The series of partial tones provide the tone material, but in its entirety it results in a too complex sound and particularly in no scale. Measurements of disaltered chords of oboes and clarinets have shown that combination tones are structured in arithmetic series. This discovery made it possible to form sonance series and selection scales out of the partial tones by means of such series. An arithmetic series is formed by repeatedly adding the same difference d to an initial value a. This is called Sequence d on a and abbreviated d || a. As an example the Sequence 3 on 2:
3 || 2 → 2 5 8 11 14 17 20 23 26 \hellip
Out of this sequence, you form a sonance series – e.g. up to the 32nd partial tone – and transpose the tones of this series into the range of one octave. Thus, you obtain an eight-step scale.
In case of a too small distance between two tones in the scale, so they can no longer be considered as independent degrees (e.g. less than ½ Limma), the first tone upward and the second tone downward, respectively, is omitted (corresponding to the melodic minor scale). As an example the Sequence 5 on 4 with 12 degrees: It includes too small distances between the 7th and 8th tone (partial tones 48, 49) and the 11th and 12th tone (partial tones 58, 59), respectively, and therefore it has 10 effective degrees.
The use of a single ekmelic scale naturally results in a tonal diatonic music which can be expanded by introducing tones that are foreign to the scale (chromaticism). The functional relations which determine the harmonic course are also derived from the partial tone series. We gain a great number of quite new, harmonious chords (in whole-numbered proportions) by including the ekmelic tones, and call them "stable sounds". In the same way, the melody shape is substantially enriched, the more so as, besides novel sequences of tones, also influences from non-European musical cultures are possible.
Too small distances between two tones are red
In the upward and downward scale, the omitted tones are marked with _ in front of the number of the respective other tone.
The Note names shown here have been designed for Ekmelily and the Ekmelic Player.
Click on a note to play it, or click Play for the entire scale (pitch 440 Hz).