31 Tone Equal Temperament

Tone Clusters in 31 Equal Temperament

A tone cluster is a chord of closely-spaced musical intervals. Although there is no clear definition of what constitutes or does not constitute a cluster, the cutoff is usually the distinction between seconds and thirds, with chords made mostly from stacked thirds normally being considered normal chords, and chords made mostly from stacked seconds normally being considered tone clusters. Here, we use the term tone cluster to refer to chords made out of stacked intervals smaller than the septimal minor third.

New opportunities for using tone clusters, relative to 12-ET

As 31-ET has six distinct "seconds", or intervals smaller than a third, this tuning provides a rich vocabulary from which to construct tone clusters. The inclusion of harmonies involving the 7th and 11th harmonics allows for the construction of tone clusters that have a number of different tonal centers, both within or outside the cluster. There is also greater consonance possible in many of these tone clusters.

To compare, 12-ET has only four distinct types of three-note tone clusters, whereas 31-ET has thirty-six.

Although tone clusters in 31-ET often do unambiguously imply a tonal center, these effects are not always evident to the untrained ear. Even the most consonant tone clusters typically sound at least somewhat dissonant, and, in the absence of strong harmonic intervals like fourths, fifths, and thirds, their root or tonal center is usually only subtly evident.

Simple (3-note) Example Tone Clusters in 31-ET

Here are some tone clusters in 31-ET that unambiguously imply a tonal center:

Some more ambiguous tone clusters:

Understanding larger tone clusters

These example of three note tone clusters (two interval stackings) can serve as a starting point for understanding more complex tone clusters. When the harmonic ratios of larger tone clusters fit consistently into a single context, like stacking two neutral seconds on top of two whole tones, it will tend to sound more consonant. When the different combinations of notes imply different roots, which corresponds to when the intervals occur out of order from their corresponding order in the harmonic series, it creates more dissonance.

The more different implied roots there are in the cluster, and the more distant the relationships between the implied roots, the more dissonant and tonally ambiguous the cluster will sound. So for example, a tone cluster with two implied tonal centers or roots a fifth apart will sound relatively consonant, but one with many implied roots, or with two strongly implied tonal centers separated by a tritone or by a second or semitone will tend to sound more dissonant and ambiguous.