for the syntonic temperament. The fingering-pattern of any given musical structure is the same in any tuning on the syntonic temperament's tuning continuum. The combination of an isomorphic keyboard and continuously variable tuning supports Dynamic tonality as described above. As shown in the figure at right, the tonally valid tuning range of the syntonic temperament includes a number of historically important tunings, such as the currently popular 12-tone equal division of the octave (12-edo tuning, also known as 12-tone “equal temperament”), the meantone tunings, and Pythagorean tuning. Tunings in the syntonic temperament can be equal (12-edo, 31-edo), non-equal (Pythagorean, meantone), circulating, and Just. The legend of Figure 2 (on the right side of the figure) shows a stack of P5s centered on D. Each resulting note represents an interval in the syntonic temperament with D as the tonic. The body of the figure shows how the widths (from D) of these intervals change as the width of the P5 is changed across the syntonic temperament's tuning continuum. At P5 ≈ 685.7 cents , the intervals converge on just 7 widths (assuming octave equivalence of 0 and 1200 cents), producing 7-edo. S/T = 0. At P5 ≈ 694.7 (19-edo), the gaps between these 19 intervals are all equal, producing 19-edo tuning. S/T = 2/3. At P5 ≈ 696.8 (31-edo), a stack of 31 such intervals would show equal gaps between each such interval, producing 31-edo tuning. S/T = 3/5. At P5 = 700.0 (12-edo), the sharp notes and flat notes are equal, producing 12-edo tuning. S/T = 1/2. At P5 ≈ 701.9 (53-edo), a stack of 53 such intervals - each just 3/44 of a cent short of a pure fifth - makes 31 octaves, producing 53-edo tuning. S/T = 4/9. etc.... at P5 = 720.0 cents , the pitches converge on just 5 widths, producing 5-edo. S/T = 1. Research projects regarding the syntonic temperament The research program Musica Facta investigates the musical theory of the syntonic temperament. The music theory of the Guido 2.0 research project is based on the syntonic temperament. Guido 2.0 seeks to achieve a 10x increase in the efficiency of music education by exposing the invariant properties of music's syntonic temperament (octave invariance, transpositional invariance, tuning invariance, and fingering invariance) with geometric invariance. Guido 2.0 is the Music Education aspect of Musica Facta (above). Notes Linear temperaments