Indian classical music (Hindustani & Karnatic) has a long tradition of rhythmic complexity that became popularized in the Western world through bands like Mahavishnu Orchestra and Shakti (both lead by John McLaughlin). In this tradition, rhythms are often learned by vocalization (spoken syllables) and gestures (claps and tapping with fingers). This tradition is known as Solkattu.
Western European music’s distinction is found in it’s harmonic system, which is rooted in the understanding of the harmonic series. Many non-Western musical traditions do not have as sophisticated a system for harmony, but they frequently excel in rhythmic complexity. In the Western tradition, rhythms are approached by counting beats with numbers, and subdivisions in syllables. If we are to take 16th notes as an example: 1e+a, 2e+a. Triplets can be counted “one-trip-let” or “1+a”. While this is effective, it can become difficult to manage multiple layers of contrasting rhythms (polyrhythms) since the voice can only produce one sound at a time.
Even a basic understanding of Solkattu can benefit your rhythmic awareness.
Hand gestures are used to keep track of the meter: IE 3/4, 4/4, 6/8, etc. Let’s take 3/4 as an example. Beat one is played with a clap. Beat two is played by tapping the pinky on to the palm. Beat three is played by the ring finger, then the cycle repeats. You can keep adding beats until you run out of digits, making a total of 6 beats possible. More beats are possible by turning the palm around.
Over top of this, you can use vocalized syllables create a second layer of rhythms. For groupings of two, “ta-ka” is used. Three note groupings: “ta-ki-ta”. Four note groupings: “ta-ka-di-mi”. Five notes: “ta-ka-ta-ki-ta” and so on. Most rhythms will be easily handled with combinations of 2 or 4 note groupings. combines with 3 note groupings. For example, seven note groupings can be expressed as “ta-ka-di-mi-ta-ki-ta” or “ta-ki-ta-ta-ka-di-mi” depending on where the rhythmic emphasis is placed.
As an exercise, try this rhythm: Using hand gestures, tap a 3/4 time signature. In eighth notes, sing a 4 note grouping over it. When you do this correctly, the claps will fall on the emphasized syllables: “TA-ki-TA, ta-KI-ta, TA-ki-TA, ta-KI-ta”. There you go, you have a polyrhythm!
This is only scratching the surface of possibilities. I highly recommend exploring different combinations of time signatures and subdivisions to create your own unique rhythmic grooves! If you’re interested in some literature on this topic, check out this link.