The most succinct analysis I can make of Arvo Pärt’s Spiegel Im Spiegel (a stunning and elegant work). Listen here: https://open.spotify.com/track/3rlqTqUOzu0zDwQFJe44gk
The most succinct analysis I can make of Arvo Pärt’s Spiegel Im Spiegel (a stunning and elegant work). Listen here: https://open.spotify.com/track/3rlqTqUOzu0zDwQFJe44gk
I’ve had this insight about palindromic scales, modes, modal groups, and the Euclidean (and sometimes maximally even) distributions of 7 notes in a one octave scale. This is what it looks like in my head. I really like that the ‘central’ scale of a group is not the traditional figurehead (Ionian, melodic minor etc.) but the palindromic parent. Nice to see the patterns emerge diagrammatically, and I will aim to use Melodic Phrygian and its modes in composing/improvising!
The next in the series of Hidden Music data sonification works. Data sonification is a long term interest/project/passion of mine, which involves the systematic translation of ‘non-musical’ data into music.
Here I’ve taken Kandinsky’s beautiful 1926 painting Several Circles and translated it systematically into sound. Colour and vertical position are translated into timbre and pitch respectively, as the red cursor scans the image horizontally.
Whether Kandinsky was a synaesthete or not is disputed, but his fusion of music and visual art metaphor, working process and concept is well documented. From the link:
“Our response to his work should mirror our appreciation of music and should come from within, not from its likenesses to the visible world: “Colour is the keyboard. The eye is the hammer. The soul is the piano with its many strings.”
Kandinsky achieved pure abstraction by replacing the castles and hilltop towers of his early landscapes with stabs of paint or, as he saw them, musical notes and chords that would visually “sing” together. In this way, his swirling compositions were painted with polyphonic swathes of warm, high-pitched yellow that he might balance with a patch of cold, sonorous blue or a silent, black void.”
Thanks as ever to Anna Tanczos for the visuals.
Here’s the first in a long series of data sonification experiments. This Hidden Music series is a long term interest/project/passion of mine, which involves the systematic translation of ‘non-musical’ data into music. Here’s a simple example, the orbital periods of the planets of the solar system translated into pitch and rhythm. The rhythms are simply created by speeding up the actual orbital periods by 25 octaves (doubling the speed 25 times), and the pitches are created by transposing them up 37 octaves. I haven’t quantized pitch or rhythm, so its both microtonal to the nearest cent (100th of a semitone) and microtemporal (to the nearest millisecond), but I hear a clockwork beauty in this irrational/chaotic collection of ratios nonetheless. Stay tuned for some even more distant harmony from some ex-planets. I recommend a sub-bass speaker to really feel Uranus and Neptune’s drones. Thanks to Rob Scott for his space science brain, and my long term partner-in-nerd Anna Tanczos for the visuals.
The next international conference of the International Guitar Research Centre has been announced. It will take place 18th to 23rd March 2016. The call for papers, keynote speakers and headline concert artists can be found here. The deadline for proposals is midnight GMT on Friday 9th October 2015.
The IGRC has no stylistic or conceptual prejudice, if you are doing work that is innovative, creative and related to the guitar, we are interested. For further info
It’s hard (for me at least) to start talking about any aspect of musical theory without talking for an hour or writing several thousand words and/or producing many diagrams. So I’m going to try and just provide some vignette posts, little moments of insight in a hugely complex field of study.
Here let’s look at the harmonic series (the pitches that emerge by multiplying a frequency by the set of integers (1,2,3,4 …) and its relationship to 12-tone equal temperament (the ‘standard’ division of the octave into 12 equal divisions).
The following diagram courtesy of the incredible programmer Dean McNamee (and Mathematica) shows how the pitches generated through the harmonic series differ from 12-tone equal temperament.
The X-axis names the harmonic number (ending at the 20th harmonic) and the Y-axis is the deviation from the nearest even-tempered note (where for example -0.2 is 20% of a semitone flatter than equal temperament). If you look carefully, you’ll see that the fundamental and all the octave equivalents (harmonic numbers 1,2,4,8, 16 etc.) align perfectly with the even-tempered equivalents. In fact these powers of 2 are the only point where the harmonic series meets up (exactly) with 12-TET. These points are circled in red below.
The ‘non-octave’ harmonics are indicated with different coloured arrows (showing in which way they differ from equal temperament). The 3rd harmonic (indicated in orange) is about 2 cents (a mere 2% of a semitone) sharper than the equal tempered equivalent (a perfect 5th), and so of course are its octave equivalents the 6th, 12th, 24th etc. The 9th harmonic is about 4 cents sharper (as it is ‘affected’ by two 3rd harmonics), and is indicated with 2 orange arrows. This ‘stacking’ (and unstacking) of the 3rd harmonic is what is used to create the Pythagorean scale, also known as a 3-limit scale, since we only allow the 3rd (and 2nd) harmonic as tools to reach musical notes.
The 5th harmonic is significantly flatter than the 12-TET equivalent (and the cause of the many historical temperaments that have emerged in polyphonic music. The 10th harmonic has the same ≈14 cents discrepancy. The 15th ends up about being 12 cents flatter, since 15 = 3*5, it uses the 3rd harmonic (which makes it ≈2 cents sharper than 12-TET) and the 5th harmonic (≈14 cents flatter) resulting in an overall drop of about 12 cents (note the contrary orange and yellow arrows). Incidentally, the use of the 3rd and 5th harmonic (together with the trivial 2nd harmonic), creates the 5-limit system of tuning, with its extensive and beautiful use in Hindustani music.
You’ll see that the other prime-numbered harmonics get their own coloured arrows (7th=green, 11th = blue, 13th = purple etc.). The 11th is about as far from 12-TET that is possible, which is why Harry Partch stops there in his 11-limit 43-note universe. Since the primes never end so the harmonic pathways of tuning are (theoretically) endless.
Another way to see the relationship between the harmonic series and 12-TET is to visualise the harmonics resting at points on an infinitely expanding spiral. Each sweep of the spiral represents an octave, and the 12 equally spaced slices of the octave pizza represent each 12-tone slice. This has the advantage of indicating where in the octave each harmonic lies, as well as the octave relationships between sets of harmonics (e.g. between the 3rd ,6th, 12th and 24th harmonics etc.). Here’s a beautiful rendering by Skye Lofander (whose website musicpatterns.dk has many awesome visualitions of musical concepts and is highly recommended).
You’ll notice that the harmonics get closer and closer together, and essentially ‘sweep’ through the 12-TET discrepancy in an ever (but never completely) flattening upward slope. Here’s Dean’s rendering which shows the same phenomenon emerging with the first 500 harmonics:
So along the way the 12-TET and harmonic series will get ‘close enough’ most certainly for human perception (which is a couple of cents on a good day) and acoustic instruments (which waver considerably in temperature and human execution). Even a slight head-turn will invoke enough doppler shift to make fractions of a cent meaningless in real terms.
So which is ‘better’ 12-TET or tuning derived from the harmonic series (also known as just (i.e. ‘true’) intonation)? And what incantation of the harmonic series is more ‘pure’? Is 4 jumps up the 3rd harmonic more ‘natural’ than one jump up the 5th harmonic? They both roughly approximate the major 3rd (the first a ‘Pythagorean third’ ≈8 cents sharper than 12-TET, the second a ‘just 3rd’ at ≈14 cents flatter). Some have attempted a measure of harmonicity (see Vals and Monzos), but its relationship to subjective experience is sketchy at best. Can one think of 12-TET as existing way, way up the harmonic series (so still harmonic), is it a ‘good enough fit’, or wholly incompatible with the harmonic series? What’s inate and wha’t encultered? Why 12 equal divisions and why not some other number?
Just intonation enthusiasts can get heated about its superiority to 12-TET, but there is no doubt that the limiting of notes to 12, close-to, or exactly evenly-spaced has led to the creation of countless, otherwise impossible, musical creations and activities.
The best answer is that they are different, and both available to every composer, get over it, embrace and enjoy.
P.S. this was 3 times longer than planned. Apologies.
It’s possible to gain an incredible fluency at music reading, absorbing large sections of music at a glance. I remember as a youngster being in awe at those who could instantly transform squiggles into beguiling sounds, as if there was no barrier between the symbols, the musical brain and the appropriate finger movements. Even without an instrument to hand, they could somehow hear the page. However, music reading seems to differ from word reading in that it can be quite easily tripped up. With word reading you can read wrds wtht vwls frly cnfdntly, or when they are uʍop ǝpᴉsdn, or even ndsᴉpǝ poʍu ɐup qɐɔʞʍɐɹps. However the odd enharmonic or dotted rather than tied note in music notation, can momentarily derail even an experienced reader.
What I’ve found puzzling is that there is no one unanimous convention for notation, nor a system that will please all the people all the time. So in this short article I will attempt to reveal some of music notation’s hidden conventions and reader preferences.
Ok so Figure 1, shows a series of numbered extracts, from which the subject indicates a preference (or no preference).
Figure 1: The Test
You may want to make a note of your preferences at this point, before we look at the results from our cohort of readers.
We’ll break these down in sections so we can discuss the various implications.
Examples 1-3 test the concept of the imaginary barline – the idea that we should notate as if 4/4 was actually 2 consecutive 2/4 bars, separated by an invisible barline. Of course, semibreves (and dotted minims) violate this regularly, so we might consider them honorary exceptions to this rule. But this begs the question, at what point does the imaginary barline ‘kick in’?
Figure 2 presents the results of the first 3 exercises
Figure 2 Preferences for Examples 1-3, testing the limits of the imaginary barline. Notice how preference is eroded by the weaker ‘bridge posts’. (NB NP= no preference and please note also that due to rounding errors, the percentages in this – and other examples – may not add up to 100% exactly, please get over it.)
You’ll notice that in all 3 cases, a central minim is preferred over an imaginary barline. At this point I’m going to suggest some terminology, let’s call the formation with a central minim (covering beats 2 and 3) as a minim bridge. It seems that readers tolerate this well. Note that positing the minim bridge allows us to talk of – among other things – crotchet bridges on beats 1& to 2& and their implications in sight reading.
Notice that the preference for the minim bridge reduces as we subdivide the material on beats 1 and 4). 1a has a minim bridge well supported by a crotchet post on either end, clearly presenting beats 1 and 4. 1b and 1c on the other hand have weaker posts, the quavers and semiquavers respectively, slightly masking the clarity of beats 1 and 4.
We could in fact imagine minim bridges of different strengths. While the majority may prefer a minim bridge to an imaginary barline (IB), as the material at beats 1 and 4 become more complex, perhaps more people prefer the IB over the bridge presentation (see Figure 3)
Figure 3 Hard and weak minim bridges with imaginary barline equivalents, and a suggested preference curve. (Click to embiggen)
The limited data supports this, but it’s only a tentative suggestion. Furthermore, I suspect that there will be a significant proportion of readers who will always prefer (or at least tolerate) a minim bridge regardless of the content in the rest of the bar.
So far we’ve seen that there is a general preference for minim bridges over imaginary barlines, less so perhaps as the minim’s supporting posts on beats 1 and 4 become more complex. But what of the minim bridge itself? How robust is it to any complexities? The answer, it seems, is not very. Figure 5 shows that when the minim bridge is divided into a quaver-crotchet-quaver pattern (a crotchet bridge formation), preference swings dramatically to the imaginary barline presentation, and slightly more so when the beats 1 and 4 posts are made more complex. So a fractal//Inception-style bridge-within-a-bridge is too much for many readers to bear, although a good 1 in 4 readers actually preferred it over IB. I suspect that some readers, don’t need any IB at all, and are happy to see a sequence of rhythmic values with no visual indication of beat 3. Let’s call these readers who can tolerate (or prefer) a sequence of rhythmic values over IB presentations as ‘sequential readers’.
Figure 4. A minim bridge collapses for most people when it is subdivided into a crotchet bridge. Still, those 1 in 4 sequential readers prefer it to IB.
So we’ve dealt to some degree with minim bridges and their relationship to the imaginary barline, and their kryptonite (the fractal bridge), but what of bridges on beats 1 and 2, and beats 3 and 4? In other words, do the same principles scale down from the whole bar to the half bar?
Figure 5 Testing the Crotchet Bridge (or crotchet IB)
Examples 6 and 7 address this question. You’ll see in Figure 6 that the majority prefer the crotchet bridge to (beat 2 and 4) imaginary barlines (6a over 6b) although this preference is less common than at the whole bar level (1a over 1b). However the crotchet bridge (surprisingly to me) seems far more susceptible to weakening than the minim bridge. Notice that as soon as we weaken the posts on the first and last quavers, preference sways over dramatically to the crotchet IB (7b over 7a). This was just a tentative study (quiz really) but if I knew of this phenomenon I would have interrogated the extent and nature of the fragile crotchet bridge more thoroughly.
Let’s look now at the quaver bridge (semiquaver-quaver-semiquaver). Figure 6 shows that a similar ratio of readers prefer quaver bridges to minim bridges (8a over 8b, as compared to 1a over 1b). However some subjects reported (without solicitation) that 8b was ‘horrible’ or ‘horrifying’. Why this ‘over-information’ created such a negative reaction (as compared to 1b) is not clear. It could be that it is simply the case of 4 instances over 1, or the shortened time scale is less tolerant of unnecessary fuss. I suspect it’s the sequential readers kicking up the fuss, I’ll check.
Figure 6 How to piss off a sequential reader.
The quaver bridge also allows us to check if the standard IB (splitting 4/4 into 2 2/4 bars) is sufficient once semiquavers are introduced. You’ll see in Figure 8 that in fact a slight majority of readers prefer to have imaginary barlines on every beat in the presence of semiquaver syncopation. A good portion preferred standard IB but one who didn’t was upset by the crotchet IB violation. He’ll recover in time.
Figure 7 Half vs. quarter imaginary barlines with semiquaver syncopation
Let’s now test sequential vs. standard IB vs crotchet IB in a syncopated semiquaver passage (Figure 9). The majority preferred crotchet IB (essentially 4 imaginary bars of 1/4), but a significant portion were happier with either no IB or standard IB presentations (Incidentally the former upset some readers presumably because it was the opposite of patronizing). Why did more prefer 10a to 10b (given 10c’s majority) is a bit puzzling. Perhaps there is an in-for-a-penny-in-for-a-pound sentiment in operation here (“if I don’t need one tie over beats 2 and 3, I don’t need any other”).
Figure 8 No vs. standard vs. crotchet IB with semiquaver syncopations.
Aside from minim bridge and the trivial semibreve and dotted minim cases, there are relatively common violations of standard IB, in the context of additive meter. To test this, let’s compare preferences for 3+3+2 vs. 2+3+3 vs. 3+2+3 quaver groups. All of these violate standard IB but will any be preferred over it. In every case standard IB is preferred (11b, 12b and 13b), but around 20-30% went for the ‘full additive’ version. This was particularly true in the 3+3+2 formation rather than the other permutations (one of which was ‘offensive’ to some). Why would this be the case? They all violate standard IB so what else differentiates them? It may be that 3+3+2 is the most commonly seen of these meters (Butler 2006) or – and perhaps because – it has a clear beat 4 ‘post’ to anchor the reader. You’ll notice that readers clearly preferred standard IB over crotchet IB (11b, 12b and 13b over 11c, 12c and 13c).
It perhaps hits the sweet spot between rhythmic clarity and patronizing over information.
Figure 9 Additive meter vs. imaginary barlines
This was a limited, uncontrolled study glorified quiz with a small number of participants, all of whom could see each other’s responses. Still, useful (and surprising) concepts emerged. In particular, I think there is mileage in terms of the bridge concept, and a more flexible concept of the imaginary barline which adapts dynamically to subdivision and syncopation, as well as the sweet spot between fussy information and pure sequentualism. I’m also going to investigate preference patterns and consistencies (or otherwise) within (rather that between) subjects’ responses.
The preferences here may be merely suggestive of experience and convention (although how these conventions emerge is interesting of itself). It’s unlikely that our preferences are the results of evolutionary pressure – quick-read-this-syncopated-passage-to-distract-the-tiger scenarios – but it may tell us something about our music reading faculties, and whether an inexperienced notator’s (and Logic notation) can be so baffling . Whether these preferences are internally consistent or optimal may be questioned, but it’s useful to actually know what a majority of readers prefer when preparing scores. So let’s ask them (ourselves).
Many thanks to those who gave up their time and composure in completing this test. Very interested to hear your preferences, and any feedback below.
Here’s some info for my Hidden Music exhibition 7-13 May 2015 at the Lewis Elton Gallery. A series of works created through translation of natural phenomena into sound.
Here’s details of a public seminar on Wednesday 29th October 4pm, TB06, University of Surrey.
4.00pm, Wednesday 29th October, TB06 FREE admission More Info
Dr Milton Mermikides (Surrey)
Musical Continua: Perception and Technology
Digital music technology has now fulfilled Varèse’s dream of “instruments obedient to […] thought”, Russolo’s call to “conquer the infinite variety of noise-sounds” and Busoni’s desire to “draw a little nearer to infinitude”. However, the staggering developments in music technology over the last 20 years has brought with it a less predictable outcome, the ability to better understand the mechanics of music itself, and to illuminate some of the mysteries of its expressive power. Through a survey of recent research projects, this seminar examines how our understanding of musical expression in pitch, rhythm and timbre can be enhanced with technological support, furthering analytical insight, artistic appreciation and creative practice.
March 2014 saw the launch of the International Guitar Research Centre, a major asset to guitar research world wide. It’s great to be involved among such eminent guitar practitioners and theorists. From the IGRC:
“The research centre will work in close affiliation with various partner institutions including the IGF (International Guitar Foundation, King’s Place, London), the IGRA (International Guitar Research Archive, CSUN, Los Angeles, California) and the University of São Paulo (Brazil). The launch was a two-day event on 29th and 30th March 2014 that included academic papers, seminars, public discussions, lecture-recitals and concerts. Guest artists included John Williams, Xuefei Yang, Newton Faulkner, The Amadeus Guitar Duo, Bridget Mermikides, Declan Zapala and Michael Partington.”
A nice promo vid is viewable here, which includes a fragment of my classical guitar and electronics concert with Bridget.
The Times Higher Education have run a well-written feature on the Bloodlines project.
Dr. Simon Park (my serial bio-art collaborator (like this) and creator of the amazing exploring the invisible site along with sound guru Professor Tony Myatt and I, have been exploring the interaction of sound/music and the Pyrocystis fusiformis bioluminescent algae. As you do. Here’s a sneaky pilot.
This is a very interesting audio example (and site). The continuity illusion in optical illusions is perfectly paralleled in the sound world. Strangely it didn’t work the first time on me, and now does consistently. How was it for you? D d y u he r t e g ps?
The Continuity Illusion | Auditory Neuroscience.
UPDATE- Since the publication of Brad Osborn’s Kid Algebra (2014), I’m going to switch to his category of Euclidean rhythms (in their 4 types) to describe the patterns below. In summary, Euclidean rhythms (ER) are rhythms in which k onsets in n divisions are as similar as possible, which essentially means that they will only differ by at most one subdivision each. So in ER the groups are as similar as possible, but the term maximally even we will reserve for ER rhythms where the smaller note groups are as separated as much as possible. For example, (2,2,3,3) and (2,3,2,3) are both ER, but only the latter is maximally even.
This is a library of all the maximally even (including strictly even) rhythms for 2-7 rhythmic onsets within 6,8,12 and 16 beat cycles.
Maximal evenness (M.E.) describes a rhythm which is as evenly spread out as possible given both a number or events (rhythmic onsets), and a number of available slots (beats). Strict evenness (marked with a º) is a subset of M.E. and occurs when the hits are equally spaced. M.E. rhythms are intrinsic to much music making in a wide range of cultures from Sub-saharan Africa, South America to EDM and much in between.
The parenthesised number shows the number of displacements (or ‘rotations’) available for the rhythm in the beat-cycle, and allows for starting on rests. When the number of rotations equals the number of beats in the cycle this is marked with an * and represents maximally independence (MI – a common trait of African timelines and clave patterns). Note that 5,6 and 7 in 12 also represents maximally even pentatonic, hexatonic and heptatonic scale sets e.g. 3,3,2,2,2 represents all the modes of the major pentatonic as well as a 5 in 12 set of ME rhythms. As another example 2,2,1,2,2,1,2 (a rotation of 2,2,2,1,2,2,1) represents both the African standard time-line and the Mixolydian mode. Enjoy.
Announcing a 2-day symposium (November 15-16 2013 at University of Notre Dame in Central London) examining the process, philosophy and products of collaborations between scientists, musicians and performing artists. It’s hosted and organised by me and my sister Dr. Alex Mermikides, and is an output of the Chimera Network – and AHRC-supported project promoting Art/Sci research.
I have a little place in Greece, on a lesser known corner of the Peloponnese, on a little beach with a derelict and rarely visited acropolis from which the islands of Ψιλι, Πλατεια and (just about) Σπετσεσ are visible.
It’s a magical (and for me painfully nostalgic) place where even when we eventually installed a phone (1996), modem (2006) and wi-fi (2013) seems eerily frozen (well baked) in time. This part of the world is home to some odd creatures: deafening cicada, scorpions, flying fish, swordfish and a plant with fruit that explode on the lightest touch.
One such unusual animal I have yet to (knowingly) see but I’ve been fasciated by its sound for years. It’s some kind of bird that emits a short tweet at intervals so regular that we use it as a metronome. (It sounds particularly good on beat 4 & in a bossa).
Here’s an unedited audio sample recorded on Tuesday, 7 July 2009 19:32
Notice how (separated by an unmeasured pause) there is a decent metronomic tempo established. Logic Pro X’s transient detector and beat mapping tools reveal that once a pulse is established it tends to stay within a couple of bpm. I’ve played with far worse time-keepers of the human species. Here are the numbers:
To get a feel for it, listen to the same unedited clip with a click track.
(non-flash) Metrobird with Click
Not bad at all. Here’s how it sounds (again completely unedited) in the context of a percussion groove.
(non-flash) Metrobird Groove
Does anyone know what type of bird it is, an what evolutionary pressures gave it such tight timing?
Total Guitar Issue 243 includes an article by me and the eminent microbiologist Dr. Simon Park (with whom I collaborated on the Microcosmos project and does many other beautiful things). Here we took a rather nasty set of strings from the Future Publishing offices and endeavoured to discover what constituted the invisible audience to our noodlings. Get it at all good newsagents. Wash your hands before and after.
My sister, Dr. Alex Mermikides, and I have recently won funding from the AHRC to set up a network of scientists, artists, writers and musicians to collaborate on Art-Science projects.
The Chimera Network brings together a network of scholars and professionals in arts and science disciplines. Through a series of events and artworks, the network explores collaborations between artists and scientists, asking:
How might collaborating with scientists generate novel creative methodologies, artistic forms and modes of spectatorship in artistic practice?
How might collaborating with artists prompt new understandings of scientific ideas and forms of science communication for both scientists and the general public?
Exciting projects afoot.
The Institute of Neurology, UCL are looking for male professional classical guitarists or pianists, aged 30-65 to put through an MRI. A 2 hour study. I’ve done this sort of thing before and it’s bloody interesting. Expenses + anecdotes. Here are the details:
For pianists aged 30-65yrs: study using state of the art MRI techniques that aims to reveal how your brain achieves such high levels of motor performance.
* Neurologists and neuroscientists at the Institute of Neurology, London are currently recruiting for an imaging project in which they will study the neural signature of piano performance and excellence of fine finger control.
* This study uses a new fMRI analysis technique that allows us for the first time to accurately map individual fingers to different parts of the brain. This figure shows the activation of one the fingers in a region called the motor cortex in a healthy control … we do not know how this differs in pianists ….
* We ask for 2 hours of your time. We understand that we are ambitious to invite a group of individuals that are phenomenally busy with performance demands and teaching and hope to offer appointment times that are convenient for you. We can pay all travel costs and will also reveal all from the data we get in the study….
* We are also examining pianists that develop dystonia of the hand which will increase knowledge about this poorly understood condition and improve existing treatment techniques.
* Please contact Dr Anna Sadnicka if you are interested in hearing more about this study (0203 4488605 or email@example.com)
For a dynamic list of Hidden Music projects click here.
Hidden Music:Sonic is a collection of electronic works using compositional systems to translate physical phenomena of the biological world into complex mesmeric soundscapes. Source material include the DNA, colour and shape of microbacterial colonies, the population of blood cells during leukaemia treatment, the shape of the coronal suture of the human skull, tree-rings, MRI scans of the human brain and the passage of molecules through the cell membrane.
Bonus material! Album purchase includes 6,000 word liner notes, detailing the philosophy and process behind these works.
[bandcamp album=2903564095 bgcol=FFFFFF linkcol=4285BB size=venti]
Milton Mermikides Research Seminar
Time-feel: the analysis, modeling and employment of sub-notational rhythmic expression
- Tuesday 22 February 2011
16:00 to 18:00
- Open to:
- Public, Staff, Students
The analysis and pedagogical focus of the jazz idiom has, historically, been largely limited to those musical features most easily described within the standard notational system. These aspects took precedence over the hugely important stylistic mechanisms of rhythmic expression that fall between the cracks of standard notation. However, with 1) the advent of digital audio analysis, 2) an increased willingness and ability of practitioners to articulate this aspect of performance and 3) a conceptual liberation from a quantized grid-view of rhythm, light has been shed on this poorly understood and yet “most basic fundamental element” (Crook 1991) of jazz and popular music virtuosity. Through the consolidation of practitioner-led research and pedagogy (Mingus, Crook, Bergonzi and Moore etc.), current analytical research (Benadon, Naveda et al, Gerischer and Friberg & Sundström etc.) and extensive use of precise digital audio analysis, this paper presents a relatively simple, powerful and usable model of expressive micro-timing in jazz and contemporary popular music, variously referred to as ‘swing’, ‘groove’ or ‘rhythmic feel’ and here collectively termed ‘time-feel’.
Central to the model is the conceptual separation of the mechanisms of swing (offset of the second quaver) from latency (the sub-notational rhythmic placement of an individual performance relative to a negotiated time-line). This separation reveals and makes quantifiable a wealth of expressive rhythmic mechanisms (dynamic swing-levels, time-line hierarchy, time-feel blocks, differential elasticity, hyper-latency, swing friction, ensemble swing, isoplacement, latency contours and temporal plasticity) lost to the discretely delineated rhythmic paradigm. Analytical methods are suggested that create useful comparisons of stylistic and performer-based variations, as well as how time-feel may be controlled dynamically during performance. A formal mathematical model, specifically written real-time software, graphic notation and digital audio techniques are presented which may be employed with great flexibility for analysis or as supporting mechanisms to performance, pedagogical practice and composition. In order to demonstrate the real-world relevance of this model, detailed analysis and commentary of precisely measured rhythmic data is also presented in case studies with a diverse range of artists including Django Reinhardt, Jimi Hendrix, Chuck Berry, Michael Jackson, Nick Mason (Pink Floyd) and a specifically commissioned recording session with Pat Martino.