User:Rperlner

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.

Diatonic Music in Meantone

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	Phrygian Fugue in 55 EDO	Phrygian Fugue in 12 EDO
Mixolydian Fugue in 31 and 12 EDO	Mixolydian Fugue in 31 EDO	Mixolydian Fugue in 12 EDO

In each case, I prefer the non-12EDO version.

To be fair to 12 EDO, I will give one example, where I prefer the 12 EDO version of a piece. This time a short Locrian Fugue (with a 31 EDO version given for contrast):

Locrian Fugue in 12 and 31 EDO

Locrian Fugue in 12 EDO

Locrian Fugue in 31 EDO

Partially De-tempered Octatonic Scale

A less well known example of the benefits of alternate tunings 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.

Here is an Octatonic jazz piece based on a shorter theme I wrote for piano in three different Jubilismic tunings that distinguish between 6/5 and 7/6 minor thirds. Ranging from narrowest to widest perfect fifths, they are 26 EDO, 48 EDO, and 22 EDO:

Octatonic Groove in 26 EDO

Octatonic Groove in 48 EDO

Octatonic Groove in 22 EDO

For contrast, here is the same piece in 12 EDO:

Octatonic Groove in 12 EDO

The 12 EDO version is pleasant enough to listen to, but I find it less interesting, and at times, less harmonious than some of the nonstandard tunings. (I especially like 26 and 48 EDO here.)