Triplets don’t swing
It’s common among non-jazz musicians to think of “swing” rhythms as having a triplet-like feel, and it’s equally common among jazz players to regard that as hopelessly incorrect. That conflict over swing style has been widely discussed elsewhere, so I won’t rehash it here.
But there’s another layer to the swing/triplets issue: It’s important to understand that real swing rhythms are essentially duple. The primary subdivision of the beat is into two parts, even though those parts aren’t equal in length.
So, writing or playing lots of triplets is a common mistake that non-jazz musicians make when they are trying to imitate a swing sound. That’s not to say that triplets can’t or don’t exist in swing rhythms, but they aren’t the underlying subdivision, and in most cases are best used sparingly.
For example, this can be played to sound like an authentic swing/jazz line:
And even this notation, while problematic, can be translated into something authentic-sounding:
But, to someone who knows jazz style well, this one never quite sounds like swing:
It might pass for a shuffle or something else, but it’s hard to make it swing.
When a well-written swing line does include a triplet, a fluent jazz player might play it to sound distinctly un-triplety:
That approach (one of several possibilities) might make sense to a jazz player because they are stretching the downbeat note, and letting the subsequent notes fall later in the beat—a very similar approach to playing a pair of swung eighth notes.
Written or improvised melodies, background figures, drum fills, and other things that are supposed to swing in an authentic way should avoid excessive triplets. Extensive listening and study of great jazz writing, interpretation, and improvisation are crucial to understanding real jazz swing style.
It seems like there’s very little I do these days without a computer. Here are some ways I have used a laptop to boost my practice sessions. 
This is wrong.
Also wrong. So is this one:
The idea of 
What I do like about the weird grace note approach is that it makes fairly clear the idea that the exact “downbeat” (quarter note) to “upbeat” (grace note) ratio is an interpretive matter. It also evokes what I find to be the most successful method of executing swing rhythms: think in quarter note pulses, and let the upbeats lead to the following downbeats. What I don’t like about this method is that it’s a hassle to write and to read.
Note the absence of the “two eighths equal triplet quarter-eighth” indication. This way is simple to read and write, reinforces the duple nature of swing rhythm, and doesn’t prescribe a specific ratio. One might hope that a jazz-untrained musician encountering this would seek out some good training or at least listen to some 
Sorry, but to me this article is just as biassed against accurate, purposefully measured swing, as it claims the triplet notation to be AGAINST swing-FEEL.
I beg to differ on this, both, in terms of the ability of even triplets to ‘swing’, and in terms of the historical predominance of triplet swing conception. Swing ratios, microtiming descrepancies, and tempo dynamics aside, triplet conception AND feel are central to jazz theory and practice. Ever read a jazz drumming manual? Triplet and/or dotted quaver – semiquaver divisions are standardly notated for PRACTICE of RHYTHM in JAZZ by good swinging drummers worldwide. In any case, several studies on the execution and perception of groove in swing, funk, and rock styles have consistently shown that, while moderate microtiming deviations in performances are acceptable, even preferred over other options, performances with strictly quantized tuplets (TRIPLETS in the case of swing examples) rate highly for sense of ‘groove’ and entrainment, and are preferred to extreme deviations of beat placement and swing ratio – yes, even for jazz. You tell us jazz is a ‘duple’-only phenomenon, while declaring the duplets to be unmeasurable, only ‘feelable’. But the great Max Roach told us that jazz rhythm is “all twos and threes” [he also said, “it’s all two over three”]. One of the main distinctions between ragtime feel and early ‘swing’ was the transition from straight/duple subdivision to a triple conception OVER the duple meter (as demonstrated by stride and boogie-woogie pianists).
Fifty years of playing, teaching, and living jazz tells me you’re trying too hard to be ‘intellectual’ about this, rather than practical. I can play you a 2-1, 3-1, 3-2, 4-1 swing, or even a 5-3, or 7-3 – by FEEL – NOT ‘counting’. However, I can do that because I HAVE counted them, have LISTENED to them, and have VISUALISED them. If I compose swing that I HEAR a particular way, then THAT’S how it gets written, and that’s how I want it PLAYED! When I play, I’m not known for ‘mechanical’ feel. So how does your statement that, “writing or playing lots of triplets is a common mistake that non-jazz musicians make when they are trying to imitate a swing sound” play out in my world? It doesn’t. Nor in Max Roach’s, nor Cannonball Adderley’s, nor Elvin Jones’, nor Jim Chapin’s, nor Art Tatum’s, nor many, many, MANY others’. Jazz is a free world man, and Western ‘classical’ notation is good enough to get us conceptually oriented to swing … So, YES – we CAN write swing in triplets if we want to (ESPECIALLY if we’re experts).
Pat Metheny believes that the triplet feel is the foundation of swing. It is the the most important subdivision and he talks of feeling triplets even when not playing them. I think this article is poorly thought out.
Jazz drummer here. I stumbled on this article looking for info on the time old argument that Max Roach couldn’t swing (I don’t subscribe to that idea). Anyway, I can see what you are saying but I have to agree with Jazz Warrior on the whole. May I suggest listening to Kenny Clarke’s ride cymbal work on the composition ‘Willow Weep for Me’ from the Dexter Gordon LP ‘Our Man in Paris’. A mixture of dotted notes and triplets. I would say they both ‘swing’ in different ways. All that being said, Jazz has become a little too dogmatic, where everything is quantified & measured and overly cerebral.