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By Timothy A. Johnson

An introductory, undergraduate-level textbook that offers a simple access element into the tough box of diatonic set idea, a department of track conception that applies the strategies of discrete arithmetic to the homes of diatonic scales. --from writer description advent -- bankruptcy 1. Spatial kinfolk and musical buildings -- bankruptcy 2. period styles and musical constructions -- bankruptcy three. Triads and 7th chords and their constructions -- end

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Also, the two bracketed pairs of dots at the top of the diagram have respective c distances of 1 (between B and C) and 3 (between C and D ), based on the number of half steps between these notes. 6 Sample procedure for counting c distances and d distances 1 1,c= d= =3 C ,c B d= 1 C A D A D G E d= G F F 2, c= 3 Definition of Maximally Even Now that we have defined c distances and d distances, we can use these terms to define the term maximally even. To determine if a circle diagram is maximally even, we will measure the clockwise distances between every pair of dots (or notes).

This fundamental arrangement of black and white keys, and therefore the intervals between the notes they represent, continues to represent our standard approach to the organization of notes, prevailing even in most computer applications through the MIDI standard. The complementary relationship between the seven-note and five-note maximally even structures, so familiar because of their arrangement on the keyboard, also can be seen in the circle diagrams. Because both the pattern of dots and the pattern of spaces in these diagrams are maximally even, the pentatonic collection and the diatonic collection are complements of each other.

5, by visual inspection rather than by using the formal definition. 7 have different intervals, as determined in reference to the tables and in the discussion that follows. 7b) is perhaps closest to maximally even; only the d distances of 3 and 4 have three different c distances, rather than the required one or two consecutive c distances. In musical terms, the scale includes diminished fourths (c distance of 4: A –D), perfect fourths (c distance of 5: B–E, C –F , F –B, G –C ), and augmented fourths (c distance of 6: D–G , E–A )—each with a d distance of 3.

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