Filtering Infinity

Soon after I began my practical study of the various grooves (phrasings) for different microtime divisions, their extraordinary diversity appeared: each of them has a different taste, a different feel, like the various accents which are applied to the different languages around the world. I wanted to explore this diversity of grooves and refine my ability to hear, identify, and play them on the piano.

In order to organize my practice I undertook to draw up a list of canonical patterns that I could morph from and consider as phrased tuplets. I first needed to reduce that list from a theoretical infinity of patterns to a set of patterns actually worth practising by taking out redundancies for example.

According to the theory, any rhythmical pattern can be considered a phrased tuplet. Also, any given tuplet can take up the function of a microtime if its total cycle coincides with the pulse cycle. But here’s where psycho-acoustics also join the game :

Practically speaking, some phrased patterns can’t be perceived as microtime. For example a pattern of three elements with duration ratios of 5:1:1 will never sound like a triplet for the human brain. A 2:1 ratio is probably the upper limit that’s never reached because at 2:1, the ear then tends to add the missing elements of a higher division. Here for example a 4-element pattern with durations of 2-1-1-2 will sound like a 6-element pattern with missing strokes 1-(1)-1-1-1-(1).

Beside duration ratios, another limitation is related to the range of perception of tempi (pulse frequencies). There is a lower limit of pulse frequency below which the human brain no longer feels a pulse and needs to subdivide in order to predict strokes with precision (apparently the limit can go as low as 0.2 Hz or 15 bpm, although for most people the limit is much higher). That’s why long patterns are either not perceptible as microtime (because their total cycle exceeds this lower limit pulse cycle), or far too fast to be heard as micropulse (micropulse becomes pitch above 16Hz aproximately), let alone to be phrased (nobody can swing eighth notes passed a certain tempo).

Last but not least one of the most interesting properties of some phrased microtimes is that they allow one to identify the pulse frequency out of the microtime structure itself, regardless of the pitches applied. This property  has an important effect: the pulse feel is emphasized, creating a feeling which might as well be the very essence of what we call groove. In the case of patterns consisting of the repetition of smaller patterns, the induced pulse feel syncs with the cycle of the smaller pattern. For example a series of 6 swinging eighth notes is perceived as 3 times the swinging duplet (ill., right) rather than a 6-tuplet (ill. left).

Taking all these psycho-acoustic elements in consideration, I chose to limit my list of canonical patterns to those ranging from two to seven elements, made of non recurring combinations of long and short elements expressed with a ratio of 2:1, and thus notated using eighth and sixteenth notes beamed together (to the beat). Have a look at the list here. The patterns are classified according to size and grouped in families of related patterns that are rotations of one another.

Of course there are much more patterns of interest to study. For instance patterns combining more than two different lengths, sometimes found in traditional music, have special qualities. But practising the canonical patterns that I propose is enough to extend one’s capacity to hear and perform very fine variations of phrasings and to quickly adapt to more complex ones if needed.

It’s all about gravity

When it comes to classifying my canonical patterns I identify 4 parameters that I name absolute size, tuplet sizepotential energy and groove balance :

  • Absolute and tuplet size:
    When considering the morphing between the pattern and its associated straight tuplet, one can say that it is a morphing between a high and a low division.
    The absolute size represents the high division, and the tuplet size the low division.

    tuplet size 5
    absolute size 7

    So the tuplet size of a pattern is simply the number of elements it contains, in other words what kind of tuplet it is considered to be a phrasing of, whereas the absolute size of a pattern is its duration expressed in 16th notes.
  • Potential energy:
    The potential energy describes how far a pattern and its associated straight tuplet are. In other terms it describes how much energy one needs to morph from the pattern to the straight tuplet and vice versa. The closer a pattern is to its straight tuplet, the easier it will be to morph back and forth between them. It is calculated by adding the distance between each element of the pattern and its corresponding element of the straight tuplet. Here below we find again the previous 5(7)-tuplet illustrated in order to show the concept of potential energy.
  • Groove balance
    The groove balance describes whether a groove feel is laid back or pushing forward:

    The pulse is often described as « ground ». This is probably because of dance where tapping the feet to the ground generally coincides with the pulse. In my view, « ground » could also depict the attraction exerted by the pulse’s « ground-point »: the beat. Like a bouncing ball is attracted to the ground, the time flow’s present is attracted to the beat.
    Now depending on how we look at it, the beat can either be the point the bouncing ball lands on, or the point from which it takes off. Musicians will describe a beat or groove as « rushing », « pushing », « moving forward » or to the contrary as « sticky », « laid back », « pulling ». These different perspectives can actually be induced by the shape of the bouncing trajectory, i.e. the phrasing of the microtime.feels
    So the shape of a phrasing pattern will affect the groove feel and make it more or less pushy or laid back. The groove balance describes that feel. To explain this better I’ll use polygons inscribe in circles. They represent tuplet phrasing patterns, so triplets will be triangles, 4-tuplets will be squares, and so on. A regular polygon illustrates a straight tuplet whereas an irregular one illustrates a phrased tuplet.
    Here, a circle represents the pulse’s cycle and the vertices of the polygon represent the different elements of the rhythmic pattern. The downmost vertex represents the first element of the pattern. It shows the beat point, or « ground point » of the groove. There is a gravity arrow pointing towards the ground to show the attraction of the beat. All polygons stand on the ground point but will tip over to either side depending on their balance. Regular polygons are perfectly balanced because of the even distribution of their vertices on the circle so they stand in equilibrium over the ground point.
    The illustration above features 3 different triplets: A is an equilateral triangle and represents a straight triplet. B and C are irregular triangles and represent phrased triplets. B tips over to the right and hence represents a « rushing » triplet. C on the contrary evokes a « laid back » feel.
    I speak of negative and positive groove balance values. The theoretical values range between -1 (extremely laid back) and +1 (extremely pushy). They are calculated by adding the signed potential energies of each pattern element, whereas the total potential energy of a pattern is calculated by adding the absolute values of the potential energies of each element.
  • Herunder a form that calculates automatically the tuplet size, absolute size, potential energy and groove balance for a given pattern. Simply enter a pattern (for example 21121) in the appropriate field. Only works up to 7 digits.


One Comment

  1. danyelnicholas

    It seems that what you are describing is essentially the old French system of notes inégales. I am grateful for your endeavours, because It is clearly necessary to draw detailed attention to the subtlety of rhythm as they indeed decide over the most essential quality of music. Interesting your attempt to align parameters of harmony (pitch proportions) and rhythm in a very different and potentially far more fruitful and enlightened way than Stockhausen in « wie die Zeit vergeht » (even though I don’t know to what extent you have experimented with tempered harmonies analogue to your morphing phrasings, might be fascinating). Any idea about the role of timbre?
    My very best wishes, danyel

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