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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox ET}} |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | {{ED intro}} |
| : This revision was by author [[User:Kosmorsky|Kosmorsky]] and made on <tt>2011-11-17 17:14:08 UTC</tt>.<br>
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| : The original revision id was <tt>276715530</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
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| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">67 equal divisions of the octave divides the octave into 67 equal parts of 17.910 cents each. It tempers out 81/80, supporting meantone temperament, with a tuning which is approximately 1/6 comma (the tuning favored by Mozart and contemporaries), or 0.16 comma, meantone. In the 7-limit the patent val tempers out 1029/1024 and 1728/1715, so that it supports [[Meantone family|mothra temperament]]. In the 11-limit it tempers out 176/175 and 540/539, supporting mosura, an alternative 11-limit mothra. In the 13-limit it tempers out 144/143 and 196/195, supporting 13-limit mosura. It tempers out the orgonisma, and on the 2.7.11 subgroup it supports [[Orgonia|orgone temperament]].
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| A promising tuning which has, as many relatively large equal temperaments do, a variety of tonal resources: it is the first edo to have both a light meantone and an orgone temperament. It has relatively good approximations of the 3rd, 7th, 11th, 13th, 15th, 17th harmonics, although the 5th, 9th, and 19th as well as certain higher ones are workable as well. 33+34 can be used to construct this temperament explaining some of its properties.
| | == Theory == |
| | 67edo [[tempering out|tempers out]] [[81/80]], [[support]]ing [[meantone]], with a tuning which is slightly sharp of [[1/6-comma meantone|1/6-comma]] (the tuning favored by {{w|Wolfgang Amadeus Mozart|Mozart}} and contemporaries, though they suggested the flatter and composite [[55edo]] as an approximation). It is indistinguishable from {{nowrap|{{frac|4|25}} {{=}} 0.16-comma}} meantone. In the 7-limit the [[patent val]] tempers out [[1029/1024]] and [[1728/1715]], so that it supports [[mothra]]. In the 11-limit it tempers out [[176/175]] and [[540/539]], supporting [[mosura]], an alternative 11-limit mothra. In the 13-limit it tempers out [[144/143]] and [[196/195]], supporting 13-limit mosura. It tempers out the [[orgonisma]], and on the 2.7.11 subgroup it supports the [[orgone]] temperament. |
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| Music:
| | It is a promising tuning which has, as many relatively large equal temperaments do, a variety of tonal resources: it is the second edo after [[26edo]] to have both meantone and an orgone temperament. It has relatively good approximations of the [[3/1|3rd]], [[7/1|7th]], [[11/1|11th]], [[13/1|13th]], [[15/1|15th]], [[17/1|17th]] [[harmonic]]s, although the [[5/1|5th]], [[9/1|9th]], and [[19/1|19th]] as well as certain higher ones are workable as well. {{nowrap|33 + 34}} can be used to construct this temperament explaining some of its properties. It does well on the 2.3.7.11.13.17.23.31.37.41 [[subgroup]]. |
| http://soonlabel.com/xenharmonic/wp-content/uploads/2011/11/67-edo.mp3 "Beginning of a piece in 67 tone", Kosmorsky
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| Cents
| | === Prime harmonics === |
| | {{Harmonics in equal|67|columns=13}} |
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| 0: 1/1 0.000 unison, perfect prime
| | === Subsets and supersets === |
| 1: 17.910 cents 17.910
| | 67edo is the 19th [[prime edo]], following [[61edo]] and before [[71edo]]. |
| 2: 35.821 cents 35.821
| | |
| 3: 53.731 cents 53.731
| | == Intervals == |
| 4: 71.642 cents 71.642
| | {{Interval table}} |
| 5: 89.552 cents 89.552
| | |
| 6: 107.463 cents 107.463
| | == Notation == |
| 7: 125.373 cents 125.373
| | === Stein–Zimmermann–Gould notation === |
| 8: 143.284 cents 143.284
| | [[Stein–Zimmermann–Gould notation]] uses sharps and flats with arrows: |
| 9: 161.194 cents 161.194
| | {{Sharpness-sharp5-szg}} |
| 10: 179.104 cents 179.104
| | |
| 11: 197.015 cents 197.015
| | === Kite's ups and downs notation === |
| 12: 214.925 cents 214.925
| | 67edo can also be notated with [[Kite's ups and downs notation|Kite's ups and downs]], spoken as up, dup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, dupflat etc. Note that dudsharp is equivalent to trup (triple-up) and dupflat is equivalent to trud (triple-down). |
| 13: 232.836 cents 232.836
| | {{Sharpness-sharp5a}} |
| 14: 250.746 cents 250.746
| | |
| 15: 268.657 cents 7/6
| | === Sagittal notation === |
| 16: 286.567 cents 286.567
| | ==== Evo flavor ==== |
| 17: 304.478 cents 304.478
| | <imagemap> |
| 18: 322.388 cents 322.388
| | File:67-EDO_Evo_Sagittal.svg |
| 19: 340.299 cents 340.299
| | desc none |
| 20: 358.209 cents 358.209 | | rect 80 0 300 50 [[Sagittal_notation]] |
| 21: 376.119 cents 5/4 -
| | rect 300 0 735 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation] |
| 22: 394.030 cents 5/4 +
| | rect 20 80 160 106 [[896/891]] |
| 23: 411.940 cents 411.940
| | rect 160 80 280 106 [[36/35]] |
| 24: 429.851 cents 429.851
| | rect 280 80 440 106 [[1053/1024]] |
| 25: 447.761 cents 447.761
| | default [[File:67-EDO_Evo_Sagittal.svg]] |
| 26: 465.672 cents 21/16
| | </imagemap> |
| 27: 483.582 cents 483.582
| | |
| 28: 501.493 cents 501.493
| | ==== Revo flavor ==== |
| 29: 519.403 cents 519.403
| | <imagemap> |
| 30: 537.313 cents 537.313
| | File:67-EDO_Revo_Sagittal.svg |
| 31: 555.224 cents 11/8
| | desc none |
| 32: 573.134 cents 573.134
| | rect 80 0 300 50 [[Sagittal_notation]] |
| 33: 591.045 cents 591.045
| | rect 300 0 759 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation] |
| 34: 608.955 cents 608.955
| | rect 20 80 160 106 [[896/891]] |
| 35: 626.866 cents 626.866
| | rect 160 80 280 106 [[36/35]] |
| 36: 644.776 cents 644.776
| | rect 280 80 440 106 [[1053/1024]] |
| 37: 662.687 cents 662.687
| | default [[File:67-EDO_Revo_Sagittal.svg]] |
| 38: 680.597 cents 680.597
| | </imagemap> |
| 39: 698.507 cents 3/2
| | |
| 40: 716.418 cents 716.418
| | In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation #Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this edo. |
| 41: 734.328 cents 734.328
| | |
| 42: 752.239 cents 752.239
| | == Scales == |
| 43: 770.149 cents 770.149
| | {{Idiosyncratic terms}} |
| 44: 788.060 cents 788.060
| | |
| 45: 805.970 cents 805.970
| | === Mos scales === |
| 46: 823.881 cents 823.881
| | * Meantone[5]: 11 11 17 11 17 |
| 47: 841.791 cents 841.791
| | * Meantone[7]: 11 11 6 11 11 11 6 |
| 48: 859.701 cents 859.701
| | * Barbados[5], Bustling Docks (original/default tuning): 14 14 11 14 14 |
| 49: 877.612 cents 877.612
| | * Barbados[9]: 11 3 11 3 11 3 11 3 11 |
| 50: 895.522 cents 895.522
| | |
| 51: 913.433 cents 913.433
| | === Modmos scales === |
| 52: 931.343 cents 931.343
| | * Cavernous (original/default tuning): 14 14 11 21 7 |
| 53: 949.254 cents 949.254
| | * Formicarium (original/default tuning): 14 7 18 14 14 |
| 54: 967.164 cents 7/4
| | * Negri Blues (original/default tuning): 14 14 3 8 14 14 |
| 55: 985.075 cents 985.075
| | * Negri Blues Septatonic (original/default tuning): 14 14 3 8 11 3 14 |
| 56: 1002.985 cents 1002.985
| | * Negri Blues Octatonic (original/default tuning): 7 14 7 11 7 11 3 7 |
| 57: 1020.896 cents 1020.896
| | * Understory (original/default tuning): 14 7 18 7 21 |
| 58: 1038.806 cents 1038.806
| | * Meantone Ionian Pentatonic: 22 6 11 22 6 |
| 59: 1056.716 cents 1056.716
| | * Meantone Minor Melodic: 11 6 11 11 11 11 6 |
| 60: 1074.627 cents 1074.627
| | * Meantone Minor Harmonic: 11 6 11 11 6 16 6 |
| 61: 1092.537 cents 1092.537
| | * Meantone Minor Hexatonic: 11 6 11 11 17 11 |
| 62: 1110.448 cents 1110.448
| | * Meantone Dorian Harmonic: 11 6 16 6 11 6 11 |
| 63: 1128.358 cents 1128.358
| | * Meantone Mixolydian Pentatonic: 22 6 11 17 11 |
| 64: 1146.269 cents 1146.269
| | * Meantone Phrygian Dominant: 6 16 6 11 6 11 11 |
| 65: 1164.179 cents 1164.179
| | * Meantone Phrygian Dominant Hexatonic: 6 16 6 11 6 22 |
| 66: 1182.090 cents 1182.090
| | * Meantone Phrygian Dominant Pentatonic: 22 6 11 6 22 |
| 67: 2/1 1200.000 octave</pre></div>
| | * Meantone Phrygian Pentatonic: 6 11 22 6 22 |
| <h4>Original HTML content:</h4>
| | * Meantone Double Harmonic: 6 16 6 11 6 16 6 |
| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>67edo</title></head><body>67 equal divisions of the octave divides the octave into 67 equal parts of 17.910 cents each. It tempers out 81/80, supporting meantone temperament, with a tuning which is approximately 1/6 comma (the tuning favored by Mozart and contemporaries), or 0.16 comma, meantone. In the 7-limit the patent val tempers out 1029/1024 and 1728/1715, so that it supports <a class="wiki_link" href="/Meantone%20family">mothra temperament</a>. In the 11-limit it tempers out 176/175 and 540/539, supporting mosura, an alternative 11-limit mothra. In the 13-limit it tempers out 144/143 and 196/195, supporting 13-limit mosura. It tempers out the orgonisma, and on the 2.7.11 subgroup it supports <a class="wiki_link" href="/Orgonia">orgone temperament</a>.<br />
| | |
| <br />
| | === Blues scales === |
| A promising tuning which has, as many relatively large equal temperaments do, a variety of tonal resources: it is the first edo to have both a light meantone and an orgone temperament. It has relatively good approximations of the 3rd, 7th, 11th, 13th, 15th, 17th harmonics, although the 5th, 9th, and 19th as well as certain higher ones are workable as well. 33+34 can be used to construct this temperament explaining some of its properties.<br />
| | * [[Lost spirit]] (approximated from [[31edo]]): 17 11 6 5 13 4 11 |
| <br />
| | * [[Blackened skies]] (approximated from [[72edo]]): 18 10 5 6 5 18 5 |
| Music:<br />
| | * Blues Aeolian Hexatonic: 17 11 6 5 6 22 |
| <!-- ws:start:WikiTextUrlRule:78:http://soonlabel.com/xenharmonic/wp-content/uploads/2011/11/67-edo.mp3 --><a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/wp-content/uploads/2011/11/67-edo.mp3" rel="nofollow">http://soonlabel.com/xenharmonic/wp-content/uploads/2011/11/67-edo.mp3</a><!-- ws:end:WikiTextUrlRule:78 --> &quot;Beginning of a piece in 67 tone&quot;, Kosmorsky<br />
| | * Blues Aeolian Pentatonic I: 17 11 11 6 22 |
| <br />
| | * Blues Aeolian Pentatonic II: 17 22 6 11 11 |
| Cents<br />
| | * Blues Bright Double Harmonic: 6 16 6 11 6 11 6 5 |
| <br />
| | * Blues Dark Double Harmonic: 11 6 11 6 5 6 16 6 |
| 0: 1/1 0.000 unison, perfect prime<br />
| | * Blues Dorian Hexatonic: 17 11 11 11 6 11 |
| 1: 17.910 cents 17.910<br />
| | * Blues Dorian Pentatonic: 17 22 11 6 11 |
| 2: 35.821 cents 35.821<br />
| | * Blues Dorian Septatonic: 17 11 6 5 11 6 11 |
| 3: 53.731 cents 53.731<br />
| | * Blues Harmonic Hexatonic: 11 6 11 11 22 6 |
| 4: 71.642 cents 71.642<br />
| | * Blues Harmonic Septatonic: 17 11 6 5 6 11 5 6 |
| 5: 89.552 cents 89.552<br />
| | * Blues Leading: 17 11 6 5 17 6 5 |
| 6: 107.463 cents 107.463<br /> | | * Blues Minor: 17 11 6 5 17 11 |
| 7: 125.373 cents 125.373<br />
| | * Blues Minor Maj7: 17 11 6 5 22 6 |
| 8: 143.284 cents 143.284<br />
| | * Blues Pentachordal: 11 6 11 5 6 28 |
| 9: 161.194 cents 161.194<br />
| | * Greyed Skies (approximated from [[91edo]]): 17 11 5 6 6 17 5 |
| 10: 179.104 cents 179.104<br /> | | * Akebono I: 11 6 11 11 17 |
| 11: 197.015 cents 197.015<br />
| | * Augmented: 17 6 16 6 16 6 |
| 12: 214.925 cents 214.925<br /> | | * Dominant Pentatonic: 11 11 17 17 11 |
| 13: 232.836 cents 232.836<br /> | | * Hirajoshi: 11 6 12 6 22 |
| 14: 250.746 cents 250.746<br />
| | * Javanese Pentachordal: 6 11 17 4 29 |
| 15: 268.657 cents 7/6<br />
| | |
| 16: 286.567 cents 286.567<br />
| | === Others === |
| 17: 304.478 cents 304.478<br />
| | * Approximation of ''[[Pelog]] lima'': 6 10 22 7 22 |
| 18: 322.388 cents 322.388<br />
| | * [[Maeve Gutierrez#Gutierrez-Lambeth quasi-subharmonic pentatonic|Gutierrez-Lambeth quasi-subharmonic pentatonic]] ''(octave-reduced: 9 6 23 16 13)'' |
| 19: 340.299 cents 340.299<br />
| | * Arcade (approximated from [[32afdo]]): 22 4 13 15 13 |
| 20: 358.209 cents 358.209<br />
| | * Cosmic (approximated from [[32afdo]]): 29 10 6 11 11 |
| 21: 376.119 cents 5/4 -<br />
| | * Mechanical (approximated from [[16afdo]]): 17 5 17 15 13 |
| 22: 394.030 cents 5/4 +<br />
| | * Moonbeam (approximated from [[16afdo]]): 11 6 12 22 6 |
| 23: 411.940 cents 411.940<br />
| | * Springwater (approximated from [[8afdo]]): 11 11 17 15 13 |
| 24: 429.851 cents 429.851<br />
| | * Volcanic (approximated from [[16afdo]]): 6 16 17 15 13 |
| 25: 447.761 cents 447.761<br />
| | * Deja Vu (approximated from [[101afdo]]): 18 21 6 12 10 |
| 26: 465.672 cents 21/16<br />
| | * Freeway (approximated from [[6afdo]]): 15 12 11 11 9 8 |
| 27: 483.582 cents 483.582<br />
| | * Mushroom (approximated from [[30afdo]]): 15 12 11 4 24 |
| 28: 501.493 cents 501.493<br />
| | * Underpass (approximated from [[10afdo]]): 18 21 12 6 10 |
| 29: 519.403 cents 519.403<br />
| | * Sourgummy (approximated from [[51afdo]]): 14 12 14 14 13 |
| 30: 537.313 cents 537.313<br />
| | * Bubblegum/Cola (approximated from [[60afdo]]/[[99afdo]]): 14 13 13 13 14 |
| 31: 555.224 cents 11/8<br />
| | * Tropicalpunch/Whitechocolate (approximated from [[62afdo]]/[[90afdo]]): 13 14 13 14 13 |
| 32: 573.134 cents 573.134<br />
| | * Lemonade (approximated from [[79afdo]]): 14 13 13 14 13 |
| 33: 591.045 cents 591.045<br />
| | * Candycorn (approximated from [[91afdo]]): 11 12 11 10 12 11 |
| 34: 608.955 cents 608.955<br />
| | * Trailmix (approximated from [[97afdo]]): 11 11 11 12 11 11 |
| 35: 626.866 cents 626.866<br />
| | * Liquorice (approximated from [[101afdo]]): 11 11 12 10 12 11 |
| 36: 644.776 cents 644.776<br />
| | * Fishcracker (approximated from [[80afdo]]): 9 11 9 9 10 9 10 |
| 37: 662.687 cents 662.687<br />
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| 38: 680.597 cents 680.597<br />
| | == Instruments == |
| 39: 698.507 cents 3/2<br />
| | * [[Lumatone mapping for 67edo]] |
| 40: 716.418 cents 716.418<br />
| | |
| 41: 734.328 cents 734.328<br />
| | == Music == |
| 42: 752.239 cents 752.239<br />
| | ; [[Bryan Deister]] |
| 43: 770.149 cents 770.149<br />
| | * [https://www.youtube.com/shorts/uwxey9_jINA ''microtonal improvisation in 67edo''] (2025) |
| 44: 788.060 cents 788.060<br />
| | * [https://www.youtube.com/shorts/L6BXGZyvK8Y ''67edo prelude''] (2025) |
| 45: 805.970 cents 805.970<br />
| | * [https://www.youtube.com/shorts/za_Ov95HbjQ ''improv in 67edo''] (2025) |
| 46: 823.881 cents 823.881<br />
| | |
| 47: 841.791 cents 841.791<br />
| | ; [[Delta Quartz]] |
| 48: 859.701 cents 859.701<br />
| | * [https://youtu.be/WOguarC1lEI ''Making microtonality accessible - "Keep It Tight"''] (2026) (also has a small amount of 24edo) |
| 49: 877.612 cents 877.612<br />
| | |
| 50: 895.522 cents 895.522<br />
| | ; [[Dolores Catherino]] |
| 51: 913.433 cents 913.433<br />
| | * [https://youtu.be/AYHpxeM6o_g ''Moments of Unexpected Beauty''] (2026) |
| 52: 931.343 cents 931.343<br />
| | |
| 53: 949.254 cents 949.254<br />
| | ; [[Peter Kosmorsky]] |
| 54: 967.164 cents 7/4<br />
| | * [http://soonlabel.com/xenharmonic/wp-content/uploads/2011/11/67-edo.mp3 Beginning of a piece in 67 tone] (2011) {{dead link}} |
| 55: 985.075 cents 985.075<br />
| | |
| 56: 1002.985 cents 1002.985<br />
| | ; [[Budjarn Lambeth]] |
| 57: 1020.896 cents 1020.896<br />
| | * [https://youtu.be/xeOjzyXJl_M 67edo Negri8 MODMOS Improvisation] (2024) |
| 58: 1038.806 cents 1038.806<br />
| | |
| 59: 1056.716 cents 1056.716<br />
| | [[Category:Equal divisions of the octave|##]] <!-- 2-digit number --> |
| 60: 1074.627 cents 1074.627<br />
| | [[Category:Meantone]] |
| 61: 1092.537 cents 1092.537<br />
| | [[Category:Listen]] |
| 62: 1110.448 cents 1110.448<br />
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| 63: 1128.358 cents 1128.358<br />
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| 64: 1146.269 cents 1146.269<br />
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| 65: 1164.179 cents 1164.179<br />
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| 66: 1182.090 cents 1182.090<br />
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| 67: 2/1 1200.000 octave</body></html></pre></div>
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