On Wednesday, November 7, 2018 at 6:43:20 AM UTC-8, Anon Anon wrote:
> On 2018-11-05 2:56 PM, John Ladasky wrote:
> > I haven't posted here in years, but a few "old-timers" from the 1990's chimed in recently, and I thought I would contribute something.
> > The early 20th century is my favorite period in orchestral music: Debussy, Ravel, Stravinsky, and their peers. My ears immediately "understand" that this lush and complex music has resonance, and deep tonal implications. My music theory courses barely scratched the surface as to why. Most people agree that the theories that were developed to explain common-practice functional harmony are inadequate for the task. I own Hindemith's _Craft_of_Musical_Composition_, and Persichetti's _Twentieth_Century_Harmony_, but even these books don't go very far in explaining what my ears already seem to know.
> > Recently, I have been experimenting with musical scales (in 12edo) which are off the beaten path, for my own compositions. My subjective impression from auditioning various scales is that I did not like the sound of two consecutive semitones in a scale. I Googled "consecutive semitone avoidance", and I found the article "Scale Networks and Debussy" by Dmitri Tymoczko:
> > http://dmitri.mycpanel.princeton.edu/debussy.pdf
> > Soon after, I also found "The Consecutive Semitone Constraint on Scalar Structure: A Link Between Impressionism and Jazz":
> > http://dmitri.mycpanel.princeton.edu/files/publications/consecutivesemitone.pdf
> > These articles have a lot to say, but the main observation that I took away from them was that the collection of scales which are used in tonal Western music, from the Renaissance to post-bop jazz, are exactly the scales which have the following two properties:
> > 1) They have no consecutive semitones.
> > 2) Consecutive intervals are either semitones or major seconds.
> > With those constraints, you obtain all the "church" modes (Ionian through Locrian), the whole-tone scale, the "diminished" scale (alternating m2 and M2), and all the "jazz" modes (ascending melodic minor, etc.). I found that to be highly interesting.
> I haven't read this or the referenced articles thoroughly at all but....
> You/he seem to be leaving harmonic minor and harmonic major out of your
> scalar palette and they both have an important role in jazz as well as
> in post-tonal classical music.
Obviously, I can't speak for Tymoczko, or the thoroughness of his survey of music.
But would you say that you can easily find persistent use of harmonic minor or harmonic major in compositions, in long passages, the same way that you find the other scales he listed? My musical experience says they're used much less commonly, in passing. Of course, if anyone wants to compose with harmonic minor and harmonic major, go right ahead! But if these scales are less common (I think they are), there might be a reason. That's what music theory is about, attempting to find a concise explanation for musical decisions that composers have made using their own ears.
> I understand why scales with consecutive semitones are problematic for
> extracting harmonies. But an augmented 2nd interval in a scale doesn't
> usually cause those types of problems. Even the harmonic major scale
> yields recognizable tertian triads and 7th chords.
I agree, that's an interesting harmonic observation. I know that I always found the harmonic minor scale to sound a bit wonky. I haven't tried composing harmonies with it. I've never even tried harmonic major.
Let me make a suggestion then: composers may have found the augmented 2nd / minor 3rd scale step to sound out of place in a heptatonic SCALE, though perhaps it causes no great difficulty with harmonies.
So what is a desirable property for scales, whose job it is to provide horizontal connections, rather than vertical? Some people say that "evenness" is acoustically important. If we're dividing 12 equal semitones into seven steps, the average step will be 12/7 steps, about 1.71. A "maximally-even" collection of seven steps will have two semitone steps and 5 whole tone steps.
If we require even one minor 3rd in a heptatonic scale, we're forced to change a M2 to a m2 to compensate. We have to push two intervals away from the mean, making one smaller and one larger.
The arrangement of those intervals matters too. If we put two semitones together, it somehow weakens the scale-like properties to many listeners, myself included (see above).
I won't say that I whole-heartedly support every reference that I post, but here's a link to an article, "Circular Distributions and Spectra Variations in Music: How Even Is Even?" It discusses a mathematical definition of evenness which might possibly be used to explain the observation "church modes first, jazz modes next, and (apropos to you) harmonic minor only occasionally, and other heptatonic combinations even more rarely":
I will propose the following: for a pitch collection to have versatility and wide use in tonal composition, in general, it has to have desirable harmonic AND melodic properties, because the composers of tonal music are generally trying to make simultaneous use of both melody and harmony. That doesn't mean that you can't take something a little off-kilter like harmonic minor, make it work as the centerpiece of a tonal composition, and make it sound great -- it just means you'll have to work harder, because the resources are more limited, and there are more "corner cases" and "avoid notes."
Think about the modern "Berklee School" chord-scale system for jazz: it seeks to map every chord to (generally, familiar) scales which are supersets of its chord tones. The system doesn't get you to everything that sounds harmonic and tonal -- but it gets you quite a lot of it.
I don't know this chord-scale system as well as a professional jazz player. But I take the idea behind the system, that "every chord fits into a scale" as implicit support for my proposal that tonal composers settled on the scales in common use because of their simultaneous utility as scales and as chord material. It wasn't completely arbitrary.
All that being said: you have inadvertently touched on an issue that I might eventually discuss in more depth. In searching for new material, I have stumbled across two observations: one is an eight-note chord, and the other a six-note chord. Both "break the rules" in interesting ways, and yet they're still strongly tonal to my ears. But this post has gone on long enough.