|
Welcome to the International Skeptics Forum, where we discuss skepticism, critical thinking, the paranormal and science in a friendly but lively way. You are currently viewing the forum as a guest, which means you are missing out on discussing matters that are of interest to you. Please consider registering so you can gain full use of the forum features and interact with other Members. Registration is simple, fast and free! Click here to register today. |
9th October 2013, 06:44 AM | #121 |
Ardent Formulist
Join Date: Jun 2005
Location: Austin, TX
Posts: 15,334
|
|
__________________
To understand recursion, you must first understand recursion. Woo's razor: Never attribute to stupidity that which can be adequately explained by aliens. |
|
9th October 2013, 07:40 AM | #122 |
Ardent Formulist
Join Date: Jun 2005
Location: Austin, TX
Posts: 15,334
|
|
__________________
To understand recursion, you must first understand recursion. Woo's razor: Never attribute to stupidity that which can be adequately explained by aliens. |
|
24th January 2014, 05:34 AM | #123 |
Penultimate Amazing
Join Date: Jul 2006
Posts: 13,001
|
Scale design explanation, post 1
I want to try to describe a process of designing the scale/tuning I'm currently practicing, using screen-shots from Lil' Miss Scale Oven.
eta: If anyone wants audible examples, ask for something specific. I'll post a link. Every composer or performer seems to have different tastes and different premises. Here are mine: --Scale repeats at the octave (2:1 frequency ratio) --Standard off-the-shelf gear is assumed, so standard keyboards of -- sadly -- no more than 88 keys are being used. With two keyboards, and assuming at least a desired two octaves of range, this means one can have up to 43 pitches per octave, resulting in a total of 4 octaves of range. --Within the home key (1/1), the scale should be able to do everything that a 12-tone scale can do, and a lot more. --The home key can be changed by pitch-bending the whole thing ("modulation"). This means that some pitches can be omitted in the home key, but reached through pitch-bend. (Instruments are set to pitch-bend range +-12 semitones.) --The scale should have ratios with primes up to 13 ("13-Limit JI") but it's not necessary to have every product of every generating number. This is a tonal scale, with important pillars at 1/1, 3/2, 4/3, 9/8, 5/4. These important tones can/should have a wider space ("interval") around them. So we can eliminate near-duplicate pitches by choosing the more important pitches, or "tempering out" near duplicates -- splitting the difference, so to speak. Here we go. We can use the "waffle iron" feature to make a JI tonality diamond with overtones 8,9,10,11,12,13,14,15 on fundamentals ("undertones") /8,/9,/10,/11,/12,/13,/14,/15. (Click on this to see a larger size, or use a magnifying glass.) (more to follow) |
24th January 2014, 06:21 AM | #124 |
Penultimate Amazing
Join Date: Jul 2006
Posts: 13,001
|
LMSO will calculate the scale, displaying it in different formats. Already, we have 49 tones, which is too many. But there are several tones which are almost the same, so we can eliminate some. Already, there are some things that the JI scale doesn't do as well as a 12-tone scale, even without considering the big advantage of an equal-tempered scale: That it can work equally well from all starting-points, all "keys".
Here's what we have so far. Ratio from 1/1: 1/1, 16/15, 15/14, 14/13, 13/12, 12/11, 11/10, 10/9, 9/8, 8/7, 15/13, 7/6, 13/11, 6/5, 11/9, 16/13, 5/4, 14/11, 9/7, 13/10, 4/3, 15/11, 11/8, 18/13, 7/5, 10/7, 13/9, 16/11, 22/15, 3/2, 20/13, 14/9, 11/7, 8/5, 13/8, 18/11, 5/3, 22/13, 12/7, 26/15, 7/4, 16/9, 9/5, 20/11, 11/6, 24/13, 13/7, 28/15, 15/8 Cents from 1/1: 0., 111.731, 119.443, 128.298, 138.573, 150.637, 165.004, 182.404, 203.91, 231.174, 247.741, 266.871, 289.21, 315.641, 347.408, 359.472, 386.314, 417.508, 435.084, 454.214, 498.045, 536.951, 551.318, 563.382, 582.512, 617.488, 636.618, 648.682, 663.049, 701.955, 745.786, 764.916, 782.492, 813.686, 840.528, 852.592, 884.359, 910.789, 933.129, 952.259, 968.826, 996.09, 1017.596, 1034.996, 1049.363, 1061.427, 1071.702, 1080.557, 1088.269 Cents difference: 111.731, 7.712, 8.855, 10.275, 12.064, 14.367, 17.4, 21.506, 27.264, 16.567, 19.13, 22.339, 26.431, 31.767, 12.064, 26.842, 31.194, 17.576, 19.13, 43.831, 38.906, 14.367, 12.064, 19.13, 34.976, 19.13, 12.064, 14.367, 38.906, 43.831, 19.13, 17.576, 31.194, 26.842, 12.064, 31.767, 26.43, 22.34, 19.13, 16.567, 27.264, 21.506, 17.4, 14.367, 12.064, 10.275, 8.855, 7.712, 111.731 Anywhere we see a "cents difference" number of less than, say, 15 cents, it might be an opportunity to eliminate a pitch or to average the two numbers. From experience, the biggest flaw of this scale so far is that there is no good 4/3 (standard term: "4th") over 16/15, and no good 3/2 (standard term: "5th") over 15/8. That would be 45/32. Also, there's no 3/2 over 9/8: That would be 27/16. (standard term: "Pythagorean major 6th".) We might try to add these pitch-relations into our waffle iron generator, and see what happens: |
24th January 2014, 06:31 AM | #125 |
Penultimate Amazing
Join Date: Jul 2006
Posts: 13,001
|
Now we have 68 tones, and even more tiny intervals between pitches that are nearly the same, so we have to try to pare down even more:
1/1, 81/80, 45/44, 27/26, 16/15, 15/14, 14/13, 13/12, 12/11, 11/10, 10/9, 9/8, 8/7, 15/13, 7/6, 13/11, 32/27, 6/5, 11/9, 27/22, 16/13, 5/4, 81/64, 14/11, 9/7, 13/10, 4/3, 27/20, 15/11, 11/8, 18/13, 7/5, 45/32, 64/45, 10/7, 13/9, 81/56, 16/11, 22/15, 3/2, 32/21, 20/13, 14/9, 81/52, 11/7, 8/5, 45/28, 13/8, 18/11, 64/39, 5/3, 27/16, 22/13, 12/7, 45/26, 26/15, 7/4, 16/9, 9/5, 20/11, 11/6, 81/44, 24/13, 13/7, 28/15, 15/8, 27/14, 64/33 Cents differences: 21.506, 17.4, 26.431, 46.394, 7.712, 8.855, 10.275, 12.064, 14.367, 17.4, 21.506, 27.264, 16.567, 19.13, 22.339, 4.925, 21.506, 31.767, 7.139, 4.925, 26.842, 21.506, 9.688, 17.576, 19.13, 43.831, 21.506, 17.4, 14.367, 12.064, 19.13, 7.712, 19.552, 7.712, 19.13, 2.376, 9.688, 14.367, 38.906, 27.264, 16.567, 19.13, 2.376, 15.2, 31.194, 7.712, 19.13, 12.064, 4.925, 26.842, 21.506, 4.925, 22.339, 16.567, 2.563, 16.567, 27.264, 21.506, 17.4, 14.367, 7.139, 4.925, 10.275, 8.855, 7.712, 48.77, 9.688, 53.273 The smallest difference is the 2.4 cent difference between 636.6 cents and 639 cents, or the difference between 13/9 and 81/56. We can eliminate one of these pitches, or split the difference. The ultimate goal is to find an equal-tempered division of the octave ("EDO") that nearly matches our target collection of JI ratios. If we find the right one, it will do a good job of splitting the difference, or "tempering out" these tiny unwanted intervals. |
24th January 2014, 06:40 AM | #126 |
Penultimate Amazing
Join Date: Jul 2006
Posts: 13,001
|
Now there's a longish process of paring down so that we preserve the tones we really need all at once, and eliminate the ones we don't need.
One consideration -- opposed to the basic JI generating process -- is that whenever possible, we want any relationship that is a bad approximation of a 3/2 ratio to be corrected to give us a viable approximation of a 3/2. The longer the chains of 3/2's ("Pythagorean chains"), the more flexible our scale/tuning will be. Here's what I came up with, after a lot of teeth gnashing. LMSO has forgotten most the original ratios, but preserved the absolute cent values and differences: 256/243, 16/15, 13/12, 150.63533, 165.0025, 182.40198, 203.90827, 231.17236, 266.86917, 294.13327, 315.63956, 347.40621, 359.46888, 386.31196, 407.81825, 435.08234, 454.21219, 498.04324, 551.31618, 563.38058, 590.22196, 609.77277, 636.61585, 648.68025, 701.95319, 745.78424, 14/9, 11/7, 8/5, 13/8, 18/11, 5/3, 27/16, 12/7, 7/4, 16/9, 9/5, 20/11, 11/6, 24/13, 15/8, 243/128, 2/1* differences: 90.225, 21.506, 26.842, 12.062, 14.368, 17.399, 21.506, 27.264, 35.697, 27.264, 21.507, 31.766, 12.063, 26.843, 21.506, 27.264, 19.13, 43.831, 53.273, 12.065, 26.841, 19.551, 26.843, 12.064, 53.273, 43.831, 19.132, 17.576, 31.194, 26.842, 12.064, 31.767, 21.506, 27.264, 35.697, 27.264, 21.506, 17.4, 14.367, 12.064, 26.842, 21.506, 90.225 The smallest interval is a little over 12 cents. There are a number of bad 3/2's ("5ths") that we hope to improve when we choose an EDO (equal division of the octave). --------------------- *My keyboard has labels which I added to memorize this. These cent values closely correspond to: 1/1, 256/243, 16/15, 14/13, 12/11, 11/10, 10/9, 9/8, 8/7, 7/6, 32/27, 6/5, 11/9, 16/13, 5/4, 14/11, 9/7, 13/10, 4/3, 18/13, 7/5, 10/7, 13/9, 16/11, 3/2, 20/13, 14/9, 11/7, 8/5, 13/8, 18/11, 5/3, 22/13, 12/7, 7/4, 16/9, 9/5, 20/11, 11/6, 24/13, 15/8, 243/128, 2/1 |
24th January 2014, 06:55 AM | #127 |
Penultimate Amazing
Join Date: Jul 2006
Posts: 13,001
|
tempering out:
Some tones will have to do double duty. So, for example, 22/13 (910.8 cents) and 27/16 (905.9 cents) will have to be represented by the same pitch. More principles: --A little detuning actually sounds better (to me) than absolutely accurate JI, for most purposes. --Pitch-relations have a zone of acceptability. Outside the zone, they sound bad or like a different relation. The size of the zone varies -- according to taste, purpose, the relative delicacy of the relationship. Now I can use the Quantize feature of LMSO to find an EDO that will approximate my target set of 43 pitches. I can literally dial up through them using the mouse. This is the button selected here called "X srutis with less than _N_ cents mean deviation": LMSO cleverly lets you enter different expressions in the boxes, so I like to enter the "cents mean deviation" as a number over 99, to find all the possibilities. Dialing up, LMSO gives us the following sequence: 53, 72, 77, 87, 94, 118, 130, (171), 183, 217, 224, 270, 388, 400 (EDO). |
24th January 2014, 07:12 AM | #128 |
Penultimate Amazing
Join Date: Jul 2006
Posts: 13,001
|
These numbers have a history.
53 is the highest EDO considered by Harry Partch in _Genesis of a Music_. 72 is the EDO favored by the Boston Microtonal Society folks: Maneri, Sims, et al. 77 is the lowest EDO that almost works for my purposes. The sweet spot is 77, 87, 94, 118, 130, 171. 87 has 3/2 approximations that are a little too wide to make a long chain. 77, iirc, fudges the distinction between 20/11 and 11/6. 171 is damn good, but has more pitches than we want. --------------------------------------------- The bottom line 43 tones of JI, with a 13-limit, tempered to 94, 118, or 130 EDO. =========== Another bottom line: With a non-standard (or "generalized") MIDI keyboard, we don't need to be restricted to 43 pitches, so we can do a lot more. Problem is, if a generalized keyboard -- made by a small company -- breaks, or the company goes out of business, you end up with an expensive paper weight. This sort of thing has happened to me before, which is why I stick to off-the-shelf standard gear. The xenharmonic folks have developed the knowledge base to an amazing degree. I only understand about one-tenth of what they talk about, but that's enough. 94EDO:https://xenharmonic.wikispaces.com/94edo 118EDO:https://xenharmonic.wikispaces.com/118edo 130EDO:https://xenharmonic.wikispaces.com/130edo |
24th January 2014, 07:39 AM | #129 |
Penultimate Amazing
Join Date: Jul 2006
Posts: 13,001
|
One final refinement as part of the process.
http://pages.central.edu/emp/LintonT...Multiples.html to check my chains of 3/2 approximations. The idea is that, in a given EDO, an approximate 3/2 will be n many srutis, so this applet makes it easier to check the chains. [/url] Here, in 130EDO, I'm checking to see if my chain goes: 76,22,98,44,120,66,12,88,34,110. (It does.) If there's a near miss, perhaps the pitch should be adjusted. And, the same process on the 4/3 side, or inversion of 3/2. At some point, (at 9/5 and 5/3) the chain will end. That's JI without tempering out the 81/80 comma. Over time, I've been favoring longer 3/2 chains over more accurate higher-limit JI. With 43 tones, there are acceptable compromises. Here's a Scala format list of my scale, tempered to 94EDO. If you have a program that reads Scala format, you can just plug it in. ! 43T94edo 43 ! 89.36170 114.89362 140.42553 153.19149 165.95745 178.72340 204.25532 229.78723 268.08511 293.61702 319.14894 344.68085 357.44681 382.97872 408.51064 434.04255 459.57447 497.87234 548.93617 561.70213 587.23404 612.76596 638.29787 651.06383 702.12766 740.42553 765.95745 778.72340 817.02128 842.55319 855.31915 880.85106 906.38298 931.91489 970.21277 995.74468 1021.27660 1034.04255 1046.80851 1059.57447 1085.10638 1110.63830 1200.00000 and here's a slightly adjusted (tweaked) version of the same scale, tempered to 130EDO: ! 43T130edo tweak 43 ! 92.30769 110.76923 138.46154 147.69231 166.15385 184.61538 203.07692 230.76923 267.69231 295.38462 313.84615 350.76923 360.00000 387.69231 406.15385 433.84615 452.30769 498.46154 553.84615 563.07692 590.76923 609.23077 636.92308 646.15385 701.53846 747.69231 766.15385 793.84615 812.30769 840.00000 849.23077 886.15385 904.61538 932.30769 969.23077 996.92308 1015.38462 1033.84615 1052.30769 1061.53846 1089.23077 1107.69231 1200.00000 Under most circumstances, I don't hear the differences between 72 through 171EDO. It's only on certain intervals, with certain instruments, at an adequate volume level. |
24th January 2014, 08:46 AM | #130 |
Penultimate Amazing
Join Date: Jul 2006
Posts: 13,001
|
Another possibility to try is 106EDO (2x53). We should treat the numbers generated by LMSO with a grain of salt, and consider some other obvious possibilities. But there won't be that many more possibilities -- given my starting assumptions. http://xenharmonic.wikispaces.com/106edo At a glance, I notice that 106 doesn't do all that well with 8/7, 7/6, 7/4: the 7-limit intervals I want. But my ear may disagree. ! 43T106edo 43 ! 90.56604 113.20755 135.84906 147.16981 169.81132 181.13208 203.77358 226.41509 271.69811 294.33962 316.98113 350.94340 362.26415 384.90566 407.54717 430.18868 452.83019 498.11321 554.71698 566.03774 588.67925 611.32075 633.96226 645.28302 701.88679 747.16981 769.81132 781.13208 815.09434 837.73585 849.05660 883.01887 905.66038 928.30189 973.58491 996.22642 1018.86792 1030.18868 1052.83019 1064.15094 1086.79245 1109.43396 1200.00000 And, if I'm willing to go to 106 or 130, I might consider going to 3x53=159EDO, which is Ozan Yarman territory. Mr. Yarman has already forgotten more about tuning today than I'll every know my entire life: http://xenharmonic.wikispaces.com/159edo |
25th January 2014, 06:39 AM | #131 |
Penultimate Amazing
Join Date: Jul 2006
Posts: 13,001
|
Checking that it's true that 77 "fudges" the difference between 20/11 and 11/6.
20/11 = 1035 cents 11/6 = 1049.36 cents difference is 14.36 cents, is ratio of 1.0083291572750366 to 1, or 121:120. This comma (121:120) doesn't have a name, that I know of. http://www.mindspring.com/~alanh/fracs.html 77EDO has pitches at: 1028.6 cents, and 1044.15 cents, and 1059.74 cents. 20/11 will be quantized down by 6.4 cents, and 11/6 will be q'd down by 5.2 cents. 16/11 @ 648.68 cents will be quantized up 5.86 cents to 654.54 cents The total error of 20/11 over 16/11 (which ideally should be 5:4) is in 77edo now around -12.26 cents (too narrow.) That's too far. We also see in the microtonal wiki, that "77et tempers out 32805/32768 in the 5-limit, 126/125, 1029/1024 and 6144/6125 in the 7-limit, 121/120, ..." So I think that's confirmation of what bothers me about 77edo for my purposes. Now, mostly you wouldn't hear that. But if we're trying to design an elegant system that works as well as it can given our limitations, that's a flaw. The reason I found this is that I was practicing my scale tempered to 77edo and the interval between what was supposed to be 20/11 to 16/11 sounded wrong. So it was a matter of something hearable. I just didn't know exactly why until now. |
27th January 2014, 05:24 PM | #132 |
Penultimate Amazing
Join Date: Jul 2006
Posts: 13,001
|
Up until now, the scales I've composed in have been either overtone series scales or the more-or-less familiar gamut of 5-limit scales -- the familiar modes, Lydian b7 (a mode of melodic minor), and the modes of harmonic minor, the 6-note scales, and the diminished or octotonic 8-note scales.
This has begun to feel too limited. Why do microtones if you're going to limit yourself to familiar-sounding scales? And, the overtone series -- to my ear -- stubbornly resists being inverted, or made into modes. That is, higher prime harmonics (7, 11, 13) in these scales tend to sound out of tune if you use them in too low a register. So overtone series scales seem to resist being used modally. They seem a little inflexible. They're perfect and they just want to sit there, being perfect. I intend, therefore, to start trying to compose with hybrid scales that are neither overtone series nor traditional scales, but -- more or less -- have "half flat" intervals, as in Arabic or Turkish maqam. However, to avoid imitating the sound of that music, I hope to avoid the other features of Arabic music. I don't want to sound like I'm going for exoticism, trying to evoke the Middle East or something. By using non-Arabic instrumentation and composition, maybe I can use similar scales without sounding like I'm trying to charm snakes, or something. But it would be silly not at least to learn a little about what these scales are, because they are in a sense tried and true. Bayati, Rast, Sabba, Siga. Some names and some tradition to start with. The tuning is really more subtle than quarter-tones, but this article gives the gist: http://en.wikipedia.org/wiki/Quarter_tone I intend this post to remind me of approximately when I started thinking seriously about this stuff. |
28th January 2014, 03:06 PM | #133 |
Penultimate Amazing
Join Date: Jul 2006
Posts: 13,001
|
A little piece just over 4 minutes.
Called to first stagger chorale The thing I like about this are the shifts to different blocks in different registers. Kind of a punky late-Stravinsky-does-science-doc effect. And the emotional reserve of it. 77edo, but conventional scales. Self-similar thing again. https://app.box.com/s/hndecii3fygwtc54npqe |
1st February 2014, 06:37 AM | #134 |
Penultimate Amazing
Join Date: Jul 2006
Posts: 13,001
|
Another list of links to pieces.
Three early-middle period pieces, when I was trying harder: Clay's Way, for Violin and Tape https://app.box.com/s/q9dknyphurezkxy7z5bj Pay No Attention to That Man (tape-only version) https://app.box.com/s/i1sl2xch8xhfl7zfx3eb Widening Gyre (tape-only version) https://app.box.com/s/qhy4trmm4utar3ibu1nk ---------------------------------------------------------------- A recent piece that some people have liked: Opening the Window https://www.box.com/s/48wc435slumb9ano9cc9 (aif version) https://www.box.com/s/oo4tlpee811uj5j7a7g9 (mp3 version) About 12 1/2 minutes. Has a little of everything I know. ---------------------------------------------------------------- Other fairly recent pieces that also combine self-similarity, microtonal, and serial techniques: Chords with Figuration https://app.box.com/s/daf63fb69db30e7d2cb0 Starting and Stopping https://app.box.com/s/9pst9o65y6nx67w6lj3u Fugazzi https://app.box.com/s/au4esop559vae2353i4n Elusive Mr. Moy https://app.box.com/s/0ac8fd057b0c8e44c66a BEADS (lighten up, Dave) https://app.box.com/s/10s67yjq1sam01o49gc4 (see here, beginning of this thread, for more info) http://www.internationalskeptics.com...d.php?t=235850 -------------------------------------------------------- Some dreamy -- or perhaps logy -- piano pieces that apply the self-similar 12-tone idea: (from: You're Not There ) #1 -- https://app.box.com/s/j9l6i4crj879so3osy6n #2 -- https://app.box.com/s/chtzh22eubqd4qug3sx3 #3 -- https://app.box.com/s/4ydcshb2ltwv9san0j3d #4 -- https://app.box.com/s/at7297ejlobphgpexsm6 #8 -- https://app.box.com/s/gi33uqpfmx1476hul47s --------------------------------------------------------- Long "found sound" collages -- made partly from recordings I made outdoors: Brighton 10 https://app.box.com/s/ktcxgt617iv94dbmv6yy Only The Searing Incomprehensible https://app.box.com/s/pbw2co34gcdagvt0easj Commons March (Local protest against US military action, etc.) https://app.box.com/s/h8t3wfr4qimx2r7jc7pm --------------------------------------------------------- Some middle-period pieces that combine composition, sampling, collage: (from: Five Sample-Based Pieces) entire folder: https://app.box.com/shared/vdrhregp02 The Aswang (Voice of Lynda Barry) https://app.box.com/s/2dtjt9ue9jmzfhqwnykn Wife and Garden (based on BBC interview with Peter Maxwell Davies, etc.) https://app.box.com/s/11ibkzjq0c6uh5xpbfvi |
25th February 2014, 07:15 AM | #135 |
Penultimate Amazing
Join Date: Jul 2006
Posts: 13,001
|
I've been practicing scales from many starting-points (in many "keys"). This is a first step to learning more exotic scales. Learning the location of the pitches in a 43-note layout is challenging, especially at my age.
It took me something like 5 years of daily practice to learn an easier tuning (or layout) of 36 pitches per octave. Eventually I got fluent to the point that it was as easy to think with 36 pitches as it is with 12. It's a little like learning a second language, but also different. Someone might find this list of the standard scales useful. To practice in a variety of keys, I randomize: I roll a 12-sided die. The "keys" or starting-points I have least facility with currently are: 16/15, 10/7, 15/8. Plus the more exotic 8/7, 16/13, and 16/11. So I try to dwell on those. ===================================== Standard Scale List: (If anyone is curious or wants an explanation, I'd be happy to discuss this a little more.) The names of the altered modes are somewhat consistent, but not entirely. Lydian Ionian Mixolydian Dorian Aeolian Phrygian Locrian Lydian #5 Lydian b7 Ionian b3 Mixo b6 Dor. b2 Aeol b5 Locr. b4 Lydian #2 #5 Lydian b3 Ion. b6 or Har. major Mixo. b2 Dor. b5 Phryg. b4 Locr. bb7 Lyd. #2 Dor. #4 Aeol. mj7 (N7) Har minor Phryg. b4 Locr. mj6 (N6) Ion. #5 Locr. b4 bb7 whole-tone hex -- minor third hex -- half-step Oct. -- dim Oct. -- dom. There are also the basic overtone scales to practice in this layout. For example: 8/5, 9/5, 2/1, 11/10, 6/5, 13/10, 7/5, 3/2, (or 8:9:10:11:12:13:14:15:16 repeat at octave) After working on this basic stuff, the fun begins. Here are some scales with "half flats" that sound pretty good: 4/3, 13/9, 11/7, 16/9, 1/1, 14/13, 32/27 and a variation on Lydian: 1/1, 9/8, 11/9, 7/5, 3/2, 27/16, 11/6, 2/1 The ratios are approximate. These scales are easy to come up with, and immediately sound good to me. The resistance I encounter to learning them comes from their newness: I can't yet fit them into the same kind of systematic framework that I can -- and many others have done -- with the "standard" scales. |
11th March 2014, 06:23 AM | #136 |
Penultimate Amazing
Join Date: Jul 2006
Posts: 13,001
|
Based on recent work, thanks to W. D. Clinger, I was able to put together a more comprehensive list of scales to practice.
(generating rules here: http://www.internationalskeptics.com...86#post9883286) Of course, they can be varied according to exact tuning. In the 43-pitch JI scale I'm currently practicing (often tempered to 118EDO, but it doesn't really matter), some of the required quarter-tones aren't available starting from 1/1. This is one reason to practice in many keys. (I can't practice in all 43 keys.) A reasonable approximation of all these scales -- without the slight problem outlined above -- can be performed in 24edo (Quarter-tone tuning.) This tuning is -- for not very good reasons -- one of the less popular "xenharmonic" tunings. Possibly because it is obvious, well-known, and not "magical" in itself. But it sounds good if used with purposeful choices. Some of the "quarter-tone" scales outlined below sound even better when slightly altered to include 13-limit intervals. For example the ratio 13/8 is 840.5 cents, or 9.5 cents off from an exact quarter-tone. The list, um, comprises: > 65 7-note scales with quarter-tones, in 10 groups > rotations of maqam Saba, not part of the computer-generated list > 5-and-6 note "no wolf" sets in 5 groups > two additions > All the possible standard scales that conform to the "no 012" rule -- with only modal names given. (ask) > two more sets of scales/maqams that have one or more 012's. |
7th April 2014, 06:28 AM | #137 |
Penultimate Amazing
Join Date: Jul 2006
Posts: 13,001
|
I sorted the 65 7-note quarter-tone scales listed above in a different way -- by left-most packing to right-most packing. Mostly this is darkest-sounding to lightest, but not always. The advantage of this way of organizing them is that you can see how one note is altered by a quarter-tone. One quarter-tone difference between each scale. Both ways of grouping them are useful. If I were smarter, I wouldn't need this at all. These groupings are aids to learning. Now, I find myself feeling fatigued and bored and distracted when trying to tackle this stuff. This is a sign that I should shift gears and try a different approach. Maybe switch to composing with them. Or maybe see a doctor about type 2 diabetes. I'm not sure. I do know that my doctor made me feel like a piece of meat on my last visit, and she was hopeless when it comes to psychology or empathy, and terse when it comes questions of ¿evidence? Apparently, what she cannot speak of she passes over in silence. Because being treated like an object is disheartening, and I'm vulnerable to such treatment, I can predict that this will make me feel worse for a long time. So a little analysis of this project is in order. Persistence is necessary. But if I persist on the wrong tack, I will have wasted my remaining time. I'm 55, there isn't all that much time left. I'm trying to learn a 43-pitch non-tempered geography, and also trying to learn 24-pitch-equal geography -- much, much easier, but not easy. With the quarter-tone scales, it's not hard to sit on one and jam with it. But I'm mystified about how to connect one scale with a different scale, so far. Maybe: It's not as strange as you think: Just do it. As Peachy Carnahan says, "We've got to brass it out, Danny. Brass it out." or as they say in AA: Fake it 'til you make it. I need the "joy and fierceness" of an Arnold in Pumping Iron. He set absurd goals for himself and somehow attained them. How to shut off the inner captious critic -- that niggling, nattering, nabob of negativism. How to not be scared by the inner Professor Terguson: "I hold music theory sacred. Sacred like a farmer holds the soil. So why don't we dive right in, and tackle one of the easiest forms of microtonality -- the quarter-tone." http://www.youtube.com/watch?v=QKBfT--rwmc It's possible to be too committed. |
16th April 2014, 09:13 AM | #138 |
Penultimate Amazing
Join Date: Jul 2006
Posts: 13,001
|
The answer to the above is, unsurprisingly, an adjustment to practice habits and expectations.
But surprisingly, there's also a technical fix. This would be to practice something very close to the 43-note fingering, but with exact quarter-tones, and with all possible quarter-tones available. That way, the strain on your elderly canine brain is reduced: You're not trying to practice two entirely different kinds of fingerings. This can be accomplished by taking a 43EDO scale and quantizing it to 48EDO to get the exact quarter-tones, then adjusting just a few pitches. Scala file here: |
11th June 2014, 04:05 AM | #139 |
Penultimate Amazing
Join Date: Jul 2006
Posts: 13,001
|
Death of Lee Hyla, composer
Lee was the chairman of the Composition Department at NEC when I was an adjunct prof there.
He was a good composer and a straight shooter. http://www.bostonglobe.com/metro/obi...vFJ/story.html I like this quote -- especially this first line that I bolded -- from the obit:
Quote:
|
26th June 2014, 01:30 AM | #140 |
Penultimate Amazing
Join Date: Jul 2006
Posts: 13,001
|
https://app.box.com/s/b70b56cwmutzmbkkn2vk (15 minutes of spacy, moody music with lots of filter-whooshes) From this series, I had the computer find this: p/0/0:...............A B F# E D Bb C# C G Ab F Eb 5x/i/3/0:............C D Eb C# B G E A Bb F Ab F# 5p/i/11/7:...........D Eb A B F Ab G C C# Bb F# E p/3/1:...............D A G F C# E Eb Bb B Ab F# C which is spread out over 15 minutes... Made a good bed from this. I'm going to try to add more, maybe change a lot. But as this stands, it could be good video-game music, or something. The tuning is slightly different from 12-tone, so that gives some of the chords a different resonance, but it's really 5-limit music -- meaning it doesn't sound that unusual. The filtering gives it all that chugging rhythm. |
29th June 2014, 09:13 AM | #141 |
Penultimate Amazing
Join Date: Jul 2006
Posts: 13,001
|
https://app.box.com/s/4pky8bwrr6t9wtxvn91b
This started to seem awfully fatiguing, like jogging through glue, so I cut some and eq'd some of the mids out. This is better, but still not all that good. As they say: Life sucks, then you die. |
29th June 2014, 04:53 PM | #142 |
Penultimate Amazing
Join Date: Jul 2006
Posts: 13,001
|
https://app.box.com/s/5ff55ygoa55f336vwqwy
More effects, more filtering. One technique that ended up working just as I'd hoped was convolving a version of this with a classical piece (had to tune the classical piece up 50 cents) using the convolution in SoundHack. This is as good as this idea is going to get. My wife is a good critic. She says that this fails to hold her interest and doesn't give her that sense of telling a story. She's never wrong about this kind of thing. So, not one of my greatest hits. But it has some production tricks new to me, so that's something. Another dystopian landscape piece, another false start. Next. |
23rd July 2014, 07:29 AM | #143 |
Penultimate Amazing
Join Date: Jul 2006
Posts: 13,001
|
https://app.box.com/s/g492do0y32vk97z50s15
the piece in the folder here called 2,3,4,5,6, git for bell bet.aif is -- at this stage in the process -- just an accretion of different speeds, each assigned to a different instrument. But it makes for a very pleasing, serene texture, with ominous looming chords. About 3/12 minutes. Future work will add more layers, then remove, sculpt, and shape. |
23rd July 2014, 12:01 PM | #144 |
Graduate Poster
Join Date: Mar 2003
Location: West London
Posts: 1,126
|
|
24th July 2014, 04:32 AM | #145 |
Philosopher
Join Date: May 2007
Posts: 6,900
|
I agree; that was very nice. In the foreground arpeggios, the quarter-tones (or are they eighth-tones? moving from 12 semitones to 48 then truncating 5... never mind; that's what i get for cutting class) don't sound strange at all, more like fragile bridges between familiar pitches; while the harmonies with the background do sound strange, slightly ominous but without overwhelming the foreground serenity, like listening to the sounds of a storm that has passed (that might return, or might not); the addition of the metronomic zillWP notes between 2,3,4,5,6 ruf and 2,3,4,5,6 bell bet give it a balancing 'calm on the horizon' feel. Looking forward to future work (& works) along these lines.
|
__________________
"Say to them, 'I am Nobody!'" -- Ulysses to the Cyclops "Never mind. I can't read." -- Hokulele to the Easter Bunny |
|
30th July 2014, 09:16 AM | #146 |
Penultimate Amazing
Join Date: Jul 2006
Posts: 13,001
|
Thanks for the nice comments, both a' yuh.
And yes, the "zill" was the late addition -- it sounds calm and metronomic, just as you say. I worried that it is too metronomic. Very perceptive comments as usual, Blobru-san. I'm going to leave this piece as is, but do another piece in a similar (self-similar) vein. One thing I've been struggling with, or at least testing, is whether altered tunings work with self-similar generation technique. They tend to be funky, because -- unlike music based on other techniques than self-sim -- every note gets combined with every other note in the tuning. That's the way this self-sim technique works out. If every note of a just-intonation major scale gets combined with every other note, sooner or later you'll hit a "wolf". JI tuning of C major scale: (Note: It's conventional to use fractions to denote ratios. They're the same thing, here. That is, 9/8 means 9:8 here.) 1/1, 9/8, 5/4, 4/3, 3/2, 5/3, 15/8 (C,D,E,F,G,A,B) The wolf, or bad interval, here is the 5/3 against 9/8. Hearing this, one substitutes 27/16 for 5/3. But then that's out of tune with 5/4. So one grimaces and substitutes 81/64 for 5/4. But that's out of tune with 15/8. So one ends up with a Pythagorean tuning for a major scale. In this kind of self-similar texture, one might as well use good ol' 12-tone equal temperament tuning for a major scale. Or one can learn to tolerate a wolf or two, or some equivocation between different versions of a pitch. In the piece linked to above, there's some subtle funkiness and a few discrepancies that I didn't fix. The moral is that self-sim technique and simple JI tuning don't play that well together. They can co-exist, but with little advantage and some strain. |
30th July 2014, 09:30 AM | #147 |
Penultimate Amazing
Join Date: Jul 2006
Posts: 13,001
|
Random notes -- some things I've been saving up.
I recently heard Not Lilacs by composer and theorist Robert Morris. http://www.mp3olimp.net/robert-morris-not-lilacs/ To my surprise, this sounds jazzier than it does self-similar or 12-tonish. Other so-called Third Stream pieces tend to err on one side or another -- either they don't swing (Babbitt, and for different reasons, Schuller) or they don't have much in the way of 12-tone rigor. Having heard this, I felt freer to pursue my own exploration of self-similar techniques, because I'm hearing that this piece doesn't seem that interested in making self-similarity audible. But it was rather fresh and pretty hip, especially compared to Babbitt -- an entirely different kind of composer. ============================= I volunteer at the library perpetual book-sale, so I get first dibs on the CD's and music books that the library is culling. It's slightly sad to see Pierre Boulez' _Notes of an Apprenticeship_ being culled, along with his recordings. He was (and is) a giant, but even here in the Athens of America, no one is reading him or listening to him. Except me. I find the atmosphere of high intellectualism and historical awareness a little stimulating, but mostly oppressive. It's hard to feel inspired by someone who would certainly think I was an ignorant hick. Hard to enjoy banging out a pretty chord when Pierre is talking about historical necessity. Thing is, for all that brilliance and knowledge, I don't find his music (Repons, etc.) all that compelling or interesting. He relies a lot on massive twittering textures -- slightly angry birds. |
30th July 2014, 11:43 AM | #148 |
Penultimate Amazing
Join Date: Jul 2006
Posts: 13,001
|
|
22nd August 2014, 11:14 AM | #149 |
Penultimate Amazing
Join Date: Jul 2006
Posts: 13,001
|
This is just the generators -- not the finished piece -- but it makes a nice minimalist piece in itself. Very happy with this.
Having trouble linking to file, but the folder is here. https://app.box.com/s/2ue7l0ujnsnj61dqtzrr The piece is titled wrong here: It's called 3 ^n mod 17 skel2, but it really should be 11 ^ n mod 17 skel2 |
24th August 2014, 05:01 PM | #150 |
Penultimate Amazing
Join Date: Jul 2006
Posts: 13,001
|
now titled Intelligent Pacman. I added a next layer to the first 4 minutes.
Sythesis sounds a little cheesy. Folder: https://app.box.com/s/g492do0y32vk97z50s15 |
31st August 2014, 06:09 AM | #151 |
Penultimate Amazing
Join Date: Jul 2006
Posts: 13,001
|
Some notes before my next piece -- to clarify my thinking, and to come back to later to see how they worked out.
-- The little innovation that makes this different from previous self-sim pieces is that the series will be only gradually explicitly stated; mostly, at first, it will be rests -- with the total result being a combination of series within the master-cycle. -- 12 tone et. -- 17-beat cycle (which is a given with a 16-note series, if you want to have all self-similar speeds available.) -- series mapped to mostly 7-note scales. This is a mapping that works well, for a bunch of reasons. Series is a permutation of indices of 3 ^ n mod 17. Like all such series, this is self-identical at every other note from the second note, every third note from the third note, every nth note from the nth note. Table of "master cycle", here: Base: 3 Mod: 17 9, 7, 10, 5, 14, 8, 4, 3, 11, 12, 0, 6, 13, 2, 15, 1 7, 5, 8, 3, 12, 6, 2, 1, 9, 10, 14, 4, 11, 0, 13, 15 5, 3, 6, 1, 10, 4, 0, 15, 7, 8, 12, 2, 9, 14, 11, 13 3, 1, 4, 15, 8, 2, 14, 13, 5, 6, 10, 0, 7, 12, 9, 11 1, 15, 2, 13, 6, 0, 12, 11, 3, 4, 8, 14, 5, 10, 7, 9 15, 13, 0, 11, 4, 14, 10, 9, 1, 2, 6, 12, 3, 8, 5, 7 13, 11, 14, 9, 2, 12, 8, 7, 15, 0, 4, 10, 1, 6, 3, 5 11, 9, 12, 7, 0, 10, 6, 5, 13, 14, 2, 8, 15, 4, 1, 3 8, 6, 9, 4, 13, 7, 3, 2, 10, 11, 15, 5, 12, 1, 14, 0 6, 4, 7, 2, 11, 5, 1, 0, 8, 9, 13, 3, 10, 15, 12, 14 4, 2, 5, 0, 9, 3, 15, 14, 6, 7, 11, 1, 8, 13, 10, 12 2, 0, 3, 14, 7, 1, 13, 12, 4, 5, 9, 15, 6, 11, 8, 10 0, 14, 1, 12, 5, 15, 11, 10, 2, 3, 7, 13, 4, 9, 6, 8 14, 12, 15, 10, 3, 13, 9, 8, 0, 1, 5, 11, 2, 7, 4, 6 12, 10, 13, 8, 1, 11, 7, 6, 14, 15, 3, 9, 0, 5, 2, 4 10, 8, 11, 6, 15, 9, 5, 4, 12, 13, 1, 7, 14, 3, 0, 2 This is a fairly well-known series, fwiw. http://www.google.com/search?q=%220%...bv=2&oq=&gs_l= And the other thought -- or resolution -- that I have going in is that I have to be inhumanly patient -- to not get excited or discouraged by what I'm hearing until the overall design is complete. That's hard, because it's always an exciting thing that a bunch of numbers seems to acquire a character, a life, of its own. Think about what a monster of toughness, of stick-to-itness, Beethoven was! He didn't say: "Oh, this sounds pretty good, I'll just go with this sketch." He re-wrote and re-wrote and re-wrote. |
10th September 2014, 07:41 AM | #152 |
Penultimate Amazing
Join Date: Jul 2006
Posts: 13,001
|
https://app.box.com/s/g492do0y32vk97z50s15 folder
File name: generators137 This is the minimalist piece resulting from only taking the two original generators, as described in the recipe below. The chord changes don't start until about a minute in. Recipe: |
12th September 2014, 05:43 PM | #153 |
Penultimate Amazing
Join Date: Jul 2006
Posts: 13,001
|
This has the next layer, the 1:2 half-speed layer. It sort of grooves in a nerdish way:
https://app.box.com/s/g492do0y32vk97z50s15 called generators137q3 |
18th September 2014, 08:41 AM | #154 |
Penultimate Amazing
Join Date: Jul 2006
Posts: 13,001
|
added layers, took out fastest, faded in so harmony moves faster at beginning.
This is quite a catchy combination of cross-rhythms. called bc 2,3,4,8 layers Folder: https://app.box.com/s/g492do0y32vk97z50s15 |
20th September 2014, 10:17 AM | #155 |
Penultimate Amazing
Join Date: Jul 2006
Posts: 13,001
|
In this somewhat odd process, before I can sculpt, I have to layer more tracks.
There are about 10 layers. When the adding is done, there will be around 18 to 20. Things in some ways are getting less interesting even as the texture gets richer, so I have to resist the feeling that the piece is getting worse. It's not, just overgrown. When I'm done adding, I'll start to remove most of what I've put in, using midi volume commands. In this particular sketch version, the bass is pounding out every 8th beat -- it's mixed way too loud. I tried using a multiband compressor to correct this, but further research is needed, as they say. https://app.box.com/s/g492do0y32vk97z50s15 Same folder, piece is called bc 10 layers. |
22nd September 2014, 12:34 PM | #156 |
Penultimate Amazing
Join Date: Jul 2006
Posts: 13,001
|
from: http://www.logicprohelp.com/forum/viewtopic.php?t=75126
Quote:
Once again, I struggle with Logic Pro 8 only to learn that there is an unfixed bug. There are so many things like this with Logic Pro. The program is so big and complicated that -- clearly -- they haven't tested it thoroughly, or they figured it wouldn't hurt sales that much if there were a few "obscure" bugs. Like Target. Tons of stuff. Quality mixed. Thing is, it's taken me years to get comfortable with this program. I don't want some new version that's redesigned. I want something that is exactly the same, except it works the way it's supposed to -- or has some really deep incremental improvements. Anyway. The piece now has 12 layers, and quite a few mix fixes. I expect to start shaping this block in about a week, maybe less. https://app.box.com/s/g492do0y32vk97z50s15 same folder version is called bc 12L m2 I'm excited about this -- about the cyber-bluegrass quality, and about the potential for making the self-similar aspect really clear. There's a way that this generating process creates repetition with slow change. That's interesting, also. |
23rd September 2014, 02:37 PM | #157 |
Penultimate Amazing
Join Date: Jul 2006
Posts: 13,001
|
https://app.box.com/s/g492do0y32vk97z50s15
name: bc channel mutes1.aiff This is the first version of this piece that I'd say is worth hearing for contrasts and textural changes. I'm maybe half-way through the whole process. Having finished the layers, I did a quick improv (captured with Audio Hijack Pro) by muting and unmuting channels, to build up and to thin out the texture. Heh. My version of Audio Hijack is a demo, so I can only capture about ten minutes. (Which is quite long enough for this version.) What's missing is the precision required to make the self-similarity element come through clearly. That will take more work. And, also, required would be more precision in bringing in the materials, to force the listener to hear certain meters. I myself can't hear this in 5, only in duples or triples. Perhaps one or two more versions to post, to complete the process. These after a lot of trial and error. |
25th September 2014, 02:04 PM | #158 |
Penultimate Amazing
Join Date: Jul 2006
Posts: 13,001
|
Well, a little trial, maybe some error.
https://app.box.com/s/g492do0y32vk97z50s15 version is called: bc 66 fx1 There is, at this stage, a strong temptation to call a piece done. Like the temptation to lie down in the snow and rest for a while. Feel pretty warm, maybe even take off my coat. Such nice, restful snow. NO! Must. Keep. Going. If I'm going to do a sort of block piece, this version is adequate. But if I want to stick to my original idea, then it's a failure. Today I added some effects, changed a bunch of other things. The effects are for the purpose of introducing slow changes of timbre, of spectrum. With slow changes, the repetitions become less abrasive, less monotonous. The balances are always changing, with different instruments fading in and out, slightly. So the effects help -- they're not just there to make it sound weird. When I took some classes with Mike Gibbs at Berklee a long time ago, he had a simple but effective approach to arranging. He'd suggest that you ask yourself how you felt about whatever the given material was. Then, how you'd like it to be different. Then, what techniques or instruments would achieve that goal. Mostly, this worked well. But, once, he played us a horrible arrangement -- what he called "Hollywood Strings" -- of a Satie piano piece that he'd done. Big lush textures. Added notes all over the place. Saccharin and schmaltz. I asked him, appalled, "Why did you do that?" He said: "I was bored with it." He'd made it different, all right. From something exquisite into something...hideous. But mostly, he was pretty tasteful. Good teacher, too, in a kind of mellow way. |
30th September 2014, 09:18 AM | #159 |
Penultimate Amazing
Join Date: Jul 2006
Posts: 13,001
|
https://app.box.com/s/g492do0y32vk97z50s15
For some reason, I can't link to the individual piece, but the folder is here. A final version, rough mix. Called 3 to the n mod 17. I'm pretty happy with the way some of this turned out. |
6th October 2014, 06:51 AM | #160 |
Penultimate Amazing
Join Date: Jul 2006
Posts: 13,001
|
On to the next. Some theory of generating rows. An attempt at a quick explanatory sketch. One tendency that guides my composition is that I simply try to do something different from the last piece. One pole of difference -- so to speak -- is between starting materials that are nearly perfect and regular, and materials that are irregular -- but which have some attributes that are interesting. Along with the starting materials goes an overall intention, a vaguely-conceived world of sound. This piece is going to be less obviously patterned, less reliant on automatic polyrhythms. Working title: Caleb's Inner Spinach. The only "perfect" series that I'm aware of are the series made by the indices of power-residues. For example, the indices of 2 ^ n mod 13. My last piece was based on the series from 3 ^ n mod 17 -- a 16-note series. Because the series was based on this power-residue formula, it easily generated lines that are related to each other, but are going at different speeds, all adding up to one big composite line -- from which each strand "grabs" notes. This next piece will be based on a less well-known, less familiar generating process. No metronomic ticking this time. Rather, dense jungle. Dense inner jungle. Hence, inner spinach. One problem with power-residue series is that there are only a few of them. (For example, 2 ^ n mod 13 generates 0,1,4,2,9,5,11,3,8,10,7,6, or C,C#,E,D,A,F,B,Eb,Ab,Bb,G,F#, also known as the Mallalieu series, or all-interval series number 44, using the numbering system of Morris and Starr.) There ain't no other 12-tone series that are perfect in this way, apart from the row-complex based on this series. But by relaxing or altering some constraints, we can find a wealth of series; a trove; indeed, a vast, rich panoply of series, enough for a lifetime of work -- should one be so inclined. To generate the series I might use for Inner Spinach, the constraints to be altered are: 1) regular permutation 2) exact self-similarity so that, 1) The series can have a similar embedded series which skips every 2,3, or 4 pitches and 2) The similar, embedded series is a transposition of the original series, but + or - 1 semitone. An additional difference is that now I can look to see whether there are series that are self-similar at some other interval rather than 1 semitone. In the example below, the series is self-similar at 2 semitones, + or - 1 semitone. To help systemize the search, I made an exhaustive list of all possible "expansion" series. After a lot of trial and error, of brute-force computer searches, I'm choosing permutation pattern #30: 0 2 4 7 B 3 6 8 A 1 5 9 *** 30.234 223443223443 This makes complete orbits with a chromatic scale (0,1,2,3,4,5,6,7,8,9,10,11) in the following 4 ways, (here written as "user row" and "grid row": Now that I'm assured of finding something, I can plug these numbers into one of my apps: Here I'm eliminating any series whose contiguous notes produce "harmonies", or cells, that I don't want. And, that produce undesired cells in the permutation and the permutation of the permutations as well. There are only 4 series found. On closer examination, these are really only two distinct series. The first and fourth are the same, and the second and third are the same. I'm calling the second series "All Permutations 026", or "AP 026", because of its many 026 cells. While I don't usually use series that contain whole-tone scales, maybe I'll make an exception. I've been listening to a little Boulez, and maybe I'm allowing a litle French influence to creep in. Here's the permutation matrix of the series. The second row is the embedded series found in the first row. The columns produce a regular sequence of 1,2, or 3 semitones -- a fairly tight "family resemblance" between all series. And no row in the matrix contains the hated 0369 chord -- instant failure -- or the equally hated triad-with-added-6th, or a dominant-seventh chord, or a 2-adjacent-semitone cluster -- 0,1,2. Working along these lines, I've also come up with five other series. I'm not sure if I'll choose only one, or whether I'll write six separate pieces -- an Inner Spinach Suite, perhaps. |
Thread Tools | |
|
|