Western music theory is notable for its rules: rules that determine which chord-pairs form a “cadence,” which chords to use to prepare for a cadence, the order in which chords should appear in a chord progression, proper voice leading, the rules of counterpoint, etc..

Some rules apply to every tuning in the syntonic temperament (Pythagorean, ¼-comma meantone, 12-tone equal temperament, etc.). For example, the I-IV-vi-ii-V-I chord progression “works” in any tuning of the syntonic temperament. “Works” means that the frequency of I is the same at the end of the progression as it was at the start  (octaves aside). This same chord progression does not work in other temperaments (e.g., the schismatic) or in Just Intonation. In them, the frequency of I would drift off-key by one syntonic comma on each cycle through the chord progression.

Other rules apply only to specific tunings of the syntonic temperament. For example, Giant Steps and Central Park West both work only in 12-tone equal temperament, because that’s the only tuning in which three major thirds (or four minor thirds) precisely equal one octave. In any other tuning, each pass through the modulatory cycle would drift off-key.

Logically, then, there is a hierarchy of “rules” to be worked out:

  • Rules that apply only to a single tuning in a single temperament
  • Rules that apply all across a given temperament (or within a sub-range there of…but what defines the sub-range?)
  • Rules that apply across all tunings of closely related temperaments (but what defines “closely related”?)
  •  …and so on.

It can be argued that the “research program” of the Common Practice Era was the exploration of the rules that applied to a very narrow sub-range of the syntonic temperament (the range that was most compatible with purely harmonic timbres). That research program gave us today’s “rules” of music theory. From this perspective, Musica Facta can be seen as a re-invigoration and expansion of the Common Practice Era’s research program. (To which Rameau might say, plus ça change, plus c’est la même chose.)

It can be argued that academics and musicians have been exploring alternative tunings for a very long time, and of course this is true. Musica Facta advances the state of the art in four specific ways:

  1. Previous research was focused almost exclusively to the tunings and temperaments that were consonant with harmonic timbres. Musica Facta can deliver similar consonance in any tuning of any temperament, which infinitely increases the set of tunings & temperaments that may be found to have emotionally-affective potential.
  2. Previous research approached each tuning as being a unique entity unto itself. Musica Facta approaches each tuning as being a bead on a string, with the string being the tuning continuum of the current temperament. This enables composers and theoreticians to explore dynamic changes in tuning – from one bead to another, and to another, and back again (see Composition, above).
  3. Musica Facta’s discovery of tuning invariance enables its new musical effects to be controlled in real time, using isomorphic keyboards.
  4. Controllers for alternative tunings were often tuning-specific and cumbersome. Isomorphic keyboards offer consistent fingering across an infinite number of tunings (with no wolf intervals), and can be implemented on your “mini”-tablet device, making them the very opposite of cumbersome.

These advances, taken together, enable dynamic tonality – a vast frontier of music-theoretical possibility, waiting to be explored.

Here are some examples of potential research projects in music theory.

Exploring the [Foo] temperament

Pick a temperament (perhaps from this list). Let’s call the temperament you chose the Foo temperament. Now, explore it using tuning-aligned timbres. What well-formed scales does Foo support, if any? What 2-dimensional note-layouts are isomorphic with Foo? What are the valid tuning ranges of these scales in Foo (at various prime limits)? What are the tonal resources of Foo – its scales, modes, cadences, chord progressions, tonnetz, orbifolds, etc.? Which of these are – at some useful level of abstraction – shared by other temperaments? Which are unique to Foo? Which are invariant all across Foo’s tuning continuum, and which are unique to specific tuning sub-ranges or to specific tunings? You goal, metaphorically speaking, is to produce an accurate (but high-level) map the New Musical World of Foo, so that the musicians and theorists who follow you can explore Foo in finer detail (perhaps through compositions that explore Foo’s structures’ “ability to reliably induce, in audiences, compositionally useful emotional responses;” see Composition, above). This task involves the scientific practices of reduction and abstraction: reducing each given structure down to its smallest components, and abstracting each such structure to the highest useful level of generalization. The process and results of this task, applied to many temperaments, should eventually reveal many new and compositionally-useful insights into music’s structure.

Assimilating other music theories into Musica Facta

Musica Facta already borrows (more or less) from other recent advances in music theory such as diatonic set theory, neo-Riemannian theory, topos, orbifolds, etc. For example, Musica Facta has already borrowed the concept of “well-formed scales” from diatonic set theory, in part because the rules for constructing such scales generalize well across tunings and temperaments. However, there is more to diatonic set theory than well-formed scales. How does the rest of diatonic set theory generalize across tunings and temperaments, in the presence of tuning-aligned timbres?  How about topos theory? Neo-Riemannian theory? Orbifolds? Etc.? Each of these can be examined in the context of Musica Facta’s generalization of the fundamental axiom of music theory, with an eye to assimilating their core concepts into Musica Facta in a parsimonious, elegant, and useful manner.

Ultimately, any useful purpose that these other theories serve, should be careful assimilated into Musica Facta, such that Musica Facta serves the same purpose more generally and parsimoniously.

Join us!

Musica Facta has opened up a vast new frontier of music theory to be explored by brave adventurers such as yourself. Let us know which research problem piques your interest, and we’ll work together to help you solve it!

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Seminal Experiments

Generally speaking, every seminal experiment in music cognition was performed with the assumption of the just-harmonic hypothesis – that is, with a combination of harmonic timbres and Just Intonation tuning (or, more often 12-EDO tuning). Each of these seminal experiments can and should be reproduced using the Musica Facta axiom instead. That is, they should be reproduced using stimuli that are:

  1. Presented with note-aligned timbres,
  2. With the stimuli varied across the valid tuning ranges of:
    1.  The syntonic temperament (which includes many notable “real world” tunings);
    2. The schismatic temperament (which is closely related to the syntonic, and which has arguably been used in traditional Turkish music), and
    3. The Magic temperament, which is included as a control, as it is more-distantly related to the syntonic and has never been used for music-making outside of the microtonal music community.

In addition, these experiments should seek to expose the above stimuli to groups of subjects whose musical experience is primarily:

  • Western (syntonic temperament, 12-edo);
  • Indonesian traditional (syntonic temperament, 5-edo slendro);
  • Thai/Mandinka traditional (syntonic temperament, 7-edo renat/balafon); and
  • Turkish (schismatic temperament, Pythagorean).

Examples of such seminal experiments include:

Universal Music Theory from 1st Principles

Musica Facta may enable the development of a truly universal music theory from 1st principles, based on experiments in music cognition.

  • First, Musica Facta provides a more-general axiom that has the potential to directly embrace non-Western cultures’ music (see Ethnomusicology).
  • Second, Music Facta enables researchers to distinguish nature from nurture through the use of two different groups experimental samples:
    • One that uses the tuning & timbre of the subject’s enculturation, and
    • One (or more) that uses tunings & timbres that are more or less different from the subject’s enculturation.

Steps in this direction have already been taken – see Milne 2011, Milne 2010a, Milne 2010b, and Milne 2009 – but there is much left to do.

Tonal space: The re-use of geo-spatial brain architecture in tonal space

The human brain appears to include many structures that are implicated in geo-spatial location, tracking, and planning (“Where am I? What route will take me home most efficiently?”). These structures include place cells, grid cells, and border cells. Perhaps these same geo-spatial structures are leveraged in the processing of tonal space.

Join us!

Post your interest in undertaking any of the experiments described above, and dive in! We’d love to have your help.

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The Musica Facta project has already shown that the valid tuning range of the syntonic temperament includes many notable tunings (Western and non-Western, equal and non-equal, regular and irregular). Among these are modern Western 12-edo (“12-equal division of the octave,” widely known as “equal temperament”), ¼-comma meantone, well temperament, Indonesian slendro, and traditional Thai & Mandinka 7-edo.

The occurrence of such diverse tunings on a single tuning continuum suggests a Chomsky-esque conjecture: that the brain is hard-wired for “syntonic music,” but that any tuning from along the syntonic tuning continuum will do. This conjecture is supported by brain scans by Petr Janata, showing that the brain contains a region that tracks tonal function using a map that is compatible with the syntonic temperament. It is also supported by Sethares’ finding that the traditional instruments of Thailand and Indonesia emit sonic spectra that are isomorphic with the notes of their tunings.

If this conjecture were validated, then it would explain both the variation in “real world” tunings, and the limitations on that variation. It would also suggest limitations on the range of alternative temperaments and tunings that can be usefully exploited in new music.

Join us!

You can help by exploring this  conjecture in a manner that is acceptable to, and publishable within, the ethnomusicological community.

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Musica Facta offers new musical effects, including (but not limited to):

  1. Polyphonic tuning bends, in which (for example) a tuning bend in the syntonic temperament from P5=696 to P5=702 (that is, from 19-edo to Pythagorean tuning) makes the sharps sharper and the flats flatter. Polyphonic tuning bends enable
    1. Tuning progressions, such as the one used in “C to Shining C” (Sethares, 2008), discussed here;
    2. Tuning color, in which a tuning is used in passing to enhance the emotional impact of its intervals (see here and here);
    3. Temperament modulations, such as a modulation from the syntonic temperament to the schismatic temperament via a “pivot tuning.”
  2. Dynamic timbre, including
    1. Dynamic sonance, which systematically mis-aligns a timbre’s partials with a tuning’s notes, thereby introducing dissonance/tension into otherwise consonant/restful notes, chords, etc.
    2. Timbre progressions, such as a progression from harmonic to tuning-aligned and back, such as the one used in “C to Shining C” (Sethares, 2008), discussed here;
    3. Dynamic primeness, in which can
      1.  Change a timbre from sounding like a closed-bore cylindrical instrument (e.g., a clarinet) to an open-bore cylindrical instrument (e.g., flute) to an open-bore conical instrument (e.g., saxophone), just by changing the amount of energy invested in the timbre’s 2nth partials (“two-ness”).
      2. Produce similar timbre effects by changing other prime-nesses, such as three-ness and five-ness.
      3. Emphasize blue notes by dynamically changing the amount of energy invested in the timbre’s 7nth partials (“seven-ness”).
    4. Dynamic regularity, in which the tuning of a temperament’s notes is made more regular (e.g., ¼-comma meantone), or less regular (e.g., well temperament).
  3. Expressive polyphony, in which on-board and external motion sensing is used to add expressive potential to a highly polyphonic keyboard, thereby enabling the real-time control of both MIDI’s traditional effects and also polyphonic tunings bends, dynamic sonance, etc..

Musica Facta needs to have composerscreate new music that exploits Musica Facta’s new effects, and discover how audiences react to them.

Join us!

You can help by using any of these tools to compose your own music using Dynamic Tonality. It would be particularly helpful to focus, initially, on composing music that can demonstrate Dynamic Tonality’s effects clearly and unambiguously within an otherwise “traditional” musical context.

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A Musica Facta-enabled controller would expose an isomorphic keyboard to control discrete notes, and also expose other means (such as motion/position sensing and/or tiny thumb-operated joysticks) to control continuous expressive variables (e.g., pitch bend, vibrato, and/or Musica Facta-specific effects such as sonance and primeness).

The design of New Interfaces for Musical Expression (NIME) is an active research area, into which the design of Musica Facta-capable controllers would fit.

Musica Facta:

  • Enables new avenues of NIME research (e.g., into tiny hand-held instruments with isomorphic keyboards), and
  • Requires new interfaces (e.g., to control the effects of Dynamic Tonality in real time).

Today, composers can use Hex – a sequencer – to compose music that explores and exploits Musica Facta. Such sequences can drive a number of synthesizers that implement Dynamic Tonality, including The Viking and 2032 (see for details & downloads).

However, there does not yet exist an expressive Musica Facta-capable music controller for real-time performance.

Musica Facta’s performers must control the usual musical effects (vibrato, pitch bend, brightness, etc.) and also the unique effects of dynamic tonality (polyphonic tuning, primeness, sonance, etc.). Therefore, a Musica Facta-capable music controller must have exceptionally high expressive potential.

Furthermore, polyphonic tuning bends are best executed on an isomorphic keyboard, so a Musica Facta-capable controller must expose such a keyboard.

Software-based controllers

Many software apps already turn mobile devices into isomorphic keyboards. However, none of them – so far – also offer the very high degree of expressive power required by Musica Facta.

To meet these needs, the Musica Facta project envisions a software app that

Dedicated hardware controller

Mobile devices were not designed to be musical instruments. It is likely that dedicated hardware controllers – jammers – will eventually be required to meet the needs of increasingly virtuosic performers of Musica Facta. Specifically, a dedicated hardware controller can implement physical note-controlling buttons, internal motion sensors (orientation), thumb-operated joysticks, and optional external motion sensing (position).

Join us!

You can help by

  • Writing code that uses a mobile device’s orientation (tracked by internal motion sensors) affect its musical expression;
  • Writing code that uses a mobile device’s position (tracked by an external video camera, e.g., Kinect) to affect its musical expression;
  • Designing a device that will affix a mobile device in “playing position” without limiting the movement of the player’s fingers (see, for example, this expired patent application);
  • Designing a dedicated hardware “jammer” (see, for example, this video for the defunct Thummer).


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Music Education

Imagine that the sole objective of music education were “to make it easy for everyone to knowledgeably compose, perform, and improvise their own music.” What innovations would be needed to attain this objective?

One early proposal is JIMS Intuitive Music System (JIMS). JIMS was designed to expose the deep structure of Musica Facta‘s syntonic temperament by combining a suite of well-known technologies whose mutual isomorphism were not previously recognized, including tonic solfa, the chromatic staff, the isomorphic keyboard, and the tonnetz.

I am  leading research into the educational implications of Musica Facta, having just begun a Master’s by Research at the University of New South Wales (Sydney, Australia). My research will attempt to [dis]prove the hypothesis that “musical novices learn musical concepts ‘better’ using JIMS than using  traditional technologies.”

I’d welcome your help! Among other things, I’d welcome assistance in extending existing open source music notation technology to support JIMS. I also need an expressive, JIMS-compatible iPhone/Android instrument — like Musix Pro (a fine app!) with the addition of expressive control through motion sensing.

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Welcome to Musica Facta!

Do not be alarmed. This is only a test.

Posted in Cognition, Composition, Education, Ethno, Theory, Tools | Leave a comment