Monday, February 24, 2020


Today just happens to mark the 13th anniversary of this blog. (MMmusing is a teenager!) And 13 just happens to be a Fibonacci number! So what better way to mark this occasion (and finish up this little blog series) than with a bit of Fibonacci fun?

In my last two posts, I talked about encounters I had with the Golden Ratio and the Fibonacci Sequence while preparing to lead some musical sessions as part of a broader academic day focused on those topics. I've already written about looking for the Golden Ratio in Beethoven and about writing a little vocal warm-up using Fibonacci numbers.

The latter is based on a simple diatonic pattern in which the primary notes of a scale (the "white notes" in C Major) are used as stepping tones for scalar ascents of 1, 2, 3, 5, and 8. Naturally, I was also interested in exploring larger numbers in the series, and though it's not practical to sing a range covering 55 notes, the piano keyboard can easily accommodate that. EXCEPT, I was actually a little surprised to realize that the 88 notes of a piano include only 52 white notes.

So, although I like the way the diatonic Fibonacci patterns emphasize the 3rd, 5th, and octave of a major scale, I set to work organizing the full chromatic complement of white AND black notes, which easily accommodates the Fibonacci 55. Sadly, the next number in the series is 89, and that's one note too far, but I also feel there might be diminishing returns if the number stretches out too far. (See postscript #1 to test this out.) It becomes difficult beyond 55 (or maybe beyond 21 or 34?) to feel the relationship to the groups preceding.

Anyway, the skeleton of my piece-in-progress is this very simple expression of Fibonacci numbers through expanding meters (Remember, the Fibonacci Sequence begins: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55):

There's not a lot of real "composing" going on there, but I then added a right hand part to emphasize some of those metrical tricks, build suspense, and also help support a vibrant ending in which a big C Major chord settles out into longer and longer notes values based on...well, you can figure it out. This little etude is called "Fibonacci Frenzy." (Yeah, yeah, yeah, I should record it like a real pianist and not subject you to this robo-performance, but I am appreciating the way Noteflight allows for the embedding of scrolling notation.)

 Since there are only a couple of hours left on this blogday, I'll just add two quick postscripts.
  • In response to my Fibonacci vocal warm-up, Twitter friend Dan introduced me to a very entertaining and ever-expanding piece based on a Fibonacci-esque sequence: Narayana's Cows. This music definitely pushes the limits of how far out we can perceive these expanding connections.
  • Rather coincidentally, this Sound Field video crossed my path a couple of days ago. Early on [0:21-0:40], one of the hosts indulges in some of that mystical "some music sounds right yada yada because...well...Golden Ratio!" As often happens with such discussions, there's not much substantive probing of what's going on and how valid this is aesthetically, though I appreciated some acknowledgement [3:28 - ] that Golden Ratios might just be the kind of thing you can always find if you look in the right place. But, most notably for me, the same host, Nahre Sol, ends the video with a little composition she wrote using both the Golden Ratio to govern the structure and some Fibonacci numbers to generate some riffs. (Oddly enough, the complete composition is not played in this video, so we don't get a chance to experience the Golden Ratio!) If you like hearing numbers dance, you might enjoy this.

    Happy MMmusing Day!

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