The flamenco dancer Israel Galván combines complete command of his medium with a phenomenally fertile range of off-beat stylistic ideas. He gives you — deliberately — the impression that traditional flamenco is too small to contain all he needs to do in terms of rhythm and drama. You see him suddenly balance on one leg and turn the sole of his raised shoe upward so that he can slap out a beat with his hands; he even taps one percussive phrase on his front teeth. These are gimmicks. As with many of the greatest flamenco dancers, the intensity with which he presents himself is always on the cusp of absurdity. But he makes his effects feel both enjoyable and necessary. They work because they’re part of the witty, odd flamboyance that characterizes his dance theater, but even more because they’re part of the rhythmic outpouring that turns his dance into music. Though he shows that he can do quite an assortment of the foot trillings that abound in flamenco, he refuses to indulge himself in that kind of bravura: he steers clear of flamenco cliché. It’s extremely rare in any genre to see a dancer of this singular imagination and authority.His show at the Joyce Theater this week is called “La Edad de Oro” (“The Golden Age”); it runs for almost an hour and a half without intermission. He is onstage throughout, with two other musicians, the singer David Lagos and the guitarist Alfredo Lagos. Lean, with a long and pointed nose, Mr. Galván is neither a hunk nor a beauty; but he has only to stand still, feet together, at the start of his first solo to show his mastery.The precision of his stance is immediately arresting. Watching, you can feel the immediate sureness and precision with which he places his body weight onto the arches of his feet. Later you realize this same skill explains the constant aplomb with which he can suddenly strike a balance with no apparent preparation: he just arrives on one foot in one striking position or another. On occasion he arches his body, in profile to the audience, like a bow ready to shoot; that kind of expressive tension is a crucial part of his style.A large part of his art consists of gesture. He can start a solo by holding his hands, fingers splayed, one in front of another above his head and beating them rapidly together in a soft clap. Frequently he holds his arms asymmetrically and with angular emphasis. Elbows, wrists, shoulders can all be given peculiar accentuations, but you always feel his sense of a larger line. Sitting, he suddenly pulls his right elbow up to one side (as if the elbow was pulling him) while his left leg points in the opposite direction: the single, slashing diagonal line from raised elbow to pointed foot makes an arresting start to a solo.Sometimes he holds one hand high and then softly brings it slowly down, fluttering it. On one occasion this movement also contained a particular kind of controlled tension, while on another the hand’s descent looked like a leaf in autumn.The title “La Edad de Oro” refers, as a program note reveals, to the widespread idea that in flamenco, as in other areas of art and life, there was once a golden age better than today. (It refers also to Luis Buñuel’s 1930 Surrealist film “L’Age d’Or.”) In flamenco that period is believed to have run from the late 19th century through the first third of the 20th. Mr. Galván’s performance suggests at once that this era is impossible to revive, and yet a new golden age can be made today in new dance terms.You feel his connection with tradition most in his close collaboration with the two Lagos brothers. Listening to the “cante jondo” of David and the guitar of Alfredo, you can easily hear the great flamenco musicians of the past; I was often reminded of the superlative recordings of La Niña de los Peines (1890-1969). The length and tension of the vocal phrases sustained by David on Tuesday were extraordinary by any standards; and the complexity and subtlety of rhythm created by the brothers flooded the program with sensuousness and brilliance. They aren’t ground-breaking artists in the way Mr. Galván is, but they have much in common with him; and on Tuesday were often more viscerally moving.Dance and music are all that occur here. The men are dressed in black; the only scenery is the chairs on which they sit. Not every flamenco show ends these days with the communal party-style dance onstage that used to occur, with all the musicians taking turns. But at the end of “La Edad de Oro” on Tuesday, the three men had fun by swapping roles: first Mr. Galván sang, Alfredo danced while David played guitar, and then Mr. Galván played guitar while David danced and Alfredo sang.