Calcul des échelles de ARTA sur des distances différentes de 64,8 cm; 100, 85, 70 cm Pour ARTA STRATO (distance chevalet/sillet : 64,8 cm) Corde Mi 53,6 cents = 1,03145854057 Calcul sur étendue de corde : 70 cm rang distance dimension chevalet/frette case 00 70 cm 0 cm 01 68,10 1,9 02 66,26 1,84 03 64,47 1,79 04 62,72 1,75 05 61,02 1,7 06 59,37 1,65 07 57,77 1,6 08 56,20 1,57 09 54,68 1,52 10 53,20 1,48 11 51,76 1,44 12 50,36 1,4 13 49 1,36 14 47,67 1,33 15 46,38 1,29 16 45,12 1,26 17 43,90 1,22 18 42,72 1,18 19 41,56 1,16 20 40,43 1,13 21 39,34 1,09 22 38,28 1,06 23 37,24 1,04 24 36,23 1,01 25 35,25 0,98 26 34,30 0,95 27 33,37 0,93 28 32,47 0,9 29 31,58 0,89 30 30,73 0,85 31 29,90 0,83 32 29,09 0,81 33 28,30 0,79 34 27,54 0,76 35 26,79 0,75 36 26,06 0,73 37 25,36 0,7 38 24,67 0,69 39 24 0,67 40 23,36 0,64 41 22,72 0,63 42 22,11 0,61 43 21,51 0,6 44 jusqu'à 17,4 cm Calcul sur étendue de corde : 100 cm rang distance dimension chevalet/frette case 00 100 cm 0 cm 01 96,95 3,05 entre 83 et 61 cents calculés à 70 cm : 3,24 et 2,54 cm dim de la 1ère case 02 94 2,95 03 91,12 2,88 04 88,35 2,77 05 85,65 2,7 06 83,04 2,61 07 80,51 2,53 08 78,05 2,46 09 75,67 2,38 10 73,36 2,31 11 71,12 2,24 12 68,95 2,17 13 66,85 2,1 14 64,81 2,04 15 62,84 1,97 16 60,92 1,92 17 59,06 1,86 18 57,26 1,8 19 55,51 1,75 20 53,82 1,69 21 52,18 1,64 22 50,59 1,59 23 49,04 1,55 24 47,55 1,49 25 46,1 1,45 26 44,69 1,41 27 43,33 1,36 28 42 1,33 29 40,73 1,27 30 39,48 1,25 31 38,28 1,2 32 37,11 1,17 33 35,98 1,13 34 34,88 1,1 35 33,82 1,06 36 32,79 1,03 37 31,79 1 39 30,82 0,97 40 29,88 0,94 41 28,97 0,91 42 28,08 0,89 43 27,23 0,85 45 26,39 0,84 46 25,59 0,8 47 24,81 0,78 48 24,05 0,76 49 23,32 0,73 50 22,61 0,71 51 21,92 0,69 52 21,25 0,67 53 20,6 0,65 54 19,97 0,63 55 19,36 0,61 56 18,77 57 18,2 58 17,65 59 17,11 60 61 Corde Si 61 cents = 1,03586308905 Calcul sur étendue de corde : 85 cm rang distance dimension chevalet/frette case 00 85 cm 01 82,06 02 79,21 03 76,47 04 73,82 05 71,27 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 66,778 cents = 1,03932606154 129 cents = 1,07735969592 Corde Ré 115 cents = 1,06868252503 rang distance dimension case chevalet/frette 00 70 cm 68 cm 0 cm 01 65,50 63,63 4,5 4,3702 61,29 59,5 4,21 4,13 03 57,35 55,7 3,94 3,8 04 53,66 52,1 3,69 3,605 50,21 48,78 3,45 3,32 06 47 45,65 3,21 3,13 07 43,97 42,71 3,03 2,94 08 41,14 39,97 2,8309 38,50 37,4 2,6410 36,02 35 2,48 11 33,71 32,75 2,3112 31,54 30,65 2,17 13 29,51 28,67 2,03 14 27,62 26,83 1,89 15 25,84 25,1 1,78 16 24,18 23,5 1,66 17 22,62 21,98 1,5618 21,17 20,57 1,45 19 19,2520 18,01 154,7 cents = 1,09347229422 Corde Mi 154 cents = 1,09303025354 rang distance dimension chevalet/frette case -2 -1 00 64,8 cm 0 cm01 59,28 5,52 02 54,24 5,04 03 49,62 4,62 04 45,4 05 41,53 06 38 07 34,76 08 31,8 09 29,1 10 26,62 11 24,35 12 22,28 13 20,38 14 18,65 15 17,06 16 15,61 17 14,28 | 0: 1/1 0.000000 unison, perfect prime 1: 160.000 cents 160.000000 2: 320.000 cents 320.000000 3: 480.000 cents 480.000000 4: 640.000 cents 640.000000 5: 800.000 cents 800.000000 6: 960.000 cents 960.000000 7: 1120.000 cents 1120.000000 8: 1280.000 cents 1280.000000 | 0: 1/1 0.000000 unison, perfect prime 1: 160.000 cents 160.000000 2: 320.000 cents 320.000000 3: 480.000 cents 480.000000 4: 640.000 cents 640.000000 5: 800.000 cents 800.000000 6: 960.000 cents 960.000000 7: 1120.000 cents 1120.000000 8: 1280.000 cents 1280.000000 9: 1440.000 cents 1440.000000 10: 1600.000 cents 1600.000000 11: 1760.000 cents 1760.000000 12: 1920.000 cents 1920.000000 13: 2080.000 cents 2080.000000 14: 2240.000 cents 2240.000000 15: 2400.000 cents 2400.000000 16: 2560.000 cents 2560.000000 | 1.09347229422 size is 154.7 cents, 38.803917 savarts/eptamerides, or 79.182246 schismas ( 871/11 ) 7.193245 syntonic commas ( 187/26 ) 6.594200 Pythagorean commas 25346.048000 MIDI tuning units 6336.512000 MIDI pitch bend units 5934.292000 flus 4747.823985 Temperament units 3880.778417 jots 2166.831333 16808-tone jinns 1582.581000 12276-tone mils 1503.684000 11664-tone decicents 1276.275000 9900-tone purdals 317.135000 2460-tone minas 219.158333 iotas 1366.516667 Türk senti 105.738569 hekt 94.109167 Woolhouse units 79.130400 grads 78.897000 612-tone schismas 46.410000 Dröbisch angles 9.282000 moria 7.912004 diaschismas 7.090417 Sauveur commas 6.832583 53-tone commas 5.674130 septimal commas 5.543417 43-tone merides 5.285583 41-tone supracommas 3.996417 31-tone normal dieses 3.767762 minor dieses 2.472623 major dieses 1.714602 Pythagorean limmas 1.325735 secors 0.816047 1/3-comma mean whole tones 0.800903 1/4-comma mean whole tones 0.786312 1/6-comma mean whole tones 119.679681 cm = 1/1 wavelength in air 59.839841 cm = 1/2 wavelength in air 29.919920 cm = 1/4 wavelength in air 167.785055 samples @ 48.0 KHz 1342.280438 samples @ 384.0 KHz 0.1289166667 octaves, 7.7569489334 / octave | 0: 1/1 0.000000 unison, perfect prime 1: 130.011 cents 130.010834 2: 260.022 cents 260.021668 3: 390.033 cents 390.032503 4: 520.043 cents 520.043337 5: 650.054 cents 650.054171 6: 780.065 cents 780.065005 7: 910.076 cents 910.075840 8: 1040.087 cents 1040.086674 9: 1170.098 cents 1170.097508 10: 1300.108 cents 1300.108342 11: 1430.119 cents 1430.119177 | 1.07860502984 size is 131 cents, 32.859167 savarts/eptamerides, or 67.051546 schismas 6.091241 syntonic commas ( 67/11 ) 5.583970 Pythagorean commas ( 67/12 ) 21463.040000 MIDI tuning units 5365.760000 MIDI pitch bend units 5025.160000 flus 4020.458578 Temperament units 3286.244167 jots 1834.873333 16808-tone jinns 1340.130000 12276-tone mils 1273.320000 11664-tone decicents 1080.750000 9900-tone purdals 268.550000 2460-tone minas 185.583333 iotas 1157.166667 Türk senti 89.539448 hekt 79.691667 Woolhouse units 67.007643 grads 66.810000 612-tone schismas 39.300000 Dröbisch angles 7.860000 moria 6.699887 diaschismas 6.004167 Sauveur commas 5.785833 53-tone commas 4.804855 septimal commas 4.694167 43-tone merides 4.475833 41-tone supracommas 3.384167 31-tone normal dieses 3.190542 minor dieses 2.093817 major dieses 1.451926 Pythagorean limmas 1.122633 secors 0.691029 1/3-comma mean whole tones 0.678205 1/4-comma mean whole tones 0.665849 1/6-comma mean whole tones 121.329321 cm = 1/1 wavelength in air 60.664660 cm = 1/2 wavelength in air 30.332330 cm = 1/4 wavelength in air 170.097769 samples @ 48.0 KHz 1360.782149 samples @ 384.0 KHz 0.1091666667 = 131/1200 octaves, 9.1603053435 / octave | 1.07735969592 size is 129 cents, 32.357500 savarts/eptamerides, or 66.027859 schismas 5.998245 syntonic commas 5.498719 Pythagorean commas ( 11/2 ) 21135.360000 MIDI tuning units 5283.840000 MIDI pitch bend units 4948.440000 flus 3959.077531 Temperament units 3236.072500 jots 1806.860000 16808-tone jinns 1319.670000 12276-tone mils 1253.880000 11664-tone decicents 1064.250000 9900-tone purdals 264.450000 2460-tone minas 182.750000 iotas 1139.500000 Türk senti 88.172433 hekt 78.475000 Woolhouse units 65.984626 grads 65.790000 612-tone schismas 38.700000 Dröbisch angles 7.740000 moria 6.597599 diaschismas 5.912500 Sauveur commas 5.697500 53-tone commas 4.731498 septimal commas 4.622500 43-tone merides 4.407500 41-tone supracommas 3.332500 31-tone normal dieses 3.141831 minor dieses 2.061851 major dieses 1.429759 Pythagorean limmas 1.105493 secors 0.680479 1/3-comma mean whole tones 0.667851 1/4-comma mean whole tones 0.655684 1/6-comma mean whole tones 121.469567 cm = 1/1 wavelength in air 60.734783 cm = 1/2 wavelength in air 30.367392 cm = 1/4 wavelength in air 170.294387 samples @ 48.0 KHz 1362.355094 samples @ 384.0 KHz 0.1075000000 = 43/400 octaves, 9.3023255814 / octave | 1.05032319891 size is 85 cents, 21.320833 savarts/eptamerides, or 43.506729 schismas 3.952332 syntonic commas ( 83/21 ) 3.623187 Pythagorean commas 13926.400000 MIDI tuning units 3481.600000 MIDI pitch bend units 3260.600000 flus 2608.694497 Temperament units 2132.295833 jots 1190.566667 16808-tone jinns 869.550000 12276-tone mils 826.200000 11664-tone decicents 701.250000 9900-tone purdals 174.250000 2460-tone minas 120.416667 iotas 750.833333 Türk senti 58.098115 hekt 51.708333 Woolhouse units 43.478242 grads 43.350000 612-tone schismas 25.500000 Dröbisch angles 5.100000 moria 4.347255 diaschismas 3.895833 Sauveur commas 3.754167 53-tone commas 3.117654 septimal commas 3.045833 43-tone merides 2.904167 41-tone supracommas 2.195833 31-tone normal dieses 2.070199 minor dieses 1.358584 major dieses 0.942089 Pythagorean limmas 0.728426 secors 0.448377 1/3-comma mean whole tones 0.440057 1/4-comma mean whole tones 0.432040 1/6-comma mean whole tones 124.596330 cm = 1/1 wavelength in air 62.298165 cm = 1/2 wavelength in air 31.149082 cm = 1/4 wavelength in air 174.677955 samples @ 48.0 KHz 1397.423642 samples @ 384.0 KHz 0.0708333333 = 17/240 octaves, 14.1176470588 / octave | 1.03227927502 size is 55 cents, 13.795833 savarts/eptamerides, or 28.151413 schismas 2.557391 syntonic commas 2.344415 Pythagorean commas ( 68/29 ) 9011.200000 MIDI tuning units 2252.800000 MIDI pitch bend units 2109.800000 flus 1687.978792 Temperament units 1379.720833 jots 770.366667 16808-tone jinns 562.650000 12276-tone mils 534.600000 11664-tone decicents 453.750000 9900-tone purdals 112.750000 2460-tone minas 77.916667 iotas 485.833333 Türk senti 37.592898 hekt 33.458333 Woolhouse units 28.132980 grads 28.050000 612-tone schismas 16.500000 Dröbisch angles 3.300000 moria 2.812930 diaschismas 2.520833 Sauveur commas 2.429167 53-tone commas 2.017305 septimal commas 1.970833 43-tone merides 1.879167 41-tone supracommas 1.420833 31-tone normal dieses 1.339540 minor dieses 0.879084 major dieses 0.609587 Pythagorean limmas 0.471334 secors 0.290127 1/3-comma mean whole tones 0.284743 1/4-comma mean whole tones 0.279555 1/6-comma mean whole tones 126.774235 cm = 1/1 wavelength in air 63.387118 cm = 1/2 wavelength in air 31.693559 cm = 1/4 wavelength in air 177.731272 samples @ 48.0 KHz 1421.850177 samples @ 384.0 KHz 0.0458333333 = 11/240 octaves, 21.8181818182 / octave | 1.03278622716 size is 55.85 cents, 14.009042 savarts/eptamerides, or 28.586480 schismas 2.596915 syntonic commas 2.380647 Pythagorean commas ( 50/21 ) 9150.464000 MIDI tuning units 2287.616000 MIDI pitch bend units 2142.406000 flus 1714.065737 Temperament units 1401.043792 jots 782.272333 16808-tone jinns 571.345500 12276-tone mils 542.862000 11664-tone decicents 460.762500 9900-tone purdals 114.492500 2460-tone minas 79.120833 iotas 493.341667 Türk senti 38.173879 hekt 33.975417 Woolhouse units 28.567762 grads 28.483500 612-tone schismas 16.755000 Dröbisch angles 3.351000 moria 2.856402 diaschismas 2.559792 Sauveur commas 2.466708 53-tone commas 2.048482 septimal commas 2.001292 43-tone merides 1.908208 41-tone supracommas 1.442792 31-tone normal dieses 1.360242 minor dieses 0.892670 major dieses 0.619008 Pythagorean limmas 0.478619 secors 0.294610 1/3-comma mean whole tones 0.289143 1/4-comma mean whole tones 0.283875 1/6-comma mean whole tones 126.712007 cm = 1/1 wavelength in air 63.356004 cm = 1/2 wavelength in air 31.678002 cm = 1/4 wavelength in air 177.644031 samples @ 48.0 KHz 1421.152250 samples @ 384.0 KHz 0.0465416667 octaves, 21.4861235452 / octave | 0: 1/1 0.000000 unison, perfect prime 1: 76.923 cents 76.923077 2: 153.846 cents 153.846154 3: 230.769 cents 230.769231 4: 307.692 cents 307.692308 5: 384.615 cents 384.615385 6: 461.538 cents 461.538462 7: 538.462 cents 538.461538 8: 615.385 cents 615.384615 9: 692.308 cents 692.307692 10: 769.231 cents 769.230769 11: 846.154 cents 846.153846 12: 923.077 cents 923.076923 13: 1000.000 cents 1000.000000 14: 1076.923 cents 1076.923077 15: 1153.846 cents 1153.846154 16: 1230.769 cents 1230.769231 | 1.04543437316 size is 76.923 cents, 19.294853 savarts/eptamerides, or 39.372566 schismas 3.576768 syntonic commas ( 93/26 ) 3.278899 Pythagorean commas ( 82/25 ) 12603.064320 MIDI tuning units 3150.766080 MIDI pitch bend units 2950.766280 flus 2360.807139 Temperament units 1929.677558 jots 1077.434820 16808-tone jinns 786.922290 12276-tone mils 747.691560 11664-tone decicents 634.614750 9900-tone purdals 157.692150 2460-tone minas 108.974250 iotas 679.486500 Türk senti 52.577427 hekt 46.794825 Woolhouse units 39.346786 grads 39.230730 612-tone schismas 23.076900 Dröbisch angles 4.615380 moria 3.934163 diaschismas 3.525638 Sauveur commas 3.397433 53-tone commas 2.821403 septimal commas 2.756408 43-tone merides 2.628203 41-tone supracommas 1.987178 31-tone normal dieses 1.873481 minor dieses 1.229486 major dieses 0.852569 Pythagorean limmas 0.659208 secors 0.405771 1/3-comma mean whole tones 0.398241 1/4-comma mean whole tones 0.390986 1/6-comma mean whole tones 125.178987 cm = 1/1 wavelength in air 62.589493 cm = 1/2 wavelength in air 31.294747 cm = 1/4 wavelength in air 175.494812 samples @ 48.0 KHz 1403.958496 samples @ 384.0 KHz 0.0641025000 octaves, 15.6000156000 / octave | 0: 1/1 0.000000 unison, perfect prime 1: 66.778 cents 66.777963 2: 133.556 cents 133.555927 3: 200.334 cents 200.333890 4: 267.112 cents 267.111853 5: 333.890 cents 333.889816 6: 400.668 cents 400.667780 7: 467.446 cents 467.445743 8: 534.224 cents 534.223706 9: 601.002 cents 601.001669 10: 667.780 cents 667.779633 11: 734.558 cents 734.557596 12: 801.336 cents 801.335559 13: 868.114 cents 868.113523 14: 934.891 cents 934.891486 15: 1001.669 cents 1001.669449 16: 1068.447 cents 1068.447412 17: 1135.225 cents 1135.225376 18: 1202.003 cents 1202.003339 | 1.03932606154 size is 66.778 cents, 16.750148 savarts/eptamerides, or 34.179910 schismas 3.105045 syntonic commas ( 59/19 ) 2.846461 Pythagorean commas ( 37/13 ) 10940.907520 MIDI tuning units 2735.226880 MIDI pitch bend units 2561.604080 flus 2049.451778 Temperament units 1675.181778 jots 935.337187 16808-tone jinns 683.138940 12276-tone mils 649.082160 11664-tone decicents 550.918500 9900-tone purdals 136.894900 2460-tone minas 94.602167 iotas 589.872333 Türk senti 45.643246 hekt 40.623283 Woolhouse units 34.157530 grads 34.056780 612-tone schismas 20.033400 Dröbisch angles 4.006680 moria 3.415306 diaschismas 3.060658 Sauveur commas 2.949362 53-tone commas 2.449302 septimal commas 2.392878 43-tone merides 2.281582 41-tone supracommas 1.725098 31-tone normal dieses 1.626397 minor dieses 1.067335 major dieses 0.740127 Pythagorean limmas 0.572268 secors 0.352256 1/3-comma mean whole tones 0.345719 1/4-comma mean whole tones 0.339420 1/6-comma mean whole tones 125.914687 cm = 1/1 wavelength in air 62.957344 cm = 1/2 wavelength in air 31.478672 cm = 1/4 wavelength in air 176.526227 samples @ 48.0 KHz 1412.209820 samples @ 384.0 KHz 0.0556483333 octaves, 17.9699901165 / octave | 1.03712695093 size is 63.111 cents, 15.830343 savarts/eptamerides, or 32.302978 schismas 2.934537 syntonic commas ( 44/15 ) 2.690152 Pythagorean commas ( 78/29 ) 10340.106240 MIDI tuning units 2585.026560 MIDI pitch bend units 2420.937960 flus 1936.909629 Temperament units 1583.192028 jots 883.974740 16808-tone jinns 645.625530 12276-tone mils 613.438920 11664-tone decicents 520.665750 9900-tone purdals 129.377550 2460-tone minas 89.407250 iotas 557.480500 Türk senti 43.136825 hekt 38.392525 Woolhouse units 32.281827 grads 32.186610 612-tone schismas 18.933300 Dröbisch angles 3.786660 moria 3.227760 diaschismas 2.892588 Sauveur commas 2.787403 53-tone commas 2.314803 septimal commas 2.261478 43-tone merides 2.156293 41-tone supracommas 1.630368 31-tone normal dieses 1.537086 minor dieses 1.008725 major dieses 0.699485 Pythagorean limmas 0.540843 secors 0.332912 1/3-comma mean whole tones 0.326734 1/4-comma mean whole tones 0.320782 1/6-comma mean whole tones 126.181675 cm = 1/1 wavelength in air 63.090837 cm = 1/2 wavelength in air 31.545419 cm = 1/4 wavelength in air 176.900531 samples @ 48.0 KHz 1415.204251 samples @ 384.0 KHz 0.0525925000 octaves, 19.0141179826 / octave | 1.03706045651 size is 63 cents, 15.802500 savarts/eptamerides, or 32.246164 schismas 2.929376 syntonic commas ( 41/14 ) 2.685421 Pythagorean commas ( 51/19 ) 10321.920000 MIDI tuning units 2580.480000 MIDI pitch bend units 2416.680000 flus 1933.502980 Temperament units 1580.407500 jots 882.420000 16808-tone jinns 644.490000 12276-tone mils 612.360000 11664-tone decicents 519.750000 9900-tone purdals 129.150000 2460-tone minas 89.250000 iotas 556.500000 Türk senti 43.060956 hekt 38.325000 Woolhouse units 32.225050 grads 32.130000 612-tone schismas 18.900000 Dröbisch angles 3.780000 moria 3.222083 diaschismas 2.887500 Sauveur commas 2.782500 53-tone commas 2.310732 septimal commas 2.257500 43-tone merides 2.152500 41-tone supracommas 1.627500 31-tone normal dieses 1.534383 minor dieses 1.006950 major dieses 0.698254 Pythagorean limmas 0.539892 secors 0.332327 1/3-comma mean whole tones 0.326160 1/4-comma mean whole tones 0.320218 1/6-comma mean whole tones 126.189765 cm = 1/1 wavelength in air 63.094883 cm = 1/2 wavelength in air 31.547441 cm = 1/4 wavelength in air 176.911874 samples @ 48.0 KHz 1415.294992 samples @ 384.0 KHz 0.0525000000 = 21/400 octaves, 19.0476190476 / octave