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33edo: Difference between revisions

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33 is also the number of years in the Iranian calendar's leap cycle, where leap year is inserted once every 4 or 5 years. This corresponds to the [[1L 7s]] with the step ratio of 5:4.
33 is also the number of years in the Iranian calendar's leap cycle, where leap year is inserted once every 4 or 5 years. This corresponds to the [[1L 7s]] with the step ratio of 5:4.
Becaus the chromatic semitone in 33edo is 1 step, 33edo is notated using sharps and flats only in [[ups and downs notation]].
{{Odd harmonics in edo|edo=33}}
{{Odd harmonics in edo|edo=33}}
== Intervals ==
== Intervals ==
{| class="wikitable center-all"
{| class="wikitable center-all"
|-
|-
! rowspan="2" |Step #
! rowspan="2" |#
! ET
! Interal
! colspan="2" | Just
! Approximate ratios
! rowspan="2" | Difference <br> (ET minus Just)
! colspan="3" |Notation
! rowspan="2" colspan="3" |Extended Pythagorean Notation
|-
! Cents
! Interval
! Cents
|-
|-
| 0
| 0
| 0¢
| 0¢
| [[1/1]]
| [[1/1]]
| 0
| 0
| 0
| Perfect Unison
| Perfect Unison
Line 39: Line 36:
| 36.364
| 36.364
| [[48/47]]
| [[48/47]]
| 36.448
| &minus;0.085
| Augmented Unison
| Augmented Unison
| A1
| A1
Line 48: Line 43:
| 72.727
| 72.727
| [[24/23]]
| [[24/23]]
| 73.681
| &minus;0.953
| Double-aug 1sn
| Double-aug 1sn
| AA1
| AA1
Line 57: Line 50:
| 109.091
| 109.091
| [[16/15]]
| [[16/15]]
| 111.731
| &minus;2.640
| Diminished 2nd
| Diminished 2nd
| d2
| d2
Line 66: Line 57:
| 145.455
| 145.455
| [[12/11]]
| [[12/11]]
| 150.637
| &minus;5.183
| Minor 2nd
| Minor 2nd
| m2
| m2
Line 75: Line 64:
| 181.818
| 181.818
| [[10/9]]
| [[10/9]]
| 182.404
| &minus;0.586
| Major 2nd
| Major 2nd
| M2
| M2
Line 84: Line 71:
| 218.182
| 218.182
| [[17/15]]
| [[17/15]]
| 216.687
| +1.495
| Augmented 2nd
| Augmented 2nd
| A2
| A2
Line 93: Line 78:
| 254.545
| 254.545
| [[15/13]]
| [[15/13]]
| 247.741
| +6.804
| Double-aug 2nd/Double-dim 3rd
| Double-aug 2nd/Double-dim 3rd
| AA2/dd3
| AA2/dd3
Line 102: Line 85:
| 290.909
| 290.909
| [[13/11]]
| [[13/11]]
| 289.210
| +1.699
| Diminished 3rd
| Diminished 3rd
| d3
| d3
Line 111: Line 92:
| 327.273
| 327.273
| [[6/5]]
| [[6/5]]
| 315.641
| +11.631
| Minor 3rd
| Minor 3rd
| m3
| m3
Line 119: Line 98:
| 10
| 10
| 363.636
| 363.636
| [[16/13]]
| 359.472
| +4.164
| Major 3rd
| Major 3rd
| M3
| M3
Line 128: Line 104:
| 11
| 11
| 400.000
| 400.000
| [[5/4]]
| 386.314
| +13.686
| Augmented 3rd
| Augmented 3rd
| A3
| A3
Line 138: Line 111:
| 436.364
| 436.364
| [[9/7]]
| [[9/7]]
| 435.084
| +1.280
| Double-dim 4th
| Double-dim 4th
| dd4
| dd4
Line 147: Line 118:
| 472.727
| 472.727
| [[21/16]]
| [[21/16]]
| 470.781
| +1.946
| Diminished 4th
| Diminished 4th
| d4
| d4
Line 155: Line 124:
| 14
| 14
| 509.091
| 509.091
| [[4/3]]
| 498.045
| +11.046
| Perfect 4th
| Perfect 4th
| P4
| P4
Line 165: Line 131:
| 545.455
| 545.455
| [[11/8]]
| [[11/8]]
| 551.318
| &minus;5.863
| Augmented 4th
| Augmented 4th
| A4
| A4
Line 174: Line 138:
| 581.818
| 581.818
| [[7/5]]
| [[7/5]]
| 582.513
| &minus;0.694
| Double-aug 4th
| Double-aug 4th
| AA4
| AA4
Line 184: Line 146:
| [[10/7]]
| [[10/7]]
| 617.488
| 617.488
| +0.694
| Double-dim 5th
| dd5
| dd5
| Abb
| Abb
Line 192: Line 152:
| 654.545
| 654.545
| [[16/11]]
| [[16/11]]
| 648.682
| +5.863
| Diminished 5th
| d5
| d5
| Ab
| Ab
Line 201: Line 158:
| 690.909
| 690.909
| [[3/2]]
| [[3/2]]
| 701.9550
| &minus;11.046
| Perfect 5th
| Perfect 5th
| P5
| P5
Line 210: Line 165:
| 727.273
| 727.273
| [[32/21]]
| [[32/21]]
| 729.219
| -1.946
| Augmented 5th
| Augmented 5th
| A5
| A5
Line 219: Line 172:
| 763.636
| 763.636
| [[14/9]]
| [[14/9]]
| 764.9159
| &minus;1.280
| Double-aug 5th
| Double-aug 5th
| AA5
| AA5
Line 228: Line 179:
| 800.000
| 800.000
| [[8/5]]
| [[8/5]]
| 813.686
| &minus;13.686
| Double-dim 6th
| Double-dim 6th
| d6
| d6
Line 237: Line 186:
| 836.364
| 836.364
| [[13/8]]
| [[13/8]]
| 840.5276
| &minus;4.164
| Minor 6th
| Minor 6th
| m6
| m6
Line 246: Line 193:
| 872.727
| 872.727
| [[5/3]]
| [[5/3]]
| 884.359
| &minus;11.631
| Major 6th
| Major 6th
| M6
| M6
Line 255: Line 200:
| 909.091
| 909.091
| [[22/13]]
| [[22/13]]
| 910.7903
| &minus;1.699
| Augmented 6th
| Augmented 6th
| A6
| A6
Line 264: Line 207:
| 945.455
| 945.455
| [[12/7]]
| [[12/7]]
| 933.129
| +12.325
| Double-aug 6th/Double-dim 7th
| Double-aug 6th/Double-dim 7th
| AA6/dd7
| AA6/dd7
Line 282: Line 223:
| 1018.182
| 1018.182
| [[9/5]]
| [[9/5]]
| 1017.596
| +0.586
| Minor 7th
| Minor 7th
| m7
| m7
Line 291: Line 230:
| 1054.545
| 1054.545
| [[11/6]]
| [[11/6]]
| 1049.363
| +5.183
| Major 7th
| Major 7th
| M7
| M7
Line 300: Line 237:
| 1090.909
| 1090.909
| [[15/8]]
| [[15/8]]
| 1088.268
| +2.640
| Augmented 7th
| Augmented 7th
| A7
| A7
Line 309: Line 244:
| 1127.273
| 1127.273
| [[23/12]]
| [[23/12]]
| 1126.319
| &minus;0.953
| Double-dim 8ve
| Double-dim 8ve
| dd8
| dd8
Line 318: Line 251:
| 1163.636
| 1163.636
| [[47/24]]
| [[47/24]]
| 1163.551
| +0.085
| Diminished 8ve
| Diminished 8ve
| d8
| d8
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