Sunday, January 29, 2012

Music in Life Artificial

The musician character in the novel (Gloves) composes in micro-tuned scales, and uses other sorts of composition techniques that we might find odd to listen to. In fact, there are hints in the novel that his music is more popular with artificials than with humans. The inspiration for Gloves' music comes largely from Daniel Thompson's blog and correspondence with him about music. He gave me permission to quote for you one of our conversations on the topic. In this exchange I was trying to  figure out exactly what sort of music UV could be. Here's the result, condensed from a series of emails into one Q and A. I also added some hyperlinks and did some very minor editing where appropriate.

Me: The idea is that UV is beyond blues in the way that it is to the right of blue on the EM spectrum, and that it uses a microtonal scale. Do you have any creative ideas about what that might look like? Just playing straight blues in 47 tones or something wouldn't be much of a change. Maybe there's an interesting twist to put on it. Heck, maybe something like that already exists. My nephew, who's a drummer, thought maybe UV should be in 19/8 time, and sent me this YouTube video. Maybe he's pulling my leg.

Dan: You describe an interesting concept. I have some ideas that I can just throw out there as part of a brainstorming phase. You can tell me if any of these ideas coincide with what you are thinking, and I can do some more thinking and research. When I think of blues and microtonality, I think of 26 tone equal temperament. It has a minor third that is a little sharper than the septimal minor third (7/6, considered to be a bluesy interval) but still can work as a replacement for the more traditional minor third. To my ear, it would be a good candidate for something that goes beyond blues since it has that minor third that is a little wider than 7/6 and it has some interesting extended scales. I have tried to develop this into something "beyond blues" but haven't yet found any approach that is entirely satisfactory. Another idea is 19 tet. It is capable of some pretty bluesy sounding music. It is also the basis of some theoretical ideas that describe it as the next evolutionary development in tonality with a twelve note diatonic scale that is intended to correspond to the seven note diatonic scale in 12 tet. I think these ideas are deeply flawed. I have never been able to make those ideas work and don't know of anyone else who has either. However, there is an established literature on the subject that could make for interesting historical references and it's always possible that someone in the future could use these ideas successfully. Another idea is if blues relates to seven limit harmony (7/4, 7/6 etc. which are sometimes sung in blues even if the instruments can't play those pitches), then UV could make use of 11 and or 13 limit harmony. In this case, just intonation might be a good choice. Otherwise, large number equal temperaments that approximate those pitches could also work. Another possibility is to take a simple scale (such as a pentatonic justly tuned scale with seven limit intervals like 1, 7/6, 4/3, 3/2, 7/4, 2/1) and use something like Shepherd tones to create ambiguity and sonic illusions so it wouldn't always be clear if the notes are are ascending or descending and it would be possible for the same interval to be heard as two different intervals in different listeners, especially when two or more notes are played at the same time. If the audience is willing to wear biofeedback devices, the relative strengths of the pitches in the notes could be subtly altered to increase or decrease the ambiguity. It could be a collaborative effort to produce an individual experience. These sonic illusions are known to vary according to region and a person's speech patterns, so I could even imagine artificial intelligences interpreting this ambiguous sonic data in different ways.

Here's an interesting video of some microtonal blues music.

Joseph Yasser wrote a book called "A Theory of Evolving Tonality". That was primarily what I was referring to when I wrote about 19 tet. It is a little complex and convoluted. I just mention it case you need to cite any obscure historical precedents. When I wrote about shepard tones, I was thinking of some obscure research where two shepard tones would be played like C and F# (a tritone apart) and the listener would answer whether it was heard as ascending or descending. It turns out that people in different regions seem to have different internal mappings of what notes seem to be higher even when shepard tones are used that make the absolute pitches ambiguous. This could influence speech patterns and accents or be influenced by them. It could also explain why some composers have insisted that certain keys have specific moods, even though others tend to disagree on which key corresponds to which mood. I think other intervals besides the tritone could be made more ambiguous by shifting the relative strengths of the sine waves in shepard tones. One reason I'm interested in microtonal blues scales and intervals is because of difference tones (tones that result from subtracting the frequencies of two tones.) The difference tones that result from many scales are disordered. Although they probably affect the musical experience it is difficult to say how and whether they improve it or not. Blues scales can be less disorganised when it comes to difference tones. For example, the pentatonic scale I mentioned yesterday produces a small set of harmonically related difference tones for adjacent notes, just two per octave. For example, going from 1 to 7/6 produces a difference tone that is equal to 7/6 to 4/3 and 4/3 to 3/2. Going from 3/2 to 7/4 produces the same difference tone as 7/4 to 2 and this tone is a perfect fifth higher than the first difference tone and two octaves below the tonic note. It is speculation on my part, but I think this might be a key reason why "blue tones" seem so natural, even though they are surrounded by other intervals that are more consonant. It is also noteworthy that the harmonic series produces the same difference tone for each set of adjacent intervals so some microtonal blues scales mimic this natural structure. It occurs to me that another way of going beyond blues is to use sympathetic vibrations to accentuate these difference tones. This could be done electronically or with sympathetic strings (like those found on a sitar and other Indian instruments), either on the instruments or in sound boxes away from the stage, perhaps near the speakers or with some other electronic help to magnify the sounds. There is a new experimental instrument called the bazantar that makes good use of sympathetic strings along with very low frequencies. Structural limitations probably prevented Indian instruments from becoming large enough to produce these peculiar sounds. Here are two videos: The Painted Bird,  Mark Deutsch playing the bazantar.

Additional Notes
When I first came across Dan's blog, I tried to calculate which micro-tuned scales gave the least error. Any equi-tempered scale has the problem that it can't play an exact major chord. This applies to pianos and any fretted stringed instrument. I created a spreadsheet to consider scales with up to 107 equally-spaced tones in the scale. Note this is geometric, not arithmetic, meaning to get from one note frequency to the next, you multiply by a fixed number (rather than adding some constant). Then I calculated how close one could come to the 3x and 5x frequencies, calculated error and sorted by descending error. Here's a bit of the result.

My error function may not be the best one--it may not correspond to the actual perception of the sounds. But with this simple mathematical metric, 87-tone equi-tempered scales are considerably better than the standard 12-tone scale. If the base frequency is 100Hz, then the closest 'fret' to 300Hz is 138 frets up, with a small negative error. 500Hz is close to the 202nd fret, with a small positive error. 400Hz will be exact in any scale since it's a multiple of two (at fret 174 = 87 + 87). So the major chord produced at frets 138, 174, and 202 would be much closer to an ideal 3:4:5 ratio than with a regular guitar or piano. By a factor of 20 using my metric. Whether your ear could tell the difference is another matter.

In case anyone wants to play with the spreadsheet itself, I've uploaded it here.

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