Music Theory

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

Tonal Harmony Flow Chart

I have been thinking about ‘nutshell’ images for a range of musical concepts. Here’s a work in progress on common progressions in a major key in 17-19th century tonal harmony. Yes caveat, WIP etc, but it seems quite useful. Comments and suggestions welcome! Minor key next, please don’t let me turn them into 3D models for mode mixtures and modulations.


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

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(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.

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

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(non-flash) Metrobird Groove

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

The Maths Behind Music

Here’s a short educational video explaining some fundamental concepts of maths and tuning. Nice production by frequent collaborator Anna Tanczos of Sci-Comm Studios.

Musicians’ Questionnaire

Musician Questionnaire

A dozen of one, or not.

It’s tempting to think that it’s only the domain of modernist composers, theorists and ethnomusicologists to talk of anything but 12 notes in an octave. After all if it was good enough for Mozart and Beethoven it should be good for everyone, right? Well, as it happens, Mozart and Beethoven understood F# and G-flat as different notes. A manuscript survives for example of Mozart’s teaching notes to his English student Thomas Attwood showing the difference between a major semitone (e.g. E to F) and a minor semitone (Fb to F). Almost universally considered as identical today, in his they were pitched slightly differently.

Very few musicians are aware that even into the 19th century fingerboard diagrams and scale exercises existed with two types of accidental (e.g. g# as distinct from a-flat) as well as keyboards with split keys so that the player could choose between accidental types.

It’s remarkable how efficiently this has been filtered out of the system so that even professional classical musicians and teachers – let alone students – are unaware of our microtonal recent history.


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A Glimpse At the Modal Universe

A diagram demonstrating a section of the huge modal universe. You may see how mirroring modes (turning them upside down) can organize them into levels of brightness. It can also identify those modes that are identical in mirror form. These include Dorian (used in a thousand tunes from Scarborough Fair, Shine on You Crazy Diamond, Brick House to The Hitchhiker’s Guide To The Galaxy), Aeolian Dominant (Babooshka) and Double Harmonic (Miserlou from Pulp Fiction).

These are just 3 of the heptatonic even-tempered modes with mirror symmetry parents. There are many others, scales with 2-12 notes, as well as scales with ‘twin’ mode systems. Regardless this technique can be applied widely and is a rich resource for composers and improvisers alike.

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Melodic Minor Harmony and Modes

An Introduction to Popular Music Harmony

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Melody and Harmony

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The Notion of Convexity in Music – Honingh & Bod

Here’s the interesting article examining inherent ster-convex properties of musical scales. Quite intriguing, will give it its due attention when I can.

Universal property of music discovered


An overblown title, but interesting nonetheless. Will comment when I have time to explore…

Trebuchet – The Interview. Geo and Milt geek out.

A transcript of Milton Mermikides’ interview with George Hrab on his latest album ‘Trebuchet’
Painstakingly transcribed by Kylie Sturgess.
The hours of audio are here:****Warning geeky musical content ****

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Upper Structure Chords

Get on top of your harmony.[scribd id=50813436 key=key-2c52bur762jfva7la0oo mode=book]

The solution to the PD/DA/PF puzzle.

Yesterday I asked the (unlikely) question if anyone noticed a little musical easter egg I laid in the Pod Delusion tribute to Douglas Adams.

The podcast was edited in a way that made it barely audible and the reference is obtuse and lateral but here goes if you are keen to know.

The moment is most clearly heard at 56:00 of the pod delusion mp3 track.

In Pink Floyd’s tribute to Syd Barrett, ‘Shine on You Crazy Diamond’ as the song is dying away the moog plays – in a very missable but achingly poignant way- the melody from Syd’s classic ‘See Emily Play’

The Hitchhiker’s theme (actually by the Eagles) that I rearranged is in a mode called Dorian (a particular scale with a lovely characteristic – see here for more:… This happens to be the same mode as ‘Shine On You Crazy Diamond’ so in my track as the last chord dies away, you hear a moog playing a little melody with the classic ‘Shine On’ four note guitar motif… What is the melody? The Pod Delusion theme.

The reason I did this is that Douglas Adams was a big Pink Floyd fan and as mentioned on the pod delusion special even played bass guitar with them on stage. which gives it all a nice symmetry. I won’t mention what happens at 42 seconds.

Here’s an annotated audio file:

Did you get it?

Complete Track Analysis Techniques

Complete Track Analysis

Popular Music Harmony: Inversions and Basslines

Time-Feel Lecture Slides

Jazz Harmony Lecture Slides

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