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Music with similar roots and characteristics may, depending on region or culture, be notated in different ways. Indeed, some forms of music lend themselves to representation using quite a variety of notations. One exchange file, multiple notations? In how far can these demands be addressed consistently and without duplication of effort, and in how far is notation diversity (transnotation) of use?
Cultivating Music Notation Diversity
World music notations have to satisfy increasingly diverging online music education usage scenarios, from the structured 2D of the web browser's DOM, through all the visual modeling possibilities offered by scalar vector graphics, tightly focussed artificial intelligence applications such as jazz chord diagram building, to the ad-hoc, bitmap-overlaid 3D objects of Web3D and virtual reality. More importantly, though, they are a bridge between musical cultures.
Associated with the various notations is an entire school of cognitive theory, and with this, established conventions for their assessment.
Where there may be wide commonalities in the underlying music systems, often music notations (their visual expression) diverge across various cultures. Nevertheless, there are similarities in the way notations are applied in teaching. Let's look at these in the context of a learning workflow. You might like to imagine how such a workflow might be supported by not just one, but interchangeable notations (so-called "transnotation"). Implementing this is decidedly not rocket science..
Notations In The Learning Process
Goal
Means
Concrete Example
Virtuosity, Musicality
Transnotation
Multiple notations from same exchange format (source), interrelationships, compatibility matrices, 'meta-knowledge'.
Accommodating Regional Pitch Preferences
Regional Microtonal Tuning Practices
Expression of differences in pitch configuration (other than 440Hz standard, ratio variances in just intonations etc).
Musicality Optimisations
Key changes, Transposition
Accommodation of instruments in other than noted keys..
Elements Of Style
IMPOVERISHED
Limited, ambiguous, poverty of notational expression.
Fingering economy, tone, dynamics
Positional and dynamics glyphs
Expression of position, dynamics and variation of tone.
Pitch-to-finger-to-position mapping
Voices, Scales, Fingering Models
Voice and fingering representations.
Initial
Orientation
Glyph Meanings, Usage, Relations
Time signatures, pitch and modal expression, simple scales.
Notation Choice
Pros & Cons Demonstrations
Musical culture, music collections, exchange formats, capabilities, compatability.
A clear limitation of notations is the representation of style, often overcome using synchronized audio to provide additional cues.
Transnotation
"Since the actual music stored in a computer notation file is the same whether it is displayed in traditional notation or an alternative notation (an F# is an F# in any notation), there is no need for a separate file, or file format for alternative notations. Transnotation does not require changing the content of the file, but only how that content is displayed. Transnotation turns out to be a task of re-presentation. So what is needed is an application that merely displays existing traditional music notation files (such as MusicXML files) in alternative notation systems". ("Transnotation and Music Notation File Formats" from The Music Notation Project)
In my previous post I touched on the relationship between music exchange file format and the resulting notation. Continuing in that wacky-go-lucky frame of mind, I focus entirely on notation and the willful application of 'what-if'. :-)
Notation needs to be culturally recognizable, expressive, capable of being visually linked with (in some cases 'drive') other screen elements, and, in as far as possible, interchangeable.
Interchangeable? For example: where a subset of musical glyphs are used across different equal temperament or just intonation music notations.
Cultivating Notation Diversity. Why?
12-tone equal temperament is far from the only music system in existence. Especially where the expressive space gets crowded (as in microtonal music), additional, or visually modified glyphs are more or less unavoidable
Extends music notation expressivity and range, and with it, our collective music-cultural 'memory'
Helps us transition from known music systems to the unfamiliar
Accommodates personal preference
Provides a base, context and impetus for the further development of online music education related web standards and conventions
More succinct, easily recognizable and meaningful iconography ('glyphs')
Musical diversity -in any form- represents niche opportunity in emerging, marginal or heavily fragmented musical cultures
Provides base for advanced, experimental and academic visualizations
Moreover, the data structures underpinning on-screen notation, can function as a repository for playback data. For any given music system, a note's visual form can change (for example with a font change), but the data content remains the same. These structures should, ideally, accommodate:
Any Number of notes per octave
Any temperament or intonation
Any note semantics (symbol meaning)
Any symbol set
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Taken across the whole spectrum of world music, the relationships between these properties are many-to-one. Just as (depending on notation type) a musical action or meaning may be associated with several different glyphs (musical symbols), a given glyph may be associated with several different actions or meanings.
Taking the number of notes per octave as an example, with two staves, the western or classical 5-line staff system allows us to accommodate the 12-tone octaval range of (say) a piano. To achieve this, each line or space can be associated with up to three notes or tones, and each of these assigned a pitch or midi number. In this way, though the norm is 88 keys, midi numbering can span a range of 128 notes.
The sequence of midi numbers can be reduced is their positions in the respective octave by applying a modulo (base or divisor) of 12, their position in the octave being the remainder. What happens, though, when we go microtonal? As far as a midi-like indexing goes, all we have to do is to adjust our modulo to match the new number of notes per octave. This holds as much for equal temperament microtonal systems (19-EDO, 22-EDO, 24-EDO, 53-EDO etc) as for just intoned systems (15-JI, 17-JI, etc). Use purely for the purposes of indexing, the number of notes in the octave and the modulo we apply are one and the same.
To continue to use our 5-line staff, however, we need to come up with additional accidentals. For other than equal temperament systems, these must, however, represent more than a simple index, namely the exact pitch. To be of What form might these take?
For trivial (equal temperament) microtonal music scenarios such as a move from 12-EDO to classical Arabic 24-EDO (a quarter-tone system), we simply use classical music's double sharp and double flat.
Visual compatibility is one thing, tonal another. In just intoned tunings, subtle differences exist in regional tuning practices. Representing these using conventional notation is a minefield. In effect, a double sharp from the classical Arabic system, when used with Persian instruments, may represent any of a half a dozen close but quite distinct pitches.
A slightly different approach is taken with Sagittal notation system, which describes notes in terms of pitch deltas from known and strong pure tones. Moreover, sagittal provides us with enough differentiated glyphs to document virtually any form of music, be it western classical or microtonal.
For the ethnic musician, though, slight regional differences in tone may not ultimately matter. Just as words can have several meanings, so, too, can notes. At the end of the day, as long as you can play your tune from the notation, who cares?
Nevertheless, there is a case for notation mapping substitution. There comes a point -both in equal temperament and just intonation systems-
where classical western notation breaks down.
Getting your head wrapped round a new system such as Sagittal can seem a formidable challenge. It would help enormously if it could be done in stages, working steadily out from the known, using direct visual mappings.
Treating one as master and the other as slave, however, there is nothing stopping us showing both on-screen at the same time.
One remains in the role of 'driver' score, the other functioning much as would a dependent instrument or theory tool animation (the possibilities can be explored under related menu items at the top of the page).
Indeed, as long as the host machine can cope with the processing demands, there is nothing stopping display of several dependent -and possibly different- scores.
Here we can compare, step for step during score playback, the glyphs in action (and -why not?) hear directly how they relate tonally.
Indeed, given suitable source files, such a configuration could provide a basis for direct, pragmatic tonal compatibility tests, including in an AI context.
Algorithmic note placement frees the underlying transfer protocol of superfluous note positioning ballast. It should be both feasible -and the norm- for all but the most complex of scores.
During score playback, notes at the current timeline position can be used as driver for various interactive, dynamic animations.
Score-driven animations may include instrument and music-theoretical models, dance step sequences or 1:1 comparative animations.
The classical or western music notation glyph set, with it's single and multiple sharps and flats, can be used in a limited range of microtonal settings - which are the primary target of microtonal notation sets such as that of the Sagittal system. So there is already some limited visual compatibility. The challenge is to be sure of tonal compatibility.
We need to be able both to automatically built notation as specified by the underlying transfer file or protocol, but in a world music context, it may be helpful to offer alternatives better matching (say) the user's music system (cultural), instrumental and theory tool preferences. If you are going to support different music system glyph sets, it may no longer be such a large step to map between them.
Taken together, these suggest the following:
A (preferably visual) notation classification system
A notation 'factory' capable of building the above from glyph libraries
Either notation set compatibility matrix or (preferable) direct mappings to or within the notation classification system.
Though potentially a useful capability, one-to-one checks on glyph compatibility are probably overkill, but it should be possible to confirm whether two sets are compatible across a widely used and well-defined subset of their symbols, and under what conditions.
So how might such an implementation behave in practice? We have discussed in past posts how the following configuration settings contribute to learning environment flexibility:
overall settings (music system)
internal defaults (notation, instrument and theory tools)
'what-if' user notation overrides (so-called 'transnotation')
The following illustrates their propagation in the context of our music visualization aggregator platform.
Finally (and in great contrast) the summary diagram from the musicnotation.org website, illustrating their perspective onto transnotation workflow. It stops where ours takes off..
Integration & Control
With Dramatic Impact
Instant Comparative Musicology
Music + Data Viz = Music Viz
Energise The Notation
Simple Ideas - Animated
Data-Driven + Algorithmic Placement
Work Out From The Familiar
Goal: Multiple Visualizations
Notation Or Audio
Notation Examples
Sagittal Microtonal Glyphs
Which HTML Gaming Backend?
Score Analysis: Practice Optimization
Compatibility Across Devices
Leveraging Instrument & Tool Data Trees
Consequently Data-Driven
Flexible Reuse Hierarchies
Comments, questions and (especially) critique welcome.