In the tonal music experience, we can give two extra levels of descriptions, namely, in terms of the scale step names and the parsing of a sequence of the diatonic scale
It is these principles of grid construction and marking our of the diatonic scale
which Balzano extends to C20, C30, and C42 scales and can also be extended to other Cn scales of the type described in his paper.
With an average consistency of over 80 per cent, this is probably the neatest system available for a diatonic scale
on a tenor-pitched slide instrument.
The fingering indicated is performed easily by a student with modest hand size and capitalizes on diatonic scale
This approach is exemplified by Stravinsky's Firebird, where the composer associates the diatonic scale
with human characters and the octatonic scale with supernatural characters, or by Alban Berg's Wozzeck, which carries the leitmotivic approach of Richard Wagner over into atonal music in that Berg associates certain set classes with the principal characters in the drama and other set classes with certain topics.
In 11 of the structures, Hawkins found ratios of small whole numbers that precisely matched the ratios defining the diatonic scale
A two-dimensional grid of eighty four cells, which charts the seven diatonic scale
degrees and twelve pitch classes, visually renders a closed tonal (US (p.
We will show how the diatonic scale
exhibits a kind of self-similarity, and prove that this self-similarity property characterizes a class of scales sharing some essential features of the diatonic.
In addition to the prose commentary, there are diagrams depicting the construction of the diatonic scale
, rhythmic and metrical relationships, key-signatures and so on, plus exercises based on scales (diatonic and chromatic, in single notes and in thirds and sixths), diminished seventh arpeggios (in various positions and configurations) and octaves, as well as an exercise to encourage finger independence (rather like one of Dohnanyi's but without the torture), and another designed to teach pivoting around the second and third fingers so that the hand can be fully extended while remaining relaxed and supple (a must in order to play countless works by Chopin).
2) My approach is structural - I seek N's and diatonic subsets which have musical structure similar to the familiar twelve-tone set with its seven-note diatonic scale
Thus, reading backwards, interval 5 ([equivalent] 12) bisected becomes interval 6, 6 becomes 3, 3 becomes 5, and we have translated the statement about hierarchies in Mozart to say something about the seven-note diatonic scale
in the abstract, to which we now turn our attention.
This matches the common musical situation, for example, where segments are all clearly subsets of a source set (such as a diatonic scale
or a combinatorial hexachord) which itself is never explicit.