Everyday Tonality II

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Preface 11

• Why this book? 11
• Why Everyday Tonality II? 13
• Basic terms 16
• Who’s the book for? 17
• Caveats about the title and contents 17
• Basic structure and contents 19
• Rationale and reservations 19
• New terms and compromise 20
• Restriction of subject area 21
• Surprising discoveries 22
• Overview of chapters 22
• Appendices 26
• Glossary 26
• References 27
• Index section 27
• Formal and practical 28
• Cross‐referencing and order of topics 28
• Musical source references 28
• Reference system 28
• Accessing and using musical sources 29
• Online recordings 29
• Online notation 30
• ‘Cit. mem.’ 30
• Tonal denotation 31
• Note names 31
• Scale degrees, scale steps and intervals 32
• Octave designation and register 35
• Scale degree chord shorthand 35
• Chords 35 — 1. Lead‐sheet; 2. Quartal chords; 3. Roman‐numeral chords
• Reflection on the ionian as default mode 37
• Music examples 37
• 8va and 15ma bassa 38
• Progressions and sections 38
• Language and typography 39
• Pronunciation 39
• Spelling and punctuation 39
• Capitals and italics 39
• Mode names 40
• Small capitals 40
• Italics 40
• Other practicalities 41
• Abbreviations 41
• Timings and durations 41
• Footnotes 41
• Fonts 41
• Acknowledgements 43

Chapter 1.

Summary in 15 points

1. A NOTE is a minimal, discrete sound of finite duration in music.
2. PITCH is that aspect of a sound which is determined by the rate of vibrations producing it —its acoustic FREQUENCY. Frequency is measured in Hertz (abbr. HZ).
3. TONE means a note with discernible fundamental pitch and TONAL is its adjective.
4. TONAL means having the properties of a tone. Notes can be tonal or non‐tonal.
5. TONALITY is an abstract noun denoting the state or quality of being TONAL (§4, above). More specifically, TONALITY means a system according to which tones are configured.
6. TONALITY includes such phenomena as KEY (Tonart), MODE (Chapters 3‐4), MELODY (Chapter 5), TONAL POLYPHONY (Chap‐ ter 6), CHORDS and HARMONY (Chapters 7‐15). It also includes certain aspects of TIMBRE (§§11‐14, below).
7. TONIC is a noun meaning keynote or reference tone for a piece or passage of music. Its adjective is TONICAL.
8. TONICAL qualifies music that has a tonic.
9. TONICALITY is the abstract noun derived from TONICAL. It means the state or quality of having a tonic.
10. Music without a tonic is NON‐TONICAL (or atonical). Music without tones is non‐tonal (or atonal). Twelve‐tone music is non‐ tonical (or atonical). It is certainly not atonal.
11. TIMBRE (a.k.a. ‘tone quality’ or ‘tone colour’) is a complex acoustic phenomenon allowing us to distinguish between two notes, tonal or otherwise, sounded at the same pitch and volume. Its adjective is TIMBRAL.
12. TIMBRE consists of an ENVELOPE containing four elements: ATTACK, DECAY, SUSTAIN and RELEASE.
13. DECAY and SUSTAIN are the most readily extendable elements of timbre and can be referred to collectively as the CONTINUANT. A tone’s CONTINUANT consists of a FUNDAMENTAL PITCH and of PARTIALS or HARMONICS pitched at integral multiples of the fundamental’s own frequency.
14. How strongly which HARMONICS are present in which parts of an envelope is an essential factor defining a particular timbre.
15. MODES are by definition TONAL. The widely disseminated binary TONALITY / MODALITY is a conceptual aberration.

Subjects

• Note, pitch, tone 45
• Note 45
• Pitch 47
• Tonal note names 49
• Tone, tonal, tonality 51
• ‘Tonal’ and ‘tonical’ 52
• ‘Tonal’ and ‘modal’ 54
• Tonality, Tonart, Tonalité, Tonicity, Tonicality 56
• Other meanings of ‘tone’ 58
• Timbre and tone 58
• Summary in 15 points + bridge 63

Chapter 2.

Summary in 14 points

1. EXTRA‐OCTAVE TUNING exists basically to ensure that all participants in a musical event perform any given note at the same pitch. CONCERT PITCH (A4=440 Hz) was established as international standard to facilitate such tuning. ABSOLUTE (OR PERFECT) PITCH is a side effect of this standardisation.
2. INTRA‐OCTAVE TUNING regulates intervals (see §9) between the octave’s (see §3) constituent pitches so that they are sounded in a consistent fashion.
3. In most Western music the OCTAVE is treated heptatonically, in the sense that it very often consists of seven basic steps (doh ré mi fa sol la ti). The OCTAVE is so called because it is the eighth note you arrive at if you ascend one heptatonic step at a time (doh ré mi fa sol la ti |doh|).
4. If doh is TONIC and numbered 1, the other six SCALE DEGREES are numbered 2 3 4 5 6 7.
5. Five of the standard Western heptatonic OCTAVE’S STEPS are WHOLE TONES; the other two are both SEMITONES.
6. The standard Western OCTAVE is also divided into TWELVE SEMITONES to cater for varying placement of tone‐ and semitone steps in different modes. SEMITONAL VARIANTS precede their relevant SCALE DEGREES, e.g. b3 as the minor third and M3 as the major third scale degree.
7. NOTE NAMES are identical for pitches separated by an octave. The pitch frequency difference factor between two such notes is 2, e.g. A3=220 Hz, A4=440 Hz, A5=880 Hz.
8. The OCTAVE is a useful unit when referring to REGISTER. A standard piano keyboard covers a range of pitches from 29.135 (A0) to 8,416 Hz (C8), equivalent to 7¼ octaves. The average human singing voice spans about two octaves.
9. An INTERVAL is the difference in pitch between two tones. Even if intervals can be measured in Hz, they are most often designated in terms of scale degree difference. In this way the interval between 1 and 4 (e.g. a and d ««in A»») as well as between 4 and 7 (d and g) is a fourth (roman counting: (x+1)‐y=z).
10. Conventional SCALE DEGREE NAMES like dominant and subdominant are useful in theories of euroclassical tonality but are irrelevant or misleading when dealing with most other types of tonality. The equation of LEADING NOTE with scale degree 7 (7 = b7 or M7) is particularly problematic.
11. ‘NATURAL INTERVALS’ are characterised by simple frequency ratios expressing pitch difference, e.g. 3:2 for the perfect fifth. Tuning based on such intervals is often called JUST‐TONE TUNING and is often heard as clearer and brighter than EQUAL‐TONE TUNING. However, while G# and Ab are pitched identically in equal‐tone tuning, they can be seriously out of tune with one another when treated as natural intervals.
12. To avoid the problem of ‘G#≠Ab’, EQUAL‐TONE TUNING adjusts each of the octaveʹs twelve constituent semitones so that each semitone step is intervallically identical. An equal‐tone semitone interval is measured as 100 cents.
13. Many music cultures configure the octaveʹs constituent pitches in ways that do not conform to the twelve semitone pitches of Western tunings. (Table 7, p. 76).
14. The individual strings of instruments like the guitar can be tuned in a wide variety of ways to suit particular tonal configurations, styles, modes and moods.

Subjects

• Tuning, octave, interval 65
• General tuning systems 65
• Extra‐octave tuning 65
• Intra‐octave tuning 67
• Intervals 67
• Octave 68
• Intervals and intra‐octave tuning 70
• Equal‐tone tuning 74
• Instrument‐specific tuning 79
• Summary in 14 points 83

Chapter 3.

Summary in 14 points

1. A MODE is the result of distilling a tonal vocabulary down to a set of individual occurrences of its constituent tones. These are normally arranged in ascending scalar order and delimited by scale degree 1 (1, the tonic) at the bottom and top of one octave.
2. Many traditions of musical learning conceive of the OCTAVE as consisting of SEVEN BASIC SCALE DEGREES, several of which (typically 3 6 and 7, but also 2 and 4) are variable in pitch.
3. The distinctive character of a mode is largely determined by its UNIQUE SCALE DEGREE PROFILE, e.g. ? ? ? ? ? ? ? (ionian), ? ?? ? ? ? ? ?? (Hijaz). Even so, music in the same mode can vary quite substantially in mood and character depending on which of its constituent tones are used in which way, as well as on other musical factors (see ‘Aeolian’, pp. 105‐112).
4. SIX HEPTATONIC DIATONIC MODES are in common use in the West: ionian, dorian, phrygian, lydian, mixolydian and aeolian. These six modes all contain a PERFECT FIFTH and consist of four scalar steps of a whole tone and two of one semitone. The locrian is less common, except in heavy metal music.
5. The IONIAN, LYDIAN and MIXOLYDIAN are called ‘MAJOR’ modes because they contain ??, the DORIAN, PHRYGIAN and AEOLIAN are called ‘MINOR’ because of their ??. The notion that major modes are happy and minor modes sad is questionable.
6. The IONIAN mode has equivalents in many music cultures but no pride of place among other modes in those traditions.
7. A vast number of heptatonic modes exist in addition to the six or seven more familiar to Westerners. Many of those other heptatonic modes are non‐diatonic. Nineteen Greek dromoi and at least thirty Arab maqamat are in daily use.
8. Many modes in the ARAB and OTTOMAN traditions contain pitches incompatible with Western tuning systems, e.g. e§, ¾‐tone above ?, ¼‐tone below ?? and ¾‐tone below ?.
9. A MAQAM octave is often theorised as a combination of two TETRACHORDS. This aspect of tonal theory is useful in the understand‐ ing of many types of mode.
10. Modes containing ?? or ?? and/or a scale step of an augmented second (1½ tones), as in the ‘harmonic minor’ —NAHAWAND— and HIJAZ, are very common in the Arab world, the Balkans, Greece and Turkey. HIJAZ is also common in ANDALUSIA as one of fla‐ menco music’s two mi modes.
11. The AUGMENTED SECOND interval (1½ tones) and the scale de‐ gree FLAT TWO (??) have been used in the West as stereotypical sig‐ nals of a remarkably wide variety of ethnic ‘Others’, most notably Arabs, Jews and Gypsies, the latter from both the Balkans and southern Spain.
12. The PHRYGIAN is the only diatonic heptatonic mode to include FLAT TWO (??), and the HARMONIC MINOR the only euroclassical mode to contain an AUGMENTED SECOND.
13. The LYDIAN FLAT SEVEN mode, found in traditional music from ROMANIA, and as used by BARTÓK, has tonal similarities to blues modes. It is also characteristic of music from Northeastern BRAZIL.
14. ‘Phrygian dominant’ and ‘lydian dominant’ are patent MISNO‐ MERS. Westerners raised on a tonal diet of V-I in the ionian mode and who fail to hear a final cadence in the phrygian or Hijaz modes are effectively deaf to the PHRYGIAN TONIC. Similarly, music in the lydian flat seven mode cannot morph into another mode with another tonic by being that tonic’s ‘dominant’ without the music ceasing to be in lydian flat seven.

Subjects

• Heptatonic modes 85
• Intro 85
• Scales, modes, tonal vocabulary 87
• Ionianisation (??) 90
• Modes and ‘modality’ 92
• Heptatonic: why seven? 93
• The heptatonic‐diatonic ‘church’ modes 94
• Theory 94
• Examples 99
• Ionian Dorian Phrygian Lydian Mixolydian Aeolian: 99 to 105
• Non‐diatonic heptatonic modes 112
• Maqamat, flat twos and foreignness 114
• Basic concepts and theory 114
• Tetrachords and jins 118
• Hijaz and phrygian 120
• ‘¡Viva España!’ 128
• Balkan modes 134
• Bartók modes 138
• Summary in 14 points 146
• One last point 147

Chapter 4.

Summary in 14 points

1. Modes containing less than seven tones are no more empty than modes containing more than seven are necessarily cluttered.
2. TRITONIC AND TETRATONIC melody is common in many parts of the world, including the urban West.
3. PENTATONIC melody is found all over the world. ANHEMITONIC PENTATONICISM (what can be played on only the black notes of a pi‐ ano keyboard) is particularly common.
4. An anhemitonic PENTATONIC OCTAVE contains three whole tone steps and two steps of 1½ tones.
5. The constituent tones in any anhemitonic pentatonic mode are related to each other by SIMPLE PITCH FREQUENCY RATIOS .
6. Anhemitonic pentatonic modes can have DOH, RÉ, MI, SOL or LA as tonal centre. The DOH‐PENTATONIC mode is also called MAJOR PENTATONIC because it’s the only one to include ?. The MI‐ and LA‐ MODEs are MINOR PENTATONIC because they include ?. The RÉ‐ and SOL‐MODE s are QUARTAL PENTATONIC because they contain ? but neither ? nor ?. MI‐PENTATONIC is unusual because it has no ?.
7. The most familiar pentatonic modes in the West are those based on DOH and LA. Blues pentatonicism is essentially based on those two modes. The DOH‐PENTATONIC BLUES mode is common in pre‐ war jazz and in gospel‐related styles. The LA‐PENTATONIC BLUES mode is more common in guitar blues, in blues‐based rock and ‘cool’ jazz.
8. HEXATONIC MELODY is extremely common but no accepted ter minology exists for the designation of tonical hexatonic modes.
9. TONICAL HEXATONIC MODES used in the West consist of a heptatonic tetrachord and a pentatonic trichord. There are nine such modes that can be played on the white notes of a piano keyboard and that contain a perfect fifth. A hexatonic octave of this sort contains four whole‐tone steps, one semitone step and one step of 1½ tones.
10. Hexatonic modes in common use are the seventhless DOH‐ HEXATONIC, the sixthless LA‐HEXATONIC and the thirdless RÉ‐HEXATONIC.
11. The WHOLE‐TONE SCALE is also hexatonic but it is non‐tonical because it contains neither perfect fifth nor perfect fourth.
12. The OCTATONIC SCALE runs in alternate steps of whole and half tones. It also has a non‐tonical character because it contains either no perfect fourth or no perfect fifth.
13. The whole‐tone and octatonic scales can only be transposed to one other position. They are both often used as mystery cues in film and TV.
14. The culturally specific use of modes to suggest geo‐cultural identity is often confused and ethnocentric but it can still work on audiences who are not the object of that identification.

Subjects

• Non‐heptatonic modes 151
• Tritonic and tetratonic 151
• Pentatonic 153
• Anhemitonic pentatonic 154
• Doh‐pentatonic 154
• La‐pentatonic 155
• Ré‐pentatonic 156
• Blues pentatonic 158
• Doh‐pentatonic blues 159
• La‐pentatonic blues 161
• Theoretical bridge from five to six 163
• Hexatonic modes 165
• No names 165
• Major hexatonic 169
• Minor or la‐hexatonic 170
• Quartal or ré hexatonic 172
• Non‐tonical modes 173
• The whole‐tone scale 173
• Octatonic 175
• Final thoughts on non‐ionian modes 175
• Summary in 14 points 177

Chapter 5.

Summary in 11 points

1. Melody is a MONODIC TONAL STRAND of music that is EASY TO RECOGNISE, APPROPRIATE AND TO REPRODUCE VOCALLY.
2. Melody occupies DURATIONS resembling those of normal or ex‐ tended EXHALATION —the EXTENDED PRESENT.
3. Melody is usually delivered at a rate ranging from that of ME‐ DIUM TO VERY SLOW SPEECH.
4. Melody is usually articulated with RHYTHMIC FLUIDITY AND UN‐ BROKEN DELIVERY of tonal material.
5. Melody is DISTINCTLY PROFILED in terms of pitch and rhythm.
6. Melody tends to be RELATIVELY SIMPLE IN TERMS OF TONAL VOCAB‐ ULARY, changing pitch more often by steps rather than leaps and rarely spanning much more than one octave.
7. TYPOLOGIES of melody can be STRUCTURAL OR CONNOTATIVE.
8. The most common STRUCTURAL TYPOLOGY of melody is based on PITCH CONTOUR —rising, falling, tumbling, terraced, V‐shaped, arched, centric, wavy.
9. JUST AS IMPORTANT as pitch contour to a melody’s specific iden‐ tity are TONAL VOCABULARY, RHYTHMIC PROFILE (including language rhythm), METRICITY, DYNAMICS, MODE OF ARTICULATION, CULTURALLY SPECIFIC MOTIFS and PATTERNS OF RECURRENCE, including REITERA‐ TION, SEQUENCE, ANAPHORA, EPISTROPHE, etc.
10. CONNOTATIVE TYPOLOGIES of melody includes such categories as ‘Dream’, ‘Supermusic’ and ‘Recitation’.
11. A MELISMA is a string of several consecutive notes sung to one syllable. Melismatic is usually contrasted with syllabic, the latter meaning that each note is sung to a different syllable. Melismatic singing is often thought to constitute a particularly emotional type of vocal expression.

Subjects

• Melody 179
• Defining parameters 179
• General characteristics of melody 179
• Metaphorical nomenclature 181
• Typologies of melody 182
• Structural typologies 183
• Pitch contour 183
• Tonal vocabulary 186
• Dynamics/mode of articulation 187
• Rhythmic profile 188
• Body and melodic rhythm 188
• Language and melodic rhythm 189
• Culturally specific melodic formulae 190
• Patterns of recurrence 193
• Connotative typologies 196
• Dream 196
• Supermusic 197
• Recitation 198
• Melisma 199
• Summary in 11 points 202

Chapter 6.

Summary in 7 points

1. POLYPHONY is music in which at least two sounds of differing pitch or timbre are heard at the same time.
2. TONAL POLYPHONY is music in which at least two tones of clearly differing fundamental pitch are heard simultaneously.
3. DRONES consist basically of ongoing or frequently recurring notes that sound at the same pitch throughout part or whole of a piece of music. A drone usually demands just intonation of the other pitches it accompanies.
4. HETEROPHONY is polyphony resulting from simultaneous differ‐ ences of pitch produced when two or more people sing or play more or less the same melodic line at the same time. Heterophony is common in music from the Eastern Mediterranean and the Arab world.
5. HOMOPHONY is a type of polyphony in which different strands of the music move in the same rhythm at the same time. It is the polyphonic antithesis of counterpoint.
6. COUNTERPOINT is a type of polyphony whose instrumental or vocal lines clearly differ in melodic and/or rhythmic profile. It is the polyphonic antithesis of homophony.
7. Differences between homophony and counterpoint are relative. There are often contrapuntal elements in more homophonic music and often homophonic passages in more contrapuntal music.

Subjects

• Polyphony 205
• Polyphony: three meanings 205
• Drone 207
• Heterophony 210
• Homophony 212
• Counterpoint 214
• Summary in 7 points 217

Chapter 7.

Summary in 7 points

1. CHORD means the simultaneous sounding of two or more differ‐ ently named tones. DYADs contain two such tones, TRIADs three, TETRADs four and PENTADs five.
2. The two most commonly used systems of chord designation are ROMAN NUMERALS and LEAD‐SHEET CHORD SHORTHAND.
3. ROMAN NUMERAL designation is RELATIVE in that it indicates the scale degree, in any key, on which a chord is based (e.g. a C major common triad is I in the key of C but bIII in A). LEAD‐SHEET CHORD SHORTHAND is ABSOLUTE (C can only be C).
4. ROMAN‐NUMERALS are mainly used to designate TERTIAL chords. LEAD‐SHEET chord shorthand is ENTIRELY TERTIAL.
5. There are four types of TERTIAL TRIAD: major, minor, augmented and diminished.
6. Lead sheet chord symbols are built from the following compo‐ nents placed in the following order: • note name of the chord’s root, e.g. C; • triad type, if not major, e.g. Cm, CP; • type of seventh, if any, e.g. C7, C^, Cm7, Cm^7; • ninths, elevenths and thirteenths, e.g. CY9, Cm^9; • altered fifth, if any, e.g. Cm7L5; TODO • added notes outside the tertial stack, or omitted notes and sus‐ pensions, if any, e.g. Cm6, C7S4; • inversions, if any, e.g. CzÌ, Cze. TODO
7. LEAD‐SHEET CHORD SHORTHAND cannot be usefully applied in its current state to quartal harmony.

Subjects

• Chords 219
• Definition and scope 219
• Tertial triads 220
• Roman numerals 220
• Inversions 225
• Recognition of tertial chords 225
• Lead sheet chord shorthand 229
• Explanations 231
• Basic rationale 234
• Symbol components 235
• Name of chord root 235
• Tertial triad type 236
• Type of seventh 236
• Ninths, elevenths, thirteenths 237
• Altered fifths 238
• Omitted notes 238
• Added ninths and sixths 239
• Suspended 4ths and 9ths 240
• Inversions 240
• Anomalies 242
• Flat, sharp, plus and minus 242
• Enharmonic spelling 242
• Non‐tertial chords 243
• Summary in 7 points 243

Chapter 8.

Summary in 6 points

The main characteristics of classical harmony, as found in hymns, national anthems and many types of popular song, as well as in most forms of jazz, can be summarised as follows.

1. Chords are constructed by stacking superimposed thirds (ter‐ tial chord structure).
2. Default mode is ionian, the only mode in which a tertial tetrad on any degree of the relevant heptatonic scale contains two leading notes in relation to the tonic triad (I); in the ionian mode that tetrad falls on scale degree 5 (V7) and is called a dominant seventh.
3. Voice‐leading (how individual notes in one chord link to indi‐ vidual notes in the following one) is important: flat sevenths de‐ scend, sharp sevenths rise, voices may move in parallel thirds or sixths but never in parallel octaves or fifths.
4. Inversions of tertial triads and tetrads are quite common, as are conjunct bass lines.
5. Initial outward harmonic movement (harmonic departure) tends to go sharpwards (clockwise) but the majority of chord changes proceed flatward (anticlockwise) round the key clock, ending with a V-I cadence ([vii?] iii?] vi?] ii or IV?] V?I) (har‐ monic return).
6. Only the V-I cadence is considered full, complete or perfect; classical harmony’s three other cadence types are called:
   1. ‘half’ or ‘imperfect’,
   2. ‘plagal’ (= ‘oblique’) and
   3. ‘interrupted’/‘false’/‘deceptive’.

Subjects

• ‘Classical’ harmony 245
• Intro 245 History and definitions 247
• Classical harmony 249 Triads and tertial 249
• Syntax, narrative, and linear ‘function 252
• Voice leading, the ionian mode, modulation and directionality 252
• The key clock (circle of fifths) 255
• Cadential mini‐excursion 258
• The key clock (reprise) 261
• Circle‐of‐fifths progressions 262
• Anticlockwise/flatwards 262
• Clockwise/sharpwards: a provisional note 264
• Partial dissolution of classical harmony 265
• Classical harmony in popular music 267
• Summary in 6 points 271

Chapter 9.

Summary in 5 points

1. Non‐classical tertial harmony uses the same basic triads as clas‐ sical harmony but applies them according to different rules and in different functions.
2. Apart from a common triad on the tonic, the most important and characteristic chords for each mode are, if played on only the white notes of a piano keyboard, the major triads on F and G.
   These major chords are positioned differently in each mode: IV and V for the ionian, bIII and IV for the dorian, bIII and bII for the phrygian, II and V for the lydian, IV and bVII for the mixoly‐ dian, bVI and bVII for the aeolian.
3. The three ‘major’ modes are ionian, lydian and mixolydian. The others —dorian, phrygian and aeolian— are ‘minor’ modes.
4. Harmony in the ‘minor’ modes often (not always) features an altered tonic triad with a permanent Picardy third —I consistently replaces i. Triads on the fifth are also frequently ‘majorised’ —v may be replaced by V.
5. Non‐classical tertial harmony is investigated in greater detail in Chapter 14 — ‘Chord loops & bimodality’. Quartal harmony is the subject of the next chapter.

Subjects

• Non‐classical tertial harmony 273
• Non‐classical tertial: intro and preliminaries 273
• Ionian and barré 275
• Tertial major triads in non‐classical harmony 276
• Permanent Picardy third 276
• Power chords 280
• ‘Acoustic’ tertiality 284
• Unaltered non‐ionian tertial harmony 286
• Phrygian tertial harmony 288
• Lydian tertial harmony 289
• Mixolydian 290
• Aeolian tertial harmony 291
• Summary in 5 points 292

Chapter 10.

Summary in 18 points

1. Unlike its tertial cousin based on the stacking of thirds, quartal harmony is based on stacked perfect fourths or on their octave complement, fifths.
2. The basic quartal chords are the open‐fifth dyad (e.g. g-d) and the quartal triad stack, for example d-g-c which can be inverted as g-c-d, c-d-g, or c-g-d.
3. Unlike tertial common triads, a quartal triad stack and its inver‐ sions share no unequivocal single root note. For example, d-g-c (DÁ) inverted as g-c-d produces G4, c-d-g produces C2, and c-g-d produces the quintal stack CÀ.
4. Since notes in quartal triads are related to each other by fourths or fifths, they are only one key‐clock step away from each other, whereas tertial harmony’s thirds are three or four steps removed from the triad’s other two notes.
5. Quartal triads contain a central note with a second note located one step flatward round the key clock and a third note one step sharpward, for example the g in d-g g-c (GÃ) in which c is one step flatward from g and d one step sharpward. Such triads constitute a tonical neighbourhood spanning three positions on the key clock.
6. Due to key‐clock proximity and the ease with which tonal centre can shift between the three notes of a quartal triad, the tonical neighbourhoods of quartal harmony are more fluid and wider than the discretely focussed ‘keys’ of tertial harmony.
7. To effectuate a clear change of quartal ‘key’ you have to shift tonical neighbourhood by at least three steps on the key clock, i.e. a minor third up or down. Changing to a counterpoise pole two steps away (e.g. from I5 to bVII5) creates enough tonal difference to allow for harmonic movement but it does not ‘change key’.
8. ‘Major’, ‘minor’, ‘dominant’ and ‘subdominant’ are to all intents and purposes irrelevant concepts in quartal harmony. ‘Suspended’ fourths and ninths are totally erroneous notions in a quartal context, as are ‘omitted’ thirds.
9. Quartal pentads contain the notes of anhemitonic pentatonic scales, typically those of the RÉ, SOL and LA modes. Quartal chords are particularly well‐suited to accompanying melody that includes ?? ? and ??.
10. The greater the number of notes in a quartal chord, the more likely it is to contain thirds and to sound tertial. The ‘eleven chord’ is one such sonority. It is often used as substitute for a tertial dom‐ inant when the melodic material includes no ??.
11. During the heyday of euroclassical tertiality, thirdless chords, particularly open fifths, were associated with olden times and ru‐ ral backwardness. Through composers like Stravinsky, Bartók and Copland, quartal dharmony acquired associations of modernity that were later used extensively in music for film, TV and advertising.
12. Quartal harmony entered the jazz world around 1960 but many musicians schooled in the II-V-I directionality of jazz stand‐ ards and bebop seem often to confuse the approximate voicing of quartal triad stacks with quartal harmony. Those voicings tend to include an augmented as well as a perfect fourth, a combination that produces chords containing double leading notes well suited to chromatic circle‐of‐fifths runs à la bebop, progressions that are quite alien to quartal harmony.
13. Quartal harmony has yet to fully enter the sphere of main‐ stream pop but it can be found in the work of prog rock artists like King Crimson. Quartal sonorities occasionally turn up in the work of bands like Police and Oasis.
14. Aside from its use in the audiovisual media to connote a sort of positive modernity (see §11), quartal harmony is probably most commonly heard in what, for want of a better label, is often called folk rock (e.g. Steeleye Span).
15. In folk rock and related styles, the factors most likely to pro‐ duce quartal harmony are drones and open tunings based on ? and ?, more often than not doubled in unison or at the octave. Quartal harmony is typically produced when ?? ? or ?? sounds simultane‐ ously with the drone notes on ? and ? (e.g. Joni Mitchell).
16. Quartal harmony in folk rock and related styles can be more or less ongoing. With drones and open tuning the music can move be‐ tween a relatively tertial and a relatively quartal sphere without compromising the tonal integrity of the music (e.g. Richard Thompson).
17. There is no consensus about how to designate the elements of quartal harmony. The ideas set out in this chapter are no more than carefully reasoned suggestions as to how some sort of viable con‐ sensus might eventually be reached.
18. Musical structures cannot be named if they have no names and they cannot be accurately named if existing concepts shoot wide of the mark. In this chapter I’ve tried to address that issue with reference to quartal harmony.

Subjects

• Quartal harmony 293
• Theory 293
• No ‘sus’, no ‘add’, no ‘omit’ 293
• Basic concepts 294
• Chord shorthand 294
• Quartal and quintal 295
• Quartal triads and the tonical neighbourhood 295
• Crossing neighbourhood borders 302
• Quartal histories and examples 306
• Elevens, the USA and corporate modernity 306
• Euroclassical thirdlessness 315
• Quartal jazz 323
• Quartal rock 328
• Quartal pop 333
• ‘Folk’ fourths and fifths 334
• Banjo tunings 334
• Counterpoise 336
• Open tuning and drones 340
• ‘The Tailor and the Mouse’ 344
• Summary in 18 points 349

Chapter 11.

Summary in 5 points

1. The dynamics of harmony in popular music tend to rely less on long‐term narrative (diataxis) and much more on tonal variation presented in bouts of the extended present (syncrisis).
2. The indication of a single chord on paper, or in theory, is in prac‐ tice rarely performed as just one single chord by competent musicians accompanying a popular tune in such styles as valse musette, rock, pop, gospel, soul, R&B, funk, etc. (see examples 250‐267).
3. Accompanying musicians have to learn how to configure a single chord in a range of style‐appropriate ways (§2). Such configuration in‐ volves the inclusion of other chords that provide the theoretical ‘one single chord’ with a sense of ongoing cyclical tonal movement. Accom‐ panimental configurations of this type constitute the tonal aspect of groove.
4. A single chord indication can in aural reality be interpreted as a sequence of up to five different chords, if the sequence were tran‐ scribed and set in front of euroclassical harmony students, as in ex‐ amples 268 and 269.
5. Equating the indication of a single chord in the sheet music to a popular song with harmonic impoverishment is a sign of musical naïvety or ignorance.

Subjects

• One‐chord changes 353
• Harmonic impoverishment‐ 353
• Extensional and intensional 356
• The wonders of one chord 358
• G — Which G? 360
• Summary in 5 points 369

Chapter 12.

Summary in 16 points

1. The observations listed below are, like the rest of this chapter, based on widely disseminated recordings of English‐language popular song released between 1955 and 2005 (p. 372).
2. A CHORD SHUTTLE involves ongoing oscillation between two chords. Each of the two chords occupies a duration of between one and four beats of the music’s underlying pulse.
3. The two chords in a shuttle are normally of equal duration and importance. The duration of a single chord shuttle does not exceed that of the extended present.
4. Many chord shuttles have an identifiable TONIC (e.g. the aeolian i←>VI: §13, below) but others do not (see §10 and §14, below).
5. The tonic in shuttles consisting of the same two chords can vary according to tonal idiom, e.g. E←>A as I←>IV in Satisfaction but as V←>I in Beethoven’s 7th symphony (ex. 270, p. 373).
6. The most COMMON general types of chord shuttle are PLAGAL (I←>IV, i←>IV, i←>iv, IV←>I, etc.) QUINTAL (I←>V, i←>v, i←>V, V←>I, etc.), SUBMEDIANTAL (I←>vi, i←>bVI, etc.), and SUBTONIC (I←>bVII, i←>bVII, bVII←>I, etc.).
7. SUPERTONIC SHUTTLES are not very common. The supertonic shuttle I←>ii is plagal in character. P HRYGIAN SHUTTLES (I/i←>bII) are quite rare in and have exotic connotations (pp. 374‐375). 34
8. M EDIANTAL SHUTTLES (I←>III, etc.) are extremely rare. While I→III works well as a harmonic departure, III→I is highly unlikely to mark a return (p. 374).
9. PLAGAL SHUTTLES are very common and of three main types: simple (I←>IV), reverse (IV←>I) and dorian (i←>IV).
10. Many DORIAN SHUTTLES have a clear minor tonic triad (i←>IV), while others act as a repeated ii←>V culminating in a final ii→V→I wih I outside the shuttle. However, it is sometimes impossible, as in the case of Pink Floyd’s Dark Side of the Moon (1973), to identify any tonic in a dorian shuttle which, like all chord shuttles, func‐ tions as an ongoing tonal state or ‘place to be’ rather than as a tonal process leading anywhere in particular (pp. 378‐380; see also §15).
11. QUINTAL SHUTTLES ( I←>V, V←>I ) are common in euroclassical music, most notably in final cadences. While by no means rare in rock music, they are much less common than plagal shuttles. Quintal shuttles seem to be absent from gospel, soul and blues‐related styles (pp. 381‐384).
12. There are two main types of SUBMEDIANTAL SHUTTLE —I←>vi and i←>bVI, the aeolian shuttle. I←>vi is common in pop music of the milksap era. It also turns up in 1960s gospel music (p. 384).
13. AEOLIAN SHUTTLES (i←>bVI) in rock music are often linked to things ominous, fateful, painful and implacable; or to modernity, cold, waiting, uncertainty, sadness, stasis, infinity in time and space, etc. (pp. 386‐388).
14. SUBTONIC SHUTTLES —bVII←>I or I←>bVII— are basically mixolydian. They are quite common in postwar English‐language popu‐ lar song. If repeated several times in succession, they may well be associated with waiting (p. 389‐395).
15. Some apparently SUBTONIC SHUTTLES , like the F←>G in Human League’s Don’t You Want Me Baby?, have, like some dorian shuttles (see §10), no clear tonic (pp. 391‐394).
16. PARTIAL SHUTTLES can be found in harmonisations of traditional melody from the British Isles but they do not fit tunes that return to the first of the shuttle’s two chords at the end of each verse. They function instead as COUNTERPOISE SANDWICHES (pp. 396‐398).

Subjects

• Chord shuttles 371
• About the material 372
• Supertonic shuttles (I←>II) 374
• Plagal shuttles 375
• Quintal shuttles (I←>V) 381
• Submediantal shuttles (I←>VI) 384
• Subtonic shuttles (I←>bVII) 389
• Shuttle or counterpoise sandwich? 396
• Summary in 16 points 399

Chapter 13.

Summary

Subjects

• Chord loops 1 401
• Circular motion 401
• Vamps, loops and turnarounds 404
• Vamp, blues and rock 411
• ‘Classic’ rock’n’roll: IV-I 412
• Outgoing, medial and incoming chords 414
• Beatles harmony: bridging the gap 416
• Summary in 8 points 419

Chapter 14.

Summary

Subjects

• Chord loops & bimodality 421
• Ionian or mixolydian? 421
• Spot the key 426
• Aeolian and phrygian 433
• Mediantal loops 442
• Rock dorian and I‐III 443
• Double shuttle excursion 445
• Ionian mediantal ‘narrative’ and ‘folk’ dorian 445
• Summary in 14 points 448

Chapter 15.

Summary

Subjects

• The Yes We Can chords 451
• The four chords 452
• Late renaissance and Andean bimodality 453
• Four chords, four changes 455
• First impressions: from zero to I 456
• Harmonic departure: from I to III 458
• Spanish‐language bull’s‐eyes 458
• English‐language misses 459
• I - iii - vi - IV 470
• I - V - vi - IV 471
• IOCM in combination 474
• Summary in 10 points 477