You’ve already seen a similar figure if you’ve read my post Marathon: Understanding Ratio Morphing. Here, I’ve added subdivisions of time from 5 to 8, but in practice they also include subdivisions of 2, 3, and 4, and we’re going to look over them relatively succinctly today.
First, how to read this graph. It’s important to know that it’s read from left to right. The leftmost boundary is the start of a measure, and the rightmost one the end of it. If you’ve ever used Guitar Pro or a similar notation software, you can easily imagine a cursor moving steadily from left to right. Every time the cursor crosses a coloured line, that’s a beat. Depending on the colour, it will be one of 5, 6, 7, or 8 beats in the measure. If the cursor crosses a black line, then that’s one note of the rhythm being hit.
Vertically, as explained in this earlier post, you see varying degrees of morphing between the two rhythms. Just as a reminder, the Gnawa rhythm as represented here is somewhere between a straight three-note triplet, a 1:1:1 ratio (𝅘𝅥𝅮𝅘𝅥𝅮𝅘𝅥𝅮), and a phrased pattern in a 2:1:2 (𝅘𝅥𝅮𝅘𝅥𝅯𝅘𝅥𝅮) ratio. The horizontal line that crosses the 0 % morph value is the 1:1:1 rhythm, and the one that crosses the 100 % value is the 2:1:2 one. As we’ve found out in our previous post, we can imagine these lines continuing beyond the 0 and 100 % thresholds into outwards morphing values, which led to a new version of the Marathon software that includes the ability to place values beyond.
In this particular instance, the absolute morphing range of the rhythm is -500 to 250 %—but due to technicalities with the Marathon software, it’s actually from -497 to 247 %—as can be calculated using Marathon’s new “Morph Range Finder” feature or manually as described here. This increases your working range from 100 to 744 units (without mentioning the use of decimal values).
Moreover, as you can see with the coloured vertical lines in the above figure, in the usual 0-100 range, you only get three orthorhythms [I created this neologism as a way of saying “correct rhythm”, meaning here a rhythm that can be written easily using European music notation, as opposed to a xenorhythm]. The 0 % triplet feel (1:1:1), the 100 % quintuplet feel (2:1:2), and the 50 % eighths feel (3:2:3). If your values differ from those, you’re into xenorhythm territory or, at the very least, orthorhythms that must be written using n-tuplets greater than 8.
When you include the absolute morphing range of the rhythm, you get the chance of feeling septuplets and other ratios of 5-, 6-, and 8-tuplets. For example, the next orthorhythm after 100 % morph would be a 3:1:3 ratio in septuplets, at around 140 % morph. Another one, rather bland, is the 2:4:2 ratio in eighths, at around -120 %. The farthest orthorhythm we have, using subdivisions of 8, is the 1:6:1 ratio, at around -310 %.
Despite being an interesting way to discover new rhythmic patterns, I believe it’s way more interesting and more likely unheard of trying to come up with xenorhythms that fall in the cracks between the orthorhythmic lines. While the Gnawa tradition usually stays within the 0-100 range, the theoretical working range of this rhythmic patterns is much more vast and can lead to different musical experiments that are out in the open for you to try.
As always, I hope you’ve enjoyed some of this, as I’ve had writing it. You can download the newest version of Marathon for Mac on our website or get the code on Github.