This is partially inspired by Pierre Baudin's recently published matrix of hybrid patterns and partially a byproduct of revisiting old work. Back in the spring as I attempted to cobble together a hybrid Gina McGrath posed as a challenge to many of us at FLAME Festival I found that my perception of how polyrhythm hybrids could be composed was only a third of the story at best. In looking at Pierre's work, I realized said insight applied to many of the shapes he was describing in the matrix table he'd composed. I'm not going to claim this is an exhaustive method for classifying all hybrids--part of the point of this work has been realizing how woefully malformed our currently classification system is, but I do hope it's a step toward not only creating a more rigorous system of classification but also providing the tools many young poi spinners will need to be able to perform all the hybrids in Pierre's chart in all the fashions I have outlined here.

At its core, this is an attempt to normalize the framing of hybrids in such a way as to focus on the feature that I believe is core to how the audience perceives them: through timing and direction. When we contrast two patterns against each other, we frequently do so by visualizing the completed pattern in our heads. In cases where we are spinning rapidly and utilizing either lit fire or LED poi, those overall patterns may become obvious to the audience but in those cases when we are not and the complete pattern may not be immediately obvious, we still perceive a hybrid as being a particular pattern--why is this? My theory is that when the complete pattern is not immediately intelligible that we instead focus on the localized aspects of it that we are able to immediately perceive. These localized aspects tend to have two major components: the alignment of the poi heads and hands in relation to each other (most especially in the case of antibrids) and the contrast of timing and direction between two patterns. It is in this latter property that I find the most compelling way to break out the different types of hybrids and their presentations that we have available to us. But first, what are we talking about?

Definitions

First, for the purposes of this work I'm defining a hybrid as the result of each hand/poi combination completing incongruent poi patterns in one or more synchronous fashions (more on this to come). Frequently (though not necessarily) these poi patterns take the form of roulette or trochoid-like patterns frequently referred to as flowers, extensions, cateyes, isolations, etc. I know this is a broad definition and it is intentionally so. For the purposes of this document, however, I will be focusing on just the trochoid-based patterns that may be used to create hybrids.

Within the context of these patterns, there is an equally important feature that both the hands and the poi share though not always in equal quantities. When performing any roulette-like move if we pick a given cardinal orientation from which to evaluate the pattern, we will find both the hand and the poi pointing in that direction in different quantities based upon the particular roulette we are working with. Nearly all require only a single point in which the hand returns to this cardinal position, but in any case where the poi head produces more than 2 self-enclosed regions (commonly known as petals), we will find that the number of times the poi head returns to the original cardinal position is now greater than the number of times the hand does. From here on I'll refer to this property as a "beat" and note that for most roulette patterns, the hand performs a single beat while the poi performs one or more beats depending upon the pattern.

The next property to define in the context of this work will be timing and direction. Timing and direction is meant to track the relative motion of two rotating objects to each other both in terms of relative directional vector and phase relationship. In the 2D space of roulettes, timing and direction is usually considered to have four major categories relating to properties of directional vector and phasing as they relate to four cardinal points or axes of symmetry. For the purposes of this work I'll use the Vulcan Tech Blog naming convention for these four categories as they abbreviate well, in which case they will be referred to from here out as Together-Same (TS), Together-Opposite (TO), Split-Same (SS), and Split-Opposites (SO).

Methodology

Given that I believe hybrids are as visually interesting for the localized effects I've described above as for the overall juxtaposition of patterns that they represent, I've endeavored to use these localized effects to help classify the different types of hybrid patterns. I use this methodology given that A) There is no hybrid pattern to which I've yet been acquainted that does not make use of localized timing and direction effects and B) it is likely to present opportunities for transitioning between patterns by finding those patterns that share localized effects in the same general areas. Given that poi hybrids present us with three possible ways of matching up localized effects with timing and direction, this classification system is based upon grouping those hybrids together that exhibit consistent timing and direction between the poi, between the hands, and the completion of both patterns simultaneously with no regard to maintaining consistent timing and direction with any of the constituent patterns. With that in mind, I've outlined a taxonomy of hybrid presentation types that includes two major categories each with at least two subcategories. Those two categories are Monorhythm and Polyrhythm Hybrids.

Monorhythm hybrids consist of those hybrids for which it is possible for timing and direction between hands, poi, and pattern completion to all be possible. This requires that both patterns in question have the same number of beats between hands and the same number of beats between poi. Matching both of these requirements also invariably leads to the patterns being completed simultaneously as well. Examples of this type of hybrid include all the 3:3 hybrids that have been explored in detail in the Vulcan Tech Gospel videos and the 2:2 hybrids I've explored in my own work. Given that all constituent patterns have equivalent beats, the timing and direction remains fixed throughout the entire pattern. No matter what timing and direction the pattern begins in, it will complete with the timing and direction unaltered by the end of the pattern.

Within this category we also find the subfamily usually noted as Unit Circle Hybrids, which are the family of hybrids for which the number of beats for all objects in the system is only one. Cateyes, unit circle extensions, and isolations make up the constituent parts of this family. Why separate out this class of hybrids? For the other type of hybrid in this class, the static nature of the timing and direction of the poi in relation to each other is due to the poi traveling an equal distance in the same amount of time. Within the unit circle, this property ceases to be so--in fact it cannot be true for any hybrid found within it.

Mathematically, unit circle hybrids superficially share timing and direction characteristics with their multiple beat cousins but do so in a completely different fashion. The consistency of timing and direction in unit circle hybrids is a result of a hiccup in the math that occurs as one approaches a singularity. For purposes of clarity, we will classify any monorhythm hybrid that does not qualify as a unit circle hybrid as being a Beat-Matched hybrid.

Moving beyond Monorhythm hybrids, we encounter Polyrhythm Hybrids. These hybrids are easy to spot in that the beat counts between patterns are inequal to each other. Examples of this include triquetra vs static and 4-petal antispin vs extension. It is here that we really get to sift apart different hybrids based upon their localized timing and direction properties. For any polyrhythm hybrid there will be two possible ways to perform it and possibly a third: if we keep timing and direction consistent between the hands, we will find that the poi become polyrhythmic and cycle through multiple timings while direction remains consistent. If, on the other hand we lock timing and direction between the poi, we will find our hands cycle through multiple timings while direction remains consistent.

For example, in performing triquetra vs extension (aka, the Mercedes) and I decide my poi will move in opposites, I can then have my hands move in TS or SS depending upon my particular preference. The poi will then seem to switch between points of TO and SO. In this case the timing and direction of the hands remain locked, and the two patterns complete simultaneously. If, on the other hand, I decide I'm going to keep the timing and direction consistent between my poi, one of my hands then has to complete two arcs for every one arc that the other hand completes and thus the two patterns will only be completed after multiple hand paths. Again, this will result in regions where my hands appear to be switching between TS and SS while my poi remain locked in either TO or SO.

All patterns that share the requirements listed above share one other characteristic beyond their being polyrhythmic: the beats of the hands or poi will be an integer (a whole number--not a fraction or decimal). If, on the other hand, one of the patterns in the hybrid does not have a beat count that is an integer (a pentagram for example, which has a beat count of 1.5 beats for every single beat of the hand), a third option becomes available: the patterns of both hands reach completion simultaneously and will result in timing and direction being locked for neither poi nor hands, in other words, both poi and hands will be seen to cycle through timings though direction will always remain constant. To distinguish between all the cases listed above, I have three labels: Poi Locked, Hand Locked, and Pattern Locked. We can note, then, that all Monorhythm Hybrids are locked in all three regards. When we move to integer-beat Polyrhythm hybrids we can either have two patterns be Pattern Locked and Hand Locked or simply Poi Locked, and when we move to fractional-beat Polyrhythms, our patterns can be Hand Locked, Poi Locked, or Pattern Locked but never all three.* Below is a handy taxonomy and diagram to help keep these elements distinguished:

Monorhythm hybrids:

• Beat-Matched
  Must be hand-locked, poi-locked, and pattern-locked
• Unit Circle/Monobeat
  Must be hand-locked, poi-locked, and pattern-locked

Polyrhythm hybrids:

• Integer beat
  Must be either hand-locked and pattern-locked or poi-locked
• Fractional beat
  Can be hand-locked, poi-locked, or pattern-locked, but cannot be all three

Thanks for reading--please send me feedback on this. Some of these ideas have been covered in some depth elsewhere, but I wanted to create a document that comprehensively brought them all together in an easy-to-read format.

* Updated 2/1/2013 after some helpful input from Pierre