Is there such a thing as "advanced"/ongoing research in melody?
Much of a Western music education, not only in the first year but also in graduate level classes, focuses on harmony. In addition, there are current scholars who work on the "cutting edge" of understanding harmony. In contrast, in my experience as an American music student, teaching of melody is confined to one or two classes in the first semester on motivic transformations.
Is there an equivalent to the third or fourth semester of a harmony course(what's considered "advanced" harmony, like using extended triads or symmetrical scales) for melody? And who are some researchers who work on coming up with new ideas about melody?
I suspect that other cultures probably have more sophisticated melodic theories than we do, so I'd love to hear what and how we can learn from hindustani/arabic/insert-culture-here about melodies as well.
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Not exactly what you are interested in, but de la Motte wrote once a wonderful book, in which he stated that this research field is nearly unexploited.
Yes there are such melody studies.
But, those studies may not be what you want or expect if you start by comparing things with the typical college harmony textbook.
I think there is a tendency in harmony textbooks to abstract the topic into something divorced from rhythm and melody as epitomized by things like this flowchart...
That may look scientific and rigorous, but it's kind of an illusion. For example, you can't really get much value out of a V-I diagram without discussing how the leading tone is handled which immediately brings in melody. Similar issues arise when dealing with chord inversion. That brings in melodic aspects. Nevertheless, harmony as mere root progressions is a persistent idea, because it's a way to present the topic with a minimum of rhythm and melody. I suppose you could say it's an attempt to teach harmony and avoid counterpoint.
The only abstracted theory of melody - similar to the harmony flowchart above - would be the "rules" for writing a cantus firmus. Those rules come from counterpoint teaching and so aren't meant to be a theory of melody. But it's the closest you will come to an abstract theory of melody.
If we embrace the fact that melody cannot be divorced from rhythm and harmony, then there are many resources for study.
Gjerdingen's Music in the Galant Style has a theory of schemea that focuses on scale degrees and idiomatic melodic frameworks. Cultural conventions and flexible grammar and important to the theory. It does not try to present a quasi-scientific law of melody. A typical analysis looks like this...
Riepel and Koch are two historical theorists who focused on melody.
Joseph Riepel's Theory of Metric and Tonal Order: Phrase and Form
Introductory Essay on Composition: The Mechanical Rules of Melody, Sections 3 and 4 (From Versuch einer Anleitung zur Composition, 1782-1793) by Heinrich Christoph Koch
There are contemporary scholars writing about their works...
"So, you want to write a Minuet?" by Stefan Eckert
Riepel on Melody and Phrases, Joel Lester
Small and Expanded Forms: Koch's Model and Haydn's Music by ELAINE R. SISMAN
Other sources are student teaching resources with extensive examples from the great masters. Books like...
Fundamentals of Musical Composition, by Arnold Schoenberg
Exercises in melody-writing; a systematic course of melodic composition... by Goetschius, Percy
Figuring Out Melody, David Fuentes
...if you look, you will find a lot of interesting material. But you probably won't anything that condenses melody into a deceptively simple system like the stuff in harmony textbooks.
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