34ed7/3: Difference between revisions
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{{Stub}} | |||
{{Infobox ET}} | |||
{{ED intro}} | |||
== Intervals == | == Intervals == | ||
Line 7: | Line 10: | ||
! colspan="2" |''Pentadecatonic'' | ! colspan="2" |''Pentadecatonic'' | ||
!''Enneadecatonic'' | !''Enneadecatonic'' | ||
! | ! colspan="2" |ed11\9~ed7/3 | ||
|- | |- | ||
| rowspan="2" |1 | | rowspan="2" |1 | ||
Line 32: | Line 18: | ||
| rowspan="2" |''Qp/W\\'' | | rowspan="2" |''Qp/W\\'' | ||
| colspan="2" rowspan="2" |''Q#/Wb'' | | colspan="2" rowspan="2" |''Q#/Wb'' | ||
| rowspan="2" |43.13725 | | rowspan="2" |43.13725 | ||
| rowspan="2" |43.1433 | |||
| rowspan="2" |43. | |||
|- | |- | ||
|Jv | |Jv | ||
Line 70: | Line 34: | ||
| rowspan="2" |''Ab'' | | rowspan="2" |''Ab'' | ||
| colspan="3" rowspan="2" |''W'' | | colspan="3" rowspan="2" |''W'' | ||
| rowspan="2" |86.2745 | | rowspan="2" |86.2745 | ||
| rowspan="2" |86.2865 | |||
| rowspan="2" |86. | |||
|- | |- | ||
|Jbb | |Jbb | ||
Line 109: | Line 51: | ||
| rowspan="2" |''W#'' | | rowspan="2" |''W#'' | ||
| rowspan="2" |''W#/Eb'' | | rowspan="2" |''W#/Eb'' | ||
| rowspan="2" |129.4118 | | rowspan="2" |129.4118 | ||
| rowspan="2" |129.4298 | |||
| rowspan="2" |129. | |||
|- | |- | ||
| colspan="2" |G#v | | colspan="2" |G#v | ||
Line 145: | Line 64: | ||
| colspan="2" |G# | | colspan="2" |G# | ||
| colspan="3" |''E(\\/b)'' | | colspan="3" |''E(\\/b)'' | ||
|172.549 | |172.549 | ||
172.57305 | |172.57305 | ||
|- | |- | ||
| rowspan="2" |5 | | rowspan="2" |5 | ||
Line 179: | Line 76: | ||
| colspan="2" rowspan="2" |''E'' | | colspan="2" rowspan="2" |''E'' | ||
| rowspan="2" |''R'' | | rowspan="2" |''R'' | ||
| rowspan="2" |215.6863 | | rowspan="2" |215.6863 | ||
| rowspan="2" |215.7163 | |||
| rowspan="2" | | |||
|- | |- | ||
|Jv | |Jv | ||
Line 218: | Line 93: | ||
|''E#/Rb'' | |''E#/Rb'' | ||
|''R#/Tb'' | |''R#/Tb'' | ||
|258.8235 | |258.8235 | ||
258.8596 | |258.8596 | ||
|- | |- | ||
|7 | |7 | ||
Line 253: | Line 106: | ||
| colspan="2" |''R'' | | colspan="2" |''R'' | ||
|''T'' | |''T'' | ||
|301.9608 | |301.9608 | ||
302.0028 | |302.0028 | ||
|- | |- | ||
|8 | |8 | ||
Line 289: | Line 120: | ||
|''R#/Tb'' | |''R#/Tb'' | ||
|''T#/Yb'' | |''T#/Yb'' | ||
|345.098 | |345.098 | ||
345.1461 | |345.1461 | ||
|- | |- | ||
|9 | |9 | ||
Line 324: | Line 133: | ||
| colspan="2" |''T'' | | colspan="2" |''T'' | ||
|''Y'' | |''Y'' | ||
|388.2353 | |388.2353 | ||
388.2894 | |388.2894 | ||
|- | |- | ||
|10 | |10 | ||
Line 360: | Line 147: | ||
|''T#/Ab'' | |''T#/Ab'' | ||
|''Y#/Ub'' | |''Y#/Ub'' | ||
|431.37255 | |431.37255 | ||
431.4326 | |431.4326 | ||
|- | |- | ||
|11 | |11 | ||
Line 395: | Line 160: | ||
| colspan="2" |''A'' | | colspan="2" |''A'' | ||
|''U'' | |''U'' | ||
|474.5098 | |474.5098 | ||
474.5759 | |474.5759 | ||
|- | |- | ||
|12 | |12 | ||
Line 431: | Line 174: | ||
|''A#'' | |''A#'' | ||
|''U#/Ab'' | |''U#/Ab'' | ||
|517.6471 | |517.6471 | ||
517.7191 | |517.7191 | ||
|- | |- | ||
|13 | |13 | ||
Line 467: | Line 188: | ||
|''Sb'' | |''Sb'' | ||
|''A'' | |''A'' | ||
|560.7843 | |560.7843 | ||
560.8624 | |560.8624 | ||
|- | |- | ||
|14 | |14 | ||
Line 501: | Line 200: | ||
|''C'' | |''C'' | ||
| colspan="3" |''S'' | | colspan="3" |''S'' | ||
|603.9216 | |603.9216 | ||
604.0057 | |604.0057 | ||
|- | |- | ||
|15 | |15 | ||
Line 537: | Line 214: | ||
|''S#/Db'' | |''S#/Db'' | ||
|''S#/Db'' | |''S#/Db'' | ||
|647.0588 | |647.0588 | ||
647.1489 | |647.1489 | ||
|- | |- | ||
|16 | |16 | ||
Line 571: | Line 226: | ||
|''Q'' | |''Q'' | ||
| colspan="3" |''D'' | | colspan="3" |''D'' | ||
|690.1961 | |690.1961 | ||
690.2922 | |690.2922 | ||
|- | |- | ||
|17 | |17 | ||
Line 607: | Line 240: | ||
|''D#/Fb'' | |''D#/Fb'' | ||
|''D#/Fb'' | |''D#/Fb'' | ||
| | |733.{{Overline|3}} | ||
|733.43545 | |||
| | |||
| | |||
733.43545 | |||
|- | |- | ||
|18 | |18 | ||
Line 640: | Line 252: | ||
|''Db'' | |''Db'' | ||
| colspan="3" |''F'' | | colspan="3" |''F'' | ||
|776.4706 | |776.4706 | ||
776.5787 | |776.5787 | ||
|- | |- | ||
|19 | |19 | ||
Line 676: | Line 266: | ||
|''F#/Gb'' | |''F#/Gb'' | ||
|''F#/Gb'' | |''F#/Gb'' | ||
|819.6078 | |819.6078 | ||
819.722 | |819.722 | ||
|- | |- | ||
|20 | |20 | ||
Line 711: | Line 278: | ||
|''Q#'' | |''Q#'' | ||
| colspan="3" |''G'' | | colspan="3" |''G'' | ||
|862.7451 | |862.7451 | ||
862.8982 | |862.8982 | ||
|- | |- | ||
|21 | |21 | ||
Line 747: | Line 292: | ||
|''G#'' | |''G#'' | ||
|''H'' | |''H'' | ||
|905.88235 | |905.88235 | ||
906.0085 | |906.0085 | ||
|- | |- | ||
|22 | |22 | ||
Line 783: | Line 306: | ||
|''Zb'' | |''Zb'' | ||
|''H#'' | |''H#'' | ||
|949.0196 | |949.0196 | ||
949.1518 | |949.1518 | ||
|- | |- | ||
|23 | |23 | ||
Line 818: | Line 319: | ||
| colspan="2" |''Z'' | | colspan="2" |''Z'' | ||
|''Jb'' | |''Jb'' | ||
|992.1569 | |992.1569 | ||
922.295 | |922.295 | ||
|- | |- | ||
|24 | |24 | ||
Line 854: | Line 333: | ||
|''Z#/Xb'' | |''Z#/Xb'' | ||
|''J'' | |''J'' | ||
|1035.2941 | |1035.2941 | ||
1035.4383 | |1035.4383 | ||
|- | |- | ||
| rowspan="2" |25 | | rowspan="2" |25 | ||
Line 889: | Line 346: | ||
| colspan="2" rowspan="2" |''X'' | | colspan="2" rowspan="2" |''X'' | ||
| rowspan="2" |''J#/Zb'' | | rowspan="2" |''J#/Zb'' | ||
| rowspan="2" |1078.4314 | | rowspan="2" |1078.4314 | ||
| rowspan="2" |1078.58155 | |||
| rowspan="2" | | |||
|- | |- | ||
| colspan="2" |Ebv | | colspan="2" |Ebv | ||
Line 925: | Line 360: | ||
|''X#/Cb'' | |''X#/Cb'' | ||
|''Z'' | |''Z'' | ||
|1121.5686 | |1121.5686 | ||
1121.7248 | |1121.7248 | ||
|- | |- | ||
| rowspan="2" |27 | | rowspan="2" |27 | ||
Line 958: | Line 371: | ||
| colspan="2" rowspan="2" |''C'' | | colspan="2" rowspan="2" |''C'' | ||
| rowspan="2" |''X'' | | rowspan="2" |''X'' | ||
| rowspan="2" |1164.7059 | | rowspan="2" |1164.7059 | ||
| rowspan="2" |1164.8681 | |||
| rowspan="2" | | |||
|- | |- | ||
| colspan="2" |Fv | | colspan="2" |Fv | ||
Line 995: | Line 387: | ||
|''C#/Vb'' | |''C#/Vb'' | ||
|''X#/Cb'' | |''X#/Cb'' | ||
|1207.8731 | |1207.8731 | ||
1208.0113 | |1208.0113 | ||
|- | |- | ||
| rowspan="2" |29 | | rowspan="2" |29 | ||
Line 1,027: | Line 398: | ||
| colspan="2" rowspan="2" |''V'' | | colspan="2" rowspan="2" |''V'' | ||
| rowspan="2" |''C'' | | rowspan="2" |''C'' | ||
| rowspan="2" |1250.9804 | | rowspan="2" |1250.9804 | ||
| rowspan="2" |1251.1546 | |||
| rowspan="2" | | |||
|- | |- | ||
| colspan="2" |Eb | | colspan="2" |Eb | ||
Line 1,059: | Line 409: | ||
| colspan="2" |E | | colspan="2" |E | ||
| colspan="3" |''V(p/#)'' | | colspan="3" |''V(p/#)'' | ||
|1294.11765 | |1294.11765 | ||
1294.2979 | |1294.2979 | ||
|- | |- | ||
|31 | |31 | ||
Line 1,092: | Line 420: | ||
|''Bb'' | |''Bb'' | ||
|''V#/Bb'' | |''V#/Bb'' | ||
|1337.2549 | |1337.2549 | ||
1337.4411 | |1337.4411 | ||
|- | |- | ||
|32 | |32 | ||
Line 1,123: | Line 429: | ||
| colspan="2" |F | | colspan="2" |F | ||
| colspan="3" |''B'' | | colspan="3" |''B'' | ||
|1380.3922 | |1380.3922 | ||
1380.5844 | |1380.5844 | ||
|- | |- | ||
| rowspan="2" |33 | | rowspan="2" |33 | ||
Line 1,155: | Line 439: | ||
| rowspan="2" |''Bp/Q\\'' | | rowspan="2" |''Bp/Q\\'' | ||
| colspan="2" rowspan="2" |''B#/Qb'' | | colspan="2" rowspan="2" |''B#/Qb'' | ||
| rowspan="2" |1423.5297 | | rowspan="2" |1423.5297 | ||
| rowspan="2" |1423.7276 | |||
| rowspan="2" | | |||
|- | |- | ||
| colspan="4" |Gv | | colspan="4" |Gv | ||
Line 1,186: | Line 448: | ||
| colspan="6" |G | | colspan="6" |G | ||
| colspan="3" |''Q'' | | colspan="3" |''Q'' | ||
| | |1466.{{Overline|6}} | ||
|1466.8709 | |||
|} | |||
| | |||
| | |||
| | |||
== Harmonics == | |||
{{Harmonics in equal | |||
| steps = 34 | |||
| num = 7 | |||
| | | denom = 3 | ||
| | }} | ||
{{Harmonics in equal | |||
| | | steps = 34 | ||
| num = 7 | |||
| denom = 3 | |||
| | | start = 12 | ||
| | | collapsed = 1 | ||
| | }} | ||
| | |||
| | |||
Latest revision as of 07:50, 5 October 2024
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This page is a stub. You can help the Xenharmonic Wiki by expanding it. |
← 33ed7/3 | 34ed7/3 | 35ed7/3 → |
34 equal divisions of 7/3 (abbreviated 34ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 34 equal parts of about 43.1 ¢ each. Each step represents a frequency ratio of (7/3)1/34, or the 34th root of 7/3.
Intervals
Degrees | Enneatonic | Pentadecatonic | Enneadecatonic | ed11\9~ed7/3 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 1# | G# | G^ | Qp/W\\ | Q#/Wb | 43.13725 | 43.1433 | |||||
Jv | Av | Jbv | Abv | |||||||||
2 | 1x/2bb | Gx | J | A | Jb | Ab | W | 86.2745 | 86.2865 | |||
Jbb | Abb | |||||||||||
3 | 2b | Jb | Ab | J^/A\\v | A^/B\\v | Jb^ | Ab^ | Wp | W# | W#/Eb | 129.4118 | 129.4298 |
G#v | ||||||||||||
4 | 2 | J | A | A\\ | B\\ | G# | E(\\/b) | 172.549 | 172.57305 | |||
5 | 2# | J# | A# | A\\^/Jpv | B\\^/Apv | G#v | E | R | 215.6863 | 215.7163 | ||
Jv | Av | |||||||||||
6 | 2x/3bb | Jx/Abb | Ax/Bbb | Jp | Ap | J | A | Ep/R\\ | E#/Rb | R#/Tb | 258.8235 | 258.8596 |
7 | 3b | Ab | Bb | Jp^/Av | Ap^/Bv | J^/Av | A^/Bv | R | T | 301.9608 | 302.0028 | |
8 | 3 | A | B | A | B | A | B | Rp/T\\ | R#/Tb | T#/Yb | 345.098 | 345.1461 |
9 | 3# | A# | B# | A^/Bv | B^/Cv | A^/Bbv | B^/Cbv | T | Y | 388.2353 | 388.2894 | |
10 | 3x/4b | Ax/Bbb | Bx/Cbb | B | C | Bb | Cb | Tp\A\\ | T#/Ab | Y#/Ub | 431.37255 | 431.4326 |
11 | 4b | Bb | Cb | B^/C\\v | C^/Q\\v | Bb^/A#v | Cb^/B#v | A | U | 474.5098 | 474.5759 | |
12 | 4 | B | C | C\\ | Q\\ | A# | B# | Ap | A# | U#/Ab | 517.6471 | 517.7191 |
13 | 4# | B# | C# | C\\^/Bpv | Q\\^/Cpv | A#^/Bv | B#^/Cv | S\\ | Sb | A | 560.7843 | 560.8624 |
14 | 5b | Cb | Qb | Bp | Cp | B | C | S | 603.9216 | 604.0057 | ||
15 | 5 | C | Q | Bp^/Cv | Cp^/Qv | B^/Cv | C^/Qv | Sp/D\\ | S#/Db | S#/Db | 647.0588 | 647.1489 |
16 | 5# | C# | Q# | C | Q | C | Q | D | 690.1961 | 690.2922 | ||
17 | 5x/6bb | Cx/Qbb | Qx/Dbb | C^/Qv | Q^/Dv | C^/Qbv | Q^/Dbv | Dp/F\\ | D#/Fb | D#/Fb | 733.3 | 733.43545 |
18 | 6b | Qb | Db | Q | D | Qb | Db | F | 776.4706 | 776.5787 | ||
19 | 6 | Q | D | Q^/D\\v | D^/E\\v | Qb^/C#v | Db^/Q#v | Fp/G\\ | F#/Gb | F#/Gb | 819.6078 | 819.722 |
20 | 6# | Q# | D# | D\\ | E\\ | C# | Q# | G | 862.7451 | 862.8982 | ||
21 | 6x/7bb | Qx/Dbb | Dx/Sbb | D\\^/Qpv | E\\^/Dpv | C#^/Qv | Q#^/Dv | Gp | G# | H | 905.88235 | 906.0085 |
22 | 7b | Db | Sb | Qp | Dp | Q | D | Z\\ | Zb | H# | 949.0196 | 949.1518 |
23 | 7 | D | S | Qp^/Dv | Dp^/Ev | Q^/Dv | D^/Sv | Z | Jb | 992.1569 | 922.295 | |
24 | 7# | D# | S# | D | E | D | S | Zp/X\\ | Z#/Xb | J | 1035.2941 | 1035.4383 |
25 | 7x/8bb | Dx/Ebb | Sx/Ebb | D^/Ev | E^/Sv | D^ | S^ | X | J#/Zb | 1078.4314 | 1078.58155 | |
Ebv | ||||||||||||
26 | 8b | Eb | E | S | Eb | Xp/C\\ | X#/Cb | Z | 1121.5686 | 1121.7248 | ||
27 | 8 | E | E^ | S^ | Eb^ | C | X | 1164.7059 | 1164.8681 | |||
Fv | D#v | S#v | ||||||||||
28 | 8# | E# | F | D# | S# | Cp/V\\ | C#/Vb | X#/Cb | 1207.8731 | 1208.0113 | ||
29 | 8x/9bb | Ex/Fbb | F^/G\\v | D#v | S#v | V | C | 1250.9804 | 1251.1546 | |||
Eb | ||||||||||||
30 | 9b | Fb | G\\ | E | V(p/#) | 1294.11765 | 1294.2979 | |||||
31 | 9 | F | G\\^Fpv | E^/Fv | B// | Bb | V#/Bb | 1337.2549 | 1337.4411 | |||
32 | 9# | F# | Fp | F | B | 1380.3922 | 1380.5844 | |||||
33 | 1# | G# | Fp^ | F^ | Bp/Q\\ | B#/Qb | 1423.5297 | 1423.7276 | ||||
Gv | ||||||||||||
34 | 1 | G | Q | 1466.6 | 1466.8709 |
Harmonics
Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | +8.0 | -3.7 | +16.0 | +18.0 | +4.4 | -3.7 | -19.1 | -7.3 | -17.1 | -9.6 | +12.4 |
Relative (%) | +18.6 | -8.5 | +37.1 | +41.7 | +10.1 | -8.5 | -44.3 | -16.9 | -39.7 | -22.2 | +28.7 | |
Steps (reduced) |
28 (28) |
44 (10) |
56 (22) |
65 (31) |
72 (4) |
78 (10) |
83 (15) |
88 (20) |
92 (24) |
96 (28) |
100 (32) |
Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | +3.2 | +4.4 | +14.3 | -11.1 | +13.4 | +0.7 | -6.6 | -9.1 | -7.3 | -1.6 | +7.8 |
Relative (%) | +7.5 | +10.1 | +33.3 | -25.7 | +31.0 | +1.6 | -15.3 | -21.1 | -16.9 | -3.6 | +18.0 | |
Steps (reduced) |
103 (1) |
106 (4) |
109 (7) |
111 (9) |
114 (12) |
116 (14) |
118 (16) |
120 (18) |
122 (20) |
124 (22) |
126 (24) |