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  1. Jun 2023
    1. The opposite situation is what Krebs calls metrical dissonance.I will argue that in jazz styles where swing rhythm is pervasive, halvingthe prevailing note-value can produce metrical dissonance, and that this dissonance is one of the main factors contributing to listeners’ perception of double time.To consider the idea of swing eighth notes in terms of Krebs’ metrical layers, I will callthe quarter-note level of rhythm the “beat layer” and the level at which quarter notes have been subdivided into swing eighths the “sub-beat layer.” The beat layer and sub-beat layer can be regarded as two different ways of grouping a third layer of
    2. Music theorists have long been aware that different levels of beat are often simultaneously available to the listener. Harald Krebs (1999) uses the term “metrical layers” to describe this phenomenon. In the normal case, metrical layers nest neatly insideone another; they are metrically consonant with each other. This occurs, for example, in Pachelbel’s Canonas the prevailing note-values are repeatedly halved. Figure 3.1 shows this nesting relationship between layers. There is no need for a separate micropulse layer because the layers are metrically consonant: both eighth notes and quarter notes can be expressed as groupings of sixteenth notes.
    3. “Double time”is defined by the New Grove Dictionary of Jazzas “the apparent doubling of the tempo [...] achieved by halving the prevailing note-value” (Kernfeld, 2002). In an explanation of the same term written for a popular audience, the book What to Listen for in Jazzclarifies that double time “involves a doubling of tempo in the rhythm section, a doubling of the general speed of the melody line, or both” (Kernfeld, 1997).The Grove’s use of the word “apparent” implies that the tempo has not in fact doubled. To emphasize this point, some authors prefer the more precise term “double-time feel,” reserving the term “double time” for a true doublingof tempo(Levine, 1995).
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    1. Chapter 25 discusses various approaches to jazz reharmonization. It begins by consideringtwo contrasting approaches to harmony: vertical and horizontal. Eleven basic techniquesof reharmonization are introduced and demonstrated using Joseph Kosma’s “AutumnLeaves.” More advanced linear techniques are shown in the context of Jerome Kern’s “Allthe Things You Are” and Victor Young’s “Stella By Starlight.”
    2. The hexatonic scale is a six-note collection that conveys characteristics similar to theseven-note modes. Just like pentatonics, hexatonic scales have more interesting intervallicproperties and provide essential notes for melodic lines and harmonic formations. Thehexatonic collections are compartmentalized in the familiar categories and scales are gener-ated from aggregates of pitches that contain all available notes from the particular category.For instance, since the pitch aggregate for the major category contains eight notes, thereare a number of options for creating different major hexatonics. Given the enormous rangeof options, it is best to pick a scale whose pitch content best conveys specific modalcharacteristics.The derivation of hexatonics from the aggregate puts the understanding of pitch hierarchyto the test. The pitch structure of different hexatonics prioritizes only those notes thatare essential to projecting the exact harmonic function and/or intended chord–scalerelationship. Each category below includes two types of hexatonic collection: regular andaltered. Regular hexatonics share common characteristics with the corresponding modes.For instance, Mixolydian ≥11 hexatonic has similar properties to the seven-note Mixolydian≥11 mode, etc. Altered hexatonics are derived from the specific pitch aggregate and theirstructure includes minor variations from regular hexatonics. In labeling altered hexatonics,use the name of the category with Roman numerals specifying different variations (i.e.Major Altered I, Dominant Altered II, etc.)
    3. The blues is an American art form. Originally, blues were primarily sung, with one of theobjectives being to tell a story as vividly as possible. To tell stories, blues singers usedsimple repeated phrases charged with a variety of expressive devices. The ability to tell thestory from one’s perspective came to represent blues performance practice in particular,and jazz improvisation in general. The familiar saying that “your solo should tell a story”takes on a completely different meaning when we consider whence it came and howintricate life’s stories can really be. Early blues practitioners were unconstrained by theform of the blues as the duration of improvised lyrics often influenced the length of
    4. The terms “turnaround” and “tag ending” are generic labels that do not indicate a partic-ular chord sequence; rather, they suggest the specific formal function of these progressions.In jazz, there is a certain subset of harmonic progressions whose names suggest specificchord successions. When jazz musicians use the term “Lady Bird” progression,for instance, it connotes a particular chromatic turnaround from Tadd Dameron’s tuneof the same title recorded in 1947. Figure 13.9 illustrates the chord structure of thatprogression using Model VI of harmonic realization
    5. Jazz musicians often use different harmonic substitutions to modify the content of diatonicprogressions. The most common harmonic modifications of the Imaj 7 –vi 7 –ii 7 –V 7progression involve the use of secondary dominant chords (V7/X), and tritone substitutions(TR/X 7). Figure 13.5 demonstrates these substitutions using Model III of harmonicrealization.The secondary dominant 7ths A7 and D7 are analyzed with two different Roman numerallabels VI7 and V 7/ii, and II 7 and V 7/V, which can be used interchangeably. The tritonesubstitutions, E≤7 and D≤7, also use two Roman numerals, ≤III7 and TR/VI7, and ≤II7and TR/V7, respectively
    6. The ii7–V7–Imaj7 progression constitutes the perfect vehicle to introduce one of the mostimportant features of jazz harmony: the tritone substitution, notated as TR/X 7. Thetritone substitution has its theoretical origins in the equal or symmetrical division of theoctave. This substitution is associated with the dominant 7th chord and capitalizes oninversional invariance of the tritone inherent to the dominant 7th formation.
    7. n order to become a successful jazz musician, one has to learn how to read, interpret,and modify lead sheets. Improvising from a lead sheet is a unique performance skill thatjazz musicians cultivate on a daily basis and perfect over a long period of time. Comparableto other shorthand notations from classical music, such as figured bass, tablature,partimento, or others, lead-sheet notation contains just enough essential information tocreate a complete performance
    8. The progression shown in Figure 9.9 exemplifies the structure of a minor blues.4The chord structure of the minor blues is characterized by the presence of traditionaltonal progressions. For instance, the tonicization of iv in m. 4 uses a secondary dominant7th, V7/iv, and the motion to V 7 in m. 10 is prepared by the ≤VI7 chord. This particularpreparation of the dominant 7th, ≤VI7–V7, is one of the harmonic trademarks of the minorblues.
    9. In the most fundamental form, the generic blues consists of only three chords: I7, IV 7,and V 7. These harmonies control the structure of the blues, even though in some chordprogressions, particularly those from the Bebop Era, they might be disguised, substituted,transformed, or omitted all together. The generic or three-chord blues, without anyadditional chord changes, was often employed in early jazz, particularly in Early Blues,Boogie-Woogie, and different New Orleans styles.3 We will now examine the harmonicstructure of a slightly modified blues (one that is probably the most common in jazz),
    10. Having examined the structure of the blues scale, we can now explore the tonal potentialof the scale.2 Figure 9.4 illustrates the structure of G blues scale.This scale has a minor feel to it; notice the use of ≤3, ≤5, and ≤7. By starting the scale onB≤3 and continuing through the octave, we are able to generate a major scale that, inaddition to having the “blue” 3rd, also contains the major 3rd needed for major anddominant 7th chords. A major blues scale, shown in Figure 9.5, starts on ≤3 of the regularblues scale, contains a perfect 5th, major 6th, and major 9th, and establishes a convincingchord–scale relationship with the B≤6/9, B≤13 or other B≤–based dominant 7th chords.In addition to more generic usage of the blues scale (where a single scale is used in thecontext of different chords), we can be more discerning and assign a regular blues scaleto minor chords and a major blues scale to major and dominant 7th chords.
    11. The musical depiction of the lyrics from Figure 9.2 illustrates an additional aspect of bluesperformance practice—the use of call and response. Originally practiced by a large groupof people, this improvisational technique involves sharing ideas between the leader andher/his followers. Mastering the call and response technique is especially important at thebeginning of our encounter with jazz improvisation. It engages us in a meaningfuldialogue that includes exchanging and communicating musical ideas. The communicativeaspect of call and response is relatively straightforward in the context of verbal conversation.

      In a musical setting, however, when spoken words and sentences are replaced with motifs and melodic phrases, the structure of the call and response might not be as obvious. To be a good communicator, we have to know how to listen, pay close attention to what the other musicians are playing, and try to be receptive to their ideas. In certain scenarios, however, the use of call and response technique might create less than desirable effects. For instance, when the call and response takes the form of exact and immediate repetition, it might be impressive but not necessarily in keeping with the surrounding musical context. A much more subtle way of thinking about the call and response technique involves musical interaction at the level of the entire performance in which non-adjacent sections relate to one another, and where the flow of the performance is regulated by logically introduced musical ideas. In creating a musical narrative, then, we can also respond to each other’s playing, but these responses are not as obvious as simple repetitions tend to be. We can demonstrate our listening skills, for instance, by incorporating an idea that we have previously heard (i.e. a rhythmic motive from the drummer, or a melodic gesture from the guitarist) and develop it in such a way that leads to a more satisfying musical discourse. The call and response aspect of improvisation means that musicians understand each other’s intentions, have an unspoken agreement, so to speak, and project them with a high level of personal expression and musical commitmen

    12. In jazz terminology, the term “voicing” refers to the arrangement of notes within a chord.That arrangement can be either close or open. In a close voicing the arrangement ofnotes is the most packed possible. In an open voicing, the arrangement of notes is

      intervallically more diverse. The most common method of generating an open voicing is to drop certain notes from a close-position chord down an octave. In a “drop 2” voicing, the second note, counting from the top note, is dropped down an octave. “Drop 2” refers to voicings above the bass in which the bass note is not counted as one of the voices being “dropped.” Each chord in Figure 4.15 includes three “drop 2” voicings because the three notes above the bass can be rotated three times.

      see figure 4.15 on p 47

    13. Broadly speaking, voice leading controls the interaction between chords and lines withinharmonic progressions. The principles of voice leading encompass several general topics,such as the role of outer-voice counterpoint, the types of melodic motion, the retentionof common tones, the treatment of dissonances, and others that will be discussedthroughout the book.At the surface level, jazz voice-leading conventions seem more relaxed than they are incommon-practice music. After all, jazz musicians use forbidden parallel perfect fifths andoctaves, move all the voices in the same direction, and tolerate voice crossings of differentsorts. The rules of jazz voice leading are different because the syntax of jazz is largelyincompatible with common-practice classical or other types of music. These differencesdo not mean, however, that the rules of jazz voice leading are any less strict. When jazzmusicians think about dissonance treatment or highlight a linear approach to harmony asopposed to a vertical one, they rely just as much on well-defined rules of voice leading asdo composers of common-practice music. The conventions of jazz voice leading dependgreatly on the soprano and bass, so-called outer-voice counterpoint.
    14. The function symbol notation is the least used notational system in jazz. As the namesuggests, this notation specifies the harmonic function of individual chords and evencomplete chord progressions. It has the potential of being useful to notate specificbehaviors of chords that may not—at least, not on the surface level—indicate that theybelong to a particular functional family of chords. As such, function symbols enable theperception of harmonic progressions from a more structural perspective. Function symbolsindicate neither the architecture nor the specific scale degrees of chords. This style ofnotation is more conceptual than it is representative of a specific surface event. The termssurface level and structural level are used to describe musical events and the degree oftheir importance. “Structural” events occur beneath the musical “surface” and areresponsible for the overall tonal, harmonic, and melodic forces controlling the piece.Function symbols use three labels: T for tonic-type chords, PD for predominant-typechords, and D for dominant-type chords.
    15. Lead-sheet notation, also known as popular-music notation, is by far the most widespreadnotational convention used by jazz musicians. It comes in a variety of forms that arisefrom its murky origins and subsequent vague implementations. There are many alternatenotational systems in use, which for better or worse every jazz musician needs to getfamiliar with for purely practical, “bandstand” reasons. Here, we will only use chordsymbols that are commonly found in published and respected fake books. Lead-sheetnotation is very specific in showing what the chord is: it indicates the letter name, theexact number and types of extensions occurring within a chord, chordal inversions, orcomplex polychordal formations. A chord symbol, then, provides a quick insight into thechord’s pitch content. As such, it can be easily transmitted into a voicing that capturesthe essence of that symbol. The downside of this labeling is the lack of contextualconsiderations, especially in regard to the underlying tonality. As a tonally “uninterpreted”notation, we are not quite sure, for instance, how chords relate to one another, how theirbehavior conveys the underlying tonality, and what the overall tonal logic of differentchord successions may be.In this book, upper-case letter names will be used to indicate major-type chords. For minor-type chords a “min” extension following an upper-case letter name will be used. The lead-sheet symbols from Figure 3.6 also employ slash notation; this specifies a chord typewith the lowest sounding pitch separated by a diagonal slash. An upper-case letter nameto the right of the diagonal indicates the chordal root. The letter name to the left of thediagonal shows a specific chord type.
    16. Figure 3.6 illustrates the structure of four triads and their inversions labeled with threesets of notational symbols: traditional lead-sheet notation above the staff, and Romannumerals and function symbols below the staff. Since we will use them interchangeablythroughout the book, let us make some general observations about their usefulness intheory and practice. Each of these notational conventions has unique advantages, but alsosome obvious shortcomings.
    17. harmonic functioncan be defined as a contextual feature that can be attributed to a chord, a family of chords,harmonic progressions, or even to complete melodic phrases. These features are uniquefor each of the following functions: the tonic, the predominant, and the dominant. Theinteraction between these three creates a system of functional tonality, which undergirdsthe structure of tonal jazz and common-practice music
    18. The use of dynamics, legato, and especially articulation can substantially improve the overallpresentation of melodic lines. Generally, the use of dynamics should roughly follow thecontour of the melodic lines. Rising lines are typically played with a slight crescendo anddescending lines with a slight diminuendo. Additionally, melodic lines should be playedalmost legato with barely perceptible note detachment. Carefully distributed articulations(dynamic accents, staccato, tenuto, marcato, etc.) are also an essential component ofphrasing.
    1. Riemann was first and foremost an empirical scientist who sought to adequatelydescribe the practice of music composition (being a composer himself) and ways of howlisteners perceive and make sense of these compositions. Neo-Riemannians, in contrast,try to forge a universal "nomothetic" music theory that would prescribe a set of "laws" thatsupposedly secure the creation of "good" musical compositions - this, in essence, is thefoundation of the Schenkerian approach. (Schenker seems to have come up with his ideasfrom his experience of correcting mistakes of his pupils in the conservatory that they madein their written harmonization exercises).

      Lewin used mathematics to abstract 2 models: the Generalized Interval System (GIS) andthe Transformational network. The former was supposed to define a set of musical objects,generalize intervals of pitch and time, and infer mathematical functions that mapped all Page 6 of 16possible pairing of musical objects. “Transformations” were supposed to model possibleactions upon the musical objects. Such modeling might be useful for automatic computer-based analysis of music and for the design of psychoacoustic experiments, but it hasnothing to do with the pragmasis of musical communication. This is not that different fromthe notorious theory of generative grammar by Chomsky, which Chomsky himself had topronounce wrong, but which nevertheless proved to be very useful for computerized studyof languages. The dichotomy between the nomothetic math-based prescriptive and empirical psychology-based descriptive approaches to music theory dates back to Classic Antiquity, to thefamous criticism of Pythagorianism by Aristoxenus (the Aristotle's pupil). A brilliant old-timeAmerican music theorist and ethnomusicologist, Norman Cazden, succinctly summarizedtheir arguments in his essay: Cazden, Norman. 1958. “Pythagoras and Aristoxenos Reconciled.” Journal of theAmerican Musicological Society 11 (2/3): 97–105.https://doi.org/10/gmnfj5.Riemann's main idea was that chords that emerge from the counterpoint of multiple partsend up forming a finite number of harmonic "classes". These classes are consistentlyreproduced in different keys and in different compositions by different composers in avariety of implementations (e.g., inversions) and can be identified by their harmonicfunctions - i.e., relative fluctuations in harmonic tension and relaxation, which determinedthe positioning of these classes within a musical form. Unlike the Neo-Riemannian"transformations", these functions reflected the conventions of musical communicationbetween composers, performers, and listeners - the common practice of engaging specificharmonies to initiate, terminate, and culminate musical phrases and sentences. Importantly, Riemann made a few critical errors in defining the functional characteristics ofminor keys and what he called iambic meters. However, these shortcomings werecorrected by his followers - especially in Russia, where the "Golden Age" of classical musicpromoted the boom of music theory, and the widespread of modal folk music, very differentfrom Western music, directed music theorists towards greater attention and deeperunderstanding of principles of tonal organization that guide creators of very diverse musiccultures. As a result, Riemann's theory of functional harmony merged with the theory ofmusical mode. In contrast, in the West, modal theory was largely abandoned after the 17th century. Thedifference between musical mode and musical scale (a principal structural unit of theSchenkerian and Neo-Riemannian theorists) is that mode incorporates not only a set ofpitch classes but also the functional relations between them as revealed in typicalprogressions of harmonies within a given musical composition. From this point of view, notall compositions nominally created in the same key share the same functionalcharacteristics. A C-Major prelude from volume I of the Well-Tempered Clavier by Bach, C-Major "Simple" sonata by Mozart, “Locus iste” by Bruckner, Bolero by Ravel, "DoctorGradus at Parnassum" by Debussy, Valse des fleurs by Stravinsky, and "Juliet - the girl",No.10 from Prokofiev's ballet "Romeo and Juliet" - all these compositions noticeably differ Page 7 of 16No.10 from Prokofiev's ballet "Romeo and Juliet" - all these compositions noticeably differin the use of harmonic progressions and therefore present different modal implementationsof the same key of C Major. Neo-Riemannian analysis fails to capture their differences(that are quite obvious from mere comparative listening to these pieces), while RussianRiemannian-based analysis easily spells out their specificities.

    1. I think that Riemannian theory applies to anymusic culture where multi-part textures occupy an important role, and music-users observe harmonic intervalsor/and chords. Technically speaking, even West African indigenous cultures that utilize parallel motion of chords (as identified and described by Kubik in his many books on African harmony) possess at least some basic harmonic functions. Although their harmony is generated by the 3-part dubbing of a melody in parallel thirds, the interaction of such dubbings with the metric grid inevitably puts in place some hierarchical distinctions between chords that are built on different degrees of melodic modes. Chords on those degrees that systemically fall on weaker metric time are likely to become subordinated to those chords that fall on stronger metric time. This is exactly the foundation of Riemannian theory.

      If you are interested, here is a thorough critical overview of Riemannian approach:Rehding, Alexander. 2003. Hugo Riemann and the Birth of Modern Musical Thought. Cambridge University Press.Below are a couple of reviews of the applicability of Riemannian principles to jazz:McGowan, James. 2010. “Riemann’s Functional Framework for Extended Jazz Harmony.” Intégral 24: 115–33. https://www.jstor.org/stable/41495296.Capuzzo, Guy Capuzzo. 2004. “Neo-Riemannian Theory and the Analysis of Pop-Rock Music.” Music Theory Spectrum 26 (2): 177–200. https://doi.org/10.1525/mts.2004.26.2.177.All Soviet and Russian musicology is based on Riemann

    1. relatively undemanding by comparison with those based on chord progressions. Because it is free of frequent harmonic interruption it can more easily create an unhurried and meditative feeling. Many performances are based on a two-chord sequence or a drone. The absence of frequent chord changes alone is sometimes regarded as defining modal jazz
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