19ed7/3: Difference between revisions

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{{Infobox ET}}
{{ED intro}}
== Intervals ==
== Intervals ==
{| class="wikitable"
{| class="wikitable"
Line 4: Line 7:
!Degrees
!Degrees
! colspan="2" |Enneatonic
! colspan="2" |Enneatonic
!ed43\36
! colspan="2" |ed11\9~ed7/3
!Pyrite<sub>v</sub>
!ed35\29
!''ed29\24=r¢<sub>v</sub>''
!ed17\14
!Golden<sub>v</sub>
!ed11\9~ed7/3
!Golden<sub>^</sub>
!ed16\13
!ed21\17
!''ed5\4=r¢<sub>^</sub>''
|-
|-
|1
|1
|Jb
|Jb
|''Ab''
|''Ab''
|75.4386
|75.6734
|76.22505
|''76.3158''
|76.6917
|76.83425
|77.193
|77.193
77.2037
|77.2037
|77.571
|77.7328
|78.0186
|''78.9474''
|-
|-
|2
|2
| colspan="2" |G#
| colspan="2" |G#
|150.8772
|151.3468
|152.4501
|''152.6316''
|153.3835
|153.6685
|154.386
|154.386
154.4075
|154.4075
|155.1421
|155.4656
|156.03715
|''157.8947''
|-
|-
|3
|3
|J
|J
|''A''
|''A''
|226.3158
|227.0202
|228.6751
|''228.9474''
|230.0752
|230.5028
|231.57895
|231.57895
231.6112
|231.6112
|232.7131
|233.1984
|234.0557
|''236.8421''
|-
|-
|4
|4
|A
|A
|''B''
|''B''
|301.7544
|302.69355
|304.9002
|''305.2632''
|306.7669
|307.337
|308.7719
|308.7719
308.8149
|308.8149
|310.5841
|310.9312
|312.0743
|''315.7895''
|-
|-
|5
|5
|Bb
|Bb
|''Cb''
|''Cb''
|377.193
|378.3669
|381.1252
|''381.57895''
|383.45865
|384.1713
|385.9649
|385.9649
386.0187
|386.0187
|387.8552
|388.664
|390.0929
|''394.7368''
|-
|-
|6
|6
|A#
|A#
|''B#''
|''B#''
|452.6316
|454.0403
|457.3503
|''457.8947''
|460.1504
|461.0055
|463.1579
|463.1579
463.2224
|463.2224
|465.4262
|466.3968
|468.1115
|''473.6842''
|-
|-
|7
|7
|B
|B
|''C''
|''C''
|528.0702
|529.7137
|533.5753
|''534.2105''
|536.8421
|537.8398
|540.3509
|540.3509
540.4261
|540.4261
|542.99725
|544.12955
|546.13
|''552.6316''
|-
|-
|8
|8
|C
|C
|''Q''
|''Q''
|603.5088
|605.3871
|609.8004
|''610.5263''
|612.5338
|614.674
|617.5439
|617.5439
617.6299
|617.6299
|620.5683
|621.86235
|624.1486
|''631.57895''
|-
|-
|9
|9
|Qb
|Qb
|''Db''
|''Db''
|678.9474
|681.0605
|686.0254
|''686.8421''
|690.2256
|691.5083
|694.7368
|694.7368
694.8336
|694.8336
|698.1393
|699.5951
|702.1672
|''710.5263''
|-
|-
|10
|10
|C#
|C#
|''Q#''
|''Q#''
|754.386
|756.7339
|762.25045
|''763.1579''
|766.9173
|768.34255
|771.9298
|771.9298
772.0373
|772.0373
|775.7104
|777.3279
|780.1858
|''789.4737''
|-
|-
|11
|11
|Q
|Q
|''D''
|''D''
|829.8246
|832.4073
|838.4755
|''839.473''7
|843.609
|845.1768
|849.1228
|849.1228
849.24105
|849.24105
|853.2814
|855.0607
|858.2043
|''868.42105''
|-
|-
|12
|12
|D
|D
|''S''
|''S''
|905.2632
|908.0806
|914.7005
|''915.7895''
|920.30075
|922.0111
|926.3158
|926.3158
926.4448
|926.4448
|930.8524
|932.7935
|936.2229
|''947.3684''
|-
|-
|13
|13
| colspan="2" |Eb
| colspan="2" |Eb
|980.70175
|983.754
|990.9256
|''992.1053''
|996.9925
|998.8453
|1003.5088
|1003.5088
1003.6485
|1003.6485
|1008.4235
|1010.5263
|1014.2415
|''1026.3158''
|-
|-
|14
|14
|D#
|D#
|''S#''
|''S#''
|1056.14035
|1059.4274
|1067.1506
|''1068.42105''
|1073.6842
|1075.6796
|1080.70175
|1080.70175
1080.85225
|1080.85225
|1085.9945
|1088.2591
|1092.26
|''1105.2632''
|-
|-
|15
|15
| colspan="2" |E
| colspan="2" |E
|1131.57895
|1135.1008
|1143.3757
|''1144.7368''
|1150.3759
|1152.5138
|1157.8947
|1157.8947
1158.0559
|1158.0559
|1163.5655
|1165.9919
|1170.2786
|''1184.2105''
|-
|-
|16
|16
| colspan="2" |Fb
| colspan="2" |Fb
|1207.0715
|1210.7742
|1219.6007
|''1221.0526''
|1227.0677
|1229.3481
|1235.0877
|1235.0877
1235.2567
|1235.2567
|1241.1366
|1243.7247
|1248.2972
|''1263.1579''
|-
|-
|17
|17
| colspan="2" |E#
| colspan="2" |E#
|1282.4561
|1286.4476
|1295.8258
|''1297.3684''
|1303.7594
|1306.1823
|1312.2807
|1312.2807
1312.4634
|1312.4634
|1318.7076
|1321.4575
|1326.3158
|''1342.1053''
|-
|-
|18
|18
| colspan="2" |F
| colspan="2" |F
|1357.8947
|1326.121
|1372.0508
|''1373.6842''
|1380.4511
|1383.0166
|1389.4737
|1389.4737
1389.6672
|1389.6672
|1396.27865
|1399.1903
|1404.3343
|''1421.0526''
|-
|-
|19
|19
| colspan="2" |G
| colspan="2" |G
|1433.3333
|1466.{{Overline|6}}
|1437.79435
|1466.8709
|1448.2759
|''1450''
|1457.1429
|1459.8508
|1466.6667
1466.8709
|1473.8497
|1476.9231
|1482.3529
|''1500''
|}
|}
== Harmonics ==
{{Harmonics in equal
| steps = 19
| num = 7
| denom = 3
}}
{{Harmonics in equal
| steps = 19
| num = 7
| denom = 3
| start = 12
| collapsed = 1
}}

Latest revision as of 09:41, 2 October 2024

← 18ed7/3 19ed7/3 20ed7/3 →
Prime factorization 19 (prime)
Step size 77.2037 ¢ 
Octave 16\19ed7/3 (1235.26 ¢)
Twelfth 25\19ed7/3 (1930.09 ¢)
Consistency limit 3
Distinct consistency limit 3

19 equal divisions of 7/3 (abbreviated 19ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 19 equal parts of about 77.2 ¢ each. Each step represents a frequency ratio of (7/3)1/19, or the 19th root of 7/3.

Intervals

Degrees Enneatonic ed11\9~ed7/3
1 Jb Ab 77.193 77.2037
2 G# 154.386 154.4075
3 J A 231.57895 231.6112
4 A B 308.7719 308.8149
5 Bb Cb 385.9649 386.0187
6 A# B# 463.1579 463.2224
7 B C 540.3509 540.4261
8 C Q 617.5439 617.6299
9 Qb Db 694.7368 694.8336
10 C# Q# 771.9298 772.0373
11 Q D 849.1228 849.24105
12 D S 926.3158 926.4448
13 Eb 1003.5088 1003.6485
14 D# S# 1080.70175 1080.85225
15 E 1157.8947 1158.0559
16 Fb 1235.0877 1235.2567
17 E# 1312.2807 1312.4634
18 F 1389.4737 1389.6672
19 G 1466.6 1466.8709

Harmonics

Approximation of harmonics in 19ed7/3
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +35.3 +28.1 -6.7 -7.0 -13.8 +28.1 +28.6 -20.9 +28.3 +17.7 +21.5
Relative (%) +45.7 +36.4 -8.7 -9.0 -17.9 +36.4 +37.0 -27.1 +36.6 +22.9 +27.8
Steps
(reduced) 		16
(16) 		25
(6) 		31
(12) 		36
(17) 		40
(2) 		44
(6) 		47
(9) 		49
(11) 		52
(14) 		54
(16) 		56
(18)
Approximation of harmonics in 19ed7/3
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +37.3 -13.8 +21.2 -13.4 +36.1 +14.3 -2.1 -13.7 -20.9 -24.3 -24.0
Relative (%) +48.3 -17.9 +27.4 -17.3 +46.7 +18.6 -2.7 -17.7 -27.1 -31.4 -31.1
Steps
(reduced) 		58
(1) 		59
(2) 		61
(4) 		62
(5) 		64
(7) 		65
(8) 		66
(9) 		67
(10) 		68
(11) 		69
(12) 		70
(13)
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