Wendelin Bitzan

Wendelin Bitzan

Musician・Researcher・Digital Content Creator

Triad Squares

Recently I’ve been fooling around with different figures to display chord relations, to some extent inspired by Euler’s and Riemann’s Tonnetz. I now came up with a 5×5 grid containing all 24 major and minor triads (with the middle position left blank) and tried to find a meaningful layout for such a triad square. There seems to be no entirely consistent way of arranging the chords so as to adhere to one single rule for the derivation of adjacent fields. Yet I found two interesting layouts, one of which tends to emphasise third relations, while the other prefers hexatonic poles. I’m curious what you think of these figures, and if they might be of any use in a transformational harmonic theory, apart from illustrating cycles of minor thirds and octatonic regions in symmetrical patterns.

To be sure, this is just thought-in-progress and by no means a fully developed approach, so I’ll be glad to hear your opinions and suggestions. In case I might have unconsciously reproduced some recent findings from Neo-Riemannian Theory which I was unaware of, I’d appreciate if somebody pointed out a source to me. Also, if you can think of another more convincing 5×5 layout, please let me know.

Whole-Tone Diatonicism?

The hexatonic or whole-tone scale (Messiaen’s mode 1) is not actually diatonic but a symmetrical scale, constructed from an equidistant division of the octave in six portions, which results in scale degrees separated by two half-tone steps from one another. This contradicts the common definition of diatonicism as a sub-category of heptatonicism, requiring seven discrete scale degrees in unambiguous alteration. However, it is possible to derive a whole-tone scale from diatonic material, which I am going to show here.

To this end I will make use of tetrachordal theory. A tetrachord consists of four adjacent diatonic pitches in the range of a perfect or augmented fourth, coming in four possible variants which differ by the existence and position of half-tone steps: Ionian (2 2 1), Dorian (2 1 2), Phrygian (1 2 2), and Lydian (2 2 2: no half-tone step). If we conceive every diatonic mode as a combination of two disjunct tetrachords transposed by a perfect fifth, there are seven combinations making up the seven diatonic modes—for instance, the Aeolian mode consists of a lower Dorian and an upper Phrygian tetrachord, while the Mixolydian mode consists of a lower Ionian and an upper Dorian tetrachord. The eighth combination, though, joins two Lydian tetrachords to a non-diatonic whole-tone scale, provided we allow the upper tetrachord to transpose by a diminished (instead of a perfect) fifth. The resulting scale (2 2 2 0 2 2 2) has six pitches, but makes use of all seven scale degrees, with a diminished second F-sharp / G-flat at the center. In the plagal variant, the scale covers the range of an augmented seventh G-flat / F-sharp.

Birdsong at the Piano

Glad to announce that I will be supervising a new edition of Mily Balakirev‘s piano transcription of Mikhail Glinka‘s song Zhavoronok (The Skylark), to be published with G. Henle Verlag. The autograph and first edition, issued in Saint Petersburg in 1864, are considered lost, which means that I will have to rely on other prints from the late nineteenth century—such as a Gutheil edition with this beautiful art nouveau title page. Looking forward to working on this project!

Teaching Remotely

An irregular and somewhat confusing semester at Robert Schumann Hochschule Düsseldorf has begun. The buildings are still closed—yet most of my department’s music theory classes are taking place, and I am teaching a number of online courses, switching between synchronous webcasting and tutorials on various e-learning platforms. Thanks to Jeannette Getrost of Studio Balu, I found a temporarily unused space where I can deliver my video conferences well-focused and without even leaving my neighbourhood, which is a great opportunity! Students are widely accepting the challenging conditions and show a remarkable level of flexibility. I am currently developing some freely accessible musical form and ear training tutorials for the ELMU platform, an open educational resource founded by Ulrich Kaiser which I invite you to check out.

Attacks by Members of DTKV Berlin

A professional body of musicians should put all its efforts into the welfare of its members, and the more so as many colleagues are severely affected by the current pandemic situation. Yet the executives of DTKV Berlin prefer to pursue their personal in-fightings against disliked persons within the organisation. The attacks and accusations I have been subjected to during the past weeks have now reached a level that leaves me with no option but going public. There has been a libelling smear campaign initiated by Gabriel Iranyi, Anka Sommer, and Christiane Edinger, who tried to do damage to my professional career by denouncing me to my university administration. After that, Detlef Bensmann has announced to expel me from DTKV Berlin just yesterday, insinuating that my behaviour has been harmful to the association. I take this as an opportunity to summarise and rebut the allegations that were brought up against me. Here is my statement (in German only).