Tone to Rhythm -- Hz to BPM

I’ve recently become entranced with the idea that rhythm is the movement between two points, and it creates a sine wave, as demonstrated in the tambourine video.  A sine wave is a geometric waveform that oscillates from top to bottom. In music, a sine wave is most commonly observed when talking about sound synthesis. It is used to talk about tone, and is measured in Hz, which means oscillations (the amount of times that the wave goes from top to bottom) per second. The tone of A above middle C on the piano is 440 Hz (thats 440 vibrations per second!). When talking about rhythm, musicians say BPM, which means beats per minute, and is used to talk about tempo, or the pace of the pulse of music. What I have become particularly fascinated by is the relationship between rhythm (BPM) and tone (Hz). Why?

60 Beats per minute (BPM) means there is one beat per second, which is 1Hz

This sounds like a pulse, but if you start speeding it up, it starts to sound like a tone, though it will be barely audible to the human ear which is only capable of hearing 20 Hz - 20,000 Hz
How many times would we have to multiply 60 BPM (1 beat per second = 1Hz) to get to baseline audible tone of 20Hz?

60 BPM x 20 = 1,200

So that means if we had rhythm with a tempo of 1,200 BPM it would make a sound at the frequency of 20 Hz, which is so low you probably wouldn’t be able to hear it, though you might be able to feel it, or sense it. Earthquakes have a frequency of .01-10 Hz, which might be why some animals can sense them, maybe they are hearing something that we are not sensitive to. In contrast to earthquakes, a more familiar and audible sound is the human voice, which has a fundamental frequency of 120 Hz.

60BPM x 120 = 7200 BPM

That means, if we were capable of turning a metronome to 7,200 BPM it would start to sound like a human voice. A more musical sound that is in the middle of the piano, is A above middle C, and this has a frequency of 440Hz. Whats the BPM of A above middle C?

60 x 440 = 26,400 BPM

Whoa! That is pretty fast, I wonder if that is how fast a hummingbird’s heart beats, or maybe closer to how fast a hummingbird flaps their wings. Thanks to google, it turns out a hummingbirds heart rate is 1,260 BPM (just a moment ago we discovered that 1,200 BPM is 20Hz, so a humming birds heart rate is just a feather over 20Hz.)

They flap their wings 80 times per second, which is 80 Hz. If you have ever had a humming bird fly by your ear, you will notice it sounds more like a tone then a rhythm, this is because humming birds flap their wings at the insanely fast rate of 80 Hz. If we multiply 80 wing flaps per second, by how many seconds are in a minute (60), we get 4800 WFPM (wing flaps per minute).

The distinction between “tone” and “rhythm” is a property of frequency. We use the measurement of Hz to talk about really sped up rhythms, and the measurement of BPM to talk about really slowed down tones. It is common to think of rhythm on a spectrum of fast or slow, and to think of tone on the spectrum of high or low, but it is less common to think of rhythm and tone to exist on the same spectrum. On this spectrum, low frequencies are measured in minutes, and as the frequency speeds up it is measured in seconds. So, what is the relevance of this spectrum?

The study of harmony looks at the relationship between tones when played simultaneously. Traditionally, this is talking about bass notes, chords, and melody notes - and how they all jive together to create a harmonic effect. What makes different notes resonate as they vibrate together has to do with the mathematical ratio between notes. This is why some notes sound like a harmony, and others do not. To go any deeper into why and how harmony works is the subject of a book! In regards to the relationship between Hz and BPM, I am fascinated by the potential of rhythms measured by BPM being in “harmony” with the tones in a piece of music. When deciding the tempo of a song, it is often seen as arbitrary, but I think our sense of wanting to adjust to the tempo that feels right has to do with the way it synchronizes with the frequencies in the song. From this perspective, changing the key (fundamental frequency of the song) could also have an effect on whether a tempo feels right. It is the same idea as trying to find a harmony note, a note that resonates with the rest, but instead of trying to find the tone that resonates, it is about finding the rhythm that is “in tune” with the fundamental tone.

Now that we have taken the idea of harmony outside the idea of only being applied to musical tones measured in Hz (oscillations per second), and seeing how it could also relate to BPM (oscillations per minute), why should we stop at seconds and minutes? The relationship between seconds and minutes is analogous to the relationship between minutes and hours. There are 60 seconds in a minute, and 60 minutes in an hour. An hour is a subdivision of a day, which is an oscillation between day and night determined by the the physical spinning of the earth. To see the earth’s spinning as a sine wave that creates a rhythm is not a metaphor, it is just as physical as the sine wave frequencies measured in seconds (Hz) and minutes (BPM), we just traded the microscope for the telescope!

When we start looking towards the rhythms of celestial bodies such as the earth, moon, planets, the moons of other planets, the sun and beyond - you can start to get an idea of what the ancient Greek philosopher Pythagoras called the “music of the spheres”. He believed the same laws that governed harmony of musical tones are also governing the frequencies of celestial bodies on a much larger scale.

Since the time of Pythagoras there have been many philosophers, mathematicians, physicists, astronomers, composers, musicians, metaphysicists, poets and mystics to try and make sense of this concept of “music of the spheres”. In my own pursuit of trying to understand what Pythagoras was referring to, I have found the more people try to fit it into a conceptual box the less interested I become. For instance, I don’t believe that the universe is a reflection of western music theory. In my quest to make sense of how all the pieces fit together, I have found it is the poets and mystics who leave a deeper impact on my understanding, the ones who approach these concepts with feeling, intuition and direct experience. I think it is for the same reason that we cannot hear an earthquake, but we can feel the ground shake beneath our feet. As with most bigger curiosities, the questions that surround them carve out a place within for an understanding to develop. I would like to end this exploration with the song lyrics of my 2 of my favorite hippies:

“You know the day destroys the night
Night divides the day
tried to run, tried to hide
break on through to the other side”
-The Doors

“And all that is now, and all that is gone
And all that’s to come and everything under the sun is in tune
But the sun is eclipsed by the moon”
-Pink Floyd