By Cree M.J.
The Phionic Series
The extended chart of the Phionic series beyond the first "Phi-Cycle" of 5 scales, reveals an interesting pattern of sweeping bridge intervals. We may question exactly what its significance is and how can it be utilised as a polytonal model.
One potentially interesting way to utilise the multiple scales of the Phionic series is to take advantage of the bridge interval over multiple scales. Relative to the middle scale 3, the scales 3 steps up or down that start the next Phi cycles are in the overall ratio of 4.016 : 3, close to a perfect fourth between the fundamental octaves.
By aligning the closest intervals or observing the bridge alignments we can see that these scales closest intervals are also precisely in the 1 : 1.00507 ratio that is the difference between the bridge interval and the standard interval.
By some creative means of utilising two scales or being able to transiently shift between them, we could take advantage of the favourable intervals of the Phionic series. This would only imply a small shift in key and basically a shift of the whole system by a fixed ratio of 1 : 1.00507.
These scales could also be played simultaneously in what would be described as a "chorus" effect, a rich shimmering caused by slightly out of phase frequencies such as found naturally when many voices are singing in unison, due to the slight differences between multiple singer's pitches and overtones. The effect could be described as ethereal, dreamy and nostalgic and contains frequencies and overtones that shimmer.
This creates a unique opportunity for acoustic instruments that have multiple strings or courses that are played together such as twelve string guitar, mandolin, lute, dulcimer etc. where if we were to tune the individual strings within the courses of these instruments to the two different scales, we can create a transient tonal centre which implies a situation where we simultaneously have an omnipresent bridge interval and standard interval. This creates the situation where at any given note we are playing at least one note as in tune as possible within the bridge interval system
As both scales are simultaneously played, exactly which scale is leading harmonically becomes vague and ambiguous. To the effect of creating a situation where either scale takes turns in leading the harmony as the most consonantly resolved interval moves from either both scales simultaneously to one scale at a time
In the case of microtonal music, we could experiment utilising two or more different scales to access unique combinations of intervals that may not be accessible with just one scale and even intervals that may be more in tune harmonically across the scales.
Given that all of the scales are geometrically fixed, we can identify between which scales does a specific interval most accurately lie and the conditions that align with it e.g. across or between the bridge. We can also observe that if for some reason we were not to cross the bridge interval in our scale and just keep increasing our ratio by 1 : 1.059, at the point of the bridge we would technically jump across to another scale.
For example if we start on scale three, and as we climb up our scale note by note toward the bridge, as we don't cross the bridge interval we then end up on the scale 5 of the previous Phi-cycle, the inverse is true were if we are going down and do not cross the bridge interval we will end up on scale 1 of the next Phi-cycle.
If we analyse the positions of the bridge, we can see that there is also a horizontal ascending pattern as well as the veritcal sweeping curve pattern. We can see how the consecutive bridges in this pattern are aligning to the other bridges along the series. We can see that a bridge occurs every 3 steps across, with 15 steps between the middle scales, crossing the bridge of each different scale before returning back..
The frequency differences between the scales are rather small, for example middle c at 261.63hz to its bridge equivalent is 262.95hz, a difference of 1.32Hz.
Practical tests acoustically suggest that the harmonics of the fundamental note begin to spread further and further apart, thus we we do hear more of this beating effect in the harmonics, in fact a very pleasant harmonic excitation and complex symphony of beating overtones could be heard in tests. The phenomenon of acoustic beating has had parallels drawn to the idea of dissonance, though when the peak of a beating note is in tune, we start to call it vibrato, as simply both ideas are just a fluctuation in frequency. So what we get with this overlapping system is a field of tones effectively beating into tune.
The pattern of these 1 : 1.00507 scales occurs in an orderly fashion that can be mapped, starting at scale 3 the bridged scales occur every 3 steps, keeping in mind that these other two scales have twin values so if we ignore them then the pattern is (scale 3 - 3 steps- 6 steps -6 steps- back at scale 3.)