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Typical spectra from five different regions.
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| Spectrum # 27 |
Spectrum #150 |
Spectrum #200 |
Spectrum #299 |
Spectrum #501 |
1, 102.73 0.000406;
2, 189.54 0.000287;
3, 247.48 0.000388;
4, 325.56 0.000149;
5, 402.96 0.000556;
6, 515.69989 0.000255;
7, 588.77002 0.000127;
8, 664.969971 0.000114;
9, 741.52 0.000261;
10, 898.90 0.000138;
11, 1074.25 0.000335;
12, 1080.84 0.000185;
13, 1208.52 0.000104;
14, 1243.73 0.000142;
15, 1384.01 0.000168;
16, 1491.96 0.000103;
17, 1578.68 0.000113;
18, 1640.39 0.000176;
19, 1857.25 0.00009;
20, 2215.92 0.000108;
21, 2293.81 0.000117;
22, 2294.10 0.000103;
23, 2696.56 0.000101;
24, 2766.48 0.000097;
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1, 42.32 0.002289;
2, 161.38 0.001966;
3, 240.71 0.010502;
4, 281.04 0.019742;
5, 393.35 0.006564;
6, 461.66 0.004629;
7, 510.61 0.00339;
8, 614.60 0.001719;
9, 672.34 0.001289;
10, 746.16 0.001492;
11, 819.02 0.000481;
12, 918.42 0.000719;
13, 980.44 0.000744;
14, 1035.26 0.000924;
15, 1115.85 0.001549;
16, 1211.43 0.001399;
17, 1265.98 0.001934;
18, 1353.09 0.000955;
19, 1522.85 0.000251;
20, 1579.85 0.000252;
21, 1657.92 0.000465;
22, 2232.92 0.000277;
23, 2254.14 0.000577;
24, 2326.82 0.000346;
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1, 56.15 0.002908;
2, 159.42 0.00169;
3, 229.97 0.000474;
4, 319.48 0.000824;
5, 497.84 0.000304;
6, 614.63 0.000134;
7, 623.52 0.000237;
8, 700.92 0.00012;
9, 784.03 0.000063;
10, 851.21 0.000117;
11, 959.19 0.00022;
12, 1054.93 0.00011;
13, 1107.14 0.00004;
14, 1304.76 0.000122;
15, 1418.68 0.000059;
16, 1481.14 0.00006;
17, 1644.00 0.000039;
18, 1890.64 0.000038;
19, 1993.53 0.000054;
20, 2065.57 0.000039;
21, 2335.64 0.00004;
22, 2797.28 0.000039;
23, 3122.45 0.00005;
24, 3260.09 0.000038;
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1, 189.11 0.002685;
2, 286.35 0.008844;
3, 411.55 0.009397;
4, 509.98 0.02783;
5, 599.31 0.005647;
6, 691.43 0.0057;
7, 815.32 0.010416;
8, 920.34 0.005869;
9, 942.91 0.005315;
10, 1056.31 0.006888;
11, 1202.61 0.004601;
12, 1353.10 0.009476;
13, 1439.47 0.003693;
14, 1530.75 0.021652;
15, 1558.65 0.004553;
16, 1683.80 0.003261;
17, 1749.76 0.003415;
18, 1830.10 0.002067;
19, 1917.61 0.001172;
20, 2076.85 0.003231;
21, 2169.67 0.00357;
22, 2248.68 0.002475;
23, 2326.06 0.002285;
24, 2874.72 0.001436;
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1, 99.36 0.000246;
2, 236.98 0.000443;
3, 298.09 0.000206;
4, 356.08 0.000239;
5, 546.65 0.000311;
6, 577.84 0.000107;
7, 732.05 0.000123;
8, 830.30 0.000073;
9, 905.47 0.000065;
10, 976.90 0.000082;
11, 1085.23 0.000093;
12, 1317.03 0.000038;
13, 1397.47 0.000047;
14, 1504.69 0.000072;
15, 1598.52 0.000066;
16, 1690.39 0.000029;
17, 1933.15 0.000064;
18, 2104.56 0.000037;
19, 2435.38 0.000036;
20, 2668.31 0.00003;
21, 2782.48 0.000034;
22, 3123.71 0.000035;
23, 3792.86 0.000031;
24, 4111.43 0.000029; |
- Data format: Index, Frequency Ampltude;
Translation into MIDI Cents and key velocities:
- Negative key velocities belong to partials below the hearing threshold.
- (In the MIDI example the velocities are normalized, so that some of the weaker partials are audible.)
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Spectrum #200
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- 1, 3336 41;
- 2, 5143 33;
- 3, 5777 14;
- 4, 6346 23;
- 5, 7114 8;
- 6, 7479 -3;
- 7, 7504 4;
- 8, 7706 -5;
- 9, 7900 -14;
- 10, 8042 -5;
- 11, 8249 3;
- 12, 8414 -6;
- 13, 8498 -21;
- 14, 8782 -5;
- 15, 8927 -15;
- 16, 9001 -15;
- 17, 9182 -21;
- 18, 9424 -22;
- 19, 9516 -17;
- 20, 9577 -21;
- 21, 9790 -21;
- 22, 10102 -21;
- 23, 10293 -18;
- 24, 10367 -22;
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- Data format: Index, MIDI Cent Velocity;
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Translation into musical notation
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- Click on image to hear a MIDI representation of this spectrum.
- Although this spectrum was extracted out of the answering-machine noise, it clearly displays the typical characteristics of a harmonic spectrum: Large intervals in the lower frequency region and increasingly smaller ones towards the higher region. This is due to a (desired) artifact of the analysis program.
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- Automatic translation of microtonal music into the Finale™ Enigma data format can be achieved by velocoding standard MIDI sequencer files; i.e. instead of using 7 bits (numbers 0 to 127) to code the velocities of the given notes, only 10 numbers are used for the dynamics (pppp to ffff) times 8 numbers for the eighth-tone deviations (from -2 8th tones to +5 8th tones).
- Once the velocoded files are transcribed by Finale into the Enigma text format (preserving the key velocities, of course), the resulting files can be altered by a MAX patch, making use of Finale’s non-standard tuning capabilities.
- For this, the MAX patch looks up the velocoded key velocities, creates dynamic markings and changes the pitch data accordingly (Finale allows a maximum of 16 steps per whole tone to which musical symbols can be assigned arbitrarily).
- This modified Enigma file can be reopened in Finale. The microtonal deviations should now display correctly.
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