Yahoo Tuning Groups Ultimate Backup makemicromusic EDOs

I've been looking at EDOs and it seems to me that 12EDO works so well because it contains both a Perfect Fourth (4/3) and a Perfect Fifth (3/2) within 2.0 cents accuracy in all keys. My favorite musical genres are Blues and Rock and this music is usually made using Fourths and Fifths which are the strongest intervals that occur between the tonic and octave. Based on this I suspect that the best EDOs are those that contain a Fourth and Fifth within 6.776 cents (256/255) accuracy. The 6.776 cents threshold is my own best guess at maximum deviation from pure and I do not claim that it should be set in stone.

I looked at all EDOs from 1EDO to 48EDO and below is a complete list of all EDOs (from 1 to 48) which contain a Fourth and Fifth within 6.776 cents accuracy.

With 12EDO there are 4 good (within +/-6.776 cents accuracy) intervals (see below) an octave or less wide: 9/8, 4/3, 3/2 and 2/1.

With 31EDO there are 14 good (within +/-6.776 cents accuracy) intervals (see below) an octave or less wide: 8/7, 7/6, 6/5, 5/4, 4/3, 7/5, 10/7, 3/2, 8/5, 5/3, 12/7, 7/4, 11/6, 2/1.

12EDO, 4 good
0.0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200

17EDO, 4 good
0.0, 70.5882, 141.176, 211.765, 282.353, 352.941, 423.529, 494.118, 564.706, 635.294, 705.882, 776.471, 847.059, 917.647, 988.235, 1058.82, 1129.41, 1200

24EDO, 6 good
0.0, 50, 100, 150, 200, 250, 300, 350, 400, 450, 500, 550, 600, 650, 700, 750, 800, 850, 900, 950, 1000, 1050, 1100, 1150, 1200

29EDO, 8 good
0.0, 41.3793, 82.7586, 124.138, 165.517, 206.897, 248.276, 289.655, 331.034, 372.414, 413.793, 455.172, 496.552, 537.931, 579.31, 620.69, 662.069, 703.448, 744.828, 786.207, 827.586, 868.966, 910.345, 951.724, 993.103, 1034.48, 1075.86, 1117.24, 1158.62, 1200

31EDO, 14 good
0.0, 38.7097, 77.4194, 116.129, 154.839, 193.548, 232.258, 270.968, 309.677, 348.387, 387.097, 425.806, 464.516, 503.226, 541.935, 580.645, 619.355, 658.065, 696.774, 735.484, 774.194, 812.903, 851.613, 890.323, 929.032, 967.742, 1006.45, 1045.16, 1083.87, 1122.58, 1161.29, 1200

34EDO, 9 good
0.0, 35.2941, 70.5882, 105.882, 141.176, 176.471, 211.765, 247.059, 282.353, 317.647, 352.941, 388.235, 423.529, 458.824, 494.118, 529.412, 564.706, 600, 635.294, 670.588, 705.882, 741.176, 776.471, 811.765, 847.059, 882.353, 917.647, 952.941, 988.235, 1023.53, 1058.82, 1094.12, 1129.41, 1164.71, 1200

36EDO, 10 good
0.0, 33.3333, 66.6667, 100, 133.333, 166.667, 200, 233.333, 266.667, 300, 333.333, 366.667, 400, 433.333, 466.667, 500, 533.333, 566.667, 600, 633.333, 666.667, 700, 733.333, 766.667, 800, 833.333, 866.667, 900, 933.333, 966.667, 1000, 1033.33, 1066.67, 1100, 1133.33, 1166.67, 1200

39EDO, 10 good
0.0, 30.7692, 61.5385, 92.3077, 123.077, 153.846, 184.615, 215.385, 246.154, 276.923, 307.692, 338.462, 369.231, 400, 430.769, 461.538, 492.308, 523.077, 553.846, 584.615, 615.385, 646.154, 676.923, 707.692, 738.462, 769.231, 800, 830.769, 861.538, 892.308, 923.077, 953.846, 984.615, 1015.38, 1046.15, 1076.92, 1107.69, 1138.46, 1169.23, 1200

41EDO, 17 good
0.0, 29.2683, 58.5366, 87.8049, 117.073, 146.341, 175.61, 204.878, 234.146, 263.415, 292.683, 321.951, 351.22, 380.488, 409.756, 439.024, 468.293, 497.561, 526.829, 556.098, 585.366, 614.634, 643.902, 673.171, 702.439, 731.707, 760.976, 790.244, 819.512, 848.78, 878.049, 907.317, 936.585, 965.854, 995.122, 1024.39, 1053.66, 1082.93, 1112.2, 1141.46, 1170.73, 1200
41 = 17 Ratio= 0.414634

43EDO, 8 good
0.0, 27.907, 55.814, 83.7209, 111.628, 139.535, 167.442, 195.349, 223.256, 251.163, 279.07, 306.977, 334.884, 362.791, 390.698, 418.605, 446.512, 474.419, 502.326, 530.233, 558.14, 586.047, 613.953, 641.86, 669.767, 697.674, 725.581, 753.488, 781.395, 809.302, 837.209, 865.116, 893.023, 920.93, 948.837, 976.744, 1004.65, 1032.56, 1060.47, 1088.37, 1116.28, 1144.19, 1172.09, 1200

46EDO, 17 good
0.0, 26.087, 52.1739, 78.2609, 104.348, 130.435, 156.522, 182.609, 208.696, 234.783, 260.87, 286.957, 313.043, 339.13, 365.217, 391.304, 417.391, 443.478, 469.565, 495.652, 521.739, 547.826, 573.913, 600, 626.087, 652.174, 678.261, 704.348, 730.435, 756.522, 782.609, 808.696, 834.783, 860.87, 886.957, 913.043, 939.13, 965.217, 991.304, 1017.39, 1043.48, 1069.57, 1095.65, 1121.74, 1147.83, 1173.91, 1200

48EDO, 9 good
0.0, 25, 50, 75, 100, 125, 150, 175, 200, 225, 250, 275, 300, 325, 350, 375, 400, 425, 450, 475, 500, 525, 550, 575, 600, 625, 650, 675, 700, 725, 750, 775, 800, 825, 850, 875, 900, 925, 950, 975, 1000, 1025, 1050, 1075, 1100, 1125, 1150, 1175, 1200

Here is the list of all intervals an octave or less wide that I consider good (in harmony)...
9/8, 8/7, 7/6, 6/5, 5/4, 9/7, 4/3, 11/8, 7/5, 10/7, 3/2, 11/7, 8/5, 5/3, 12/7, 7/4, 9/5, 11/6, 13/7, 2/1.

John.

🔗Kraig Grady <kraiggrady@...>

🔗cityoftheasleep <igliashon@...>

Well, based on my practical experience playing rock (and some blues) in a variety of EDOs, I can safely say that 6.776 cents is too narrow. I'd broaden it to at least 8 cents, to include 19-EDO and 22-EDO, as these both produce triads of superior consonance to 12-EDO. Of course, on a guitar (where intonation fluctuates wildly and tuning is seldom accurate to more than a 2-cent margin of error), I've found fifths as wide as 720 cents and as narrow as 685 cents to be more than reasonable for rock music. Interestingly, fifths on the narrower side (flat of pure) seem to sound better than those on the wider side (sharp of pure) given a constant value of deviation from Just--i.e. a 10-cent flat fifth sounds better than a 10-cent sharp fifth.

-Igs

--- In MakeMicroMusic@yahoogroups.com, "john777music" <jfos777@...> wrote:
>
> I've been looking at EDOs and it seems to me that 12EDO works so well because it contains both a Perfect Fourth (4/3) and a Perfect Fifth (3/2) within 2.0 cents accuracy in all keys. My favorite musical genres are Blues and Rock and this music is usually made using Fourths and Fifths which are the strongest intervals that occur between the tonic and octave. Based on this I suspect that the best EDOs are those that contain a Fourth and Fifth within 6.776 cents (256/255) accuracy. The 6.776 cents threshold is my own best guess at maximum deviation from pure and I do not claim that it should be set in stone.
>
> I looked at all EDOs from 1EDO to 48EDO and below is a complete list of all EDOs (from 1 to 48) which contain a Fourth and Fifth within 6.776 cents accuracy.
>
> With 12EDO there are 4 good (within +/-6.776 cents accuracy) intervals (see below) an octave or less wide: 9/8, 4/3, 3/2 and 2/1.
>
> With 31EDO there are 14 good (within +/-6.776 cents accuracy) intervals (see below) an octave or less wide: 8/7, 7/6, 6/5, 5/4, 4/3, 7/5, 10/7, 3/2, 8/5, 5/3, 12/7, 7/4, 11/6, 2/1.
>
>
> 12EDO, 4 good
> 0.0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200
>
> 17EDO, 4 good
> 0.0, 70.5882, 141.176, 211.765, 282.353, 352.941, 423.529, 494.118, 564.706, 635.294, 705.882, 776.471, 847.059, 917.647, 988.235, 1058.82, 1129.41, 1200
>
> 24EDO, 6 good
> 0.0, 50, 100, 150, 200, 250, 300, 350, 400, 450, 500, 550, 600, 650, 700, 750, 800, 850, 900, 950, 1000, 1050, 1100, 1150, 1200
>
> 29EDO, 8 good
> 0.0, 41.3793, 82.7586, 124.138, 165.517, 206.897, 248.276, 289.655, 331.034, 372.414, 413.793, 455.172, 496.552, 537.931, 579.31, 620.69, 662.069, 703.448, 744.828, 786.207, 827.586, 868.966, 910.345, 951.724, 993.103, 1034.48, 1075.86, 1117.24, 1158.62, 1200
>
> 31EDO, 14 good
> 0.0, 38.7097, 77.4194, 116.129, 154.839, 193.548, 232.258, 270.968, 309.677, 348.387, 387.097, 425.806, 464.516, 503.226, 541.935, 580.645, 619.355, 658.065, 696.774, 735.484, 774.194, 812.903, 851.613, 890.323, 929.032, 967.742, 1006.45, 1045.16, 1083.87, 1122.58, 1161.29, 1200
>
> 34EDO, 9 good
> 0.0, 35.2941, 70.5882, 105.882, 141.176, 176.471, 211.765, 247.059, 282.353, 317.647, 352.941, 388.235, 423.529, 458.824, 494.118, 529.412, 564.706, 600, 635.294, 670.588, 705.882, 741.176, 776.471, 811.765, 847.059, 882.353, 917.647, 952.941, 988.235, 1023.53, 1058.82, 1094.12, 1129.41, 1164.71, 1200
>
> 36EDO, 10 good
> 0.0, 33.3333, 66.6667, 100, 133.333, 166.667, 200, 233.333, 266.667, 300, 333.333, 366.667, 400, 433.333, 466.667, 500, 533.333, 566.667, 600, 633.333, 666.667, 700, 733.333, 766.667, 800, 833.333, 866.667, 900, 933.333, 966.667, 1000, 1033.33, 1066.67, 1100, 1133.33, 1166.67, 1200
>
> 39EDO, 10 good
> 0.0, 30.7692, 61.5385, 92.3077, 123.077, 153.846, 184.615, 215.385, 246.154, 276.923, 307.692, 338.462, 369.231, 400, 430.769, 461.538, 492.308, 523.077, 553.846, 584.615, 615.385, 646.154, 676.923, 707.692, 738.462, 769.231, 800, 830.769, 861.538, 892.308, 923.077, 953.846, 984.615, 1015.38, 1046.15, 1076.92, 1107.69, 1138.46, 1169.23, 1200
>
> 41EDO, 17 good
> 0.0, 29.2683, 58.5366, 87.8049, 117.073, 146.341, 175.61, 204.878, 234.146, 263.415, 292.683, 321.951, 351.22, 380.488, 409.756, 439.024, 468.293, 497.561, 526.829, 556.098, 585.366, 614.634, 643.902, 673.171, 702.439, 731.707, 760.976, 790.244, 819.512, 848.78, 878.049, 907.317, 936.585, 965.854, 995.122, 1024.39, 1053.66, 1082.93, 1112.2, 1141.46, 1170.73, 1200
> 41 = 17 Ratio= 0.414634
>
> 43EDO, 8 good
> 0.0, 27.907, 55.814, 83.7209, 111.628, 139.535, 167.442, 195.349, 223.256, 251.163, 279.07, 306.977, 334.884, 362.791, 390.698, 418.605, 446.512, 474.419, 502.326, 530.233, 558.14, 586.047, 613.953, 641.86, 669.767, 697.674, 725.581, 753.488, 781.395, 809.302, 837.209, 865.116, 893.023, 920.93, 948.837, 976.744, 1004.65, 1032.56, 1060.47, 1088.37, 1116.28, 1144.19, 1172.09, 1200
>
> 46EDO, 17 good
> 0.0, 26.087, 52.1739, 78.2609, 104.348, 130.435, 156.522, 182.609, 208.696, 234.783, 260.87, 286.957, 313.043, 339.13, 365.217, 391.304, 417.391, 443.478, 469.565, 495.652, 521.739, 547.826, 573.913, 600, 626.087, 652.174, 678.261, 704.348, 730.435, 756.522, 782.609, 808.696, 834.783, 860.87, 886.957, 913.043, 939.13, 965.217, 991.304, 1017.39, 1043.48, 1069.57, 1095.65, 1121.74, 1147.83, 1173.91, 1200
>
> 48EDO, 9 good
> 0.0, 25, 50, 75, 100, 125, 150, 175, 200, 225, 250, 275, 300, 325, 350, 375, 400, 425, 450, 475, 500, 525, 550, 575, 600, 625, 650, 675, 700, 725, 750, 775, 800, 825, 850, 875, 900, 925, 950, 975, 1000, 1025, 1050, 1075, 1100, 1125, 1150, 1175, 1200
>
>
> Here is the list of all intervals an octave or less wide that I consider good (in harmony)...
> 9/8, 8/7, 7/6, 6/5, 5/4, 9/7, 4/3, 11/8, 7/5, 10/7, 3/2, 11/7, 8/5, 5/3, 12/7, 7/4, 9/5, 11/6, 13/7, 2/1.
>
> John.
>

🔗john777music <jfos777@...>

Hi Igs, thanks for the reply.

An 8 cents tolerance to include 19 and 22 EDOs isn't all that far away from my 6.776 cents (256/255) tolerance but I always try to err on the side of caution (I have tested an 8 cents deviation from a pure 3/2 and I swear I can detect the very slightest hint of dissonance).

I'm curious, is my criterion of having good Fourths and Fifths important or can other EDOs that don't have good Fourths and Fifths be any good?

John.

--- In MakeMicroMusic@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> Well, based on my practical experience playing rock (and some blues) in a variety of EDOs, I can safely say that 6.776 cents is too narrow. I'd broaden it to at least 8 cents, to include 19-EDO and 22-EDO, as these both produce triads of superior consonance to 12-EDO. Of course, on a guitar (where intonation fluctuates wildly and tuning is seldom accurate to more than a 2-cent margin of error), I've found fifths as wide as 720 cents and as narrow as 685 cents to be more than reasonable for rock music. Interestingly, fifths on the narrower side (flat of pure) seem to sound better than those on the wider side (sharp of pure) given a constant value of deviation from Just--i.e. a 10-cent flat fifth sounds better than a 10-cent sharp fifth.
>
> -Igs
>
> --- In MakeMicroMusic@...m, "john777music" <jfos777@> wrote:
> >
> > I've been looking at EDOs and it seems to me that 12EDO works so well because it contains both a Perfect Fourth (4/3) and a Perfect Fifth (3/2) within 2.0 cents accuracy in all keys. My favorite musical genres are Blues and Rock and this music is usually made using Fourths and Fifths which are the strongest intervals that occur between the tonic and octave. Based on this I suspect that the best EDOs are those that contain a Fourth and Fifth within 6.776 cents (256/255) accuracy. The 6.776 cents threshold is my own best guess at maximum deviation from pure and I do not claim that it should be set in stone.
> >
> > I looked at all EDOs from 1EDO to 48EDO and below is a complete list of all EDOs (from 1 to 48) which contain a Fourth and Fifth within 6.776 cents accuracy.
> >
> > With 12EDO there are 4 good (within +/-6.776 cents accuracy) intervals (see below) an octave or less wide: 9/8, 4/3, 3/2 and 2/1.
> >
> > With 31EDO there are 14 good (within +/-6.776 cents accuracy) intervals (see below) an octave or less wide: 8/7, 7/6, 6/5, 5/4, 4/3, 7/5, 10/7, 3/2, 8/5, 5/3, 12/7, 7/4, 11/6, 2/1.
> >
> >
> > 12EDO, 4 good
> > 0.0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200
> >
> > 17EDO, 4 good
> > 0.0, 70.5882, 141.176, 211.765, 282.353, 352.941, 423.529, 494.118, 564.706, 635.294, 705.882, 776.471, 847.059, 917.647, 988.235, 1058.82, 1129.41, 1200
> >
> > 24EDO, 6 good
> > 0.0, 50, 100, 150, 200, 250, 300, 350, 400, 450, 500, 550, 600, 650, 700, 750, 800, 850, 900, 950, 1000, 1050, 1100, 1150, 1200
> >
> > 29EDO, 8 good
> > 0.0, 41.3793, 82.7586, 124.138, 165.517, 206.897, 248.276, 289.655, 331.034, 372.414, 413.793, 455.172, 496.552, 537.931, 579.31, 620.69, 662.069, 703.448, 744.828, 786.207, 827.586, 868.966, 910.345, 951.724, 993.103, 1034.48, 1075.86, 1117.24, 1158.62, 1200
> >
> > 31EDO, 14 good
> > 0.0, 38.7097, 77.4194, 116.129, 154.839, 193.548, 232.258, 270.968, 309.677, 348.387, 387.097, 425.806, 464.516, 503.226, 541.935, 580.645, 619.355, 658.065, 696.774, 735.484, 774.194, 812.903, 851.613, 890.323, 929.032, 967.742, 1006.45, 1045.16, 1083.87, 1122.58, 1161.29, 1200
> >
> > 34EDO, 9 good
> > 0.0, 35.2941, 70.5882, 105.882, 141.176, 176.471, 211.765, 247.059, 282.353, 317.647, 352.941, 388.235, 423.529, 458.824, 494.118, 529.412, 564.706, 600, 635.294, 670.588, 705.882, 741.176, 776.471, 811.765, 847.059, 882.353, 917.647, 952.941, 988.235, 1023.53, 1058.82, 1094.12, 1129.41, 1164.71, 1200
> >
> > 36EDO, 10 good
> > 0.0, 33.3333, 66.6667, 100, 133.333, 166.667, 200, 233.333, 266.667, 300, 333.333, 366.667, 400, 433.333, 466.667, 500, 533.333, 566.667, 600, 633.333, 666.667, 700, 733.333, 766.667, 800, 833.333, 866.667, 900, 933.333, 966.667, 1000, 1033.33, 1066.67, 1100, 1133.33, 1166.67, 1200
> >
> > 39EDO, 10 good
> > 0.0, 30.7692, 61.5385, 92.3077, 123.077, 153.846, 184.615, 215.385, 246.154, 276.923, 307.692, 338.462, 369.231, 400, 430.769, 461.538, 492.308, 523.077, 553.846, 584.615, 615.385, 646.154, 676.923, 707.692, 738.462, 769.231, 800, 830.769, 861.538, 892.308, 923.077, 953.846, 984.615, 1015.38, 1046.15, 1076.92, 1107.69, 1138.46, 1169.23, 1200
> >
> > 41EDO, 17 good
> > 0.0, 29.2683, 58.5366, 87.8049, 117.073, 146.341, 175.61, 204.878, 234.146, 263.415, 292.683, 321.951, 351.22, 380.488, 409.756, 439.024, 468.293, 497.561, 526.829, 556.098, 585.366, 614.634, 643.902, 673.171, 702.439, 731.707, 760.976, 790.244, 819.512, 848.78, 878.049, 907.317, 936.585, 965.854, 995.122, 1024.39, 1053.66, 1082.93, 1112.2, 1141.46, 1170.73, 1200
> > 41 = 17 Ratio= 0.414634
> >
> > 43EDO, 8 good
> > 0.0, 27.907, 55.814, 83.7209, 111.628, 139.535, 167.442, 195.349, 223.256, 251.163, 279.07, 306.977, 334.884, 362.791, 390.698, 418.605, 446.512, 474.419, 502.326, 530.233, 558.14, 586.047, 613.953, 641.86, 669.767, 697.674, 725.581, 753.488, 781.395, 809.302, 837.209, 865.116, 893.023, 920.93, 948.837, 976.744, 1004.65, 1032.56, 1060.47, 1088.37, 1116.28, 1144.19, 1172.09, 1200
> >
> > 46EDO, 17 good
> > 0.0, 26.087, 52.1739, 78.2609, 104.348, 130.435, 156.522, 182.609, 208.696, 234.783, 260.87, 286.957, 313.043, 339.13, 365.217, 391.304, 417.391, 443.478, 469.565, 495.652, 521.739, 547.826, 573.913, 600, 626.087, 652.174, 678.261, 704.348, 730.435, 756.522, 782.609, 808.696, 834.783, 860.87, 886.957, 913.043, 939.13, 965.217, 991.304, 1017.39, 1043.48, 1069.57, 1095.65, 1121.74, 1147.83, 1173.91, 1200
> >
> > 48EDO, 9 good
> > 0.0, 25, 50, 75, 100, 125, 150, 175, 200, 225, 250, 275, 300, 325, 350, 375, 400, 425, 450, 475, 500, 525, 550, 575, 600, 625, 650, 675, 700, 725, 750, 775, 800, 825, 850, 875, 900, 925, 950, 975, 1000, 1025, 1050, 1075, 1100, 1125, 1150, 1175, 1200
> >
> >
> > Here is the list of all intervals an octave or less wide that I consider good (in harmony)...
> > 9/8, 8/7, 7/6, 6/5, 5/4, 9/7, 4/3, 11/8, 7/5, 10/7, 3/2, 11/7, 8/5, 5/3, 12/7, 7/4, 9/5, 11/6, 13/7, 2/1.
> >
> > John.
> >
>

🔗Michael <djtrancendance@...>

John>"I'm curious, is my criterion of having good Fourths and Fifths important
or can other EDOs that don't have good Fourths and Fifths be any good?"

All a fourth is...is a fifth going the other direction (IE downward). Note
that the octave 2 over (3/2) AKA 2/(3/2)= 4/3. So if you get the fifth accurate
by about 6 cents, you also get the fourth accurate by the same amount.

I have an admittedly odd approach to this...which is try to handle the most
error-effected (and often more dissonant) intervals first...and then check the
intervals that allow more error (including the fifth and fourth) last.
*****************
Here is my order of analysis.........

A) Worry about the minor third (6/5) and the sixth (5/3) since these are very
intolerant to error (IE 1.65 sounds a world different than 5/3 and 1.21 sounds a
world different than 6/5)

B) Next think about the augmented fourth around 7/5. It is fairly sensitive to
error but, IMVHO, not as sensitive as the minor third. There is a dead zone
(very dissonant) between 7/5 and 11/8 where it begins to sound awful...between
7/5 and 10/7 it seems much more tolerant of error..

C) Next consider the minor second (and major seventh...since they are also
"reversed around the octave") should be dealt with first as they are the most
dissonant. Note that, IMVHO, 11/6 and 9/5 can be used as alternatives to
15/8...but there's a bad area around 1.818 that sounds terrible you should avoid
at all costs...which makes accuracy a bit tricky at times. You can also
occasionally use 11/9 as an alternative minor second.

D) Next handle the augmented sixth around 7/4 and 12/7. Note there is a dead
spot between 7/4 and 12/7. Note around 16/9 (1.7777) can also be used as an
alternative.

E) Then the the fifth (and fourth) should be dealt with. Both have fairly good
tolerance for error: try 1.515 vs. 3/2 and 1.49 vs. 3/2...you'll likely be
amazed how alike they sound. Same goes for 1.32 vs. 4/3.

------------------------
IMVHO using an occasional 22/15 diminished fifth within a few cents, if you
can't get a perfect one, is NOT a crime so long as the majority of fifths in
your scale are perfect. The real dead area comes if you drop under 1.49 into
the wolf fifth area from 1.475-1.487'ish...it sounds horrific. Usually, I've
found, end up with a wolf fifth...try to get the intervals around it that
normally form chords with it to be very accurate to help cancel out the effect
(Igs does this a lot in his compositions).

>>>> Trying to optimize this tends to favor scales like 31TET which both has good
>>>>regular and diminished fifths. Note that using up to around 1.515 as a fifth is
>>>>OK too.<<<<<<<<<<

**************************************************
So, in general my motto is AVOID the following DEAD (dissonant/very sensitive)
zones such as these:
*) Around 1.21
*) Between 9/7 (1.285) and 1.32
*) Near around 11/8 (about 1.385 to 1.39)
*) Between 1.475 and 1.49 (typical wolf fifth zone)...note 22/15 (1.4666) can be
OK to use on occasion
*) Between about 1.52 and 1.59
*) Around 1.61 (near 13/8)...note the 18/11 (1.6363) area can be OK to use on
occasion
*) Around 1.65
*) Around 1.73-1.74
*) Over about 15/8
Near these errors, getting notes accurate can be much more important than in
other areas...especially like the areas between 1.49 and 1.515...or 15/11
(1.36363) to 11/8 (1.375).......or between around 11/6 to 15/8 (including 13/7):
areas where tones over a relatively wide range sound rather alike.

[Non-text portions of this message have been removed]

🔗Mike Battaglia <battaglia01@...>

On Tue, Dec 28, 2010 at 5:59 PM, john777music <jfos777@...> wrote:
>
> Hi Igs, thanks for the reply.
>
> An 8 cents tolerance to include 19 and 22 EDOs isn't all that far away from my 6.776 cents (256/255) tolerance but I always try to err on the side of caution (I have tested an 8 cents deviation from a pure 3/2 and I swear I can detect the very slightest hint of dissonance).
>
> I'm curious, is my criterion of having good Fourths and Fifths important or can other EDOs that don't have good Fourths and Fifths be any good?

If you know how to finesse the timbre of the instruments you're using,
lots of things can sound good. With a no-3's timbre, or a timbre with
some kind of vibrato, for instance, things like mavila really pop out,
because the fifths just sound like narrow fifths - they don't sound
like dirty, beating, grungy narrow fifths. Then you end up with a
setup where 4 fifths end up leading to a minor third, which is pretty
trippy.

Or if brightness is more your thing, try messing around with
blackwood[10] in 15-tet or 20-tet (I prefer 20-tet and I believe Igs
does as well). Use it with a suitable timbre and the 720-cent fifths
will just sound like wide fifths.

You might also want to consider evaluating a temperament by the
"damage" it causes to certain key triads, rather than the error to
individual dyads.

-Mike

🔗Kraig Grady <kraiggrady@...>

I am always reluctant to say i am going to avoid anything. So often a context comes up where it is the right thing.

/^_,',',',_ //^/Kraig Grady_^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere:
North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

a momentary antenna as i turn to water
this evaporates - an island once again

On 29/12/10 12:11 PM, Michael wrote:
>
> John>"I'm curious, is my criterion of having good Fourths and > Fifths important
> or can other EDOs that don't have good Fourths and Fifths be > any good?"
>
> All a fourth is...is a fifth going the other direction (IE > downward). Note
> that the octave 2 over (3/2) AKA 2/(3/2)= 4/3. So if you get > the fifth accurate
> by about 6 cents, you also get the fourth accurate by the same > amount.
>
> I have an admittedly odd approach to this...which is try to > handle the most
> error-effected (and often more dissonant) intervals > first...and then check the
> intervals that allow more error (including the fifth and > fourth) last.
> *****************
> Here is my order of analysis.........
>
> A) Worry about the minor third (6/5) and the sixth (5/3) since > these are very
> intolerant to error (IE 1.65 sounds a world different than 5/3 > and 1.21 sounds a
> world different than 6/5)
>
> B) Next think about the augmented fourth around 7/5. It is > fairly sensitive to
> error but, IMVHO, not as sensitive as the minor third. There > is a dead zone
> (very dissonant) between 7/5 and 11/8 where it begins to sound > awful...between
> 7/5 and 10/7 it seems much more tolerant of error..
>
> C) Next consider the minor second (and major seventh...since > they are also
> "reversed around the octave") should be dealt with first as > they are the most
> dissonant. Note that, IMVHO, 11/6 and 9/5 can be used as > alternatives to
> 15/8...but there's a bad area around 1.818 that sounds > terrible you should avoid
> at all costs...which makes accuracy a bit tricky at times. You > can also
> occasionally use 11/9 as an alternative minor second.
>
> D) Next handle the augmented sixth around 7/4 and 12/7. Note > there is a dead
> spot between 7/4 and 12/7. Note around 16/9 (1.7777) can also > be used as an
> alternative.
>
> E) Then the the fifth (and fourth) should be dealt with. Both > have fairly good
> tolerance for error: try 1.515 vs. 3/2 and 1.49 vs. > 3/2...you'll likely be
> amazed how alike they sound. Same goes for 1.32 vs. 4/3.
>
> ------------------------
> IMVHO using an occasional 22/15 diminished fifth within a few > cents, if you
> can't get a perfect one, is NOT a crime so long as the > majority of fifths in
> your scale are perfect. The real dead area comes if you drop > under 1.49 into
> the wolf fifth area from 1.475-1.487'ish...it sounds horrific. > Usually, I've
> found, end up with a wolf fifth...try to get the intervals > around it that
> normally form chords with it to be very accurate to help > cancel out the effect
> (Igs does this a lot in his compositions).
>
> >>>> Trying to optimize this tends to favor scales like 31TET > which both has good
> >>>>regular and diminished fifths. Note that using up to > around 1.515 as a fifth is
> >>>>OK too.<<<<<<<<<<
>
> **************************************************
> So, in general my motto is AVOID the following DEAD > (dissonant/very sensitive)
> zones such as these:
> *) Around 1.21
> *) Between 9/7 (1.285) and 1.32
> *) Near around 11/8 (about 1.385 to 1.39)
> *) Between 1.475 and 1.49 (typical wolf fifth zone)...note > 22/15 (1.4666) can be
> OK to use on occasion
> *) Between about 1.52 and 1.59
> *) Around 1.61 (near 13/8)...note the 18/11 (1.6363) area can > be OK to use on
> occasion
> *) Around 1.65
> *) Around 1.73-1.74
> *) Over about 15/8
> Near these errors, getting notes accurate can be much more > important than in
> other areas...especially like the areas between 1.49 and > 1.515...or 15/11
> (1.36363) to 11/8 (1.375).......or between around 11/6 to 15/8 > (including 13/7):
> areas where tones over a relatively wide range sound rather alike.
>
> [Non-text portions of this message have been removed]
>
>

🔗genewardsmith <genewardsmith@...>

🔗Michael <djtrancendance@...>

Me>> E) Then the the fifth (and fourth) should be dealt with. Both have fairly
good

>> tolerance for error: try 1.515 vs. 3/2 and 1.49 vs. 3/2...you'll likely be
>> amazed how alike they sound.

Gene>No good for harmony, sorry.

Well, isn't that assuming everyone has ears that yell at them when a dyad
(particularly the fifth) is even more than a few cents off?... I seriously
doubt many people have such sensitive ears...

Now if you DO insist on only near-perfect fifths for harmony...and don't
allow any alternative 5ths (IE 50/33, 22/15, 11/7, etc.), I figure you have a
few options
A) Meantone, meantone, and meantone (IE 31TET for a near quarter-comma-meantone
tuning or good old 12TET) :-D
B) Some huge tunings IE 53TET+ that become increasingly complex to play and/or
make instruments for
C) Gene and others...what are your alternatives for preserving 5ths so well
without meantone tunings in EDOs?

Correct me if I'm wrong Gene, but aren't you saying that anything that isn't
mean-tone compatible thats a TET is no good for harmony?

Seems to kind of kill the point for me in composing microtonally...which is
to strengthen intervals OTHER than those strong in meantone-type tunings (IE
22/15, 11/9, 18/11, 11/8, 15/11, 9/7, 12/7 , 16/9, 11/10, 7/6, etc. Instead of
getting less harmony, you often end up with simply different harmony (maybe in
some cases, gasp...chords not using 5ths) :-D Looking particularly at things
like Iglashion Jones' map of an Internal Landscape IE
http://www.cityoftheasleep.com/releases/moail.zip
....it seems obvious to me there is life beyond perfect fifths so far as
harmony...and even (occasionally) ways to make even types of fifths I can't
stand IE 16/11 work in triads and such.

[Non-text portions of this message have been removed]

🔗genewardsmith <genewardsmith@...>

🔗cityoftheasleep <igliashon@...>

--- In MakeMicroMusic@yahoogroups.com, "john777music" <jfos777@...> wrote:

> I'm curious, is my criterion of having good Fourths and Fifths important or can other
> EDOs that don't have good Fourths and Fifths be any good?

Oh my goodness yes. Or rather, it depends on what you mean by "good". Having access to dissonant intervals is very important to express certain moods and emotions. I look at beating and beatlessness as just "effects", like a phaser or distortion or whatever, affecting the texture more so than the emotional quality. I've spent a lot of time exploring EDOs that look pretty nasty from a consonance/Just Intonation perspective, and have found that without exception, they are all capable of making worthwhile music--it just takes a judicious hand and an adventurous ear.

However, in my explorations I have also found chords that sound VERY restful and pretty and nice despite lacking anything like a fifth. In 13-EDO, for instance, a "minor" chord made up of 0-277-462 cents and a "major" chord made up of 0-185-462 cents (these are rounded to the nearest integer cent-values) sound as sweet to my ears as anything in 12-tET, and their nearest equivalents in 18-EDO and 23-EDO sound even nicer. I believe these chords approximate 16:18:21 triads, being made up of a 9/8 and 7/6. You should check them out.

-Igs

🔗Mike Battaglia <battaglia01@...>

On Wed, Dec 29, 2010 at 1:06 AM, cityoftheasleep
<igliashon@...> wrote:
>
> Oh my goodness yes. Or rather, it depends on what you mean by "good". Having access to dissonant intervals is very important to express certain moods and emotions. I look at beating and beatlessness as just "effects", like a phaser or distortion or whatever, affecting the texture more so than the emotional quality. I've spent a lot of time exploring EDOs that look pretty nasty from a consonance/Just Intonation perspective, and have found that without exception, they are all capable of making worthwhile music--it just takes a judicious hand and an adventurous ear.

I think you're somewhat of a pioneer in this field, Igs, as you have
this masterful ability to see ET's as different subgroup temperaments,
whereas most people focus more on the full 13-limit spectrum or
something like that. Your insight here is what led to me trying to do
a more formal search on the tuning list.

> However, in my explorations I have also found chords that sound VERY restful and pretty and nice despite lacking anything like a fifth. In 13-EDO, for instance, a "minor" chord made up of 0-277-462 cents and a "major" chord made up of 0-185-462 cents (these are rounded to the nearest integer cent-values) sound as sweet to my ears as anything in 12-tET, and their nearest equivalents in 18-EDO and 23-EDO sound even nicer. I believe these chords approximate 16:18:21 triads, being made up of a 9/8 and 7/6. You should check them out.

0-277-462 sounds like 6:7:8 to me. I'm screwing around in scala with
the "recorder" timbre, which is really tame, and if you put a 738 cent
fifth below it, it sounds like a distorted 4:6:7:8 to me. The sharp
fifth is especially pungent and I like it quite a bit.

-Mike

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

🔗Kraig Grady <kraiggrady@...>

both are fun pieces but if i had instruments in this tuning and nothing else, i think i would become a painter. imagine a 45 min piece you listened to 5 times a week.
really thinking about it, if this was is 12 ET i would not like it any less.

/^_,',',',_ //^/Kraig Grady_^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere:
North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

a momentary antenna as i turn to water
this evaporates - an island once again

On 29/12/10 6:51 PM, Mike Battaglia wrote:
>
> On Wed, Dec 29, 2010 at 2:48 AM, genewardsmith
> <genewardsmith@... > <mailto:genewardsmith%40sbcglobal.net>> wrote:
> >
> > --- In MakeMicroMusic@yahoogroups.com > <mailto:MakeMicroMusic%40yahoogroups.com>, Mike Battaglia > <battaglia01@...> wrote:
> >
> > > Have you heard knowsur's 14-tet experiments? I'm now a > believer in blown fifths:
> > >
> > > http://www.split-notes.com/spnt004.php
> > >
> > > Haneru is one of the trippiest things I've ever heard in > my life.
> >
> > I remain highly unconvinced.
>
> How about this one, where the main chord in this piece is two > 7-tet
> fourths stacked on top of each other?
>
> http://www.youtube.com/watch?v=m9NlHaWllwU
>
> Does that grab you any better?
>
> -Mike
>
>

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

On Wed, Dec 29, 2010 at 3:11 AM, Kraig Grady <kraiggrady@...> wrote:
> both are fun pieces but if i had instruments in this tuning and
> nothing else, i think i would become a painter. imagine a 45 min
> piece you listened to 5 times a week.
> really thinking about it, if this was is 12 ET i would not like
> it any less.

That's interesting that you say that, because when I listened to this
piece I felt as thought I was being launched through a rocket into the
sky and becoming one with the blue and green fireworks that were all
around in the air, and then I'd proceed to surf down those fireworks
on a surfboard made of diamond down onto a racetrack where I'd jump
into a checkered NASCAR car, and then drive through a rollercoaster
course that defies gravity and launches me into antigravity in
4-space, where I'd merge with the 4-dimensional self-transforming
machine elves whose dance defines existence and then become one with
the universe.

If I listened to this in 12-tet, I'd feel like all of the above was
happening on a Nintendo Wii game that's being played on an old TV with
crappy speakers. But that's just me, anyway.

-Mike

🔗Kraig Grady <kraiggrady@...>

I glad it does this for you!

/^_,',',',_ //^/Kraig Grady_^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere:
North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

a momentary antenna as i turn to water
this evaporates - an island once again

On 29/12/10 7:17 PM, Mike Battaglia wrote:
>
> On Wed, Dec 29, 2010 at 3:11 AM, Kraig Grady > <kraiggrady@... <mailto:kraiggrady%40anaphoria.com>> > wrote:
> > both are fun pieces but if i had instruments in this tuning and
> > nothing else, i think i would become a painter. imagine a 45 min
> > piece you listened to 5 times a week.
> > really thinking about it, if this was is 12 ET i would not like
> > it any less.
>
> That's interesting that you say that, because when I listened > to this
> piece I felt as thought I was being launched through a rocket > into the
> sky and becoming one with the blue and green fireworks that > were all
> around in the air, and then I'd proceed to surf down those > fireworks
> on a surfboard made of diamond down onto a racetrack where I'd > jump
> into a checkered NASCAR car, and then drive through a > rollercoaster
> course that defies gravity and launches me into antigravity in
> 4-space, where I'd merge with the 4-dimensional self-transforming
> machine elves whose dance defines existence and then become > one with
> the universe.
>
> If I listened to this in 12-tet, I'd feel like all of the > above was
> happening on a Nintendo Wii game that's being played on an old > TV with
> crappy speakers. But that's just me, anyway.
>
> -Mike
>
>

🔗Michael <djtrancendance@...>

🔗Mike Battaglia <battaglia01@...>

On Wed, Dec 29, 2010 at 11:12 AM, Michael <djtrancendance@...> wrote:
>
> Funny, this sounds good enough it has very confident feel harmonically and a
> playful and steady rhythm. It wouldn't be an inaccessible "intro to
> microtonallity" for someone who has never heard it at all. But, on the other
> hand, the tonality is distorted enough that my mind is always lagging a bit
> behind in interpreting it.

I dunno man, my friends at school dug it. And almost everyone liked
knowsur's album, which was also in 14-tet. For a lot of people it was
the first microtonal music they had ever heard and they really liked
it.

> So my mind keeps trying to round it to 12TET, sadly. Especially that fourth
> chord, which happens after the first two alternate several times in the main
> riff....it sounds like is supposed to function as a resolve point because it is
> held at the end of the riff for a long time...but never resolves..

It sounds like it's in mixolydian mode, yes. The neutral thirds sound
either like major or minor thirds depending on how they're voiced
1-4-7-10 makes the 10 sound like a "minor" third, and 1-5-8-10 makes
it sound like a "major" third. What's cool is when you can exploit
this equivalence to make puns which sound both major and minor at the
same time, as opposed to sounding "ambiguous" as a lot of neutral
thirds do.

Knowsur was the first person I've ever heard really succeed at doing
that and I didn't even know it was a musical possibility until I heard
his 14-tet experiments. I'm not sure how he's doing it exactly, but
there's the characteristic "sound" of dicot temperament for you.

I think that there are some psychoacoustic reasons why shades of
"minorness" and "majorness" can be heard in this tuning, and that it's
something to be embraced and explored, rather than assuming that it
shouldn't be that way. There are plenty of scales that sound nothing
like 12-tet, and the fact that shades of diatonic harmony can be heard
in 7-tet shouldn't really be that big of a deal. Sometimes I can hear
it as a distorted 1+6 scale too, although that I was hearing it that
way was never exactly clear until I got really familiar with 1+6
scales. Knowsur's song "Haneru":
http://ia700103.us.archive.org/14/items/Knowsur-NanaWodori/03Knowsur-Haneru.mp3

-Mike

🔗Michael <djtrancendance@...>

MikeB>"I dunno man, my friends at school dug it. And almost everyone liked
knowsur's album, which was also in 14-tet. For a lot of people it was the first
microtonal music they had ever heard and they really liked

it."

It's actually good news :-D...perhaps they can tolerate it more than I thought
"even" without fixing the "dud" 4th chord at the end of the progression.
Perhaps the obvious steady-ness of the rhythm and catchy-ness of the melodies
simply overrides that issue.

>"It sounds like it's in mixolydian mode, yes. The neutral thirds sound either
>like major or minor thirds depending on how they're voiced 1-4-7-10 makes the 10
>sound like a "minor" third, and 1-5-8-10 makes
it sound like a "major" third."

Right, you can/should-be-able-to interpret it as both. Only my mind still
trips a bit over that as implemented in 7TET.

>"I think that there are some psychoacoustic reasons why shades of "minorness"
>and "majorness" can be heard in this tuning, and that it's something to be
>embraced and explored, rather than assuming that it
shouldn't be that way."

Agreed.
This works well for the 18/11 and 11/9-ish intervals in 7TET. Those appear to
be two of the gems in that tuning, and two intervals I use a whole lot in my own
scales.

However the 7th interval, to me, sounds horrid (right smack between the
IMVHO far less distorted-sounding intervals of 9/5 and 11/6) and the high 4th in
7TET sounds OK by itself to me, but terribly mis-tuned when played against the
octave IE 2/(1.3459 AKA the 7tet 4th) = 1.485...a big time wolf fifth (neither
in the 22/15 diminished fifth or 3/2 pure fifth areas my mind tends to favor).
That "wolf fifth" also, of course, if the fifth in 7TET...and, to me, it means
less triads will be available since the other dyads will have to work to help
"cancel out" the impurity of the 5th (not to say it's impossible, just hard to
do/"prime"....for the composer).

IMVHO, 7TET, though obviously having its virtues, hints at something purer
that still keeps a high degree of major/minor swap-ability in tact at the
composer's creative disposal. Try the following "skewed 7TET" scale which,
IMVHO, keeps the feel while increasing the "steadiness" of the scale:

1/1
10/9
11/9
4/3
3/2
18/11
11/6
2/1

Now granted...temper this beast and you will likely get something "even"
better sounding... I really wonder what that song you found on Youtube would
sound like tuned to this...

>"Knowsur's song "Haneru":
http://ia700103.us.archive.org/14/items/Knowsur-NanaWodori/03Knowsur-Haneru.mp3"

Funny you gave that as an example...because it just happens to be about my
favorite song of his. Out of his album there were maybe 2 I really liked (yep,
I'm picky)...and that was one of them.

[Non-text portions of this message have been removed]