Why No Classification System For Music Theory Visualisations?

Music theory models and tools help students understand and contextualize thematic musical development. Both teaching and learning of music theory are hamstrung by a range of problems, however, not the least the lack of a theory (or, more relevant, theory tool) classification system.

The presentation formats of most music theory models are already very visual - but almost universally static, isolated from musical context, and their very different application and strengths poorly differentiated.

In keeping with our push towards music visualization as a central, unifying platform concept, we try to break the theory tool domain down into suitable model families.

It would be nice to know what you think. Maybe you have some ideas? Comments welcome.

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Note: the images in this post are drawn from external sites which you are encouraged to visit for further information.

Periodic Table (Sic) of Musical Instruments

Why No Classification System For Music Theory?

The Challenges

• proficiency at music theory takes time and effort
• students often consider music theory a drag
• conventional notation software is of only limited help as an interrogation interface
• theory tools are still widely presented in a static (usually printed) form, leaving them difficult to relate to specific pieces of music
• apps present a very fragmented view of the problem space

These difficulties stem more from issues of accessibility and immediacy than from difficulty. As a result, even amongst professional musicians, music theory is neither well understood, nor consequently applied.

Were music theory directly context-relevant and immediate, it could be absorbed quickly and easily. Bringing the relationships between notation, instrument fingerings and abstract theory tools to visual life is one of the key goals of our aggregator platform.

Qualification

We immediately need to distinguish between music theory tools and 'raw' music theory (their 'content').

Music theory takes the form of rulesets linking physical or mathematical properties. Theory tools are an abstraction, a visual aid to understanding these. Theory tools remove elements of configuration to reveal the fundamental relationships between characteristics such as pitch or (in relation to some modular base such as that used in MIDI) note index.

For ease of access and use (and especially in the context of an integrated, customizable platform), the tools need to be at very least:

• disambiguated through classification
• indexed for easy retrieval
• according to user preference, intimately linked to and configurable by music sources and/or instrument models.

There is, however, currently no classification system - neither for music theory, nor for theory tools. Here I hope to explain why at least the latter is necessary.

First of all, though -and as an analogy- let's look at an established approach to a classification in a closely related area, that of music instruments.

Instrument Classification Systems

The widely-used Hornbostel-Sachs instrument classification system allows us to identify specific families of instruments sharing similar features. Though instrument descriptions are written, it is in essence a visual classification system focussed on instrument construction forms.

World Music Instrument Classification Systems

Hornbostel-Sachs' classification system ignores underlying physical and mathematical properties, concentrating instead on appearance and handling.

Decoupling Form and Function

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As first-level instrument classification systems go, Hornbostel-Sachs is, in the sense that it describes only the general construction forms,entirely sufficient.

In this way, the next natural level of classification - purely musical characteristics such as temperament or intonation, number of notes per octave, number of channels, tunings etc remain entirely decoupled.

This is of clear practical value, allowing musical characteristics both to be configured and saved separately, yet all within a formal and widely accepted classification system.

Different musical instruments often share musical characteristics. If you look at the number associated with guitar (321.322), for example, you find many related instruments.

Once defined, then, a guitar’s musical configuration can be saved directly to this node in the Hornbostel-Sachs classification tree, and shared with all other related instruments. How this is done is beyond the scope of this blog, but will certainly be explained as part of aggregator platform documentation.

Music Theory Tools Visual Classification

Similarly, any music theory or tool classification system should allow us to identify groups of theory topics - and relate general application or tool types to these, but *without going into detail about musical characteristics*.

Music theory is founded on three key cornerstones, some inherent or naturally occurring, some configurable:

• physical properties such as time, amplitude, wavelength
• imposed musical conveniences such as temperament, intonation or tuning
• mathematical properties dependent on the above, such as harmonic ratios, or the number and extent of equal temperament intervals.

This is not rocket science, yet again: to date there is no formal classification system linking these. The reasons for this appear to be partly historical, partly rooted in 'higher order' concerns amongst music researchers.

From a user experience / design perspective, we can probably get away without a music theory classification system, but, because of their visual nature, would certainly need a theory tool classification system.

Just as with Hornbostel-Sachs in the instrument context, we need some kind of breakdown of the problem space allowing me to progressively identify suitable models.

Tentative Solutions

Our anchor point must be the visual result in the GUI. We need to pull all the threads together in a way that makes instant and intuitive sense to the user. Depending on the degree of configuration flexibility offered to users, this can be a big leap.

There are many ways of graphically relating and instrument (for example guitar) and a theory tool (e.g. circle of 5ths) via their common configuration characteristics : here a hypothetical example using a simple 5-cornered radar chart.

Joint configuration of musical instruments and theory tools using a radar chart.

Adjusting any of temperament or intonation, notes per octave, scale length, channels or layout would result in changes both to the instrument model and theory tool geometry.

Alone the fact that a given aspect of music theory may be related to more than one area of physics (eg. time, frequency and/or dynamics) suggests that a purely hierarchical (tree) structure may be insufficient: perhaps a Venn or other diagram would be better suited. It’s this structure -whatever it’s form- that is missing.


It should, however, be becoming clear that our immediate classification focus needs to be on the visual models, rather than the underlying detail.

By Venn Diagram

Though not indexed and one can argue about topic and allocation, the outline of a classification structure I find reasonably intuitive is this:

Contentious -But Promising- Music Theory Classification Approach

This is, however, a breakdown of music theory, not music theory tools. Though an entirely worthy goal in itself, for our immediate needs, it represents overkill.

By Theory Tool Visual Form

The practicality of the Hornbostel-Sachs classification system suggests an analagous, visual approach to theory tool classification.

Platonic Solids

It is tempting to imagine, for example, a collection of tools whose geometric layout, both as solid and as net, reflect -amongst others- some of the platonic solids. 

Their use has indeed, in some cases, been borne out in music-theoretical works.
Perhaps more intuitive in the sense of end-user needs is a simple hierarchy based on patterns of visual recognition. In the diagram below, you can see a (simplified) first cut for such a visual classification tree. You will find something similar actually applied in the Theory Tools menu structure for this blog site.


So here the approach: use the simple visual form of each theory tool as a classification node.

This follows the more or less intuitive labels given to theory tools in many images returned by internet search engines.

Clearly, even for the simplest of forms, we can expect further branches.

A clear advantage is that immediate visual confirmation can be provided (in image form) at each and every level of the hierarchy.

Examples? Alone for linear theory models:

• arc diagrams
• tonal interval diagrams
• tonal ratio diagrams

2D to 3D Transformations

Classification by Form + 2D or 3D

In effect, however, 3D models may simply be adding an abstract third dimension to an existing 2D model. 

There may be good cognitive arguments in favour of this, but to a certain extent this may simply be encouraging information redundancy.

There may, nevertheless, be something to be said for rearranging the above to a matrix with each form mapped (where available) against it's 2D and 3D manifestations.

Where there are no compelling arguments for moving from 2D to 3D (in the form of an additional data dimension), the latter should be used with caution.

The accompanying diagram shows a few of the numerous theory tool forms possible. For each, there is a 2D and a 3D version.

There are many ways to visually combine the basic theory tool properties, and certainly many more waiting to be discovered.

Music Theory Tool Classification Goals

Important is that a progressive, uniquely indexable decomposition of the problem space is achieved, while leaving musical form (construction) and function (musical characteristics) entirely decoupled.

These musical characteristics, though common both to instruments and the related theory tools find redundant expression on instruments, and abstract or essential expression in theory tools.

This allows us to both define and re-access instrument models and theory tools in an aggregator platform, and (more importantly) directly and mutually configure the instrument models and associated theory tools onscreen, via their common musical characteristics.

In this way, a circle of fifths can be progressively (on-screen, in-browser and above all in step) adjusted for use directly with a given equal temperament or just intoned instrument, or with any of 12, 15, 17, 19, 22 (or whatever) notes per octave.

Further, it can be shown in a 3D version as a helix.

Theory Topics Classification: the Last Word

The real challenge, though, may be to find a workable bridge between the visual forms exhibited by theory tools and specific, underlying theory topics.

My feeling is that a music theory (as opposed to theory tool) classification system will prove unavoidable. With one theory topic, multiple views, and one view, multiple theory topics..

No structure? -->  Spaghetti.

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