A simplified schematic diagram may be created by using rectangles to
represent each of a chord's relative frequencies. To construct such a diagram,
find the least common multiple, or smallest number into which each of the
members of the set can evenly divide. Then for each note, divide the least
common multiple by its relative frequency.
In the case of the C major triad, the least common multiple of the relative frequencies 1, 3, and 5, is 15. The next step is to measure off 15 equal divisions, or units. To find the length of rectangle C1, divide the least common multiple by 1, which provides the length of 15 units. Likewise, the length of rectangle G3 is 15 divided by 3, or 5 units. Finally, the length of rectangle E5 is 15 divided by 5, or 3 units.
Figure 7
Simplified Schematic Diagram of C Major Triad
(1 Period)
Figure 8
Simplified Schematic Diagram of C Major Triad
(3 Periods)
In the case of the F minor triad, the least common multiple of the relative
frequencies 3, 5, and 15 is 15. The next step is to measure off 15 equal
divisions, or units. To find the length of rectangle A-flat 3, divide the
least common multiple by 3, which provides the length of 5 units. Likewise,
the length of rectangle F5 is 15 divided by 5, or 3 units. Finally, the
length of rectangle C15 is 15 divided by 15, or 1 unit.
Figure 9
Simplified Schematic Diagram of F Minor Triad
(1 Period)
Figure 10
Simplified Schematic Diagram of F Minor Triad
(3 Periods)
Two observations based on simplified schematic diagrams of the previous two chords can readily be made:
The above statements hold true for any chord whose constituent frequencies
are all integer related.
The following conclusions may be drawn from the observations of vertical alignment and symmetry of chords represented as simplified schematic diagrams. (Chord is defined here as a fixed set of continuous frequencies equal in duration and occurring simultaneously.)
