He acknowledged that a great deal of familiarity was needed with these more complex ratios before they could be heard and reproduced accurately, and that this complexity was hierarchical: the intervals derived from the eleventh partial, which form the limit of his own pitch usage, Partch held to be more complex relationships both physiologically and in terms of historical usage than the intervals derived from the seventh partial, and the septimal intervals in turn as more complex than those derived from the fifth partial, which were (and are) the familiar basis of Western tuning practice.
More complex relationships, such as the septimal minor triad 1/1-7/6-3/2, can be "explained" by examining its geometrically more elaborate configuration on the lattice.
live has been that you spend the first four hours becoming familiar with the cozy septimal minor third, the expansive septimal major third, and by the fifth hour you can hardly remember that intervals had ever been any other sizes.
These show that Young's initial interest in the tuning was the possibility of septimal thirds and septimal triads (9/7/6).
Section 5 (1:21:54-2:06:06): In theory, the Magic Harmonic Rainforest Chord combines the pitches of the Magic Chord with those of the Harmonic version of the Opening Chord, spread through all octaves; in this performance, however, the section primarily reduces the pitch spectrum back to the Opening Chord, though with the addition of a mournfully dissonant minor third, 147/128 [G.sub.b], and occasionally the "flat" septimal fourth 21/16 G as an alternative.
the lower note is resolved downward by step, as in the Simple Sequence (Example 14).(8) The upper note of the septimal major seventh 27/14 is also usually resolved downward by step in the Theme of the Dawn of Eternal Time and in the Romantic Cadence.
Young favors these notes as pedal points because of the 9/7 major third and the septimal major seventh 27/14, the latter available over no other tonic.
Not only does this scheme encompass the familiar intervals from the lower reaches of the series - the octave (2/1), perfect fifth (3/2), perfect fourth (4/3), just major third (5/4), and just minor third (6/5) - but also unfamiliar kinds of every interval class, derived from the seventh partial and the eleventh partial: for example, the septimal
tritone 7/5 and its inversion 10/7 (also a "tritone" but a slightly wider one); the septimal
minor third 7/6, the "median third" 11/9, and the septimal
major third 9/7; and fixe kinds of "major second" - from smaller to larger: 12/11, 11/10, 10/9, 9/8, 8/7.