User:Aura/Aura's Ideas on Tonality: Difference between revisions

Because the 3-limit and the 11-limit are the primes that have all of this foundational functionality, they are naturally very important in musical systems that have their roots in 24edo, and their pivotal role in laying the groundwork for key signatures means that they can be referred as the "navigational primes".  In both the traditional and quartertone-based key signatures, it is the Pythagorean Diatonic Scales that arise as the standard variants for the various key signatures, as these are the simplest diatonic scales that can be formed with the 3-limit, and the pure 11-limit is not capable of forming diatonic scales at all.  Although the 5-limit, 7-limit and 13-limit also play a role in defining key signatures, these primes define variations on the standard key signatures as opposed to the standard key signatures themselves.  For the sake of simplicity, it can generally be assumed that higher primes are ill-suited for serving as anything other than accidentals.

Now, some may have additional questions as to good reasons for elevating the 11-limit to the status of "navigational prime", and why 11-limit quartertones in particular are better than others in this department.  Well, perhaps we should start with the fact that quartertones are the most readily accessible among microtones.  Furthermore, research seems to show that quartertones are the smallest musical intervals that can be regularly used in musical capacities without being considered a variation of one of the surrounding pitches.