This chapter shares common aspects with work done at the IRISA research institute in collaboration with Frédéric Bimbot, along with Gabriel Sargent and Emmanuel Vincent. Academic publication of this work is in progress, with a first paper having been presented at ISMIR 2011 [48].

About “structure”

Generally speaking, we will consider “structure” as the description of both elements and relations between elements belonging to a system.

This particular interpretation of the term “structure” is consistent with its use in other fields. For instance:

• In the field of sociology, “structure” refers to “the distinctive, stable arrangement of institutions whereby human beings in a society interact and live together” [44].
• In the field of chemistry, the Lewis structure is a representation of bonds between atoms (chemical bonding) [45].
• In the field of linguistics, the term “structuralism” refers to school of linguistics committed to the principle that a language is a self-contained relational structure, the elements of which derive their existence and their value from their distribution and oppositions in texts or discourse [46].
• In the field of computer sciences, a “control structure” such as IF-THEN-ELSE refers to the relations between statements so that they can constitute an algorithm [47]

“Formal structure” and “grouping structure”

This leads us to two conflicting definitions for “musical structure”.

1. On the one hand, we can consider “musical structure” as an ensemble encompassing both musical elements and relations between musical elements.
2. On the other hand, we can consider “musical structure” as “the variety of discrete time spans organized hierarchically in a work” [42] p.4 [51] pp.13-16.

The first definition will correspond to what we call “formal structure” and the second definition to what we call “grouping structure”.

“Formal structure”

Caplin distinguishes between several entities in relation to formal structure:

1. Formal types, archetypes of organization of formal functions and formal processes. ”Sentence”, “period”, “small ternary”, “sonata”, “rondo”, are examples of such formal types [42] p. 9.
2. Formal functions, the specific role played by a particular musical passage in the formal organization of a work [42] p. 254. ”Presentation”, “continuation”, “cadential”, “antecedent” and “consequent” are examples of such formal functions [42] pp. 10-12.
3. Formal processes: transformations of a musical passage that results into another musical passage. “Repetition”, “fragmentation”, “extension”, “expansion” [42] p.9.

If we want to consider “formal structure” as the description of both elements and relations between elements belonging to a system, then we can deduce that:

1. a formal type corresponds to a particular, recurring model of system.
2. a formal function correspond to a particular property of an element of the system.
3. a formal process corresponds to a particular relation between two elements of the system.

In this chapter, we will identify formal types, functions and processes that are best suited to “pop” music.

Phrase. Antecedent/consequent. Sentence/period.

We focus our attention on the notions of “phrase”, “antecedent/consequent” (two formal functions) and “sentence/period” (two formal types).

“Phrase”.

According to Schoenberg [41], “the smallest structural unit is the phrase, a kind of musical molecule consisting of a number of integrated musical events, possessing a certain completeness, and well adapted to combination with other similar units. The term phrase means, structurally, a unit approximating to what one could sing in a single breath […]. Its ending suggests a form of punctuation such as a comma” [41] p.3.

“Period”, “sentence”, “antecedent”, “consequent”.

Schoenberg [41], and after him Caplin [42], define two types of what Caplin refers to as formal types [42] p.9: the period and the sentence. Both types are normatively eight-measure segments [42] p.9 [42] p.12, even though they may last sixteen or even thirty-two measures [41] p.21. They begin with what Schoenberg calls a “two-measure phrase” [41] p.21, Caplin a “two-measure idea” [42] p.9 or a “basic idea” [42] p. 10, that occupies the first quarter of the segment.

Time-scales

We consider two time-scales, in accordance with [48]:

• The high-level structure of the musical piece, which describes the long term regularities and relationships between its successive parts, and which we will call the level of the  semiotic structure, or semiotic level.
• The mid-level organization of the musical content,  based on compositional units such as bars or hyper-bars or on perceptual units such as musical cells and phrases [...] We will refer to this level as the morpho-syntagmatic level, or MS level for short.

Sentences and periods are objects that belong to the semiotic level. Phrases, antecedents and consequents belong to the morpho-syntagmatic level. One particular object at the semiotic level correspond to one particular system of relations between elements at the MS level (a formal type corresponds to a set of formal functions and formal processes).

De facto formal processes

Caplin studies Mozart, Haydn and Beethoven. In this context, it is only natural that he wants to emphasize on “the role of local harmonic progression as a determinant of form”, since “theorists and historians widely recognize that the form of a classical work is determined in large part by its pitch organization” [42] p.4. As mentioned before, this is not the case with “pop” music. What, then, is the determinant of form in “pop” music? That we don’t know yet. To answer this question, we have to identify the musical degrees of freedom on which the structural form is expressed.

Let’s consider the period. If we write it as [A A'], then there exists a relation between antecedent and consequent that can be described. This relation is de facto a formal process. Therefore, a simple way to start with formal functions is to identify an {antecedent – consequent} couple, and examine the relation between one and the other. Let’s now write the period as [a b a' x]. There is also a de facto formal process between a and a’. If the period is of the particular sort [a b a' b'], then we also want to consider the de facto formal process linking b to b’.

Let’s now consider the sentence [a a' x y]. There is a de facto formal process between a and a’. If the sentence is of the particular kind [a a' a" x], then we want to consider the de facto formal process between a and a’ on the one hand, and a’ and a” on the other hand.

Fundamental and realized states

In a given period, let f be the relation (or formal process) between the antecedent and its consequent. Let’s A be the antecedent, and C its consequent. We have: C=f(A). The actual sequence of the antecedent and its consequent can be written as [A C], of [A f(A)]. We define [A A] as being the fundamental state of the sequence, and [A C] or [A f(A)] as being its realized state. From a Schenkerian perspective [49] pp.81-85, the fundamental state [A A] is a reduction (Reduktion) of [A C], and [A A] is one layer (Schicht) “behind” [A C].

Similarly, if we write a period as [a b a' x], then it can be considered as a [a b f(a) x], and its fundamental form is [a b a x]. If the period is of the [a b a' b'] kind, then its fundamental form is [a b a b]. A sentence written as [a a' x y] will have [a a x y] as its fundamental form, and the particular sentence [a a' a" x] will have [a a a x] as its fundamental form.

[Deruty, Emmanuel: Elements of "Popular" Music Analysis, April 2012]

Next page: Example: formal processes in Britney Spears’ “If You Seek Amy”

Transcription

We consider Britney Spears, “If You Seek Amy” [D41][this example on YouTube], 32 bars from 1′06 to 2′06.

The image below shows a transcription corresponding to these 32 bars. Click to enlarge.

The transcription shows, from bottom to top:

• Four staves corresponding to instrumental / sampled parts: “Bass”, “Vocal Samples”, “Horns”, “Upwards Synth”.
• Three staves corresponding to vocal parts: “Vocals Bottom”, “Main Vocals”, “Vocals Top”, with annotations in regards to the relations between the parts.
• A transcription of the vocal parts in terms of Square Space Units.
• A decomposition in terms of sentences and periods (upper case letters), along with phrases (lower case letters). This decomposition is based on the melodic patterns followed by the vocal parts.

A, B, D and E are periods. C is a sentence. Periods A, D and E last 8 bars, whereas period B and sentence C last 4 bars.

Formal functions and formal processes at the MS level

• Bars 1 to 8: {antecedent = a b}, {consequent = a’ b’}
• Bars 9 to 16: {antecedent = c d}, {consequent = c’ d’}, then sentence.
• Bars 17 to 24: {antecedent = g h}, {consequent = g’ h’}
• Bars 25 to 32: {antecedent = i j}, {consequent = i ø}

The transcription below highlights the differences between each antecedent and its consequent, i.e. the formal process f according to which consequent = f(antecedent). The sentence C = {e e’ e” f} is examined under the angle according to which e’=f(e) and e”=f(e).

This transcription contains four staves. From top to bottom:

• Stave 1 shows the vocal parts as heard, in terms of both melodic patterns and Square Space Units.
• In stave 2, the consequent is replaced by its corresponding antecedent. Each antecedent is thus repeated twice. This corresponds to the fundamental form of the period ([A A]). Similarly, the sentence is written in its fundamental form [a a a b].
• Staves 3 and 4 show the difference between each consequent and its corresponding antecedent. Stave 3 shows added elements, stave 4 shows removed elements. Staves 3 and 4 thus show the realization of the antecedent into its consequent.

List of formal processes f

Following is the list of formal processes f where consequent = f(antecedent):

• Bar 5: addition of an anacrusis
• Bar 6 and 7: addition of an upper voice whose sound image is Left+Right
• Bar 8: replacement of a lower voice by an upper voice, without a sound image change
• Bar 12: motivic change, along with the addition of an upper voice whose sound image is Left + Right
• Bar 22: addition of an upper voice whose sound image is Left+Right
• Bar 24: addition of an upper voice whose sound image is Left+Right

Bars 31 and 32 being almost empty, we dont consider them as being a variation of bars 27 and 28. Therefore, consequent = f(antecedent) doesn’t apply.

Functions inside sentence C:

• Bar 14: downwards transposition following the scale, addition of a lower voice whose sound image is Left + Right
• Bar 15: downwards transposition following the scale, addition of an upper voice whose sound image is Left + Right

The formal process that we meet the most is the “addition of an upper voice whose sound image is Left+Right”. In the case of this song, the determinant of form near this time-scale is based on the addition of an upper voice whose sound image is Left + Right. This shows that the most pertinent formal aspect for the MS level belongs to the arrangement and the sound image.

[Deruty, Emmanuel: Elements of "Popular" Music Analysis, April 2012]

Previous page: About “structure” and “form”

There are three criteria we’ve met during this study that we can associate with the notion of quantitative vocal complexity:

1. number of simultaneous vocal lines
2. SSU density
3. single SSU type density

The image below shows the evolution of vocal complexity throughout the song.

There are two classes of questions that can be immediately asked around this notion of ‘quantitative vocal complexity’:

1. Perceptively speaking, how do we define vocal complexity? Can it be measured in the context of a cognitive study?
2. If we suppose that we can define vocal complexity from a perceptive point of view, how would we link our three quantitative criteria to it? What would be their respective importance?

It is not the purpose of this study to give answers to those questions. However, we think that this notion of ‘quantitative vocal complexity’ might be an interesting subject for future studies.

[Deruty, Emmanuel: Elements of "Popular" Music Analysis, August 2011]

Previous page: “Bad Girl”: Vocal Instrumentalization
Next page: “Bad Girl”: Conclusion

It is the author’s opinion that this song features several elements that ‘instrumentalize’ the vocal part. Vocals are treated as instruments on several occasions, both from compositional and perceptual points of view. There are two practical aspects of this ‘instrumentalization’.

The first aspect lies in similarities between the keyboard part and the vocal parts. Following are observations relevant to this first aspect:

1. Vocal and melodic keyboard parts sometimes share the exact same frequency register. This is particularly obvious near 2’46, where it’s difficult to perceptively distinguish keyboard and vocal parts.
2. As described in this chapter, vocal and harmonic parts often share the same melodic pattern.

The second aspect lies in intrinsic properties of the vocal parts. Following are observations relevant to this second aspect:

1. There are many vocal parts throughout the song that come without lyrics. Some are perceptively close to the vocal parts that are based on lyrics, in which case they’re displayed on the MVAC. For instance, this is the case for the ‘aaaas’ between 1’38 And 1’53. On the other hand, some are so close to an instrumental part that they’re not displayed on the MVAC. This is the case for the sampled vocal-like loop that takes place between 3’10 and 3’23 (instrumental section). This results in a continuum between ‘instrumental vocal parts’ and ‘vocal vocal parts’.
2. This continuum can be heard literally at 3’10”5. On the word ‘around’, the vocal part’s timbral characteristics are gradually morphed so that they closely resemble the vocal-like loop that follows.
3. From 2’57 to 3’10, inside section B”, we can hear a phaser on the vocal part. This way of modifying a part’s timbral characteristics is a concern that’s typical to arrangement/orchestration. As such, it’s traditionally associated to instrumental parts. In this regard, it instrumentalises the vocal part on which the effect’s applied.
4. Such vocal part instrumentalisation using modifications of timbral characteristics also takes place throughout the whole song: anytime two same-pitch, homorhythmic vocal lines are superimposed,it modifies the singer’s original timbre. This means that such instrumentalisation methods are intrinsic to the very way the vocals are written and arranged, therefore intrinsic to the song itself.

[Deruty, Emmanuel: Elements of "Popular" Music Analysis, August 2011]

Previous page: “Bad Girl”: keyboard / vocal track relationship
Next page: “Bad Girl”: quantitative vocal complexity

There is a keyboard part that runs continuously throughout the song, and which exhibits two particular behaviors. Either it’s a mostly melodic one, like in sections A, E, and F first part, or it’s a harmonic one, like in sections B, B’, B”, C, C’, D, and F second part. We’re going to focus on three phases of the relationship between this keyboard part and the vocal parts: when the keyboard’s melodic, when the keyboard’s harmonic, and during particular cases that feature timbral links between keyboard and vocal parts. Those three phases have a common point: each one of them creates links between keyboard and vocal parts, whatever the method that’s used in each case.

Vocal parts and melodic keyboard

Vocal parts and melodic keyboard parts are interlaced using the following tricks:

1. From 0’07 to 0’11, section A, the vocal part follows a melody, which we’ll call ‘theme 1’. It’s the first vocal melody of the song, therefore it’s naturally associated with vocals. This melody is repeated by the keyboard from 0’10 to 0’14.
2. From 0’14 to 0’18, section A, the keyboard follows theme 1. Also, the keyboard is homorhythmic to the vocal parts.
3. From 0’56 to 1’03, section E, the keyboard follows a variation of theme 1.
4. From 1’14 to 1’21, section A, the keyboard follows a variation of theme 1. It is also homorhythmic to the vocal parts.
5. From 1’28 to 1’30, section B’, the vocal part follows a relatively stable melody, and so does the keyboard. From 1’28 to 1’32, ita est during the end of the sentence, the vocal part follows a more mobile melody, and so does the keyboard in homorhythmy.
6. From 2’00 to 2’14, section F first part, the keyboard follows theme 1. Also, the vocals are accentuated following patterns studied here. The keyboard line is interrupted during some of those accents.
7. From 2’28 to 2’35, section E, the keyboard follows theme 1.
8. From 2’42 to 2’46, section A, the vocals follow theme 1 again. Just after, from 2’46 to 2’49, the keyboard repeats theme 1.
9. From 3’32 to 3’38, section E, the keyboard follows theme 1. (10)From 3’46 to 3’49, section A, the vocals follow theme 1 again. Just after, from 3’49 to 3’52, the keyboard repeats theme 1, in unison to one of the vocal lines. From 3’53 to 3’57, the keyboard also follows theme 1.

Vocal parts and harmonic keyboard

Vocal parts and harmonic keyboard parts are synchronised using the following tricks:

1. From 0’21 to 0’34, section B, there are two sentences, each one being sung in one breath, one interjection, and again two sentences, each one being sung in one breath. Notice how the harmonic keyboard part follows those elements, as it was sharing the singer’s breath. It plays one chord under ‘Look in my eyes covered in Maybelline’, and one other chord under ‘Looking like something fresh out of a magazine’. Then it changes chord again in perfect synchronisation with the interjection. It changes again synchronously to ‘I can be part of your deepest fantasies’, and though the notes don’t change, an attack can clearly be heard at the beginning of ‘You’re the detective come solve my mysteries’.
2. From 0’33 to 0’48, section C. The accentuation of this section is studied in chapter 4.3.1. Notice how the harmonic keyboard changes chords exactly and only during the accentuated syllables.
3. From 1’24 to 1’28, section B’, the sentence ‘Something about me is getting you hypnotized’ is sung in one breath, with a downward portamento on the syllable ‘tized’. The keyboard plays one chord during that time, with an upward portamento at the end.

Timbral links

Two particular cases of sound manipulation result in a natural link between vocal and keyboard parts:

1. At 1’38, end of section B’, the vocal part follows a singular pattern, consisting in an upward melody based on a single syllable, that’s clearly reminiscent of theme 1. During this pattern, it’s possible to hear artifacts that are typical to pitch-shift processes. In particular, anomalies in the quality of the formants. This denaturation of the vocal timbre makes the vocal part closer to a virtual instrument, and further from a vocal part.
2. At 3’03, section B”, there is a pattern whose timbre can be identified as being half-vocal, half- keyboard. At 3’06, this hybrid ‘instrument’ has been morphed into something that’s more vocal and less keyboard-ish.

[Deruty, Emmanuel: Elements of "Popular" Music Analysis, August 2011]

Previous page:  “Bad Girl”: kick drum / vocal track relationship
Next page: “Bad Girl”: vocal instrumentalization

We describe the grouping structure of the song, not its formal structure.

We define three observation scales. Scale 0 is the song. Scale 1 refers to the largest possible structural objects that are contained in the song. Scale 2 refers to the largest possible structural objects that are contained in scale 1 objects. As a way of consequence, level 2 objects are necessarily more numerous than level 1 objects, which are necessarily more numerous than the single level 0 object, the song.

The image below shows a possible interpretation of the song’s structure according to those three scales of observation. This is the structure that will be used as a reference throughout the study.  The main vocal analysis chart features level 2 structural information.

[Deruty, Emmanuel: Elements of "Popular" Music Analysis, August 2011]

Previous page: Example: Analysis of “Bad Girl”’s vocal parts
Next page: “Bad Girl”: main chart

As stated in the introduction, the band Danity Kane was primarily formed to be a commercial product. The song ‘Bad Girl’, as well as the album it comes from, is also a commercial product. On the other hand, our analysis of the vocal parts in this song shows a lot of craftsmanship in the making of vocal arrangements. Many details are not immediately audible, and the author of this article needed to listen to the song repeatedly to understand what is actually going on. Listening to ‘Bad Girl’ is like listening to a piece from Schumann’s “Carnaval”: it’s possible to discover something new each time we listen to it. What’s more, our analysis doesn’t encompass all the song’s aspects. Many more things could be said about the instrumental arrangement.

This indicates that purposely commercial music can be interesting to listen to, even from an “intellectual”, analytical point of view. It is the author’s belief that there is no contradiction between music as a business and music as an art, and that mainstream hits can exhibit craftsmanship and complexity, even though the first audition can be disorienting to ‘serious’ music specialists. Naturally, ‘Bad Girl’ is not the only song in this case. In the same modern R&B trend, the author can recommend the following tracks, that also show high vocal production complexity: “If you seek Amy” and “Womanizer” from Britney Spears [D41], “Wait a Minute” and “Bite the Dust” by The Pussycat Dolls [D19], “Single Ladies” by Beyoncé [D20], and “What Goes Around… Comes Around” by Justin Timberlake [D18].

There are several conclusions that we can draw:

1. Vocal part construction in ‘Bad Girl’ relies heavily on the layering of monodic vocal lines. Such a layered architecture prompts the use of particular vocal patterns such as: accentuation of certain words from the vocal part, and fancy overlapping between consecutive vocal parts.
2. MVAC and SSUs are particularly well-suited to the analysis of such a layered architecture. SSUs can display, in a clear and concise form, audio informations that are sometimes difficult to picture. From the MVAC, many useful observations can be drawn, such as count of simultaneous vocal lines and vocal pattern density.
3. In ‘Bad Girl’, vocal parts are linked to non-vocal parts using a variety of techniques, be it techniques based on synchronisation, or techniques based on timbre.

Those observations lead to several concepts and hypotheses:

1. Pitch and harmonic analysis may not be necessary in such a context. In fact, they may be harmful to the analysis, by diverting the attention from the really important aspects of the music.
2. There exists a notion of vocal part complexity, which may be quantified using a combination of three criteria: number of simultaneous vocal lines, SSU density, SSU unique type density.
3. In this song, vocal parts may be subject to a process of ‘instrumentalisation’. From a compositional point of view, they are neither considered as entirely vocal, nor as entirely instrumental.
4. Aspects of the vocal parts that vary the most between successive verses may depend on musical style and era. In other words, there may be a connection between instrumentalisation and musical style.
5. Vocal part instrumentalisation and complexity may be linked. Perceptual instrumentalisation may be a consequence of compositional complexity.

Most generally, this study shows that a thorough perceptual analysis of commercial popular music is possible and can lead to numerous observations, even in the case of a mainstream product that was recorded in the context of a reality show on MTV.

[Deruty, Emmanuel: Elements of "Popular" Music Analysis, August 2011]

Previous page: “Bad Girl”: quantitative vocal complexity

The image below shows respective kick drum and vocal part placements in sections D. There are three remarks to be made.

1. Notice how the vocal parts are regular. In particular, there is always a word ‘bad’ on each first beat. On the contrary, the kick drum elements around the first beats are irregular: one time out of two they end on a first beat, and one time out of two they begin on a first beat. As a way of consequence, the ‘bad girl’ stanza falls at different places of the rhythmic pattern depending on the measure, even though it remains at the same place.
2. Notice how ‘maybe I’m just a’ always begins in synchronisation with a kick drum element. Similarly, notice how in bars 1, 2 and 3, the syllable ‘girl’ exactly lasts until another occurrence of a kick drum element. This creates a link between kick drum and vocal parts.
3. Notice the symmetrical structure of the last measure. It contains 4 vocal syllables. Syllable 1 goes along with three kick drum elements, and symmetrically, so does syllable 4. Syllables 2 and 3 go along with a kick drum element right in their middle. Try to listen to this measure again and feel the groove this setup induces.

[Deruty, Emmanuel: Elements of "Popular" Music Analysis, August 2011]

Previous page: “Bad Girl”: accents
Next page: “Bad Girl”: keyboard / vocal track relationship

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Accents in sections C

Two sections show a particular vocal production method that consists in accentuating one or several consecutive syllables using the interruption of a monodic setup by a different, polyphonic one. Those are section C (0’34 to 0’48) and section C’ (1’38 to 1’52).

Section C, 0’34 to 0’48. Following are the lyrics from this section, with the accentuated syllables in bold characters:

Some say that love is all that I’m missing / Some call it Jezebel, I call it attention / But what they don’t know they can’t even imagine / Say I don’t have no self-esteem but it’s my passion

Notice how the accents come with great regularity: on the 3rd and 4th beat of each measure. Accentuation methods are shown on the image below, left. Notice how vocal accentuation gets increasingly complex until ‘magine’, then gets back to a simpler state.

Section C’, 1’38 to 1’52. Lyrics and accentuation are practically the same as in section C, 0’34 to 0’48. The accents still come with great regularity, on the 3rd and 4th beat of each measure. These accentuation methods are shown on the image below, right.

Notice that a more fundamental difference between this section and section C, 0’34 to 0’48, lies in the simultaneous existence of another vocal part, that features between 4 and 6 monodic vocal lines by itself.

Accents in section F

Section F, 1’58 to 2’28, shows another particular vocal production method that also consists in accentuating one or several consecutive syllables, this time using the addition of vocal lines on a main monodic line. It is different from the method described above, due to the fact that there is no interruption of the main vocal line. We’ll divide this section into two separate parts. One goes from 2’00 to 2’14, the other one goes from 2’14 to 2’28. We’ll let aside the vocal pickups that go from 1’58 to 2’00.

Section F from 2’00 to 2’14

Following are the lyrics from the first part, with the accentuated syllables in bold characters:

B-A-D-C-H-I-C, lookin’ so sexy / Make them bitches hate me / She not me cause there’s just one me / I’m the M to the I-double S-Y-E / Lights come on, I tr-transform /Gimme that dick, baby, com-come on / I can do it all night ’til the break of dawn /On-On and on, I keep on goin’.

Regularity is not as great as it was the case for sections C and C’. Though accents still come near the 3rd and 4th beat, the length of the actual accentuation is more variable. Additionally, there are two measures during which there is no accentutation. Accentuation methods are shown below, left.

Section F from 2’14 to 2’28

Following are the lyrics from the second part, with the accentuated syllables in bold characters:

They call me a Jezebel cause I freaks, I does it well / Got extensions in my hair, bad girls is ya’ll up in here /Tonight we just gonna let it do what it do / I can put this pretty young thing on you / I ain’t lookin’ for attention, I just want you / Let me be your addiction, I can be that too.

The first three accentuated groups of syllables follow the usual pattern of being near the 3rd and 4th beat of each measure. They’re followed by two full measures of accentuation. The last three measures follow the standard pattern again. Length of accentuation duration is as variable as it was for the first part of section F. Accentuation methods are shown below, right.

[Deruty, Emmanuel: Elements of "Popular" Music Analysis, August 2011]

Previous page: “Bad Girl”: SSU density
Next page: “Bad Girl”: kick drum / vocal track relationship

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The table on the right shows the measurement of Square Space Unit density over level 2 structural objects. Column ‘Number of SSUs per second’ shows densities of vocal arrangement setups during each level 2 section. Column ‘Number of unique SSU types per second’ shows densities of unique SSU types during each level 2 section.

Intuitively, ‘Number of SSUs per second’ is a marker of how frequently the vocal track setups change. ‘Number of unique SSUs per second’ is a marker of how variable is the vocal track setup. Those two criteria can be taken into account for the evaluation of quantitative vocal complexity.

There are specificities during the count of SSUs that we want to highlight.

1. Specificity 1, example. Let’s focus on the transition between E and D near 1’02. There is an overlap between those two sections. The SSU for ‘I can be your addiction if you wanna get hooked on me’, from section E, overlaps with the SSUs for ‘Maybe’ and ‘I’m just a’ from section D. In such case, we consider (in the context of this SSU density study only) that section ‘E’ lasts until 1’03”5, and section D starts at 1’02”5. Generally speaking, a section will last until the end of all the SSUs in contains, even if that means it overlaps with the following section. As a consequence, sum of all durations in Table 3, column 5 is greater than the actual song duration.
2. Specificity 2, example. Let’s focus on the transition between C’ and D near 1’52. The pattern on SSU track 3 doesn’t belong to any section. In such cases, we will count the pattern as being part of the section it precedes. In this specific case, it means that this pattern on SSU track 3 belong to section D.

[Deruty, Emmanuel: Elements of "Popular" Music Analysis, August 2011]

Previous page: “Bad Girl”: number of simultaneous vocal lines
Next page: “Bad Girl”: accents

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