Saturday, August 25, 2018
The Harp and Lou Harrison
“There is however one exception,” he said, “and that is the harp which, if you think about it, does have a hollow tone. That however, to me, is remedied by the fact that it is plucked, and a series of harp tones is to me very activating, very beautiful, indeed I score for it very often."
That’s an understatement. Harrison not only published a whole book of his scores for the instrument but also frequently featured it in his chamber and orchestral music. He included the harp, along with the harpsichord and clavichord, in an informal list of “Europe’s most perfect treasures.” The harp came to play a distinctive and crucial role in his explorations of mode, pitch, and harmony later in his career.
For Harrison, the foundation of all these musical dimensions was tuning. The harp embodied a role in his tuning experiments that, for him, connected the instrument to the marvels of ancient Greece and Rome — “the most wondrous time of music anywhere, of intelligent beauty, of loveliness enabled in Apollo’s rules (regulations).”
Harrison’s love of the harp’s “dulcet tones” started early, while still a teenager in the California Bay Area in the 1930s, and he regularly included it in his early compositions. He must have made the acquaintance of a student harpist at Mills College, because he included it in scores he wrote for theater productions there.
A decade later, a much more experienced Harrison brought his love of the instrument to several influential scores he wrote during his troubled New York period, beginning with The Perilous Chapel for flute, cello, harp, and percussion. Composed after his series of atonal scores influenced in part by his study with Schoenberg, that 1949 ballet score signaled a shift towards modalism. Despite the unusual choice of the harp’s sweet timbre over that of the piano, Harrison, like other modernists, avoided the cloying harmonies familiar in Hollywood scores. In The Perilous Chapel, the harp becomes an almost entirely melodic instrument, alternating between detached counterpoint and cascades of tones flowing between the other instruments.
The same year, in response to a commission from his friend, cellist Seymour Barab, Harrison again chose the harp over the more obvious piano. The harpist for the premiere of his Suite for Cello and Harp was Lucille Lawrence, ex-wife and a former student of innovative new music harpist Carlos Salzedo, who was also close to Harrison’s own teacher, Henry Cowell. She likely advised Harrison on the extended techniques used in this piece, including selective damping of strings, the use of fingernails, and plucking while muting with the left hand to produce xylophone-like timbres.
Harrison adapted the suite’s most haunting movement from his not-yet-completed Symphony on G. Titled “Aria” and dedicated to his friend John Cage, the movement pairs an ethereally floating cello melody with impressionistic harp arpeggios. While using Schoenberg's twelve-tone method, Harrison also freely combined quasi-tonal pitch sets from the row to create a gently bittersweet lyricism.
The Suite is still one of Harrison’s most performed works, and if he had never written anything else for the instrument, his name would still be familiar to many harpists. But in the early 1950s, the instrument became newly significant as Harrison began studying musical tuning. He learned from Harry Partch’s book Genesis of a Music that when ancient musicians marked off lengths of strings, they found that octaves occur when the string is stopped at its halfway point, again at a quarter of its length, an eighth, and so on — that is, a 2:1 ratio. The next simplest ratio less than the octave, 2/3s of the string length, is the “perfect fifth” so common in musical scales all over the world, and so on. These ratios exist in the harmonic series present in the acoustics of string and wind instruments, and harmonies with these relationships reinforce each other and ring out with a remarkable purity. The intervals of equal temperament, our standard system of tuning pianos and harps, sounded, by comparison, rough and grating.
Two of Harrison’s earliest experiments in just intonation from 1955 take advantage of the ability to easily tune the harp and keep the tuning stable. His Four Strict Songs asks the harpist to prepare up to three different instruments to accommodate the different tunings or otherwise retune one or two harps between movements. His wildly impractical Simfony in Free Style requires five harps each tuned to different scales. The original version has never been performed, but it has been realized on computer long after its composition.
But Harrison’s real use of the harp to explore these ideas came in the 1960s, when he bought a small Lyon & Healy diatonic harp. Before tuning his harp, he decided that he needed an instrument like the ancient Greek canon or monochord, which they used to find pitches by precisely measuring off lengths of a stopped string. Harrison built a version of this zither with a meter stick inserted between the bridges, so that once he worked out the decimal equivalents of the scale ratios, he could precisely find each of the pitches on the string. In order to save the resulting intervals as a scale, the Greeks transferred the pitches to a seven-string lyre, usually called the lyra, the instrument of the lyric poets, so Harrison built a homemade harp on which he could save the tuning before finally transferring the pitches to his Lyon and Healy harp or other instrument. He therefore called this instrument a “transfer harp,” because he used it to transfer the monochord pitches to a stable instrument. In later years, Harrison’s partner Bill Colvig would refine these designs and build several versions of their monochord and transfer harps.
For example, after tuning the monochord’s open string, say to F, he could find C by stopping the string at exactly of 2/3 of its length, creating a frequency that is 3/2 of the frequency of the F. He could then continue the process, finding the next pitch in the sequence of fifths, G at 2/3 of the length of string that produced the C, which is 2/3 of 2/3, or 4/9 the length of the open string, and so on. This tuning system, a sequence of multiplying by lengths 2/3, follows the circle of fifths and is known as Pythagorean tuning, after its supposed inventor in 6th-century BCE Greece. When Harrison first retuned his piano to this scale after reading about it in Partch’s book, he was startled that his pieces composed in quintal, that is, fifth-based, counterpoint gained an amazing new vibrancy next to which the equal temperament of the standard equal tuned piano sounds positively muddy.
This tuning system gained all the more currency for Harrison in the 1970s, when he met Ann Kilmer, a UC Berkeley archaeologist who was also working with Harrison’s friend and ethnomusicologist Robert Brown. Kilmer had translated a nearly 4000-year-old clay tablet from ancient Sumer known as UET VII/74 that outlined this very tuning system — used not only in Greece but also Arabic countries, China, India, medieval Europe and elsewhere — more than a thousand years before Pythagoras. Pointing out the inaccuracy of the “Pythagorean” label, Harrison and others instead called it a “ditone” tuning or a “3-limit” tuning, referring to the fact that 3 is the largest prime number in these ratios. 3-limit tuning works well for music based on fifths, such as the Sonata in Ishartum he composed at this time in one of the modes mentioned by this tablet.
But for European composers around the time of the Renaissance, 3-limit tuning imposed significant shortcomings. First, the circle of fifths is not really a circle at all. If we continue the process of multiplying 3s and 2s, we find that after 12 iterations we arrive at the pitch E#, which is not the same as the pitch F. In fact, E# overshoots F by about an eighth of a tone or roughly 24 cents, an interval known as the Pythagorean comma, though it was well known in China and other cultures. It means that one of the “fifths” on a keyboard (in this example A# to F) will be smaller and dissonant, known as a “wolf” fifth.
Although the wolf fifth could be avoided by keeping to simple keys, a more serious shortcoming for European composers was the interval of a third, which composers used more and more by about the 14th century. The major third in 3-limit tuning has a ratio of 81/64, or 407 cents, a complex number that medieval theorists classified as a dissonance. But narrowed just a little bit to 386 cents, it reduces to the very simple ratio 5/4, which Renaissance composers called a very sweet interval. Tuning systems that include the 5/4 major third, the 6/5 minor third, and related intervals are known as 5-limit tunings, because a new prime number has been introduced.
For several Harrison harp works, in addition to some works for Asian zithers, metallophones, and refretted guitar, Harrison used these 5-limit thirds to create beautifully sonorous triads and other harmonies, including a scale that the ancient Alexandrian Claudius Ptolemy called syntonic diatonic, or more generally since then, just intonation. This is the tuning Harrison used, for example, in his Jahla in the Form of a Ductia to Pleasure Leopold Stokowski on his Ninetieth Birthday, in the key of F. (Jhala refers to a section and technique in North Indian music in which repeated drone pitches are inserted between notes of a fast melody.) Unfortunately, tuning the D to be the sweet 5/4 over the subdominant Bb, means that the fifth on the ii triad becomes a wolf. In essence, we need two Ds, to have both consonant triads. In this piece, he simply avoids the G/D fifth, but in other works he sometimes deliberately used the wolf fifth to create points of dissonance and instability. In 1967’s Music for Bill and Me — referring to the times he would play harp with his partner Bill Colvig — Harrison decided to keep the fifth on the second scale degree consonant (D-A in this key) and avoid the F-A major third.
Philosophers such as Pythagoras and Plato observed that whole numbers and their ratios represented abstractions intelligible only in human intellects and the phenomenon of music, where they were manifest in the tuning of musical scales. Well-formed music is therefore our opportunity sensually experience the mathematical framework that not only describes the universe but, in a very real sense to these thinkers, actually is the universe.
But Harrison didn't need the mystical justifications of numerology to enjoy the splendor of just intonation. Throughout his life he continued to speak of tuning as an empirically aural experience and remained convinced that the perception of simple ratios, aurally as well as visually, is emotionally powerful. He viewed just intonation as a place where ancient philosophy, physics, and perception converge. “The music sounds better, it just does,” he said. “Because I’m a sensualist, the hearing of those just intervals just pulls me in, whereas in equal temperament, I feel as though I’m on ice skates.”
The European tradition of triadic harmony essentially reflects a five-limit ideal in the compromised form of equal temperament. But beyond the five-limit, Harrison found delicious and exotic intervals not even remotely approximated in the tempered twelve-tone scale. He wrote Threnody for Oliver Daniel in a tuning that uses 7-limit intervals, including the 7/4 or natural seventh harmonic, the 7/6 ratio or small minor third, and the 8/7 ratio or large major second. These last two intervals approximate the step sizes in the Javanese gamelan tuning known as slendro, in which the octave is divided into five roughly equal intervals. Unlike slendro, this 1990 elegy for Harrison’s good friend also includes a mournful semitone, actually a small semitone of 21/20, which Harrison, like Baroque composers, often uses as a symbol of grief.
But the 7-limit was just the beginning. Harrison’s harp adventures continued when he would invite like-minded friends over for a weekend lunch and then spend the afternoon resurrecting the ancient sounds of Archytas’s enharmonic, Didymus’ chromatic, or Ptolemy’s equable diatonic scale. After tuning his harp in one of these scales, Harrison would improvise until the distinctive character and musical possibilities of the scale began to sink in. Harrison said that just intonation opens limitless possibilities, “a sort of paradise garden of delights,” that he never tired of exploring. One piece to come out of these experiments was his 1974 Little Homage to Eratosthenes, which uses a distinctive 19-limit scale invented by this librarian of ancient Alexandria.
“I have always been ‘exceedingly enamored’ of the harp,” Harrison wrote in a letter to John Schneider, who was then transcribing Harrison’s harp compositions for guitar, “and approve of a quote from the 16th- and 17th-century Spanish that Zabaleta wrote about—‘A gentleman will not be for long without his harp.’ Indeed, what you are doing with guitar and harp brings vividly to mind the manuscript pictures of the court of Alfonso the Wise, especially since those instruments were then properly tuned.”