19EDO
If you have a web broswer with good support for HTML5, and WebAudio you can try out the keyboards below to compare 19 Equal Divisions of the Octave and 12EDO. The keys show the note names (including the most common enharmonic equivalents) and the distance in cents from the A below.
To play a single note, click and hold the left mouse button. To play a chord, start one note at a time by clicking it, then moving the mouse outside the key before letting go of the button. The Volume slider sets the master volume, and the "Tacet" button sets all keys up.
Three keyboards are presented. In the centre is a normal 12EDO layout tuned to A=440Hz. Above it is a keyboard inspired by claviers of the early Baroque where the accidentals are split front-to back with additional keys inserted between E and F and between B and C. This keyboard is tuned with the keys layed out to facilitate chromatic scales: the sharper of the accidentals is to the top of the screen. There is a 1/19th of an octave per chromatic step, so a "hyperchromatic" scale fits easily under the hand, with fingering +,1,2,+,1,2,+,1,+,1,2... Baroque keyboards would most probably be tuned using an extended mean-tone temperament which does not divide the octave equally. This gave rise to "remote keys" which had less than perfect intonation. Some of the accidentals were therefore less frequently used than others. Although using 19EDO tuing, the third keyboard uses the layout common on Baroque instruments which places more frequently used notes (C- and F-sharp, and E- and B-flat) to the front of the instrument. G-sharp is also brought forward as it occured more frequently than A-flat, being the sharpened leading note of A minor.
A is the same for all of the keyboards. Some 19EDO pitches deviate from their 12EDO namesakes by a few tens of cents. This results in a clear and rapid beat if, for example, two Fs are played simultaneously, one on the 12EDO keyboard and one on a 19EDO one. Also noteworthy in 19EDO is the availability of the intervals of the augmented second, third and fourth, and their inversions, the dimished seventh, sixth and fifth. The augmented 19EDO second and third provide the composer with an interval which is almost equidistant between the semitones of the 12EDO instrument: the 19EDO augmented second lies between a major second and minor third in 12EDO, and the 19EDO augmented third lies between the minor and major thirds in 12EDO.