Posted in For Project 7 Examples

Example 4 Research, Part 1: Nonatonic Scale and its Coincidental Use until Tcherepnin

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

Looking at the three versions, we see that all of them contain three augmented triads. Interestingly, since the whole-tone scale is made of two, it can be a constituent of the nonatonic scale. (Fig. 3) Except by the major-third division and the augmented triads, the scale can also result by combining a specific form of hexatonic scale with its inversion.

This hexatonic scale is built within the interval of a major seventh, with the alternation of half-step and one-and-a-half-step intervals. Depending on their order, the two intervals build two versions of the tetrachord called major/minor tetrachord, which are inversions of one another. With these two overlapping, we get the hexatonic scale, which in turn has two versions as well, one being the inversions of the other. Finally, as expected, if we combine the latter two, we get the nonatonic scale. (Fig. 4)

Similarly to the other symmetrical scales, the earliest examples of the nonatonic scale occurred coincidentally. Much like the octatonic scale, it appeared as a incidental outcome of transposition. As I’ve already written in the previous research, the eight-note scale could appear in melodic transposition of minor third cycles, but while  nine-tone scale did emerge in the major-third cycle transpositions, it is a lot more hidden – its existence is in the harmony, and not melody of the transpositions, established through the hexatonic space, as an overall pitch content of chords.

Usually this involves the use the chromatic mediant relationships and progressions. In fact, the earliest instances of nonatonic scale I could find all belong to the 19th century, when the chromatic mediant relations became widely recognized and had a prominent role in music. Before that, the chromatic mediants were characterized as alterations or combinations of other, basic progressions; They were ornamental, secondary-voice leading events or coloristic phenomena.

Diatonic mediant relationship is formed between two chords whose roots are minor or major third apart within a certain diatonic key. To remain in the key, the chords need two tones in common, and they need to have contrasting qualities – if one is major, the other is minor, or the other way around. (Fig. 5) Chromatic mediant relationship is formed between two chords whose roots are major or minor third apart without conforming to a given key. If the chords have one common note, they share the quality – both are major, or both minor, and we have a single or conjunct chromatic mediant relationship. (Fig. 6) If there are no common notes at all, the qualities are contrasting, and this is called the double or disjunct chromatic mediant relationship, completely outside the diatonic key – the most distant mediant relationship. (Fig. 7)
Back to the nonatonic scale, in his introduction from Ich scheide, Liszt has a melodic line of descending hexatonic scale A G F E C# (Db) C , created by major-third transposition of the first bar A G E# (F) to the second F E C# (Db) and the third covering the beginning (Db C). The remaining notes of the chords are also major-third lower –
E# B C# G to A
in the middle voices of bar 1 to
B G# G E to Eb

The bass is the augmented triad, C# in the first bar, A in the second and F in the third. If we add together the pitch content of the chords, we get the descending nonatonic scale: A G# G F E Eb Db C B, the version semitone/tone/semitone. This nonatonic pitch content is created by the harmony – the major-third cycle of chromatic mediant progression. (C#7 A7 F7) It is these dominant-seventh types of chords and the motion of their descending 7-6 half-step suspensions, that contribute to the passage being in nonatonic tonality rather than hexatonic, with the F major upbeat before the first bar, representing the only brief hint of tonic in this introduction.
Another example is from the first movement of Liszt’s Faust Symphony, which also features a descending major third sequence that encompasses the similar harmony. Here, the nonatonic pitch content is created by harmonizing the descending chromatic melodic line, which is made from the major third transposition – focusing on the augmented triad E – C – Ab. The transposing major third cycle is again harmonized by chromatic mediants, but interlaced with their dominants. (E6 Am – C6 Fm – Ab6 C#m)
As Cohn points out, Liszt may have become familiar with this type of chord progression from the music of Schubert. One passage that features the same progression can be found in the first movement of Schubert’s Symphony no 4 in C minor. Although, the claim for nonatonicism is weaker because of the inclusion of some other harmonies.
As we see, the examples above are quite coincidental. In the overture of Glinka’s Ruslan and Lyudmila, however, there is a better symmetrical design, which may hint at the presence of nonatonicism in the composer’s mind. This sequence is created by the chromatic mediant progression of arpeggiated chords D, Bb and F# major, which create the hexatonic melodic line, with the basses stating the complete descending whole-tone scale. Both are created by major third transposition – upward for melody and downward for bass notes. In other words, the nonatonic pitch content is created by the union of the whole-tone scale and hexatonic scale. However, soon the melody gives way to the tonal melody, and so passage of nonatonicism is only brief, very distinct comparing to the rest of the diatonic overture.
Act II of Korsakov’s opera The Tale of Tsar Saltan also demonstrates a nonatonic passage. This passage shows the creation of nonatonic tonality by combining two hexatonic scales. The melodic line of the swan’s song is the descending hexatonic scale version of semitone/tone and a half – C H Ab G E D#. The accompaniment creates a statement of the other version, parsed into constituent triads, harmonized through the single chromatic mediant relationship progression Am Db (C#) – Fm A – C#m (Db) F. I already pointed out in the previous post, how Korsakov became the pioneer of consciously using the octatonic scale after noticing the minor-third progression in Liszt’s Symphonic poem. In the same way, Veenstra points out, Korsakov’s musical context in which nonatonic scale appears, may have been the possible wellspring that inspired Tcherepnin’s conscious development of the nine-step scale in his music. Eventually, the scale itself was referred to as the Tcherepnin scale. More about that, read my next post.

List of illustrations:

Fig. 1. Three versions of the major-third tetrachord

Fig. 2. Three versions of the nonatonic scale


Cohn, Richard (1996)  ‘Maximally Smooth Cycles, Hexatonic Systems, and the Analysis of LateRomantic Triadic Progressions’ In Music Analysis, Vol. 15, No. 1 , pp. 9-40 (Published by: Wiley Stable URL:


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