Harmonization of Brazilian Popular Songs

Harmonization of popular songs in Brazil has, for quite some time, been considered worthy of the attention of both music theorists and musicologists. Theaccompanimentsattract attention due to their varied and sometimes original character. The peculiarit ies of the harmonizat ion of popular Brazilian songs may not always be immediately comprehensible, nor correspond exact ly to conventions found in analyses of the tradit ional concert repertoire. The chief reference treatises and manuals adopted in music schools can certainly provide satisfactory explanations, when appropriately used. Yet many specialists consider problematic some concepts and definitions that should facilitate the task of analysing popular songs.The Manual of Harmony by Igor VladimirovichSpossobin, 1955 ed ition, is the textbook adopted for harmony classes in the undergraduate program at the Universidade Federal do Estado do Rio de Janeiro – Unirio. Considered one of the most complete on the topic,it is also used at the Tchaikovsky Conservatory in Moscow. The 2007 edit ion is also used for reference.Nevertheless, it is worth mentioning that the book has not been used intensively for the analysis of popular songs. The Manual covers 60 topics, some of which are useful in explaining harmonic language frequently present in popular songs. Concepts such as inclination, the major-minor system, augmented sixth chords, Neapolitan harmonies, ellipse, dimin ished-seventh chords and chords with non-chord tones, can be used to explain many of the harmoniesheard in Brazilian popular songs.


Introduction
Music theorists and musicologists in Brazil have been turning their attention to the harmonizat ion of popular songs for decades, because of its variable and sometimes original uses.The harmonic peculiarities of Brazilian popular songs necessitate clarification since they do not correspond exactly to the time-honoured conventions of the tradit ional repertoire.
The best-known instructional manuals adopted by music institutions provide acceptable explanations. These books contain concepts and definitions ready to use in exercises, but up to now have seemed difficu lt for some experts, and thus have not been used intensively for the analysis of popular songs.
The undergraduate music program at the Un ivers idade Federal do Estado Rio de Janeiro -Un irio, has adopted the Manual for Harmony by Igor VladimirovichSpossobin as its textbook fo r the field. While the 4th edition has been used at Unirio since 1970 [1],the more recent, 2007 edition is now being used as well. The book has also been adopted at the Moscow Conservatory. The Manual covers 60 topics, some of wh ich are usefu l inexp lain ingh armon ic langu age of

Selecting the Repertoire to be Analyzed
Brazilian popular song refers as much to the object of study as to the production of tunes sung in Po rtuguese. In any event, the current analysis encompasses songs with Brazilian Portuguese lyrics. The study is not restricted to a particular time period, since doing so might lead to mistakes. As an example, the harmonic co mplexity frequently associated with Bossa Nova would seem to be at odds with the fact that songs recorded before 1950 contained non-diatonic harmonic progressions similar to those used after that period of time. For this reason, questions about the correspondence between genres, styles and period of time were put aside.
As an illustration, examp les of the use of inclination include "Vira a casaca", a song originally recorded in 1923 and remastered in 1996, p layed by Pixinguinha and the band Os Oito Batutas.

Spossobin's Concepts and Their
Applicability to the Concepts Used in the Analysis of Popular Songs 1

Inclination
In the 31st Theme of the Manual, page 235[1],Spossobin defines inclination as "briefly leaving the principaltonality and moving into a secondary tonality during the exposition of a monotonic or modulat ing structure (period). There are two types of inclination: passing and cadential. The passing inclination occurs inside the structure, without the cadence, it is similar to the passing tone or passing chord." On page 234 of the Manualthe author distinguishes inclination fro m modulation as "passing into a new tonality to conclude the musical structure in that tonality. As a rule, modulation ends in a co mplete cadence. The simp lest modulation is that which substitutes the tonality at the end of the first period [1]." This defin ition coincides with the notion of inclination as taught in both schools of music and in well-known manuals. Inclination is a harmon ic technique that appears in the majority of songs. For this reason it may not be appropriate to group repertoire by its country of origin or a specific time period.However it is important to note that the process of inclination applied to some songs can be slightly different fro m the above definit ion.
The notion of inclination is frequently replaced by the concept of secondary dominants, more o ften used to explain harmonizat ion in popular music. AlmirChediak [2] and Ian Guest [4] have consistently used it as an alternative to the term inclination. The concepts of secondary dominants and tonics are also explained in the 32nd Theme of the Spossobin´s Manual. There are many songs in which secondary dominants are combined with secondary or interpolated subdominants and followed by deceptive cadences (ellipsis), as in the passages shown below.
Most of the examp les listed below have already been discussed in my dissertation, "Bossa Nova: a permanência do samba entre a preservação e a ruptura" (Bossa Nova: the endurance of samba amid preservation and rupture) [9].

Major-Mi nor System
The major-minor system is an important aspect of harmonic analysis. Spossobindefines the concept on page 374 [1] of the 49 th Theme: "in the development of the idea of modality, the major and the minor modes have never had an isolated, independent existence. On the contrary, it has long been noted that changes, linked to the interaction of both modes, have produced complexit ies through the insertion of harmonic elements fro m either mode, which, as a result, become richer. The major and minor modalities beco me more co mplex due to their interaction and form the ma jor-minor system, named major-minor or minor-ma jor, depending on the leading tonic, major or minor.The system can be homony mous if they share the same tonic (for example C major -C minor) or parallel (for examp le C ma jor -A minor)." Modal interchange has been widely used in popular music. Philip Tagg points out that bitonality is common in many popular styles of Latin American music (page 10) [8]. Chords fro m the minor mode are often inserted in a song whose prevailing tonality is in the major mode. On the contrary, inserting majo r mode chords in a progressionwhose principal tonality is in the minor mode is much less common. The exception to this is the Picardy third, used both in traditional and popular music.
The idea of modal interchange comes closer toSpossobin's definit ion, due to the fact that major and minor mode are often mixed together. It is important to consider additional modal interchanges, which occur in the church modes:Mixo lydian, Lydian, Phrygian and Dorian. In his book, Theory of Harmony, Arnold Schoenberg describes the genesis of the major and minor modes and considers them "both a residue of the seven church modes" [3].
However, modal interchange in popular music typically occurs when the major and minor tonics are the same, or homonymous. In Walter Piston's Harmony [10] he exp lains modal interchange along with the idea that the minor mode runs parallel to the major. The same notion appears in Spossobin'sManual, yet the minor mode is not the homonymous but the relative, which shares the same key signature as the corresponding major.
The major-minor system comprises the modal interchange concept as demonstrated below:

Aug mented Sixth Chord
The harmonic structure known as subV has been increasingly used in popular music, both in the harmonizat ion and re-harmonizat ion of songs. The so-called subV chord has as its main characteristic the augmented sixth, which is derived fro m the inversion of the d iminished third between the majo r third and the diminished fifth of the dominant chord. Hence, it may be mo re useful to think of it as the second inversion of the do minant chord with a lo wered fifth, where its diminished third is converted to an augmented sixth. Both Schoenberg and Pistonconsidered this an important topic, and dedicated complete chapters to it.
The repeated use of this chord may overshadow the fact that it is simply an alteration or variation of a do minant chord with a lowered fifth.
Spossobin describes these altered chords as comprising not only the lowered II degree of the major mode (which is the fifth of the dominant chord) but other possible altered tones inserted in a variety of chords on different scale degrees. He states, "As is well known, the alteration represents the intensification of a semitone in the tension of a whole tone existing in the mode, withoutchanging the chord function and without leaving the respective tonality. The corresponding chord is called an altered chord. A ltered harmonic co mpounds have their origin in chro matic passing tones in different voices inside the diatonic mode. The basic alteration present in most harmonic functions is associated with the change of the II degree of the scale. Its alteration in the major mode can be done by raising or lowering it; in consequence, the intensification of the tension occurs toward the tones of the lower third of major tonic t riad, i.e., toward the I and the III scale degrees. In the minor mode, raising the II degree is not possible, thus the alteration in that mode is based exclusively by lo wering the II degree and, to some extent by altering the IV degree. Consequently the intensification of the tension occurs toward the lower third of the tonic minor triad [1]." This quotation makes clear the orig in of the chord alteration.The harmonic situation is quite co mmon and can be heard in various songs, of which three were selected. Key: C minor Chord progression: D7(9) |Dm7(9) | Db7 G7(b5)|Cm7 (9) Analysis:V7(b9) | IIm7(9) |V7/b5 V7(b5) | Im7(9) Corresponding lyrics: " ...Acordaamor, queeuseiqueembaixodesta neve mora um coração..." 2. " Sótinha de ser com você" (It must be you) by Tom Jobim Key: F major Chord progression:F7M|C7(#9)|F7M|Gb7(b13)|Cm7(9)|Bm7(b5) Bbm6 (9) Analysis:I7M |V7(#9)|I7M|subV7(b13) | IIm7(9)/IV |#IVm7(b5) IVm6(9) Placed inthe first phrase. 3. "Derradeira primavera" (Ultimate springtime) by Tom Jobim and Vinícius de Moraes Chord progression: Dm7 | E7 |Bb7 |Am7 Analysis:IVm7|V7 |bII7|Im7 Placed at the end of the song.

Neapolitan Harmonies
The lowered II degree can often be detected in the harmonizat ion of popular songs. It shows up most frequently in the bII 7M root position form. The most common way to explain it is through its origin fro m the Phryg ian mode, considered a modal interchange.
The shape of this structure however, may be explained by its origin, as described by Spossobin on page 352 of the 47 th Theme: "The most significant and commonaltered subdominant chord is b1 sII, fo rmed by the sII of the minor and the harmonic major mode, through the alteration of the chord's root. In addition to the lowered fifth of the minor subdominant chord, the first inversion contains an altered sixth, formed between the lowered root and the third of thechord.This lowered II major triad in its first inversion isthe Neapolitan sixth chord, sometimes called Neapolitan harmony. It first appeared in works of XVII century composers from the Neapolitan Opera School (A. Scarlatti, A. Stradella and others), as a Ph rygian minor mode harmon ic compound [1]." Spossobingoes on to explain the use of the seventh in Neapolitan harmony: "A passing tone between the b1 sII 6 altered tone and the dominant third gradually created a new Neapolitan harmony -the Neapolitan seventh chord ( b1 sII 7 ). Co mbin ing s and b1 sII 6 in the majo r and minor mode altogether shaped it. It is a majo r chord due to themajor triad and its seventh [1]." Indeed, the appearance of the Neapolitan chord in root position is quite peculiar: "Later, the lowered II triad in root position appeared. Originating fro m the Neapolitan sixth chord, it emerged in a singular way, as if it had been an inversion form the original chord [1]." Table 4. Examples of Songs with Neapolitan Harmonies

Elli psis
In linguistics, ellipsis (fro m the Greek élleipsis, "omission") refers to the absence of one or mo re words fro m a clause. In Spossobin's Manual it refers to the lapse of an expected resolution. Other designations, such as deceptive cadence, deceptive resolution and irregular resolution appear in Schoenberg's Theory of Harmony, page 136 [3], and Piston's Harmony, page 191 [10]. The concepts of ellipsis and irregular resolution have not been applied to the harmonic analysis of popular music. In some cases these terms were rep laced by extended and consecutive dominants that deal specifically with a do minant chord resolution in which the tonic preserves the major triad but adds a minor seventh, changing it to a dominant chord (Chediak, page 266 [2], and Guest, page 99 volu me 1 [4]). The concept of extended dominants is related to a generic jazz notion that defines a dominant chord as a preparation chord: due to its tension it can prepare or precede any chord placed a fifth below. For examp le, the dominant of the do minant chord (V7 -V7), a secondary dominant, involves a situation in which a do minant chord precedes another chord with the same structure and does not have the expected resolution, typically to a stable major or minor chord. According to Spossobin, the double dominant chord, as defined in the Manual, does not characterize ellipsis as long as the resolution is not omitted. On the other hand, ellipsis does take place in the case of consecutive dominants since the resolution chords are continuously replaced.
The notion of ellipsis does not appear in Chediak and Guest, but is replaced by the deceptive resolution, the same as described by Schoenberg, (page 137): "This term is understood to mean the substitution for the expected progression, V-I" [3], and mentioned by Philip Taggon in his article Troubles with tonal terminology, page 9 [8]. Guest (page 70, volu me 2) describes it as follows: "The deceptive resolution occurs when the dominant chord does not lead to the predictable resolution" [4].
Spossobin exp lains the term on page 426 of the 56 th Theme: "Literally meaning absence or o mission, ellipsis is formed by replacing the expected chord with any other without delay, in the functional sequence of the first chord. Ellipsis ju xtaposes two chords that have no immediate relation such as dominant and tonic, subdominant and tonic or DD and D [1]." Harmonic progressions, understood as extended and consecutive dominants, are exp lained on page 430: "the expected tonic chord is replaced by the dominant seventh chord, built on the same bass note of the tonic chord, so as to create the dominant cycle, ending, in most cases,with D7 of S or SII [1]." The use of extended dominants is one of the harmonic situations that can be called ellipsis in popular music. Somet imes the resolution to extended dominants is delayed due to the interpolation of a subdominant chord. Interpolated subdominants can appear in situations as often in ellipsis as in inclinations. (See the examp les of inclination above).

The Seventh Di minished Chord
The seventh diminished chord is commonly designated as a diminished chordon the VII degree of the harmonic minor scale. This chord has become, fo r many reasons, one of the most useful harmonic elements in popular music. As a result, its origin fro m the harmonic minor scale has been forgotten in various harmonic progressions and does not even appear in the chord symbol used to notate the dimin ished chord.
Chord symbol notation is, by and large, insufficient to represent harmonic elements. Conventionally it does not indicate the inversion as commonly used for all other chord labels, as for example, Dº would stand for Bº/D. In so me harmonic progressions the chord symbol of a root position is given, though it is actually an inversion. This kind of simp lification has some advantages, though it may cause misunderstandings. In any case, one should note that the same chord symbol used for root positionmightbe used to represent an inversion of other chords, sometimes as an enharmonic equivalent.
In general, in popular music diminished chords has two different functions: • As a dominant chord of the seventh degree, wh ich precedes the tonic chord.
• As an element derived fro m the combination of altered tones.
Both can appear as auxiliary or chro matic passing chords, sometimes without the dominant function. A passing chord can be explained as follows: the bass note of a d iminished chord becomes a passing tone between two other bass notes, in ascending or descending stepwise motion.
Dimin ished chords preceding secondary tonics can be easily seen as having dominant function because they are related to the tonic as its seventh degree.
Dimin ished chords, however, do not have a dominant function when resulting fro m some other chords in which altered notes or non-chord tones are inserted. In any case, the melodic relation prevails over the harmon ic relat ion: melodic motion in inner voices is made by chromatic or diatonic approach notes and prevails over the harmon ic relat ion. They are voice-led chords and are designated as approach chords having no dominant function at all, regard less of whether the root moves up or down stepwise.
On the contrary, the seventh degree diminished chord is always connected to the resolution, up one degree in root positionor other intervals, depending on its inversion.
Dimin ished chords may lin k neighbouring diatonic chords by moving the bass up or down. They are known as passing dimin ished chords because of the chromatic passing tone in the bass. However, they can function as auxiliary chords (Iº or Vº) when they have the same bass note as the first and the fifth degrees.
In Spossobin´sManual,diminished chords are not dealt with in one exclusive Theme (chapter). In the 22 nd Theme they are explained in the context of the seventh degree of the minor scale, together with the seventh degree of the major scale, which, though built differently, has the same dominant function. The use of the VII chord of the major scale is not as widespread as that of the minor. However, the examples presented in the book are useful for both major and minor modes.
In the 57 th Theme, devoted to enharmonic modulation, the dimin ished chord is dealt with exhaustively on page 439: "Enharmonic modulation by way of the diminished seventh chord is one of the most widespread examples of abrupt changes in tonality and a consequence of the universal possibilit ies inherent in this chord. Th is type of modulat ion is based on the fact that dimin ished chords, in terms of sonority, have only three possibilities, though they can be formed on any of the twelve pitches of the chro mat ic scale. Thus each of the three inversions of the seventh diminished chord can resolve to any tonality as the leading tone of T, S or D [1]." The examp les are very specific and comply with the chord resolution and in every enharmonic situation. The co rrect notation is consistent with the expected tonality and the prevailing key signature.
The 57 th Theme deals with the diminished chord involving only the dominant function on the seventh scale degree. In other harmonic situations that include the dimin ished chord, the chord in question is built with non-chord tones.
The examp les below demonstrate two types of dimin ished chords: as a seventh degree chord and as an auxiliary chord formed with auxiliary notes. Both types can feature passing chords, unlike the auxiliary chord that can never have dominant function. Harmonic co mpounds, or сосвучие, refer to non-harmonic tones or non-chord tones. Similar to the`non-harmonic´ tones discussed by Schoenberg, (page 309 [3]) and Piston, (page 109 [10]): these are also defined in the introduction but developed in later chapters. So me of them are dealt with in separate chapters, for examp le the delayed notes are in the 36 th and 37 th Themes, passing tones in the 38 th , 39 th and 41 st The mes.
Unlike tert ian chords, harmonic co mpounds are formed by intervals other than thirds: they are random structures that appear accidentally in the melodic-harmonic relat ionship. The 44 th Theme defines how these structures can be shaped, rather differently than the tertian chord.
Nevertheless, the accumulation of non-chord tones can occasionally form structures in thirds and are similar to the diatonic chords without the corresponding harmonic function. Dimin ished chords without dominant function are included here. While their structure is actually tertian,their function does not correspond to the seventh scale degree of the harmonic minor.
There are other harmonic situations in which chords do not correspond to their apparent function, such as minor chords that become dominant chords through the insertion of an altered tone. Despite this modificat ion they maintain their original function.
The sus4 chord can be explained in much the same way: the perfect 4 th is inserted as a suspended tone, but is considered part of the chord because of its intensive use. Due to its repeated use over time, the delayed tone lost its sense of novelty.There are nu merous songs containing the perfect 4th, of which a few were selected for the list below.