The Mixolydian scale flattens the seventh scale degree to the Ionian while maintaining the pentachord
and is third.
Furthermore, most other musical parameters undergo little or no change once they have been established, such as the setting (voice alone), mode (minor), range (pentachord
), tempo (slow, inexorable), meter (in one), rhythmic pulse (weak strong), dynamics (within a small range), and register (chest voice).
Suggest an ostinato and ask student to experiment with a melody within a certain scale structure: pentachord
, major, minor, modal and so on.
In this work he also developed a theory of chromatic progressions (those in which a melody proceeds directly from, say, C-natural to C-sharp), adapting earlier melodic theories to the musical realities of his day, and expounded a theory of modes in plainchant (predecessors of present-day major and minor keys) based on pentachord
and tetrachord species (arrays respectively of five and of four consecutive pitches); his doctrine of modes became the basis of later such theories applicable to both plainchant and polyphony.
They operate in what is clearly the lower pentachord
of the G minor scale.
It is a sort of iterative operator, which starts from the lower category of tetrachords and their derivatives, the pentachord
and the octochord, and builds up a chain of more complex organisms, in the same manner as chromosomes based on genes....
In a short alap this ascent-descent pattern might be accomplished in two stages, comparable to the A and B sections of ex.4: the first (called sthayi in the classical tradition) concentrating on the lower pentachord
of the octave, the second (antara) completing the ascent to the upper tonic.
In addition, Z is based on the 01369 pentachord
which is a subset of the 013679 hexachord on which T is based.
Part develops a cyclic, permutational approach to musical time in several ways: the solo percussion sections unfold a four-beat pattern in all rotational orderings within an ever tapering repetition scheme, while the sections for two tenors combine the pitches of a pentachord
both in a palindrome and in an exhaustive imitative reordering.
There is a strong sense in which the upward-moving seconds form a 'Phrygian' pentachord
on D and the downward-moving ones a whole-tone pentachord
It seems to me, for example, that a critique of a particular similarity relation would be much more convincing if it showed the similarity relation to make such counterintuitive judgments as a numerically high similarity measure for, say, the mostly-whole-tone pentachord
 and the octatonic hexachord .
Nonetheless, careful reading of Kurtzman's analyses reveals sound reasons for his reliance on older modal traditions, with their emphasis on the range or ambitus of melodies, the positions of the pentachord
and tetrachord in relation to the finalis, and the melodic emphasis on the reciting tone.