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Fucos, Part 1

Sometimes when I listen to music I get a flurry of ideas for my own music creation. After one event last year, the thought popped into my head that I should write a string quartet about drones. I figured I would explore the different instruments taking turns droning while the others played something-yet-to-be-determined.

This semester at Austin Community College (ACC), where I’m studying again with my first composition teacher, Dr. Steven Sodders, there was to be an end-of-semester recital with a string quartet performing student compositions. I decided to set aside what I was working on and write my first string quartet.

As I considered the concept and contemplated the meaning of “drones” beyond a continuous sound, what came to mind was 1) male bees, 2) those small personal or commercial drones that are a toy or a tool, and 3) large military weapons. This suggested a structure of three parts to the piece.

Drone Bees

Reading about male bees* has been fascinating – they only have a mother and not a father, so they are haploid (one set of chromosomes). We humans are diploid (two sets of chromosomes). When considering the genealogy of drones, then, the number of ancestors per generation is different than for humans. For us, we have 2 parents, 4 grandparents, 8 great-grandparents, 16 great-great-grandparents, etc. Number in previous generation x 2, right? Or 2n, where n = number of the generation. Drone bees, however, have 1 parent, 2 grandparents, 3 great-grandparents, 5 great-great-grandparents… it’s the Fibonacci sequence! As soon as I came across that little nugget of information, I decided to use it as much as possible in the piece and it made my process really enjoyable.

The Fibonacci Sequence

Let me back up a bit. What’s the Fibonacci sequence? It’s the sequence of numbers where the next number is the sum of the two previous numbers. So it starts like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, … and continues indefinitely.

Drone Lengths and Dynamics

I maintained my original pre-process idea of droning throughout by at least one instrument. I used the Fibonacci sequence  as much as possible in choosing the length (in measures) that particular drones are played. For instance, the viola at measure 40 holds that drone for 3 measures, so the next one needs to be held for either 2 measures or 5 measures (I chose 5) to maintain the sequence. In general, when deciding how long one element should be before introducing another element in a different voice, I strove to decide based on the sequence. I also did my best to apply dynamics relative to Fibonacci patterns. I’m sure it’s not exact, but the result pleases my ear. There are a lot of 2s, 3s, and 5s, with the occasional 8 or 13, in my decision-making about lengths and dynamics. Pretty simple, really.


Perhaps the funnest application of the Fibonacci sequence was in choosing pitches. Since the numbers in the sequence get really large really fast, one way to make the concept more “wieldy” is applying a modulo function (divide by a number, keep the remainder). Fibonacci mod 12 yields a pattern of 24 numbers within the range 0 to 11 that repeats.

In studying atonal music, one learns the concept of pitch classes and applying numbers to the 12 semi-tones of Western music starting with C = 0 and counting up the half-steps to 11. Fibonacci mod 12 is very easily mapped to the 12 pitch classes this way.

For my piece, I briefly considered transposing the set (C = something besides 0), but the thought flittered away quicker than a drone looking for a queen.

While the opening pitches are simple open fifths as I establish droning, the cello at measure 21 starts at 1 (D-flat) and climbs up the Fibonacci sequence, just to 8 (A-flat). Most of the tonality remains within the first 8 rows of the table above, though I ventured into little patches of the Fibonacci mod 12 sequence occasionally.

Morse Code

Another adventure I explored with this piece is to embed Morse code. What does my little drone bee have to say? “I have no stinger.” Another fun fact about drones! The cello makes the first statement in measure 60. The viola restates it, overlapping with the cello. Then there is a bit of space where other things happen, violin II restates it then violin I says “No stinger.” The multiple statements, to me, imply multiple bees, which is relevant to the life cycle of drones as they aspire to their life’s dream.

The spacing/rhythms of the Dahs and Dits of the Morse code is not perfect. I calculated spacing precisely with 16th notes but it was “scary to read.” Teacher and I came up with a compromise that’s more playable. Imprecise, perhaps, but it definitely sounds like Morse code to me. Besides, I like how it sounds.

Besides rhythmic notation of the letters, I used different pitches for them as well. Starting with A = 0, I numbered the letters through 11, then started over. This gave me assigned pitch classes for letters. So, for example, R – Dit Dah Dit – was assigned the number 5, so it sounds at pitch F.

The Queen

The Morse code plays against a drone of E (4) and A-flat (8), which, for me, symbolizes the queen. Though the queen likewise has only 3 grandparents, she does have 2 parents, so the selection of 4 and 8 (22 and 23) for me represents the diploid nature of the queen.


Bees fly up-up-up during swarming, with drones from different colonies flying around a specific zone with many other drones. When a queen enters their area, they all try to mate with her. When they succeed, they die. This suggested the form of my piece and I’m pleased with how well that representation comes across to me. The little funeral dirge at the end, after the death, states the complete set of pitches of the Fibonacci mod 12 pattern in a slow fashion, setting up the next section that I plan to write later.


Using the Fibonacci sequence as guidance for my decision-making made writing this one of the most pleasant projects I’ve tackled in a long time!


* Disclaimer – I only browsed the internet, looking for ideas. No deep research here…

Permanent link to this article: https://ashleyhkraft.com/fucos-part-1/

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