Spiral tunings

Spiral tuning systems encompass the diverse configurations of a spiral polygonal chain, known as a "spirangle," utilizing the segment's length as the fundamental determinant for pitch.^{[clarification needed]}

These systems are non-periodic and possess an infinite range of possibilities. Among these configurations defined by their sides and segments, many prove musically practical, with potential for some to manifest as tangible instruments, such as spiral harps.

For instance, a six-sided spiral harp comprised of 120 segments spans approximately five octaves.

Each unique configuration unveils distinct chords and progressions, often showcasing geometric patterns.

Furthermore, the inversions of these tunings hold musical merit. Instead of the segment's length dictating string length, it determines frequency. However, this approach forfeits the utilization of the spiral as an instrument.

Another aspect influencing pitch is the spiral margin. This alteration also sacrifices the characteristic spider-web appearance and eliminates the possibility of a spiral harp.

Additionally, concerning the margin/radius property, the same algorithm used for calculating the spirals can be (unnecessarily) employed to generate equal-division systems. For example, when sides are 1, 1/2, or 1/4, etc., the angle is calculated with "PI*2/spiralSides," leaving the margin as the sole control for segment length increase, with the rest of the calculation following Pythagoras' theorem.

For instance, a one-sided spiral with a radius of approximately 1.05946 (twelfth root of 2) generates a 12 equal division system.

An open-source, virtual playable spiral harp is accessible in https://kepleriandreams.github.io.