This week was not conducive to good writing. I haven’t been sleeping well, and I had lots of extra errands to run that took up some of my time. However, I managed to get a kinda-terrible chunk (10 pages!) organized on Riemann, his predecessors, and successors. Much of it was from a previous paper for a class, but my writing was not as good then, and the purpose of the paper was different, so I’m sure I have not enough of somethings and way too much of others. I’m glad that I’ll get other eyes on it soon to tell me what’s lacking.
While I did get the writing accomplished, there was no progress on readings this week. That’s ok, because I have time to read while I’m waiting for edits to come back later this quarter.
I’m not super happy with this writing, but here’s the chunk on 19th century predecessors:
Subsection: 19th Century functional ideas
Some thoroughbass writers as early as the 1750s were already advising continuo players to organize a key around three primary chords, instead of to diatonic scale pitches, such as Johann Frederick Daube in his 1756 General-Baß in drey Accorden. As mentioned in the previous section, Weber also related his Roman numerals to 3 or 4 most important harmonies, and two Spaniards in London (1850) were using the names the cadence, precedence, and transcadence, which roughly correspond to our tonic, dominant, and predominant. The most developed system of this style of the time was Portmann (look up dates/treatise!) who had only 4 categories of chords instead of Stufentheorists’ seven. Riemann, in his historical surveys and other acknowledgements, only briefly touches these predecessors.
However, Riemann does more closely acknowledge his scholarly lineage through Hauptman, Helmholtz, and Öttingen. Daniel Harrison describes Moritz Hauptmann (The Nature of Harmony and Meter 1853) and Herman Helmholtz (On the Sensations of Tone 1863) as harbingers of a new age in music theory. Part of the Hauptmann/Helmholtz tradition is the urge to revise, adapt, and update previous theories, and urge which I also feel!
One of the hallmarks of Hauptmann’s theory that carries over into Riemann’s theory is dualism. Hauptmann had a very philosophical, Hegelian interpretation of music, and used nested, logical relationships to try to explain why music works the way it does and where minor keys come from. The best way I’ve found to think about Hauptmann’s dualism is a having/being dichotomy: major chords/keys have overtones, and minor chords are overtones of different fundamentals; this means that minor triads have their roots as the highest note. Some critique Hauptmann saying he is too idealist, but there are interesting insights that come from thinking about music in this different way.
Later, Öttingen and Riemann back off of the dualistic dialectic by trying to aurally justify undertones, which actually hurts their cause; Hauptmann’s work might have arbitrary relationships, but his instincts about the nature of keys and tonal relationships seem reasonable and even insightful.
Helmholtz relies on the research methods of contemporary physics and physiology, being one of the first to study and understand acoustics, to the point where his writings are still a standard in acoustics and physiology. His understanding of acoustics led him to believe that minor triads were inferior, which led others to vehemently disagree with him, but his impeccable scientific methods often set the terms of the debate and made him somewhat unassailable for a time. 
While many dualists took Helmholtz very seriously based on his physiological foundation, a different option was taken by Öttingen. Hauptmann and Helmholtz’s ideas are merged by Arthur Öttingen in his Harmoniesystem in dualer Entwicklung, which began at least in part because Öttingen thought Helmholtz was wrong about minor keys.
A picturesque analogy describing the difference between Öttingen and Helmoltz uses bridge building; saying Helmholtz built a bridge to span from science (acoustics) to art, while Öttingen built an alternate bridge using the same raw materials, but starting from art and trying to span back to science; both bridges start well-founded, but by the time they cross the gap the other side (whether science or art) the bridge is not as solid or well-supported as at first. That is to say, Helmholtz’s acoustical reasoning did not lead to fertile musical ground, and when Öttingen tried to start in fertile musical ground, he ran into what we now understand as problems trying make solid acoustical justifications for undertones.
Damschroder, Thinking about Harmony, 9. CHOWMUT, 19th cent harm. Th. 795.
 Damschroder, 12. Also something else?
 Joaqui’n de Viretue’s y Spi’nola and FT Alphonso Chaluz de Vernevil; Damschroder, 13.
 Damschroder, 13, 90.
 Damschroder 16.
 Harrison, 216.
 Harrison 217.
 Harrison, 218, 223.
 Harrison, 227-8. Others?
 Klumpenhauer, 459
 Harrison, 232.
 Harrison, 234/
 Harrison 241-2.
 Klumpenhauer, 457.
 Harrison, 216, 242, Klumpenhauer, 458.
 Harrison 243.
 Klumpenhauer 464.
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