By Timothy A. Johnson
An introductory, undergraduate-level textbook that gives a simple access element into the not easy box of diatonic set idea, a department of tune idea that applies the recommendations of discrete arithmetic to the houses of diatonic scales. --from writer description advent -- bankruptcy 1. Spatial kinfolk and musical constructions -- bankruptcy 2. period styles and musical buildings -- bankruptcy three. Triads and 7th chords and their constructions -- end
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Extra resources for Foundations of diatonic theory : a mathematically based approach to music fundamentals
E harmonic minor scale B C CLOCKWISE DISTANCE BETWEEN DOTS C D A A d distance c distance D E G G F F Maximally even? b. B melodic minor scale (ascending) B C CLOCKWISE DISTANCE BETWEEN DOTS C D A A d distance c distance D E G G F F Maximally even? qxd 9/4/02 11:21 AM Page 36 c. F melodic minor scale (descending) B C CLOCKWISE DISTANCE BETWEEN DOTS C D A A d distance c distance D E G G F F Maximally even? 7 is maximally even. 7c, is maximally even? 5 on p. 20). Are there any similarities? 5, by visual inspection rather than by using the formal definition.
Chromatic notes are labeled in these circle diagrams with sharps only, for consistency; to plot a flat note, use the corresponding enharmonically equivalent note (for example, A for B ). 6 Check the musical structures indicated on the staves to determine if they are maximally even according to the definition. Plot each structure on the circle diagram, and complete each interval table. a. B C CLOCKWISE DISTANCE BETWEEN DOTS C D A A d distance c distance D E G G F b. B C Maximally even? F CLOCKWISE DISTANCE BETWEEN DOTS C D A A d distance c distance D E G G F F Maximally even?
However, no matter how an augmented triad is inverted, it still can be interpreted as a root position augmented triad by sound alone (disregarding enharmonic spellings). 1a, suggest that any of the three dots can serve as the root (or starting dot) of this chord. It is only the spelling (or specific note names) that designates a root. When you play the notes on the piano, you can identify the structure as an augmented triad by sound, regardless of which note you use as the starting note. In this way, you can identify the chord by ear, even if the actual spelling of the notes diverges from the pattern you would have expected.