So I'm coming to this ten days late, but Ethan Hein discussed quartal harmony and melody and I had to, eventually, write a response post.
No surprise the musical soundworld of Star Trek came up. Space, the final frontier ... I loved that opening music bit from the original series. When I got to college and started exploring music I stumbled upon the composer from whom that whole chain of rising melodic fourths probably came from.
Check out the second movement of Paul Hindemith's symphony Mathis der Maler (from 1934, drawn from the opera by the same name, which arguably makes Paul Hindemith's best symphonic work a sampler plate of moments from his opera)
The ascending stack of fourths in the oboe starts at 01:36 above pizzicato strings
Then check out 02:20 and tell me that the Star Trek TOS opener soundtrack didn't just rip this one off cold. ;) Not quite the famous Trek fanfare went up where Hindemith went down, and Hindemith being who he was he had counterpoint using melodies with stacked fourths. Back in the day copyright lasted about twenty-four years (give or take) and if you didn't renew it whatever it was went public domain. Perhaps more important was that something that was copyrighted decades ago in Germany was not going to be regarded as an IP infringement if you "sampled" it thirty years later for incidental music for an American television show. So my pet theory has been that it's hard to understand musical elements from the TOS Trek soundworld without having at least some reference to Hindemith's mid-20th century influence (he taught in the United States for years)
Now check out the fugal finale of Paul Hindemith's Piano Sonata No. 3 written in 1936. Here's a performance of the Hindemith by Maria Yudina (starts at 14:57) A faster, spunkier opening version of the fugue was recorded by Glenn Gould. Gould uses virtually zero pedal in his performance and goes for a more brittle, staccato take on the double fugue. Yudina swamps several passages with pedal. I actually like Hindemith's music by and large and enjoy both takes on this fugal finale.
One of the things Hindemith played with in the 1930s onward was blending stacks of thirds and fourths. Ethan Iverson did a three-part talk with Henry Threadgill who mentioned he met Hindemith briefly.
Herbie Hancock: “When I was eleven, I performed at a young people’s concert with the Chicago symphony. I played the first movement of a Mozart concerto. In fact, I studied classical piano all the way through college, until I was twenty.” [How are you preparing for a duo piano tour with Chick Corea?] “I just got out my Oscar Beringer scale book, the Chopin études, Hindemith’s Ludus Tonalis, Bach’s Well Tempered Clavier, some Debussy and Ravel, and Slominsky’s Thesaurus of Scales and Melodic Patterns. I’ve heard that McCoy Tyner and John Coltrane used to practice out of that.”
Ludus Tonalis is a favorite of mine. Famously (if only for Hindemith fans) the second fugue in Ludus Tonalis is not only in 5/8 it is based on a subject made from stacked fourths. Hindemith wasn't the first to write a fugue in three voices using quintuple meter, the Bohemian-French composer Anton Reicha did that long before)
So when Iverson wrote:
Herbie Hancock mentions Hindemith. Fair enough, although I find most Hindemith pretty square, with the Ludus Tonalis being especially deadly…
…but, hey, nothing Herbie is going to play onstage in his own music will ever be square. The point is to rummage through stuff that you can use, stuff that can rattle around in your subconscious.
It would seem that Hancock and I don't quite share his sentiment about Hindemith being square or, if he was, so what? :) The Italian guitarist composer Angelo Gilardino found useful inspiration in Hindemith's music and writings. I realize that here in 2025 the German composer has been regarded as super-square and passe but part of music history and digging into chains of influences is going back and discovering that, back while he was alive, Hindemith was an actually important and influential composer.
Yeah, yeah, I admit I'm a bit of a Paul Hindemith fan so when I saw Ethan Hein discussed fourth chords it jogged my memory about Ethan Iverson and, of course, the Star Trek tie-in jogged my memory about Mathis der Maler symphony's second movement, and got to thinking about the second fugue from Ludus Tonalis. The thing about music history is that stuff we like can turn out to be indebted to stuff we hate. Hindemith was influenced by Debussy (okay, he's okay) and both Hindemith and Debussy admitted to influence by Wagner (whose music drives me up the wall and who I admit I find to have been a reprehensible human being). Iverson likes Hancock but not Hindemith? Well, that's part of musical life, people whose music we love can draw inspiration from composers that bore us. I like Shostakovich, for instance, but have just never warmed up to Mahler, whose influence on the Soviet composer is hard to miss.
Probably because Hindemith became so wildly unfashionable even within classical music he's so square that he's cubed in jazz and non-classical scenes. Nevertheless, as Iverson himself has shown, if someone like Herbie Hancock actually played Ludus Tonalis it's an influence to keep in mind.
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