a mode, a toad, a road

[bachus]

Please refer to the thread “Program in Progress” for an introduction to what is going on here.

To avoid confusion I would like to start with a definition of terminology which is not entirely standard. If someone strongly objects and thinks they have a less confusing terminology I would gladly hear it.

A mode is a succession of intervals the sum of which lies within the span of one octave.
Example, the Major (Ionian) Mode:
whole-step
whole-step
half-step
whole-step
whole-step
whole-step
half-step

A scale is defined by a mode and a starting pitch:
Example, the D Major Scale:
D (the starting pitch)
whole-step E
whole-step F#
half-step G
whole-step A
whole-step B
whole-step C#
half-step D

A modality is a set of relationships between a scale designated as the controlling tonic and other scales. Thus we can say Classical Tonality is the best understood form of modality and it and its variants were virtually the exclusive basis of western music from the late renaissance to the 20th century.

At present, when it comes to algorithmic models of Classical Tonality, Jackendoff and Lerdahl’s “A “Generative Theory of Tonal Music” is the only game in town. In that domain (the Classical) it is extremely powerful at least down to the phrase and its cadence. In phrases that are not extended cadences or cadential elaborations (i.e. in phrases that have non-trivial chord successions or non-cadential chord progressions) or in music much out side the realm of the classical I find it less convincing and less useful. (I should note that Jackendoff and Lerdahl explicitly state that the domain of application is limited to Classical music). It seems to me that its power is generally retained at the higher levels of abstraction but as one moves closer to modernity it applies less well to the lower levels of abstraction.

I want Heuristic Muse to provide tools for working with multiple modalities (though only one at a time (except in explicit transitions)) and I want those tools to be primarily graphic. For example if the modality is Tonal and the controlling tonic is C I want to be able to draw lines over the time domain that quantitatively represent the influence of other scales in a manner consistent with Tonality.

Say I raise the line that represents A-major. Because we are in Tonal C the C# of A-major will be used in a way that ultimately supports C (unless we are in a modulation). Thus we might expect the consequence to be something that eventually reduces to a progression from A to D to G to C in a sequence of applied dominants (but there are many other consequences to an occurrence of C# in C that fit Tonality equally well ) Now, in Tonality, C remains the controlling tonic, period. My subjective experience tells me that the ear experiences a “flux” in tonal location on which current theories are mute. What I would like to quantify in this context is the moment to moment flux of the perceived strength of C (the controlling tonic) . This would allow the user or the program to vary that parameter and have other algorithms work out what other scale strengths need be raised or lowered to meet those conditions.

Any and all ideas on this and the idea of modalities in general would be very welcome.

[jksuperstar]

One way is to use a vector represetation of frequencies over time...much like a waterfall FFT looks like. All raw frequencies are containted. Relationships would then ride "on top" of that, such as an A4 = 440Hz. Then, the program would do it's "work" in the same domain we would hear it in: FFT over time. This gives you access to infomation like sibilence, harmonics, "chords", etc. I would think this would make it easier for you to import information about the sounds/instruments used. The FFT of a sound created over a certain amount of time time has the exact same type of information as a score representated in this manner.

Vectors come from how the frequencies or harmonics move over time. Say you have a single frequencey, a sine wave. Starts at 440Hz, and 4 seconds later, or 8 beats@120 bps, the has swept up to 880Hz in a linear fashion. The vector is a straight line from 440 to 880 at this rate. You could change vectors from linear to non-linear (or as described by some other function as well, such as an envelope).

Thus, you could do a pre-processing step of translating standard score into FFT/time, do the work on this, then a post-processing step (if necessary) of fft/time back into score, or directly into sound via inverse FFT. This also allows your engine to work with western scales, microtonal, etc since they are defined as parts of the pre-processor or post-processor. It also means the engine could work in various levels of detail: 10K point FFTs, 8K pt FFT, 4 Tera-point FFTs, or as many points as the length of the song & sample rate determine. This could be a daunting amount of data on a harddrive, and/or take lots of time to deal with, but I think it's ultimately the most flexible for audio generation.

Just an idea...

[bachus]

[Kassen]