Recent work has revealed several new and significant aspects of the dynamics of theory change. First, statistical information, information about the probabilistic contingencies between events, plays a particularly important role in theory-formation both in science and in childhood. In the last fifteen years we’ve discovered the power of early statistical learning.

With the exception of the blues, the rhythm changes progression is probably the mostimportant chord progression in jazz. The term “rhythm changes” refers to a 32-bar AABAform based on the harmonic structure of “I Got Rhythm” by George and Ira Gershwin.The song appeared in the Aarons and Freedley production Girl Crazy (1930) andoriginally featured a 34-bar AABA form with a two-bar extension in the last A section.The two-bar extension was eventually cut and the chord changes of the last A sectionreplicated those from the second A. A newly composed line based on the rhythm changesprogression is known as a contrafact. The enormous popularity of rhythm changes hasbeen well documented by an ever-increasing number of composed contrafacts andrecordings

During the Baroque Era, the “Rule of the Octave” was a practical tool that enabledmusicians to gain harmonic flexibility at the keyboard.5 The rule prescribed how toharmonize a scale in the bass using stylistic tonal progressions. In jazz, a similar rule canalso be developed. Instead of placing the scale in the bass, the major scale is placed in thesoprano voice. The jazz rule of the octave explains how to harmonize a descending majorscale with idiomatic jazz progressions. By examining different harmonic outcomes, therelationship of melodies to chords and chords to melodies becomes clear. The jazz ruleof the octave also helps us to realize the harmonic potential of different melodic segmentsand examines their behavior in the context of underlying chord progressions. Figures21.3a–21.3d illustrate four distinct harmonizations of the descending major scale

John Coltrane’s recording of Giant Steps in 1959 epitomized his three-year period ofharmonic explorations, most notably with symmetrical intervallic cycles. 3 Hiscomposition “Countdown,” which is based on Miles Davis’s “Tune Up,” illustrates theuse of so-called “Coltrane” substitutions. Characterized by fast harmonic rhythm, thissubstitution projects a major-third cycle in which each local major 7th chord is tonicizedwith the corresponding dominant 7th. In the context of the Dmin7–G7–CMaj7progression shown in Figure 13.10, the first member of the major-third cycle, ≤VImaj7,is accessed through its dominant 7th that follows the structural predominant, ii 7. Thenext member of the major-third cycle, IIImaj7, is also preceded by its dominant, V 7/III,before the progression completes its trajectory with the structural dominant 7th resolvingto the tonic.

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.”

chromatic [ii≤57–V7]/x interpolation

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

Figure 9.8 establishes a couple of chord–scale relationships for the basic blues progressionin the key of B≤. Figure 9.8a uses major and minor blues scales and Figure 9.8b combinesblues scales and modes

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),

Chapter 6 investigates the most important progression in jazz—the II–V–I—and its twotonal variants: ii7–V7–Imaj7 and ii≤57–V7–i7. A discussion of guide tones, secondary dominant7ths, and diminished 7th chords and their subsequent voice-leading transformations furtheramplifies the importance of the progression

The Blues Progression

Standard Chord Progressions

II–V–I

Idiomatic Jazz Progressions

at the targeted level

The goal of this progression is to build up gradually, with each step building on the previous one,

progression starts with Beginning, where the student tries to write a conclusion

Speech and thought arc inseparable, in Vico'., view: They evolve together.

But in this brightest and kindest world, the philosophical problems themselves become intimidating. A mind that stays at the same capacity cannot live forever; after a few thousand years it would look more like a repeating tape loop than a person. (The most chilling picture I have seen of this is Larry Niven’s story “The Ethics of Madness.”) To live indefinitely long, the mind itself must grow … and when it becomes great enough, and looks back … what fellow-feeling can it have with the soul that it was originally? The later being would be everything the original was, but vastly more. And so even for the individual, the Cairns-Smith or Lynn Margulis notion of new life growing incrementally out of the old must still be valid.

Medicine, when fully taught, is usually subdivided into several professorships, but this cannot well be without the accessory of an hospital, where the student can have the benefit of attending clinical lectures & of assisting at operations of surgery. With this accessory, the seat of our university is not yet prepared, either by its population, or by the numbers of poor, who would leave their own houses, and accept of the charities of an hospital. For the present therefore we propose but a single professor for both medicine & anatomy.