19ed7/3: Difference between revisions

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m Intro, harmonics
 
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{{Infobox ET}}
{{Infobox ET}}
{{ED intro}}
== Intervals ==
== Intervals ==
{| class="wikitable"
{| class="wikitable"
Line 16: Line 18:
| colspan="2" |G#
| colspan="2" |G#
|154.386
|154.386
|[[Tel:154.4075|154.4075]]
|154.4075
|-
|-
|3
|3
Line 22: Line 24:
|''A''
|''A''
|231.57895
|231.57895
|[[Tel:231.6112|231.6112]]
|231.6112
|-
|-
|4
|4
|A
|A
|''B''
|''B''
|[[Tel:308.7719|308.7719]]
|308.7719
|[[Tel:308.8149|308.8149]]
|308.8149
|-
|-
|5
|5
|Bb
|Bb
|''Cb''
|''Cb''
|[[Tel:385.9649|385.9649]]
|385.9649
|[[Tel:386.0187|386.0187]]
|386.0187
|-
|-
|6
|6
|A#
|A#
|''B#''
|''B#''
|[[Tel:463.1579|463.1579]]
|463.1579
|[[Tel:463.2224|463.2224]]
|463.2224
|-
|-
|7
|7
|B
|B
|''C''
|''C''
|[[Tel:540.3509|540.3509]]
|540.3509
|[[Tel:540.4261|540.4261]]
|540.4261
|-
|-
|8
|8
|C
|C
|''Q''
|''Q''
|[[Tel:617.5439|617.5439]]
|617.5439
|[[Tel:617.6299|617.6299]]
|617.6299
|-
|-
|9
|9
|Qb
|Qb
|''Db''
|''Db''
|[[Tel:694.7368|694.7368]]
|694.7368
|[[Tel:694.8336|694.8336]]
|694.8336
|-
|-
|10
|10
|C#
|C#
|''Q#''
|''Q#''
|[[Tel:771.9298|771.9298]]
|771.9298
|[[Tel:772.0373|772.0373]]
|772.0373
|-
|-
|11
|11
|Q
|Q
|''D''
|''D''
|[[Tel:849.1228|849.1228]]
|849.1228
|849.24105
|849.24105
|-
|-
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|D
|D
|''S''
|''S''
|[[Tel:926.3158|926.3158]]
|926.3158
|[[Tel:926.4448|926.4448]]
|926.4448
|-
|-
|13
|13
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|1466.8709
|1466.8709
|}
|}
== 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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