My name is Ray Perlner (the only one as far as I know.) I have a longstanding hobby of writing music for a standard acoustic piano and playing it for friends and family. I also enjoy writing and studying microtonal music, which is by definition, music which cannot be played on my chosen instrument. Why would I do this to myself? Of course, this wiki has a general page on why a person might opt for microtonalism, but I would like to give it a more personal spin using my compositions as examples.
First of all, sometimes music I can play on the piano may sound better in a different tuning. A well known example is that music based on the diatonic scale can be rendered in any meantone temperament, and not just 12-EDO. Baroque and Renaissance music in particular generally will sound better in tunings ranging from about sixth comma meantone (~55EDO) to quarter-comma meantone (~31edo). Indeed this was what was used when these styles were the hot new thing in Europe. I have tried my hand at this style, and I find my compositions to sound better in these tunings as well.
Here are two short fugues I wrote in Phrygian and Mixolydian mode, respectively. Each is rendered in my favorite meantone tuning for that piece, as well as 12 EDO for comparison.
| Phrygian Fugue in 55 and 12 EDO | ||
| Mixolydian Fugue in 31 and 12 EDO |
In each case, I prefer the non-12EDO version.
A less well known example concerns music written using the Octatonic scale -- one of the better-known non-diatonic scales used in 12 EDO music. The standard treatment of this scale is as a MOS of the Rank-2 Diminished temperament, which tempers out the 7-limit commas 50/49, and 36/35. In this analysis, 12 EDO is pretty much optimal already. However, I have found that there is little downside to treating the Octatonic scale as a Rank-3 temperament that only tempers out 50/49 in the 7-limit (Jubilismic Temperament.) This allows the 6/5 and 7/6 minor thirds to be tuned differently, improving the fit to just intonation and the expressiveness of the system, Something similar is done with the Diatonic scale in Indian music, where 5-limit JI (effectively a rank 3 temperament) is used instead of Meantone temperament, rendering 9/8 and 10/9 as separate intervals. The downside of using 5-limit JI for diatonic music, in general, though, is that one is often faced with hard decisions regarding whether the D in C major, for example, should be rendered as being 9/8 or 10/9 relative to the tonic.
There are no such difficult decisions in the Octatonic scale in a rank-3 Jubilismic temperament. If we render the semitone-wholetone Octatonic scale as
1 : 15/14 : 7/6 : 5/4 : 7/5=10/7 : 3/2 : 5/3 : 7/4 : 2,
we find that while we have two different versions of a number of 9-limit consonant chords that appear in the 12-edo version, both versions are consonant in the 9-limit also in the partially de-tempered version. For example, a dominant 7th chord might either be 4:5:6:7 or 1/9:1/7:1/6:1/5. Likewise, if we treat the half octave as representing 17/12 in addition to 10/7 and 7/5, we can always render some inversion of any diminished 7th chord as 10:12:14:17. The melodic structure is also only moderately more complex than the 12-edo version, featuring a small (s) semitone, and medium (M) and large (L) wholetones in a sMsLsMsL pattern.