Music in Steadman Space...
Patterns in Steadman Space
In this chapter I explore some of the patterns that Steadman space supports and further show how simple pattern recognition can support more complex harmonic structures.
One of the nice things about Steadman space is that cells that are close together are close harmonically as well. For instance if we consider the major triad, which is constructed from a root note, a major third and a perfect fifth, it should be immediately obvious that it is made up from the basic intervals of harmony. If we represent this in Steadman space by highlighting a root cell, a cell a perfect fifth away and a cell a major third away we arrive at a closely packed downwards pointing triangle. What is more, it soon becomes apparent that any downwards pointing triangle anywhere in the space represents a major chord whose root note is the cell in its top left corner.
We can construct a shape in this way for any chord and due to the ordering of the space harmonically consonant chords tend to be closely packed shaped, whereas dissonant chords form broken patterns.
Continuing the process with the remaining triads we yield the following patterns:
The suspended fourth is included on this diagram even though it isn't traditionally thought of as a triad because it fits the pattern quite well. What is more, a suspended fourth usually resolves to a major or minor triad when used within a chord progression. Graphically this amounts to the left-most cell in the suspended fourth pattern making a jump to either above or below the other two cells to make a major or minor triad.
These shapes work in both kinds of Steadman space, although in equal temperament space the augmented triad is ambiguous because of the connected edge. This means that an augmented triad feature could be interpreted with any of its cells acting as a root note. The same thing happens with the diminished seventh chord as we shall see later.
Because these chords are fundamental to music theory it is possible to recognise more complex chords just by considering these features. For instance a dominant seventh chord is a major triad with a diminished triad overlapping it. The following diagram shows how several types of seventh chord can be constructed from these tri-note features.
As an aside, it is feasible that the human brain might process music in a similar way. We know that in the visual cortex there are cells that respond to lines of different orientation, and that these features are passed on to further layers of perception. Is it possible therefore that the brain processes music in a similar way to this?
Time Averaging
Many of the patterns that could be recognised within Steadman space don't occur simultaneously but instead occur over time. For instance consider an input stream consisting of the following sequence of notes: C, E, G, C, E, G, C, E, G, C, E, G. These are the notes of a C major triad, but because they are being interpreted one at a time the downwards pointing triangle in Steadman space that would identify it as a major triad is never apparent. One solution to this would be to treat the cells in Steadman space as having continuous values, rather than bipolar ones. An incoming note could then activate the relevant cell location, which would then decay in activation at a rate dependent upon how much it was perceived to reinforce the current harmonic key centre.
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