Beyond the Imaginary Barline

Patterns in Sight Reading Preferences

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.

Some disclaimers:

  • This is a ‘study’ of a mere 54 participants, ranging from intermediate to highly experienced note readers. All from Facebook, and most of whom are my friends, so make of that what you will.
  • We are limiting ourselves to 4/4, single notes and no rests. A major restriction, but one must start somewhere.
  • This is very lazy research. I spent a few seconds googling relevant terms, but basically wanted to follow through these ideas prima vista. I’m sure if I looked for 7 seconds longer I’d find Ideathief & Twatamaholey’s comprehensive and beautifully argued 1973 thesis on the topic. So be it.
  • I have no affiliation with Big Quaver.


Ok so Figure 1, shows a series of numbered extracts, from which the subject indicates a preference (or no preference).

Figure 1

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.

The Extent of Imaginary Barlines

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

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

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.

Bridge Stability

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

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.

 Crotchet Bridges and Imaginary Quarter-Barlines

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

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.

Quaver Bridges, Patronizing Over-information and Even More Imaginary Barlines

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

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

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

Figure 8 No vs. standard vs. crotchet IB with semiquaver syncopations.


Additive Meters vs. Imaginary Barlines

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

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.

Hidden Music Exhibition Lewis Elton Gallery

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.

Hidden Music

Musical Continua Research Seminar

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.

Changes Over Time

Here’s the theoretical section of my PhD Changes Over Time (2010)

Changes Over Time:Theory – Milton Mermikides by Milton Mermikides

And the practice portion:

Changes Over Time Practice Milton Mermikides by Milton Mermikides


International Guitar Research Centre

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.

Bloodlines feature in Times Higher Education

The Times Higher Education have run a well-written feature on the Bloodlines project.

Transplant inspires siblings’ Bloodlines project | News | Times Higher Education.

Shine On You Crazy Bioluminescent Algae

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.

The Colour of Sound: Whale Song | Exploring The Invisible.

Filling in the gaps

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.

Maximally Even Library

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.Maximal Evenness Library

The Splice Symposium

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.

Presentation and paper proposals

Book a place


The Amazing Metrobird

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.

Shore it is

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

Audio clip: Adobe Flash Player (version 9 or above) is required to play this audio clip. Download the latest version here. You also need to have JavaScript enabled in your browser.

(non-flash) Metrobird

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.

Audio clip: Adobe Flash Player (version 9 or above) is required to play this audio clip. Download the latest version here. You also need to have JavaScript enabled in your browser.

(non-flash) Metrobird with Click
Not bad at all. Here’s how it sounds (again completely unedited) in the context of a percussion groove.

Audio clip: Adobe Flash Player (version 9 or above) is required to play this audio clip. Download the latest version here. You also need to have JavaScript enabled in your browser.

(non-flash) Metrobird Groove

Does anyone know what type of bird it is, an what evolutionary pressures gave it such tight timing?

What’s Growing on Your Strings?

GuitarMacTotal 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.

Images ©2013 Milton MermikidesGuitar gunkGuitar swabVery cultured

The Chimera Network

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.


Here’s the theoretical section of my PhD Changes Over Time (2010)

Changes Over Time:Theory – Milton Mermikides by Milton Mermikides

And the practice portion:

Changes Over Time Practice Milton Mermikides by Milton Mermikides


Are you a male professional guitarist or pianist aged 30-65? Then get your head examined.

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

Hidden Music

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.

Time-Feel Lecture Slides

Milton Mermikides Research Seminar – University of Surrey – Guildford

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.

A Little Drag – Time-feel analysis in Michael Jackson’s ‘The Way You Make Me Feel’

Download now or preview on posterous

A Little Drag.pdf (321 KB)


Extract from my PhD, an analysis of time-feel (rhythmic groove that escapes standard notation) in Michael Jackson’s ‘The Way You Make Me Feel’ – rehearsal in This Is It (2010)
Audio extracts below.All transcription analysis and text ©2010 Milton Mermikides

The Way You Make Me Feel – Extract A by Michael Jackson  
Download now or listen on posterous

1.23 Michael Jackson Swing – Extract A.mp3 (198 KB)


Extract A Clicks by Milton Mermikides  
Download now or listen on posterous

1.24 Extract A clicks.mp3 (221 KB)


The Way You Make Me Feel – Extract B by Michael Jackson  
Download now or listen on posterous

1.25 Extract B.mp3 (506 KB)


Extract B 2 Of 67,69,71,73,75 by Milton Mermikides  
Download now or listen on posterous

1.26 Extract B 2 of 67,69,71,73,75.mp3 (740 KB)

The Science and Art of Tuning – Lecture Slides

Menu Title