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Notably an axis of reflection can occur directly on a tone or half way between two tones.Ī palindromic scale has the same pattern of intervals both ascending and descending.Ī chiral scale can not be transformed into its inverse by rotation. It also implies that the scale has Ridge Tones. If a scale has an axis of reflective symmetry, then it can transform into itself by inversion. If there are any rotational symmetries, these are the intervals of periodicity. Some scales have rotational symmetry, sometimes known as "limited transposition".
#D harmonic minor code#
The tones in this scale, expressed as numbers from 0 to 11Ī code assigned by theorist Allen Forte, for this pitch class set and all of its transpositional (rotation) and inversional (reflection) transformations. On the Tonic Pedal, the Subject is used in the second and third voices by inversion, and at the same time by direct motion in the fourth and fifth voices (Bar 43), forming a succession of rich harmonies in six part, for the conclusion.Cardinality is the count of how many pitches are in the scale.The Episodes are constructed from material taken from the Counter-subject.At Bar 7 the Counter-subject is transferred from the Treble to the Alto, halfway through.This Fugue contains the device of Inversion of the Subject and Answer.After the Exposition the theme is used no less than eight times with the major third. The treatment of the Subject is remarkable on account of its frequent employment of the major instead of the minor third.This Fugue has a “real” Answer, and would be called a “real” Fugue.
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The entries are all exactly at one bar’s distance from each other.įree Inversion of the Subject and Answer: Several instances. Stretti: Six, one being complete and five incomplete. RECAPITULATORY SECTION:īars 40-42: Subject in Alto. īars 36-39: Episode IV, modulating from G minor to D minor. īars 31-33: Episode III, modulating from G minor to D minor by way of F.īars 33-34: Subject in Alto (incomplete). īars 29-31: Answered by Inversion in Bass, passing to G minor. īars 27-29: Answered by Inversion in Treble. īars 25-27: Episode II, modulating from D minor to G minor.īars 26-27: Subject by Inversion in Bass. īars 23-25 : Subject by Inversion in Bass. īars 22-24: Answered by Inversion in Treble. īars 21-23: Subject in Bass. Counter-subject in Treble. Subject in Bass and Subject in Alto successively, in Stretto. Ascending sequential figure in the Bass in Bars 15-16.īars 17-20: Fragment of Counter-subject in Treble. īars 14-16: Answered by Inversion in Alto. Counter-subject (first part only) in Bass. Answer in Alto (first five notes only) by Inversion. īars 10-13: Episode I, modulating from D to A, forming a descending sequence.īars 12-13: Subject (fragment of) in Bass, the first note being altered (E flat instead of F). MODULATORY SECTION:īars 8-10: Subject (irregular as to position) in Treble. īars 7-8: Second limb of Counter-subject in Alto. First limb with counter-subject in Treble. īars 5-6: Codetta, founded on Counter-subject.īars 6-8: Subject in Bass. Fugueīars 3-5: Real Answer in Alto, with Counter-subject in Treble. Period II is Modulatory its first Phrase, Bars 6-8, modulating to G minor (Subdominant), its second Phrase to A minor (Dominant), and so on, proceeding finally to the Tonic Major (Bar 15), where the Coda is commenced. It is then broken for two bars, but re-appears in Bars 12-14. In the early part of this Prelude the sequential character of some of its Phrases should be notes, for instance, Bars 6-8 are imitated by Bars 8-10 in an ascending Sequence. Bars 15-26: Period III. Tonic Pedal (Bars 15-21), Dominant Pedal (Bar 23). Coda.