Palindromes, sequences that read the same backward as forward, are appreciated by many. They are normally known in numbers (like 11, 232 and, by the way, did you know that every integer is a sum of 3 palindromes? E.g.: 389 = 11 + 55 + 323. For the advanced readers, the above is true for every base, except for base two, which requires four palindromes), dates (22.02.2022), words (mom, pop, madam, noon, tattarrattat – an onomatopoeic word for a knock on the door), and phrases (“Was it a car or a cat I saw?”, “never odd or even”).
But what about music? Musicians, are they up to the challenge? Well, of course! And it shouldn’t come as a surprise. After all, there is something aesthetically appealing in symmetry, and we, humans, enjoy patterns, puzzles, and wit. Musical palindromes, in their basis, are very similar to the written ones: Music that is the same when played forward or backward. However, they are often interpreted in multiple forms and variations, and many times are not quite literal palindromes, but inspired by the palindromic idea.
Musicians are known for their subtle sense of humor, and musical palindromes are a great way to express that. Gary Bachlund notes in his opera “Alice”, an adaption of Lewis Carroll’s “Alice’s Adventures in Wonderland“ and “Through the Looking-Glass“ that:
“Though tonal and tuneful, because the Ur-text is filled with various kinds of verbal humor, it seemed necessary to reflect varying forms of humor in the music itself”
According to Bachlund, the score has many such palindromes. These palindromes, small and simple, look as if they wink at us, hinting about the backward world of the Looking-Glass, and especially The White Queen, which lives backward in time. Well, we aren’t surprised that it’s Lewis Carroll who inspires such humor, even in music.
Sometimes, it’s much harder to spot a musical palindrome, for example, in a fragment from “Six unison melodies” by Béla Bartók. The diagram below represents the symmetry of the melody.
Bach, of course, took the idea to another level, and in his “Musikalisches Opfer” created a “crab canon”: A canon in which one line of the melody is reversed in time and transformed in pitch from the other. On May 7, 1747, Johann Sebastian Bach met with Frederick the Great (King Frederick II of Prussia). The king, knowing Bach’s skill at improvising, gave him a long and complex (and honestly, quite despairing) theme. He ordered Bach to improvise a three-voice fugue based on the theme, which Bach did. Then, the king challenged Bach to improvise a six-voice fugue, to which Bach requested some time to work on, and after four months sent back what is known today as The Musical Offering.
The offering is a collection of multiple fugues and canons, and the amount of creativity Bach put there is absolutely astounding. It includes musical riddles; an endlessly rising canon that feels like walking up spiral stairs, climbing higher and higher and endlessly going in circles; a mirror canon in which the leading voice is being played alongside its own inversion (i.e., upside-down), and of course, the crab canon. In it, one can play the melody forward, backward, or, folding it in the middle and playing it in two voices at the same time. The name ‘crab’ refers to the fact that crabs are known to walk backward (although they can also walk forward and sideways).
The Netherlands Bach Society described these works as “a sort of visual music”. They also created music and video recordings, in which they attempted “to give a literal picture of this ‘visual music’. So for example, wherever a part is doubled, the player will be in view twice. And where a part is mirrored, then the player appears in a mirror too.” The result is fascinating:
Another famous palindrome-inspired piece is written by Mozart, and it’s a version of a table canon. A table canon is a canon that is meant to be placed on a table in between two musicians, who both read the same sheet of music in opposite directions. Many musicians wrote such canons, but Mozart’s “Der Spiegel” duet is one of the most known:
It’ll take all day long to show or even mention the most famous works that are inspired by palindromes. Joseph Haydn’s Symphony No. 47 in G is nicknamed “The Palindrome”, the interlude from Alban Berg’s opera Lulu is a palindrome, Igor Stravinsky’s final composition, The Owl and the Pussy Cat, is as well a palindrome, and there are many many more. Some lesser-known examples, but not less interesting, include a modern electrical guitar solo (by Bradley Hall), a combination of jazz and bluegrass music (“UFO Tofu”, a palindromic name for a palindromic song, by Béla Fleck and the Flecktones), some fragments in a rock song (“Divided Sky” by Phish, the first half of the palindrome, and the second half), mathematics-inspired electrical music (“The Nørgård Palindrome” by Morten Bach and Jonas Lindstrøm), and a forty-two-minute piece for large orchestra, written by the American composer John Luther Adams, and titled Become Ocean (premiered on June 2013 and won the 2014 Pulitzer Prize the 2015 Grammy Award).
One fact remains curious: Although musical palindromes exists for centuries, it seems that it’s really hard for us to recognize them. Some studies suggest that even trained musicians have trouble recognizing them, both aurally, by hearing them without knowing in advance that they are palindromes, or visually, by reading static notes (check Sound of picture vs picture of sound: Musical palindrome, Petrović et al, 2017). Taking that into account, one may wonder: Why bother? If auditorily they don’t have some special aesthetic appeal, and normally not even noticed, why work so hard to make them in the first place?
While the question certainly remains open, we can guess the answer together: We love challenges and keeping our minds busy. There is something special in puzzles, riddles, and brain teasers. Sometimes, we struggle to solve them, and yet keep going. When we finally figure it out and find the answer, that “aha!” or “eureka!” moment is worth it all. That insight-, satisfaction-, and even elevation-feeling, is so strong, that it lifts us, keeps us motivated, and encourages us to look for the next challenge. These challenges and complementary “eureka!” moments meet us everywhere, in arts, sciences, engineering, and even in our everyday life – it seems that they just must be in our nature.
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