For this next (and maybe long-overdue) interactive, I’m exploring the relationships between pitch intervals and polyrhythms. The main difference is how we audibly perceive pitch and rhythm:
- Musical notes are recognizable as having a discernible pitch to them because they vibrate at a specific frequency in hertz. This can also be thought of as cycles per second. Pitches happen to cycle A LOT per second which is why we hear those vibrations as notes rather than rhythms.
- Polyrhythms literally means “many rhythms” but typically these polyrhythms are understood to be ostinati or cyclic. However, our ears have a difficult time hearing vibrations as pitches once they reach slower than about 20 to 30 hertz. This is when we can start thinking about vibrations or impulses as rhythms.
So when I say, “pitch = rhythm” I’m really talking about pitch intervals are equivalent to polyrhythms. Both are ratios and sometimes those ratios are exactly the same. For example, a 3:2 rhythmic ratio could be one part playing three triplet 8th notes in the same space of the other part playing two 8th notes. As a pitch interval, this would work out to be a perfect 5th, a chord of perhaps 660Hz to 440Hz. I should note that this integer ratio works for Just Intonation and Pythagorean tuning, NOT Equal Temperament.
I experimented with this idea in my work Quocíente for six berimbaus. The musical process of Quocíente was to play the rhythmic ratio first (i.e., 6:5, one player plays every six 8th notes while another player plays every five 8th notes) and when the cycles completes, you will hear an interval of a minor 3rd (6:5). If this is too confusing, hopefully the interactive will help. Below, the first part about pitch is a simulated divided string. You’ll get the sense of what it’s like to tune a berimbau! Many of these tuning ratios come from Arcomusical’s notation and style guide for composers. Enjoy, and feel free to contact me for questions or suggestions. If you’re having trouble viewing on a mobile device, try this version.