally submitted under the title ‘Troubles with tonal terminology’ as a contribution to the Festschrift for Coriún Aharonián and Graciela Paraskevaídis (Montevideo), November-December 2011. Subsequent changes were made in April 2012, and a substantial revision was posted in February 2013. This text is a radically expanded version of the February 2013 revision.

2. References: [1] The Tailor and the Mouse (Eng. trad., Tagg 2009c); [2] If You Were The Only Girl (0 Como 1946); [3] What Shall We Do With The Drunken Sailor? (Eng. trad.); [4] Hickory Dickory Dock (Eng. nursery rhyme).

3. ‘Complete this motet in the style of Palestrina’, ‘this invention in the style of Bach’, ‘this piano quartet in the style of Brahms’ etc. were typical end-of-year composition exam questions.

4. See ‘Extended present’ in Chapter 8 of Tagg (2013). According to Hall (1992: 209), ‘[b]asic to [Leonard B] Meyer’s argument are the differences between primary and secondary parameters… The primary parameters—melody, rhythm, harmony— are syntactic because they can define closure… The secondary parameters—tempo, dynamics, texture, timbre—are statistical rather than syntactic because they change only in quantity and therefore cannot create closure… A central theme [of Meyer (1989), under review] is that secondary parameters… gain increasing dominance over primary parameters and syntactic processes through the nineteenth century and into the twentieth. This trend leads… to the increasing structural importance of statistical plans as opposed to syntactic scripts, and to the overwhelming statistical climaxes by which “unrealized implications… [and] unresolved tensions… are absorbed and ‘absolved’” (p. 268).’ Since Meyer himself seems well aware of the incongruity (the ‘increasing dominance’ of secondary ‘over primary parameters’, etc.), it is not his historical observations that are the problem but the actual terms ‘primary’ and ‘secondary’. The Concise Oxford Dictionary (1995) presents the first meanings of primary as ‘of the first importance, chief; fundamental’ while secondary is primarily (sic) defined as ‘coming after or next below what is primary; derived from or depending on or supplementing what is primary’. If what seemed once to be primary and secondary can, in the light of musical evidence, no longer be usefully conceptualised in such clearly hierarchical terms, more accurate, non-hierarchical concepts become a necessity. Perhaps we should be talking about ‘scribal’ and ‘non-scribal’, or ‘notatable’ (transcriptible in French) and ‘non-notatable’ (non-transcriptible) parameters.

5. See Chapters 10-12 in Tagg (2009a). ‘Shuttle’ = lanzadera, vaivén (repeated to-and-fro between two chords); ‘loop’ = lazo, vuelta (short, repeated ‘circle’ of usually three or four chords). Vega’s concept of bimodality was useful in explaining harmony in many different types of popular music.

6. All italics and underlinings are mine. For a thorough discussion of the Scotch snap, see Tagg (2011a).

7. Neither Sub-Saharan cross-rhythm nor the fluctuating to-and-fro patterns of downbeat placement in styles like candombe, merengue, rumba or son montuno constitute syncopation because what sounds like metric disturbance in our ears is an intrinsic part of the ongoing norm. It should also be noted that the term polyrhythm (literally = more than one rhythm at the same time) is often used erratically to denote Sub-Saharan cross-rhythm. Unless the music is strictly homophonic and contains no contrapuntal elements, all polyphonic music features more than one simultaneous rhythm and is therefore polyrhythmic. Polymetricity (more than one metre at the same time) may be a viable term for people brought up in a monometric music culture who want to grasp the rhythmic principles of Sub-Saharan musics but that is not how the music’s users and scholars hear it. For them it’s cross-rhythm, ‘a single metre in a permanent state of contradiction’ (Tagg, 2013: 457-465, quoting Ladzekpo (1995) and Peñalosa (2009)). Moreover, medieval, baroque and Tudor music performance practice, with its use of tactus instead of metric conducting, suggests that symmetric monometricity, visualised in later types of notation by the ubiquitous bar line, is also foreign to European musics of that time. The term syncopation, applied to frequent hemiola shifts (as in the Galliard), is in other words questionable, especially in contrapuntal sections where duple and triple metre occur simultaneously in different voices as simple composite cross-rhythm.

8. See Tagg (2013: 256-260).

9. For more on poïetic and aesthesic descriptors, see under ‘Musical knowledges’ in chapter 3 and under ‘Aesthesic focus’ in chapter 6 of Tagg (2013).

10. It goes without saying that chords consisting of stacked fifths are also quartal, not ‘quintal’, because the fifth is the octave complement of the fourth, just as no-one refers to ‘sextal’ harmony when a sixth, the octave complement of a third, is featured in a tertial chord.

11. It’s another case of ‘us’ as ‘normal people’ against ‘them’ as ‘foreigners’ or ‘others’, including the ‘Other’ inside ourselves (Kristeva, 1988: Étrangers à nous-mêmes); see also ‘Popular Music Studies versus the “Other”’ (Tagg 1996).

12. Wikipedia features authoritative articles on all these musicians.

13. Modes were often named after the regions or nations of which they were considered typical— the Ionian and Dorian modes, for example, or the Hijjaz and Kurd ajnas, or, in vernacular European parlance, a ‘Gypsy scale’. See also the semantic contortion of ‘inverse’ v. ‘normal’ dotting according to the Harvard Dictionary of Music under §4, pp. 4 -5, above.

14. See section on monomodality/bimodality, p. 19, ff.

15. Thanks to Luana Stan (Iaşi / Montréal) who informed me (2011-12-04) that in Romania sistem tonal denotes solely euroclassical ionian tonality in contradistinction to other tonalities such as sistem atonal, as in twelve-tone music (!), and sistem modal (all those ‘non-tonal’ modes!). If similarly muddle-headed notions exist in other Neo-Latin languages this problem will not be easily solved.

16. Cadence suspendue and cadenza sospesa are the French and Italian names for half cadence: harmonic completion has been suspended, left hanging in the air.

17. See comments about monomodality and bimodality (p. 19, ff.).

18. Trompeuse, rompue, évitée are French, Trugschluss is German and inganno Italian.

19. Um Um Um Um Um was written by Curtis Mayfield and first recorded by Major Lance (1963). The verses are resoundingly in A major as, indeed, is the first half of each refrain. The Lance original ends with a fade-out but the Fontana cover leaves no doubt about the identity of the tune’s final chord.

20. The contradictory expression ‘uninterrupted “interrupted” cadence’ is intended to highlight the absurdity of applying euroclassical cadence nomenclature to non-euroclassical musics. ‘Pre-’ and ‘post-tonal’ are included here as jokes on those nonsensical terms.

21. = ‘There are no major and minor tunes: there are just bimodal tunes’.

22. For more on æolian/phrygian reversibility, see Tagg (2009a: 227-234).

23. C5 = open 5th dyad c-g, B$5 = b$-f, etc.

24. The secondary mode might theoretically be lydian, but I am unaware of any traditional melody from the British Isles being in that mode.

25. See ‘Propulsive reiteration’ in Tagg (2013: 518-520).

26. Diataxis [daI(!tQksIs; fr. Gk. διάταξις) means ‘order of service’ in Byzantine Orthodox liturgy. As a chronological ordering of constituent episodes into an overall form, diataxis can be used to designate what concepts like ‘sonata form’ and the ‘32-bar aaba jazz standard’ have in common. See also ftnt. 30, p. 27.

27. Since composition has a particular meaning in music studies —the musical work— it cannot be used to denote musical form, since that is only one aspect of (musical) composition.

28. Extended present (a.k.a. ‘present-time experience’ and, misleadingly, ‘specious present’). As a duration the extended present lasts no longer than a musical phrase (exhalation), or a few footsteps, or a short gestural pattern, or a few heartbeats. It’s a duration experienced as a single unit (Gestalt) in present time, as ‘now’ rather than as an extended sequence of musical ideas. The extended present can also be imagined as the human brain’s equivalent to a computer’s ram where information is processed immediately, rather than as its hard drive (longer-term memory) where access and retrieval times are longer. For further explanations, see Tagg (2013: 19-20, 272-273, 588).

29. The extract starts at 1:44 in the recording. Transcription in Davis (2005: 299).

30. Syncrisis [!sINkrIsIs], from Ancient Greek σύγκρισις, means a putting together, an aggregate, combination, etc., from the verb συγκρίνω = to combine, compound, etc. While native speakers of English might have preferred expressions like ‘stack form’ or ‘now form’ to syncrisis, and ‘string form’ or ‘narrative form’ or ‘episodic form’ to diataxis, those more popular-sounding terms have three disadvantages: [1] they are longer; [2] they are not easy to use adjectivally or adverbially (unlike syncritic[ally] or diatactical[ly]); [3] they are more difficult to translate satisfactorily into other languages.

31. Narrative n. ‘a spoken or written account of events in order of happening’. Musical narrative means the overall presentation of musical events ‘in order of happening’.

32. See Tagg (2013: 272-273, 383-385, chapter 12, esp. pp. 417-425). The notion of texture covers no more than one aspect of syncrisis.

33. Æolian-phrygian bimodality is discussed in b Tagg (2009a: 227-234) and illustrated in t Tagg (2009b) which also includes the bizarre ‘perfect’ cadence add-on. Phrygian final cadences are of course two a penny in tertially harmonised music from the Balkan, for example in such popular recordings as Alexiou/Αλεξίου (1976), Er Malyk/Ер Малък (1992), Málamas/Μάλαμας (2006).

34. Between October 2011 and August 2013 I gave presentations relating to this text at conferences in Rome, Edinburgh, Granada and Cáceres, as well at university schools of music and/or media in Glasgow, Aarhus, Durham, Newcastle, Liverpool, Lancaster, Nottingham, Huddersfield, Cambridge (Anglia Ruskin, not Disneyland!), Keele, Trento, Turin, Paris, Nantes and Santiago de Chile.

35. The two conservative agendas were: [1] old-style musical absolutism (see Tagg, 2013: 83-100); [2] 1990s-style poststructuralist theorising, i.e. the sort of meta-contextual absolutism critiqued in Tagg (2013: 101-115).

36. Thanks to Dave McGuinness (davidmcguinness.com/ [13-02-18]).

37. See Chapter 1 in Tagg (2013) for statistical details.

38. See Chapters 6 (‘Intersubjectivity’), 10 (‘Notes on Vocal Persona’) and 12 (‘Analysing Film Music’) in Tagg (2013). See also stage 5 (p. 6) in this article.

39. IASPM: International Association for the Study of Popular music G iaspm.net.

40. See stage 1 at the start of this article (p. 2).