The film-music scholar Frank Lehman, an assistant professor at Tufts University, works fast: within a day of the opening of “Star Wars: The Last Jedi,” he had updated his “Complete Catalogue of the Motivic Material in ‘Star Wars,’ Episodes I-VIII,” which can be found online. The catalogue now includes fifty-five distinct leitmotifs—thematic ideas that point toward characters, objects, ideas, and relationships—and forty-three so-called incidental motifs, which, Lehman says, “do not meet criteria for proper leitmotifs” but nonetheless possess dramatic significance. Such beloved tunes as “The Force,” “Han and Leia,” and the dastardly “Imperial March” are here, along with more esoteric items like “Planetary Descent Figure,” “Ominous Neighbor Figure,” and “Apocalyptic Repeated Minor Triads.”

All this refers, of course, to the eight scores that John Williams has composed for the “Star Wars” cycle, with a ninth in the works. In decades past, it was fashionable for self-styled serious music types to look down on Williams, but the “Star Wars” corpus has increasingly attracted scholarly scrutiny: Lehman’s catalogue will be published in “John Williams: Music for Films, Television, and the Concert Stage,” a volume forthcoming from the Centro Studi Opera Omnia Luigi Boccherini. This attention has come about not only because of the mythic weight that George Lucas’s space operas have acquired in the contemporary imagination; the music is also superbly crafted and rewards close analysis. Williams’s latest score is one the most compelling in his forty-year “Star Wars” career: Rian Johnson’s film complicates and enriches the familiar template, and Williams responds with intricate, ambiguous variations on his canon of themes.

The word “leitmotif,” like much else emanating from the gaseous Planet Wagner, has caused considerable confusion over the years. The term was coined by Hans von Wolzogen, one of a coterie of intellectual sycophants who surrounded the composer in the years before his death, in 1883. Wagner had spoken of “melodic moments” and “ground-motifs” in his work, but he criticized his acolyte for treating such motifs purely as dramatic devices, neglecting their internal musical logic. As happened so often, Wagner’s idea took on a life of its own. Wolzogen lived long enough to hail Hitler in the pages of the Bayreuther Blätter, the dismal Wagner fanzine that he edited for decades.

In the basic definition, leitmotifs are identifying musical tags: when someone talks about the sword, you hear the sword’s melody. In the “Ring” cycle, there are motifs for the spear, Valhalla, Fate, the giants, the dragon, and dozens of others. But they are less finished themes than suggestive fragments, which transcend their immediate context and point forward or backward in time—signals of foreboding and remembrance, in Wagner’s words. As the cycle proceeds, Wagner treats the leitmotifs in oblique, even subversive ways. The theme known as Renunciation of Love first sounds in “Das Rheingold,” when Alberich forswears love and thereby gains access to the magic gold. It is heard again in “Die Walküre,” as Siegmund prepares to pull the sword from the tree. Why should a lusty hero be linked to a loveless dwarf? Much ink has been spilled trying to resolve that contradiction, but contradiction may be the point. Likewise, the descending scalar motif of Wotan’s spear progressively deteriorates in the course of the cycle. When Siegfried defeats the Wanderer, it shatters into whole-tone fragments; when Hagen, Alberich’s son, dreams of world domination by the Rhine, it turns demonically black.

Leitmotifs surfaced early in film-music history. In 1911, Clarence Sinn, the musical director at the Orpheum Theatre, in Chicago, proposed that Wagner’s alleged system was “ideally perfect” for the accompaniment of motion pictures. Sinn summarized the system thus: “To each important character, to each important action, motive or idea, and to each important object (Siegmund’s sword, for example), was attached a suggestive musical theme. Whenever the action brought into prominence, any of the characters, motives, or objects, its theme or motif was sung or played.” The conductor and composer Ernö Rapée followed the same line, writing that Wagner’s “method of investing each one of his characters with a certain motive, called ‘Leit Motiv’ and applying this motive at every appearance of the character, but in different shadings to suit the surrounding conditions, is the one which can best be applied in scoring pictures.”

These definitions have only a tenuous relation to Wagner’s unsystematic method. In reality, silent-film accompanists relied on a fixed library of stock themes, usually not of their invention. The scholar James Buhler argues that such a system was an inevitable development, given the novelty of long-form visual stories: “Musical accompaniment became an obvious red thread of orientation within the confusing field of narrative integration.” Wagner was at the top of the stockpile. The “Ride of the Valkyries” quickly became a favorite device, serving to illustrate scenes involving battles, chases, and galloping horses. Most notoriously, it accompanied the ride of the Ku Klux Klan in D. W. Griffith’s “The Birth of a Nation.”

When sound came in, leitmotifs proliferated, although their function was less clear than before. In some cases, they become superfluous and overbearing: if we see British naval officers speaking in British accents with a British flag waving in the background, we don’t also need to hear “Rule, Britannia!” Nonetheless, Golden Age Hollywood composers, such as Max Steiner and Erich Wolfgang Korngold, made lavish and often creative use of musical tags in Wagnerian style. Steiner said, “If Wagner had lived in this century, he would have been the No. 1 film composer.” In truth, because Wagner would have wanted to write and direct films as well, Hollywood might have been a less hospitable place than was King Ludwig’s Bavaria.

Williams’s first “Star Wars” score was a deliberate throwback to the grand manner of Steiner and Korngold. Lucas liked the idea of a sci-fi saga unfolding against a Romantic, swashbuckling musical backdrop, and Williams responded artfully. The composer said in an interview, “It was not music that might describe terra incognita but the opposite of that, music that would put us in touch with very familiar and remembered emotions, which for me as a musician translated into the use of a nineteenth-century operatic idiom, if you like, Wagner and this sort of thing.” Such a method activated, Williams said, a “cross-cultural mythology.” The constant underlining of characters and situations—robust, rag-tag heroic themes for the Rebels, or monumental, ominous music for Darth Vader and the Empire—has a playful obviousness, a knowing air. In this sense, it conforms to the grinning naïveté of Lucas’s film.

Something more substantial happens in the celebrated scene in which young Luke Skywalker looks longingly toward a horizon lit by twin setting suns, dreaming of a life beyond the desert planet Tatooine. Williams writes a melancholy, expansive G-minor theme for solo horn, which is soon taken up by full strings. Akin to the noble C-minor melody that Wagner writes for Siegfried, this leitmotif represents not only Luke but also the mystical medium known as the Force. Buhler points out that the music is heard before the Force has been explained; thus, in classic Wagnerian fashion, it foreshadows the not-yet-known. This may be the point at which “Star Wars” steps out of the adolescent-adventure arena and into the realm of modern myth.

Scholars like Lehman are exulting in “The Last Jedi” because the score is full of such echt-leitmotivic moments. Williams manipulates his library of themes with extreme dexterity, often touching on a familiar motif for just a couple of bars. (Spoilers loom ahead.) In early scenes set at a remote, ruined Jedi temple, we keep hearing an attenuated, beclouded version of the Force motto: this evokes Luke’s embittered renunciation of the Jedi project. As the young heroine Rey begins to coax him out of his funk, the Force stretches out and is unfurled at length. Sometimes, the music does all of the work of explaining what is going on. In one scene, Leia, Luke’s Force-capable sister, communicates telepathically with her son Kylo Ren, who has gone over to the dark side and is training his guns on her vessel. Leia’s theme is briefly heard against a dissonant cluster chord. Earlier in the saga, we might have been subjected to dialogue along the lines of “Don’t do this! I’m your mother!” Williams’s musical paraphrase is more elegant.