30ed7/3: Difference between revisions

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m Intro harmonics
 
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Line 1: Line 1:
{{Stub}}
{{Infobox ET}}
{{ED intro}}
== Intervals ==
== Intervals ==
{| class="wikitable"
{| class="wikitable"
!Degrees
!Degrees
! colspan="2" |Enneatonic
! colspan="2" |Enneatonic
!ed11\9~ed7/3
! colspan="2" |ed11\9~ed7/3
|-
|-
|1
|1
Line 9: Line 13:
|''G+/Abd''
|''G+/Abd''
|48.{{Overline|8}}
|48.{{Overline|8}}
48.8957
|48.8957
|-
|-
|2
|2
|G#/Jb
|G#/Jb
|''G#/Ab''
|''G#/Ab''
|97.{{Overline|7}}97.7914
|97.{{Overline|7}}
|97.7914
|-
|-
|3
|3
Line 20: Line 25:
|''G#+/Ad''
|''G#+/Ad''
|146.{{Overline|6}}
|146.{{Overline|6}}
146.6871
|146.6871
|-
|-
|4
|4
|J
|J
|''A''
|''A''
|195.{{Overline|5}}195.5828
|195.{{Overline|5}}
|195.5828
|-
|-
|5
|5
Line 31: Line 37:
|''A+/Bbd''
|''A+/Bbd''
|244.{{Overline|4}}
|244.{{Overline|4}}
244.4785
|244.4785
|-
|-
|6
|6
|J#/Ab
|J#/Ab
|''A#/Bb''
|''A#/Bb''
|293.{{Overline|3}}293.3742
|293.{{Overline|3}}
|293.3742
|-
|-
|7
|7
Line 42: Line 49:
|''A#+/Bd''
|''A#+/Bd''
|342.{{Overline|2}}
|342.{{Overline|2}}
342.2699
|342.2699
|-
|-
|8
|8
|A
|A
|''B''
|''B''
|391.{{Overline|1}}391.1656
|391.{{Overline|1}}
|391.1656
|-
|-
|9
|9
|A+/Bd
|A+/Bd
|''B+/Cd''
|''B+/Cd''
|440(.0613)
|440
|440.0613
|-
|-
|10
|10
|B
|B
|''C''
|''C''
|488.{{Overline|8}}488.957
|488.{{Overline|8}}
|488.957
|-
|-
|11
|11
Line 63: Line 73:
|''C+/Qbd''
|''C+/Qbd''
|537.{{Overline|7}}
|537.{{Overline|7}}
537.8527
|537.8527
|-
|-
|12
|12
|B#/Cb
|B#/Cb
|''C#/Qb''
|''C#/Qb''
|586.{{Overline|6}}586.7484
|586.{{Overline|6}}
|586.7484
|-
|-
|13
|13
Line 74: Line 85:
|''C#+/Qd''
|''C#+/Qd''
|635.{{Overline|5}}
|635.{{Overline|5}}
635.6441
|635.6441
|-
|-
|14
|14
|C
|C
|''Q''
|''Q''
|684.{{Overline|4}}684.5398
|684.{{Overline|4}}
|684.5398
|-
|-
|15
|15
Line 85: Line 97:
|''Q+/Dbd''
|''Q+/Dbd''
|733.{{Overline|3}}
|733.{{Overline|3}}
733.43545
|733.43545
|-
|-
|16
|16
|C#/Qb
|C#/Qb
|''Q#/Db''
|''Q#/Db''
|782.{{Overline|2}}782.33115
|782.{{Overline|2}}
|782.33115
|-
|-
|17
|17
Line 96: Line 109:
|''Q#+/Dd''
|''Q#+/Dd''
|831.{{Overline|1}}
|831.{{Overline|1}}
831.22685
|831.22685
|-
|-
|18
|18
|Q
|Q
|''D''
|''D''
|880(.1225)
|880
|880.1225
|-
|-
|19
|19
Line 107: Line 121:
|''D+/Sd''
|''D+/Sd''
|928.{{Overline|8}}
|928.{{Overline|8}}
929.0182
|929.0182
|-
|-
|20
|20
|D
|D
|''S''
|''S''
|977.{{Overline|7}}977.9139
|977.{{Overline|7}}
|977.9139
|-
|-
| rowspan="2" |21
| rowspan="2" |21
Line 118: Line 133:
|''S+''
|''S+''
| rowspan="2" |1026.{{Overline|6}}
| rowspan="2" |1026.{{Overline|6}}
1026.8096
| rowspan="2" |1026.8096
|-
|-
| colspan="2" |Ebd
| colspan="2" |Ebd
Line 126: Line 141:
|''S#''
|''S#''
| rowspan="2" |1075.{{Overline|5}}
| rowspan="2" |1075.{{Overline|5}}
1075.7053
| rowspan="2" |1075.7053
|-
|-
| colspan="2" |Eb
| colspan="2" |Eb
Line 133: Line 148:
|D#+
|D#+
|''S#+''
|''S#+''
| rowspan="2" |1124.4444
| rowspan="2" |1124.{{Overline|4}}
1124.601
| rowspan="2" |1124.601
|-
|-
| colspan="2" |Ed
| colspan="2" |Ed
Line 140: Line 155:
|24
|24
| colspan="2" |E
| colspan="2" |E
|1173.{{Overline|3}}1173.4967
|1173.{{Overline|3}}
|1173.4967
|-
|-
|25
|25
| colspan="2" |E+/Fbd
| colspan="2" |E+/Fbd
|1222.{{Overline|2}}
|1222.{{Overline|2}}
1222.3924
|1222.3924
|-
|-
|26
|26
| colspan="2" |E#/Fb
| colspan="2" |E#/Fb
|1271.{{Overline|1}}1271.2881
|1271.{{Overline|1}}
|1271.2881
|-
|-
|27
|27
| colspan="2" |E#+/Fd
| colspan="2" |E#+/Fd
|1320(.1838)
|1320
|1320.1838
|-
|-
|28
|28
| colspan="2" |F
| colspan="2" |F
|1368.{{Overline|8}}1369.0795
|1368.{{Overline|8}}
|1369.0795
|-
|-
|29
|29
| colspan="2" |F+/Gd
| colspan="2" |F+/Gd
|1417.{{Overline|7}}
|1417.{{Overline|7}}
1417.9725
|1417.9725
|-
|-
|30
|30
| colspan="2" |G
| colspan="2" |G
|1466.{{Overline|6}}1466.8709
|1466.{{Overline|6}}
|1466.8709
|}
|}
== Harmonics ==
{{Harmonics in equal
| steps = 30
| num = 7
| denom = 3
}}
{{Harmonics in equal
| steps = 30
| num = 7
| denom = 3
| start = 12
| collapsed = 1
}}

Latest revision as of 07:47, 5 October 2024

This page is a stub. You can help the Xenharmonic Wiki by expanding it.
← 29ed7/3 30ed7/3 31ed7/3 →
Prime factorization 2 × 3 × 5
Step size 48.8957 ¢ 
Octave 25\30ed7/3 (1222.39 ¢) (→ 5\6ed7/3)
Twelfth 39\30ed7/3 (1906.93 ¢) (→ 13\10ed7/3)
Consistency limit 3
Distinct consistency limit 3

30 equal divisions of 7/3 (abbreviated 30ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 30 equal parts of about 48.9 ¢ each. Each step represents a frequency ratio of (7/3)1/30, or the 30th root of 7/3.

Intervals

Degrees Enneatonic ed11\9~ed7/3
1 G+/Jbd G+/Abd 48.8 48.8957
2 G#/Jb G#/Ab 97.7 97.7914
3 G#+/Jd G#+/Ad 146.6 146.6871
4 J A 195.5 195.5828
5 J+/Abd A+/Bbd 244.4 244.4785
6 J#/Ab A#/Bb 293.3 293.3742
7 J#+/Ad A#+/Bd 342.2 342.2699
8 A B 391.1 391.1656
9 A+/Bd B+/Cd 440 440.0613
10 B C 488.8 488.957
11 B+/Cbd C+/Qbd 537.7 537.8527
12 B#/Cb C#/Qb 586.6 586.7484
13 B#+/Cd C#+/Qd 635.5 635.6441
14 C Q 684.4 684.5398
15 C+/Qbd Q+/Dbd 733.3 733.43545
16 C#/Qb Q#/Db 782.2 782.33115
17 C#+/Qd Q#+/Dd 831.1 831.22685
18 Q D 880 880.1225
19 Q+/Dd D+/Sd 928.8 929.0182
20 D S 977.7 977.9139
21 D+ S+ 1026.6 1026.8096
Ebd
22 D# S# 1075.5 1075.7053
Eb
23 D#+ S#+ 1124.4 1124.601
Ed
24 E 1173.3 1173.4967
25 E+/Fbd 1222.2 1222.3924
26 E#/Fb 1271.1 1271.2881
27 E#+/Fd 1320 1320.1838
28 F 1368.8 1369.0795
29 F+/Gd 1417.7 1417.9725
30 G 1466.6 1466.8709

Harmonics

Approximation of harmonics in 30ed7/3
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +22.4 +5.0 -4.1 +0.7 -21.5 +5.0 +18.3 +10.0 +23.1 +4.8 +0.9
Relative (%) +45.8 +10.2 -8.4 +1.5 -44.0 +10.2 +37.4 +20.4 +47.3 +9.9 +1.8
Steps
(reduced) 		25
(25) 		39
(9) 		49
(19) 		57
(27) 		63
(3) 		69
(9) 		74
(14) 		78
(18) 		82
(22) 		85
(25) 		88
(28)
Approximation of harmonics in 30ed7/3
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +9.0 -21.5 +5.7 -8.2 -15.4 -16.5 -12.4 -3.4 +10.0 -21.7 -0.9
Relative (%) +18.4 -44.0 +11.7 -16.8 -31.5 -33.8 -25.3 -6.9 +20.4 -44.4 -1.7
Steps
(reduced) 		91
(1) 		93
(3) 		96
(6) 		98
(8) 		100
(10) 		102
(12) 		104
(14) 		106
(16) 		108
(18) 		109
(19) 		111
(21)
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