has recently been "emancipated" from harmonic timbres and their related tunings. Using electronically controlled pseudo-harmonic timbres, rather than strictly harmonic acoustic timbres, provides tonality with new structural resources such as dynamic tonality. These new resources provide musicians with an alternative to pursuing the musical uses of ever-higher partials of harmonic timbres and, in some people's minds, may resolve what Arnold Schoenberg described as the "crisis of tonality".( Neo-classic harmonic consonance theory George Russell, in his 1953 Lydian Chromatic Concept of Tonal Organization, presents a slightly different view from classical practice, one widely taken up in Jazz. He regards the tritone over the tonic as a rather consonant interval due to its derivation from the Lydian dominant thirteenth chord. In effect, he returns to a Medieval consideration of "harmonic consonance": that intervals when not subject to octave equivalence (at least not by contraction) and correctly reproducing the mathematical ratios of the harmonic series are truly non-dissonant. Thus the harmonic minor seventh, natural major ninth, half-sharp (quarter tone) eleventh note (untempered tritone), half-flat thirteenth note, and half-flat fifteenth note must necessarily be consonant. Most of these pitches exist only in a universe of microtones smaller than a halfstep; notice also that we already freely take the flat (minor) seventh note for the just seventh of the harmonic series in chords. Russell extends by approximation the virtual merits of harmonic consonance to the 12TET tuning system of Jazz and the 12-note octave of the piano, granting consonance to the sharp eleventh note (approximating the harmonic eleventh), that accidental being the sole pitch difference between the major scale and the Lydian mode. (In another sense, that Lydian scale representing the provenance of the tonic chord (with major seventh and sharp fourth) replaces or supplements the Mixolydian scale of the dominant chord (with minor seventh and natural fourth) as the source from which to derive extended tertian harmony.) Dan Haerle, in his 1980 The Jazz Language, extends the same idea of harmonic consonance and intact octave displacement to alter Paul Hindemith's Series 2 gradation table from The Craft of Musical Composition. In contradistinction to Hindemith, whose scale of consonance and dissonance is currently the de facto standard, Haerle places the minor ninth as the most dissonant interval of all, more dissonant than the minor second to which it was once considered by all as octave-equivalent. He also promotes the tritone from most-dissonant position to one