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Wednesday, October 6, 2010

Natural Microtonality

After extensive playing slowly with fretless mode, it is finally starting to sink in with respect to what is going on with natural microtonality (as seen in maqam). Instead of speaking in terms of cents, I will speak in terms of *pixels* in Mugician. Since the fret width is uniform due to it not being a real string instrument, this makes things easy. I will roll my eyes at suggestions to take measurements and pick some equal temperment that will allow frets, as these are the findings of my ears; which ultimately are how these temperments are attempting to approximate (or at least tame to some degree).

First turn up all the reverb and echo that you can stand, so that there is much resonating going on as you can make happen! Turn the yellow slider all the way up for full polyphony. Turn the gray slider all the way to 0 until the green frets disappear.

I am going to speak in terms of D Dorian mode, which means all white keys. In Maqam, this can be viewed as the standard central drone pitch. Arabic violins are tuned DGDG, with G tuned to a perfect fifth (not the piano fifth, the one that arises from sound physics) so that they resonate in a fifth chord on D. I couldn't tell you if that D is the piano D, but I will assume that it is.

First note that to make a real fifth, you have to push up 5 pixels or so (-5 for a fourth), and for minor third you need to go up about 5 pixels (towards quarterflat), and major third is a little too sharp and needs to go down by similar amount...about 5 pixels to quarterflat. Of course, octaves are always perfect. Knowing that, you get an intuition for how to bend these microtones in general.

First, we do the D minor pentatonic and ignore the quartertones for a moment. Play D and F together, then slide F up a few pixels until you get maximum resonance. Do this slowly so that the echo and reverb don't make this hard to hear.

D + 0 pixels
F + 6 pixels

This is a minor third interval adjusted to match up with physics. Play that F when you play F in your scale. Now play a fourth interval. Again, keep D fixed, but slide G around until you get maximum resonance.

D + 0 pixels
G - 5 pixels

Because that was a perfect fourth, a perfect fourth down is similar. So play first an octave down for this. Then do the same thing for G an octave up.

D + 0 pixels
A + 5 pixels

Note that F and G are approximately 10 pixels farther apart than normal. In short, when you play a fifth you should augment about 5 pixels. When playing a fourth, taking octaves into account you basically do the same thing and drop a fourth by 5 pixels.

Now for Equarterflat, the quarterflat would be exactly between E and E-flat, but...

D + 0 pixels
Equarterflat - 3 pixels

Flatten that quarterflat until it resonates at about 3 pixels. Likewise, Bquarterflat, because A was 5 pixels too high, do it relative to A. 5-3=2, so:

A + 5 pixels
Bquarterflat + 5 - 3 pixels
C + 5 + 5 - 3 pixels

The C wants to be higher in the context of A,Bquarterflat,C. This is all about drifting around until the notes resonate.

When coming down from D,

D + 0 pixels
C + 3 pixels
Bflat + 3 pixels

The descending scale wants a slightly lower C, and using the fully flat B still needs to be up a few pixels.

And when playing the tetrachord Hijaz, I have a feeling that this is correct:

D +0
Eflat + 5
F# - 3
G + 3

In this case, the perfect fourth is messed up... it's actually 6 pixels sharp. Or this:

D + 0
Equarterflat - 3
F + 5
F# + 3

With the common theme being to stretch the interval wider if it's a half-step until it resonates, or to shrink intervals that are larger than a whole step to the closest resonation point. These may not be right, but this is exactly the kind of thing that happens when fretless.

When playing a quartertone, when going up I want to do +3 pixels so that when I hit the minor third interval it's the same width as I would get if I did -3 pixels from the note below it. So the quartertone isn't exactly in the dead center... it's either a little above or below based on which note you want to emphasize.

Anyways... I don't know the math behind it other than knowing that it is related to creating the shortest standing wave (with respect to what?...not always obvious). The only thing I can assure is that it has *nothing* to do with how many equally spaced frets to have in an octave, as this number is actually infinity.

So I am beginning to see how in Maqam, the exact pitches depend on the tetrachord you are working in.

All this crazy microtonal stuff is just a consequence of what happens when you try to have perfect fifths and fourths...more generally, picking the closest standing wave that is shortest. If Mugician were tuned to *perfect* fourths, then each row would have to walk over 5 pixels from its current position, or tuned to perfect fifths would do the opposite (but might be useful for making the fretlessness 2 dimensional in the case of perfect fifths). Microtonality is inevitable when you try to handle resonance, sympathetics, and overtones. All of the equal temperments attempt to gloss over this with "$N tet is close enough" (where N is usually a large-ish prime number) when it's typically unable to play along with 12tet instruments and still isn't matching up with physics.

The point of this is *not* to figure out where frets and snapping need to be. The point is that you need to adjust to make perfect intervals (until sound give maximum resonance). Where these resonances happen is dependent upon any notes you already have down, or are still reverbing from previous play.