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Cloud Rhyme
This piece is a bit floatier than many of the others, like super mario when you driftin around up in the clouds.  The tuning makes a bit of a judgement on that as well, using higher-numbered ratios for their minute difference (can we tell) compared to other smaller number ratios that could take the place.   Questions of perception can ultimately go quite deep in tuning analysis.  The mode is like a locrian, with all the flats.  1 b2 b2 4 b5 b6 b7 .  The tuning is: 

19/18 (93.6¢), 

95/81 (276¢) __ 5/3 * 19/27

4/3 (498¢)

7/5 (582.5¢)

128/81 (792.2¢) __ 2*2*2*2*2*2/ 3*3*3*3

16/9 (996.1¢)

2/1 (1200¢)


I don't know why I chose 95/81, other than it contains the only other sense of the 19 that the 19/18 brings.  

Looking at the soon the disappear "Gallery of Just Intervals", the only neighbours within +/-10¢ are

90/77
270.079867
swetismic subminor third
62/53
271.531027
orwell subminor third
75/64
274.582429
classic augmented second
20/17
281.358304
17qy2 = 17esque yellow 2nd
septendecimal augmented second, septendecimal minor third


None of these (especially given the context of the 19 being the only high prime in the set (not really counting 7 as high, and it only exists in 1 place), really seem like a markedly better choice than the 95/81, though the 75/64 is 5-limit.  I guess I wanted the 19, still don't know how I derived it / decided it.

I just got back from the Microtonal Adventures Festival in Bellingham.  Super great festival which I hope happens again soon (in addition to other like it in other locations).  Lots of interesting questions it has brought to me, especially that of perception.  Many of these questions have been long terms answers I've been seeking, which have been reframed in my mind, or positioned closer to the front.  Two of the main points of this include:

1. Do intervals have an objective sound?  How much is cultural / experiential?  

___ For example: If many different musical traditions placed high value on the 2nd and 3rd harmonics (octave & perfect fifth), we can therefore hypothesize that either: there is a fundamental property of the sound in which music seeks to use that relation as a symbol in its music (ie. in Chinese music the 3/2 was necessarily perfect to represent the relation of man to god (thanks John Platter)), or that there was an unknown musical mother culture in which all of these particular musical traditions stemmed from.  The former seems strong to me as the phenomenon of "locking in" to just tuned intervals is both a physically testable reality, and a well-known psychoacoustic phenomenon.  Though it is easier to consider 2/1 and 3/2 as mathematical phenomena which depend on physics to better describe their reality (which is often a claim to the fallibility of just intonation), the lack of beating as we approach these nodes (and extended to at least 5 and 7 limit) is well tested.  In musical systems which do not value the 3/2 as highly, there still generally exist a tempered form of it (ie African music, where the purity of the tuning of the 3/2 is not of tantamount importance), and this interval category still tends to be present (would like to find an example of a musical tradition which completely excludes any form of the fifth or octave).  In addition, the gamelan tradition seems to intentionally detune the 5th for the shimmering effect which also has a holy representation.  This actually can also bring about the greatest counter-claim and the strongest case towards culture -- the materials in which instruments were created.  If the fifths were decided, in gamelan for example, by tuning to the harmonics (on in gamelan's case, in inharmonicity of the material), then it is the materials which resonate the 3rd harmonic, and we are not in fact drawn as heavily to that naturally.  However, from that, why are there not more Bohlen-Pierce like clarinets occurring naturally.


2. To what resolution can we hear the effects of tuning?  And, how to we "parse" commas?

___ for example, if we had chosen a different note from Cloud Rhyme for the subminor 3rd, to what degree would it have an effect on the piece?  MORESO, could those different notes have a markedly more profound effect if given the proper context for their internal structure.  Say, the 11-lim neutral 3rd: 11:9.  Two of them make 121:81 (which is ~8¢ flat of 3:2).  This is almost identical to the 5th in 19EDO.  So why in 19EDO do we speak of the fifth as 3:2 instead of 121:81, and is there a situation in which 121:81 can have the resolution to exist as in independent entity, or is this tempering necessarily going to happen in the natural course of events.  For a reference, we are only stacking 2 intervals (though they are not a harmonic from the root).  3/2 and 3/2 make 9/8 which is commonly used as a whole tone and an important interval (however 3/2 is a natural harmonic *octave reduced).  Though 5/4 is as well, 25/16 is a bit odd, but not really foreign, as the third of the third.  *Thanks Aaron Wolf for sharing the idea yesterday of the pumping of a comma perhaps being interpreted by the brain as a syntax error.  How deep are we processing this syntax, and is it ever extending as we increase harmonic limit and train our ears to hear higher resolution differences?