While I knew about the whole-tone and octatonic scales prior to the course, I never heard about nonatonic or nine-step scale. None of my teachers mentioned it to me, nor did I find it among any of my earlier study material. Even online, there was very little information about this scale. As it seems, it has been rather neglected by musicians.
Similar to the whole-tone scale, but especially the octatonic scale with whom it shows a strong link, nonatonic scale also occurs from the symmetrical division of the octave. While this is done using the whole/semitone alteration within four minor third sections, which equally divide the octave in the octatonic scale, the nonatonic scale is formed by the alternation of whole/semitones in the octave divided into three equal major third sections. In the major-third tetrachord, the tones may be arranged in following ways: semitone/whole tone/semitone, whole/semitone/semitone, and semitone/semitone/whole tone. (Fig. 1) Depending on this arrangement, there are three versions of the nonatonic scale. (Fig. 2)
Fig. 1. Three versions of the major-third tetrachord
Fig. 2. Three versions of the nonatonic scale Continue reading “Example 4 Research, Part 1: Nonatonic Scale and its Coincidental Use until Tcherepnin”
For my first example, I chose to explore the whole-tone scale. It belongs to the category of symmetrical scales, in which the scales are built from symmetrical repetition of an interval or a short intervallic pattern. In the case of the whole-tone scale, the interval of major second is repeated between the neighboring tones, resulting in the scale having six tones within an octave – being a type of hexatonic scale. (Fig. 1a) It can also be conceived as two augmented triads a major second apart. (Fig. 1b)
Continue reading “Example 1 Research, Part 1: The Use of Whole-tone Scale until Liszt”
After writing my first example using the whole-tone scale, I decided to employ octatonic scale for my second example, which results from the alternation of whole and semitone steps. There are two versions, depending on whether the order begins with a whole tone or a semitone. (Fig. 1) Note that there are several other manners to notate the scale, depending on whether sharps or flats are utilized for specific notes. (Fig. 2) With no standardization, all of these notational variants are used, varying from composer to composer, depending on the musical ideas.
Fig. 1. Two versions of the octatonic scale
Fig. 2. Some notational variations of the octatonic scale
But before I focus on the properties of the octatonic scale, I have to address how puzzled I was as to why it was associated with Middle East in the West. I’ve already started my research on the Middle Eastern modes, which you can read in my three-part research here. As I wrote there, the modern practice of Arabic maqam, Turkish makam and Persian dastgah, and the related Afghanistan, Central Asian and Caucasus systems, actually use heptatonic modes. It is in the older traditions that we see the octatonic modes. Continue reading “Example 2 Research: Octatonic scale and Orientalism”