12/16/2023 0 Comments Fibonacci sequence golden ratio![]() ![]() This is a rhythm that you hear in all kinds of places – think of the opening chords of Michael Jackson's Billie Jean. It's standard four-four time, with one added feature: if you were to step to the beat, you'd hear a chord when you take your first step, and then another chord while your knee is aloft between the second and third steps. The harmonic rhythm in Foster's original is asymmetric in a Fibonacci way: a short chord and then a long chord, three beats plus five beats, totalling eight beats. But what do I mean by as vague a term as "similar"? This is a question I explore musically with my trio's version of Mystic Brew, a 70s soul-jazz classic by Ronnie Foster. ![]() Because the ratios get successively closer to the golden ratio, the ratio 5:3 is not the same as, but "similar" to the ratio 8:5, which is "similar" to the ratio 13:8, or 144:89, or 6,765:4,181. ![]() What interests me about Fibonacci numbers is their scaling property. (Coleman introduced me to this whole idea.) That ratio has been observed frequently in dimensional proportions across many different contexts – in architecture from the Pyramids of Giza and the Parthenon, to constructions by Le Corbusier and Mies van der Rohe images by artists from Da Vinci and Albrecht Dürer to Juan Gris, Mondrian and Dalí and rhythmic durations and pitch ratios in works by composers from Bartók and Debussy to John Coltrane and Steve Coleman. If you look at the ratios of two successive Fibonacci numbers, and keep going up the sequence, you get: 1, 2, 1.5, 1.667, 1.6, 1.625, 1.615, 1.619, 1.618 … As you go up the sequence, this ratio gets closer and closer to a famous irrational number called the "golden ratio": 1.6180339887. Each number in the sequence is the sum of the previous two numbers, and it continues ad infinitum. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |