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| <h2>IMPORTED REVISION FROM WIKISPACES</h2> | | <span style="display: block; text-align: right;"> |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | __FORCETOC__ |
| : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2017-11-23 15:46:12 UTC</tt>.<br>
| | [[:de:übermässige_Temperaturen Deutsch]]</span> |
| : The original revision id was <tt>622276421</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"><span style="display: block; text-align: right;">[[toc]]
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| [[xenharmonie/übermässige Temperaturen|Deutsch]] | |
| </span>
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| The 5-limit parent comma for the **augmented family** is 128/125, the [[128_125|diesis]]. Its [[monzo]] is |7 0 -3>, and flipping that yields <<3 0 -7|| for the [[wedgie]]. Hence the period is 1/3 octave, and this is what is used for a major third. The [[generator]] can be taken as a fifth or a semitone, and [[12edo]], with its excellent fifth, is an obvious tuning for [[5-limit]] augmented, though a sharper fifth might be preferred to go with the sharp third.
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| =Seven limit children=
| | The 5-limit parent comma for the '''augmented family''' is 128/125, the [[128/125|diesis]]. Its [[monzo|monzo]] is |7 0 -3>, and flipping that yields <<3 0 -7|| for the [[wedgie|wedgie]]. Hence the period is 1/3 octave, and this is what is used for a major third. The [[generator|generator]] can be taken as a fifth or a semitone, and [[12edo|12edo]], with its excellent fifth, is an obvious tuning for [[5-limit|5-limit]] augmented, though a sharper fifth might be preferred to go with the sharp third. |
| The second comma of the [[Normal lists|normal comma list]] defines which [[7-limit]] family member we are looking at. August adds 36/35, augene 64/63, hexe 256/245, hemiaug 245/243, and hemis 49/48. Hexe splits the period to 1/6 octave, and hemiaug the generator, giving quarter-tones instead of semitones.
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| =August= | | =Seven limit children= |
| [[Comma]]s: 36/35, 128/125 | | The second comma of the [[Normal_lists|normal comma list]] defines which [[7-limit|7-limit]] family member we are looking at. August adds 36/35, augene 64/63, hexe 256/245, hemiaug 245/243, and hemis 49/48. Hexe splits the period to 1/6 octave, and hemiaug the generator, giving quarter-tones instead of semitones. |
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| [[POTE tuning|POTE generator]]: 696.011 | | =August= |
| | [[Comma|Comma]]s: 36/35, 128/125 |
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| [[Map]]: [<3 0 7 -1|, <0 1 0 2|] | | [[POTE_tuning|POTE generator]]: 696.011 |
| [[Wedgie]]: <<3 0 6 -7 1 14||
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| [[edo|EDOs]]: [[9edo|9]], [[12edo|12]], [[45edo|45cd]], [[57edo|57cd]], [[69edo|69cd]]
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| [[Badness]]: 0.0265
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| ==11-limit== | | [[Map|Map]]: [<3 0 7 -1|, <0 1 0 2|] |
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| | [[wedgie|Wedgie]]: <<3 0 6 -7 1 14|| |
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| | [[EDO|EDOs]]: [[9edo|9]], [[12edo|12]], [[45edo|45cd]], [[57edo|57cd]], [[69edo|69cd]] |
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| | [[Badness|Badness]]: 0.0265 |
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| | ==11-limit== |
| Commas: 36/35, 45/44, 56/55 | | Commas: 36/35, 45/44, 56/55 |
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| Map: [<3 0 7 -1 1|, <0 1 0 2 2|] | | Map: [<3 0 7 -1 1|, <0 1 0 2 2|] |
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| EDOs: 9, 12, [[21edo|21]], [[33edo|33e]], [[45edo|45cde]] | | EDOs: 9, 12, [[21edo|21]], [[33edo|33e]], [[45edo|45cde]] |
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| Badness: 0.0202 | | Badness: 0.0202 |
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| ==13-limit== | | ==13-limit== |
| Commas: 27/26, 36/35, 45/44, 56/55 | | Commas: 27/26, 36/35, 45/44, 56/55 |
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| Line 39: |
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| Map: [<3 0 7 -1 1 -3|, <0 1 0 2 2 3|] | | Map: [<3 0 7 -1 1 -3|, <0 1 0 2 2 3|] |
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| EDOs: 9, 12, [[21edo|21]], [[33edo|33ef]], [[54edo|54bcef]] | | EDOs: 9, 12, [[21edo|21]], [[33edo|33ef]], [[54edo|54bcef]] |
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| Badness: 0.0184 | | Badness: 0.0184 |
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| ==Augustus== | | ==Augustus== |
| Commas: 26/25, 36/35, 45/44, 56/55 | | Commas: 26/25, 36/35, 45/44, 56/55 |
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| Line 48: |
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| Map: [<3 0 7 -1 1 11|, <0 1 0 2 2 0|] | | Map: [<3 0 7 -1 1 11|, <0 1 0 2 2 0|] |
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| EDOs: 9, 12, 21f | | EDOs: 9, 12, 21f |
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| Badness: 0.0222 | | Badness: 0.0222 |
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| =Augene= | | =Augene= |
| Commas: 64/63, 126/125 | | Commas: 64/63, 126/125 |
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| [[POTE tuning|POTE generator]]: 709.257 | | [[POTE_tuning|POTE generator]]: 709.257 |
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| Map: [<3 0 7 18|, <0 1 0 -2|] | | Map: [<3 0 7 18|, <0 1 0 -2|] |
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| Wedgie: <<3 0 -6 -7 -18 -14|| | | Wedgie: <<3 0 -6 -7 -18 -14|| |
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| EDOs: [[12edo|12]], [[27edo|27]], [[39edo|39d]], [[66edo|66cd]] | | EDOs: [[12edo|12]], [[27edo|27]], [[39edo|39d]], [[66edo|66cd]] |
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| Badness: 0.0248 | | Badness: 0.0248 |
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| ==11-limit== | | ==11-limit== |
| Commas: 56/55, 64/63, 100/99 | | Commas: 56/55, 64/63, 100/99 |
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| Line 67: |
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| Map: [<3 0 7 18 20|, <0 1 0 -2 -2|] | | Map: [<3 0 7 18 20|, <0 1 0 -2 -2|] |
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| EDOs: 12, 15, 27e | | EDOs: 12, 15, 27e |
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| Badness: 0.0196 | | Badness: 0.0196 |
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| ===13-limit=== | | ===13-limit=== |
| Commas: 40/39, 56/55, 64/63, 66/65 | | Commas: 40/39, 56/55, 64/63, 66/65 |
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| Line 76: |
Line 84: |
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| Map: [<3 0 7 18 20 16|, <0 1 0 -2 -2 -1|] | | Map: [<3 0 7 18 20 16|, <0 1 0 -2 -2 -1|] |
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| EDOs: 12f, 15, 27ef | | EDOs: 12f, 15, 27ef |
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| Badness: 0.0208 | | Badness: 0.0208 |
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| ===Ogene=== | | ===Ogene=== |
| Commas: 56/55, 64/63, 91/90, 100/99 | | Commas: 56/55, 64/63, 91/90, 100/99 |
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| Line 85: |
Line 95: |
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| Map: [<3 0 7 18 20 -8|, <0 1 0 -2 -2 4|] | | Map: [<3 0 7 18 20 -8|, <0 1 0 -2 -2 4|] |
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| EDOs: 12, 15, 27e, 69bcef | | EDOs: 12, 15, 27e, 69bcef |
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| Badness: 0.0229 | | Badness: 0.0229 |
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| ===Agene=== | | ===Agene=== |
| Commas: 56/55, 64/63, 78/77, 100/99 | | Commas: 56/55, 64/63, 78/77, 100/99 |
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| Line 94: |
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| Map: [<3 0 7 18 20 35|, <0 1 0 -2 -2 -5|] | | Map: [<3 0 7 18 20 35|, <0 1 0 -2 -2 -5|] |
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| EDOs: 12f, 27e | | EDOs: 12f, 27e |
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| Badness: 0.0231 | | Badness: 0.0231 |
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| ==Eugene== | | ==Eugene== |
| Commas: 55/54, 64/63, 77/75 | | Commas: 55/54, 64/63, 77/75 |
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Line 117: |
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| Map: [<3 0 7 18 -4|, <0 1 0 -2 3|] | | Map: [<3 0 7 18 -4|, <0 1 0 -2 3|] |
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| EDOs: 15, 27, 42 | | EDOs: 15, 27, 42 |
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| Badness: 0.0356 | | Badness: 0.0356 |
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| [[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Sad%20Like%20Winter%20Leaves.mp3|Sad Like Winter Leaves]] by [[http://soundcloud.com/cityoftheasleep/sad-like-winter-trees|Igliashon Jones]]
| | [http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Sad%20Like%20Winter%20Leaves.mp3 Sad Like Winter Leaves] by [http://soundcloud.com/cityoftheasleep/sad-like-winter-trees Igliashon Jones] |
| [[http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of27sonatina.mp3|Galticeran Sonatina]] by [[http://soundcloud.com/joelgranttaylor/galticeran_sonatina|Joel Taylor]]
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| =Inflated= | | [http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of27sonatina.mp3 Galticeran Sonatina] by [http://soundcloud.com/joelgranttaylor/galticeran_sonatina Joel Taylor] |
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| | =Inflated= |
| Commas: 28/27, 128/125 | | Commas: 28/27, 128/125 |
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| Map: [<3 0 7 -6|, <0 1 0 3|] | | Map: [<3 0 7 -6|, <0 1 0 3|] |
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| Wedgie: <<3 0 9 -7 6 21|| | | Wedgie: <<3 0 9 -7 6 21|| |
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| EDOs: 15, 48bc, 63bc, 78bc | | EDOs: 15, 48bc, 63bc, 78bc |
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| Badness: 0.0547 | | Badness: 0.0547 |
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| ==11-limit== | | ==11-limit== |
| Commas: 28/27, 55/54, 128/125 | | Commas: 28/27, 55/54, 128/125 |
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Line 145: |
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| Map: [<3 0 7 -6|, <0 1 0 3|] | | Map: [<3 0 7 -6|, <0 1 0 3|] |
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| EDOs: 15, 48bce, 63bce, 78bce | | EDOs: 15, 48bce, 63bce, 78bce |
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| Badness: 0.0312 | | Badness: 0.0312 |
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| =Deflated= | | =Deflated= |
| Commas: 21/20, 128/125 | | Commas: 21/20, 128/125 |
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| Line 134: |
Line 156: |
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| Map: [<3 0 7 13|, <0 1 0 -1|] | | Map: [<3 0 7 13|, <0 1 0 -1|] |
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| Wedgie: <<3 0 -3 -7 -13 -7|| | | Wedgie: <<3 0 -3 -7 -13 -7|| |
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| EDOs: 3, 9, 18bd, 21d, 30bd | | EDOs: 3, 9, 18bd, 21d, 30bd |
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| Badness: 0.0591 | | Badness: 0.0591 |
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| =Hexe= | | =Hexe= |
| Commas: 50/49, 128/125 | | Commas: 50/49, 128/125 |
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| [[POTE tuning|POTE generator]]: 710.963 | | [[POTE_tuning|POTE generator]]: 710.963 |
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| Map: [<6 0 14 17|, <0 1 0 0|] | | Map: [<6 0 14 17|, <0 1 0 0|] |
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| Wedgie: <<6 0 0 -14 -17 0|| | | Wedgie: <<6 0 0 -14 -17 0|| |
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| EDOs: [[6edo|6]], [[12edo|12]], [[30edo|30d]], [[[42edo|42d]], [[54edo|54cd]] | | EDOs: [[6edo|6]], [[12edo|12]], [[30edo|30d]], [[[42edo|42d]], [[54edo|54cd]] |
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| Badness: 0.0577 | | Badness: 0.0577 |
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| ==11-limit== | | ==11-limit== |
| Commas: 50/49, 56/55, 125/121 | | Commas: 50/49, 56/55, 125/121 |
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| Line 154: |
Line 182: |
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| Map: [<6 0 14 17 21|, <0 1 0 0 0|] | | Map: [<6 0 14 17 21|, <0 1 0 0 0|] |
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| EDOs: 6, 12, 30de | | EDOs: 6, 12, 30de |
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| Badness: 0.0384 | | Badness: 0.0384 |
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| ==13-limit== | | ==13-limit== |
| Commas: 50/49, 56/55, 66/65, 105/104 | | Commas: 50/49, 56/55, 66/65, 105/104 |
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| Line 163: |
Line 193: |
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| Map: [<6 0 14 17 21 13|, <0 1 0 0 0 1|] | | Map: [<6 0 14 17 21 13|, <0 1 0 0 0 1|] |
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| EDOs: 12f | | EDOs: 12f |
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| Badness: 0.0359 | | Badness: 0.0359 |
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| =Hemiaug= | | =Hemiaug= |
| Commas: 128/125, 245/243 | | Commas: 128/125, 245/243 |
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| [[POTE tuning|POTE generator]]: ~28/27 = 45.118 | | [[POTE_tuning|POTE generator]]: ~28/27 = 45.118 |
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| Map: [<3 1 7 -1|, <0 2 0 5|] | | Map: [<3 1 7 -1|, <0 2 0 5|] |
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| Wedgie: <<6 0 15 -14 7 35|| | | Wedgie: <<6 0 15 -14 7 35|| |
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| EDOs: [[24edo|24]], [[27edo|27]], [[105edo|105bc]] | | EDOs: [[24edo|24]], [[27edo|27]], [[105edo|105bc]] |
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| Badness: 0.0705 | | Badness: 0.0705 |
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| ==11-limit== | | ==11-limit== |
| Commas: 56/55, 128/125, 245/243 | | Commas: 56/55, 128/125, 245/243 |
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Line 217: |
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| Map: [<3 1 7 -1 1|, <0 2 0 5 5|] | | Map: [<3 1 7 -1 1|, <0 2 0 5 5|] |
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| EDOs: 24, 27e, 51ce, 78ce | | EDOs: 24, 27e, 51ce, 78ce |
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| Badness: 0.0382 | | Badness: 0.0382 |
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| ==13-limit== | | ==13-limit== |
| Commas: 56/55, 91/90, 128/125, 245/243 | | Commas: 56/55, 91/90, 128/125, 245/243 |
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| Line 191: |
Line 228: |
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| Map: [<3 1 7 -1 1 13|, <0 2 0 5 5 -1|] | | Map: [<3 1 7 -1 1 13|, <0 2 0 5 5 -1|] |
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| EDOs: 24, 27e, 51ce, 78ce | | EDOs: 24, 27e, 51ce, 78ce |
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| Badness: 0.0302 | | Badness: 0.0302 |
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| =Triforce= | | =Triforce= |
| Commas: 49/48, 128/125 | | Commas: 49/48, 128/125 |
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| [[POTE tuning|POTE generator]]: ~7/6 = 247.049 | | [[POTE_tuning|POTE generator]]: ~7/6 = 247.049 |
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| Map: [<3 0 7 6|, <0 2 0 1|] | | Map: [<3 0 7 6|, <0 2 0 1|] |
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| Wedgie: <<6 0 3 -14 -12 7|| | | Wedgie: <<6 0 3 -14 -12 7|| |
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| EDOs: 6, 9, [[15edo|15]], [[24edo|24]], [[39edo|39]], [[63edo|63cd]], [[102edo|102cd]] | | EDOs: 6, 9, [[15edo|15]], [[24edo|24]], [[39edo|39]], [[63edo|63cd]], [[102edo|102cd]] |
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| Badness: 0.0202 | | Badness: 0.0202 |
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| [[image:triforce9.jpg]] | | [[File:triforce9.jpg|alt=triforce9.jpg|triforce9.jpg]] |
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| ==11-limit== | | ==11-limit== |
| Commas: 56/55, 77/75, 128/125 | | Commas: 56/55, 77/75, 128/125 |
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| [[POTE tuning|POTE generator]]: ~7/6 = 247.068 | | [[POTE_tuning|POTE generator]]: ~7/6 = 247.068 |
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| Map: [<3 0 7 6 8|, <0 2 0 1 1|] | | Map: [<3 0 7 6 8|, <0 2 0 1 1|] |
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| EDOs: 6, 9, 15, 24, 39, [[63edo|63cd]], [[102edo|102cd]] | | EDOs: 6, 9, 15, 24, 39, [[63edo|63cd]], [[102edo|102cd]] |
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| Badness: 0.0262 | | Badness: 0.0262 |
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| ===Musical example:=== | | ===Musical example:=== |
| [[http://soundcloud.com/cityoftheasleep/the-triforce-of-courage15|The Triforce of Courage (tuned in 15edo)]] by Igliashon Jones
| | [http://soundcloud.com/cityoftheasleep/the-triforce-of-courage15 The Triforce of Courage (tuned in 15edo)] by Igliashon Jones |
| ==13-limit== | | |
| | ==13-limit== |
| Commas: 49/48, 56/55, 66/65, 77/75 | | Commas: 49/48, 56/55, 66/65, 77/75 |
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| [[POTE tuning|POTE generator]]: ~7/6 = 248.313 | | [[POTE_tuning|POTE generator]]: ~7/6 = 248.313 |
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| Map: [<3 0 7 6 8 4|, <0 2 0 1 1 3|] | | Map: [<3 0 7 6 8 4|, <0 2 0 1 1 3|] |
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| EDOs: 6, 9, 15, 24, [[63edo|63cdf]], [[87edo|87cdf]] | | EDOs: 6, 9, 15, 24, [[63edo|63cdf]], [[87edo|87cdf]] |
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| Badness: 0.0202 | | Badness: 0.0202 |
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| [[triphi|Triforce(9) with L:s = phi]] | | [[triphi|Triforce(9) with L:s = phi]] |
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| ==Semitriforce== | | ==Semitriforce== |
| Commas: 49/48, 56/55, 77/75, 507/500 | | Commas: 49/48, 56/55, 77/75, 507/500 |
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| Line 234: |
Line 281: |
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| Map: [<6 0 14 12 16 27|, <0 2 0 1 1 -1|] | | Map: [<6 0 14 12 16 27|, <0 2 0 1 1 -1|] |
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| EDOs: 6, 24, 54cd, 78cd, 102cdf | | EDOs: 6, 24, 54cd, 78cd, 102cdf |
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| Badness: 0.0592 | | Badness: 0.0592 |
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| === === | | === === |
| =Hemiug= | | |
| | =Hemiug= |
| Commas: 128/125, 1323/1250 | | Commas: 128/125, 1323/1250 |
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| Line 244: |
Line 294: |
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| Map: [<3 1 7 14|, <0 2 0 -3|] | | Map: [<3 1 7 14|, <0 2 0 -3|] |
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| Wedgie: <<6 0 -9 -14 -31 -21|| | | Wedgie: <<6 0 -9 -14 -31 -21|| |
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| EDOs: 21, 24, 45c, 69cd | | EDOs: 21, 24, 45c, 69cd |
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| Badness: 0.1378 | | Badness: 0.1378 |
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| ==11-limit== | | ==11-limit== |
| Commas: 56/55, 128/125, 1323/1250 | | Commas: 56/55, 128/125, 1323/1250 |
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| Line 254: |
Line 307: |
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| Map: [<3 1 7 14 16|, <0 2 0 -3 -3|] | | Map: [<3 1 7 14 16|, <0 2 0 -3 -3|] |
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| EDOs: 21, 24, 69cd, 93cd | | EDOs: 21, 24, 69cd, 93cd |
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| Badness: 0.0681 | | Badness: 0.0681 |
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| ==13-limit== | | ==13-limit== |
| Commas: 56/55, 66/65, 105/104, 507/500 | | Commas: 56/55, 66/65, 105/104, 507/500 |
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| Line 263: |
Line 318: |
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| Map: [<3 1 7 14 16 13|, <0 2 0 -3 -3 -1|] | | Map: [<3 1 7 14 16 13|, <0 2 0 -3 -3 -1|] |
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| EDOs: 21, 24, 69cdf, 93cdf | | EDOs: 21, 24, 69cdf, 93cdf |
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| Badness: 0.0423 | | Badness: 0.0423 |
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| =Trug= | | =Trug= |
| Commas: 128/125, 360/343 | | Commas: 128/125, 360/343 |
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| Line 272: |
Line 329: |
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| Map: [<3 1 7 6|, <0 3 0 2|] | | Map: [<3 1 7 6|, <0 3 0 2|] |
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| EDOs: 9bd, 12 | | EDOs: 9bd, 12 |
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| Badness: 0.1383 | | Badness: 0.1383 |
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| =Oodako= | | =Oodako= |
| Commas: 128/125, 2401/2400 | | Commas: 128/125, 2401/2400 |
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| Line 281: |
Line 340: |
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| Map: [<3 3 7 8|, <0 4 0 1|] | | Map: [<3 3 7 8|, <0 4 0 1|] |
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| Wedgie: <<12 0 3 -28 -29 7|| | | Wedgie: <<12 0 3 -28 -29 7|| |
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| EDOs: 6, 21, 27, 75c, 102cd, 129bcd | | EDOs: 6, 21, 27, 75c, 102cd, 129bcd |
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| Badness: 0.1132 | | Badness: 0.1132 |
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| ==11-limit== | | ==11-limit== |
| Commas: 56/55, 128/125, 3773/3750 | | Commas: 56/55, 128/125, 3773/3750 |
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| Line 291: |
Line 353: |
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| Map: [<3 3 7 8 10|, <0 4 0 1 1|] | | Map: [<3 3 7 8 10|, <0 4 0 1 1|] |
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| EDOs: 6, 21, 27e | | EDOs: 6, 21, 27e |
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| Badness: 0.0592 | | Badness: 0.0592 |
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| ==13-limit== | | ==13-limit== |
| Commas: 56/55, 78/77, 128/125, 507/500 | | Commas: 56/55, 78/77, 128/125, 507/500 |
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| Line 300: |
Line 364: |
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| |
|
| Map: [<3 3 7 8 10 12|, <0 4 0 1 1 -2|] | | Map: [<3 3 7 8 10 12|, <0 4 0 1 1 -2|] |
| | |
| EDOs: 6, 21, 27e | | EDOs: 6, 21, 27e |
| | |
| Badness: 0.0423 | | Badness: 0.0423 |
|
| |
|
| =Hemisemiaug= | | =Hemisemiaug= |
| Commas: 128/125, 12005/11664 | | Commas: 128/125, 12005/11664 |
|
| |
|
| Line 309: |
Line 375: |
|
| |
|
| Map: [<6 1 14 4|, <0 2 0 3|] | | Map: [<6 1 14 4|, <0 2 0 3|] |
| | |
| Wedgie: <<12 0 18 -28 -5 42|| | | Wedgie: <<12 0 18 -28 -5 42|| |
| | |
| Edos: 18, 24, 42, 66c, 108bc | | Edos: 18, 24, 42, 66c, 108bc |
| | |
| Badness: 0.2110 | | Badness: 0.2110 |
|
| |
|
| ==11-limit== | | ==11-limit== |
| Commas: 56/55, 128/125, 3773/3645 | | Commas: 56/55, 128/125, 3773/3645 |
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| |
|
| Line 319: |
Line 388: |
|
| |
|
| Map: [<6 1 14 4 8|, <0 2 0 3 3|] | | Map: [<6 1 14 4 8|, <0 2 0 3 3|] |
| | |
| EDOs: 24, 42e, 66ce, 108bce | | EDOs: 24, 42e, 66ce, 108bce |
| | |
| Badness: 0.0807 | | Badness: 0.0807 |
|
| |
|
| =Niner= | | =Niner= |
| Niner gives 9 as the complexity of an otonal tetrad, tying it with augene as a temperament supported by 27edo. Niner[18], therefore, has nine such tetrads. | | Niner gives 9 as the complexity of an otonal tetrad, tying it with augene as a temperament supported by 27edo. Niner[18], therefore, has nine such tetrads. |
|
| |
|
| Line 330: |
Line 401: |
|
| |
|
| Map: [<9 0 21 11|, <0 1 0 1|] | | Map: [<9 0 21 11|, <0 1 0 1|] |
| | |
| Wedgie: <<9 0 9 -21 -11 21|| | | Wedgie: <<9 0 9 -21 -11 21|| |
| | |
| EDOs: 9, 18, 27, 63c, 90c | | EDOs: 9, 18, 27, 63c, 90c |
| | |
| Badness: 0.0672 | | Badness: 0.0672 |
|
| |
|
| ==11-limit== | | ==11-limit== |
| Commas: 56/55, 128/125, 540/539 | | Commas: 56/55, 128/125, 540/539 |
|
| |
|
| Line 340: |
Line 414: |
|
| |
|
| Map: [<9 0 21 11 17|, <0 1 0 1 1|] | | Map: [<9 0 21 11 17|, <0 1 0 1 1|] |
| | |
| EDOs: 9, 27e, 36, 63ce | | EDOs: 9, 27e, 36, 63ce |
| | |
| Badness: 0.0349 | | Badness: 0.0349 |
|
| |
|
| ==13-limit== | | ==13-limit== |
| Commas: 56/55, 78/77, 91/90, 128/125 | | Commas: 56/55, 78/77, 91/90, 128/125 |
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| |
|
| Line 349: |
Line 425: |
|
| |
|
| Map: [<9 0 21 11 17 19|, <0 1 0 1 1 1|] | | Map: [<9 0 21 11 17 19|, <0 1 0 1 1 1|] |
| | |
| EDOs: 9, 27e, 36, 63ce | | EDOs: 9, 27e, 36, 63ce |
| | |
| Badness: 0.0241 | | Badness: 0.0241 |
|
| |
|
| ==Music== | | ==Music== |
| [[https://www.prismnet.com/~hmiller/music/temp-augmented.html|Herman Miller's page about augmented temperament]]</pre></div>
| | [https://www.prismnet.com/~hmiller/music/temp-augmented.html Herman Miller's page about augmented temperament] [[Category:augmented]] |
| <h4>Original HTML content:</h4>
| | [[Category:family]] |
| <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>Augmented family</title></head><body><span style="display: block; text-align: right;"><!-- ws:start:WikiTextTocRule:78:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --><div style="margin-left: 1em;"><a href="#Seven limit children">Seven limit children</a></div>
| | [[Category:theory]] |
| <!-- ws:end:WikiTextTocRule:79 --><!-- ws:start:WikiTextTocRule:80: --><div style="margin-left: 1em;"><a href="#August">August</a></div>
| |
| <!-- ws:end:WikiTextTocRule:80 --><!-- ws:start:WikiTextTocRule:81: --><div style="margin-left: 2em;"><a href="#August-11-limit">11-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:81 --><!-- ws:start:WikiTextTocRule:82: --><div style="margin-left: 2em;"><a href="#August-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:82 --><!-- ws:start:WikiTextTocRule:83: --><div style="margin-left: 2em;"><a href="#August-Augustus">Augustus</a></div>
| |
| <!-- ws:end:WikiTextTocRule:83 --><!-- ws:start:WikiTextTocRule:84: --><div style="margin-left: 1em;"><a href="#Augene">Augene</a></div>
| |
| <!-- ws:end:WikiTextTocRule:84 --><!-- ws:start:WikiTextTocRule:85: --><div style="margin-left: 2em;"><a href="#Augene-11-limit">11-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:85 --><!-- ws:start:WikiTextTocRule:86: --><div style="margin-left: 3em;"><a href="#Augene-11-limit-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:86 --><!-- ws:start:WikiTextTocRule:87: --><div style="margin-left: 3em;"><a href="#Augene-11-limit-Ogene">Ogene</a></div>
| |
| <!-- ws:end:WikiTextTocRule:87 --><!-- ws:start:WikiTextTocRule:88: --><div style="margin-left: 3em;"><a href="#Augene-11-limit-Agene">Agene</a></div>
| |
| <!-- ws:end:WikiTextTocRule:88 --><!-- ws:start:WikiTextTocRule:89: --><div style="margin-left: 2em;"><a href="#Augene-Eugene">Eugene</a></div>
| |
| <!-- ws:end:WikiTextTocRule:89 --><!-- ws:start:WikiTextTocRule:90: --><div style="margin-left: 1em;"><a href="#Inflated">Inflated</a></div>
| |
| <!-- ws:end:WikiTextTocRule:90 --><!-- ws:start:WikiTextTocRule:91: --><div style="margin-left: 2em;"><a href="#Inflated-11-limit">11-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:91 --><!-- ws:start:WikiTextTocRule:92: --><div style="margin-left: 1em;"><a href="#Deflated">Deflated</a></div>
| |
| <!-- ws:end:WikiTextTocRule:92 --><!-- ws:start:WikiTextTocRule:93: --><div style="margin-left: 1em;"><a href="#Hexe">Hexe</a></div>
| |
| <!-- ws:end:WikiTextTocRule:93 --><!-- ws:start:WikiTextTocRule:94: --><div style="margin-left: 2em;"><a href="#Hexe-11-limit">11-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:94 --><!-- ws:start:WikiTextTocRule:95: --><div style="margin-left: 2em;"><a href="#Hexe-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:95 --><!-- ws:start:WikiTextTocRule:96: --><div style="margin-left: 1em;"><a href="#Hemiaug">Hemiaug</a></div>
| |
| <!-- ws:end:WikiTextTocRule:96 --><!-- ws:start:WikiTextTocRule:97: --><div style="margin-left: 2em;"><a href="#Hemiaug-11-limit">11-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:97 --><!-- ws:start:WikiTextTocRule:98: --><div style="margin-left: 2em;"><a href="#Hemiaug-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:98 --><!-- ws:start:WikiTextTocRule:99: --><div style="margin-left: 1em;"><a href="#Triforce">Triforce</a></div>
| |
| <!-- ws:end:WikiTextTocRule:99 --><!-- ws:start:WikiTextTocRule:100: --><div style="margin-left: 2em;"><a href="#Triforce-11-limit">11-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:100 --><!-- ws:start:WikiTextTocRule:101: --><div style="margin-left: 3em;"><a href="#Triforce-11-limit-Musical example:">Musical example:</a></div>
| |
| <!-- ws:end:WikiTextTocRule:101 --><!-- ws:start:WikiTextTocRule:102: --><div style="margin-left: 2em;"><a href="#Triforce-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:102 --><!-- ws:start:WikiTextTocRule:103: --><div style="margin-left: 2em;"><a href="#Triforce-Semitriforce">Semitriforce</a></div>
| |
| <!-- ws:end:WikiTextTocRule:103 --><!-- ws:start:WikiTextTocRule:104: --><div style="margin-left: 3em;"><a href="#toc25"> </a></div>
| |
| <!-- ws:end:WikiTextTocRule:104 --><!-- ws:start:WikiTextTocRule:105: --><div style="margin-left: 1em;"><a href="#Hemiug">Hemiug</a></div>
| |
| <!-- ws:end:WikiTextTocRule:105 --><!-- ws:start:WikiTextTocRule:106: --><div style="margin-left: 2em;"><a href="#Hemiug-11-limit">11-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:106 --><!-- ws:start:WikiTextTocRule:107: --><div style="margin-left: 2em;"><a href="#Hemiug-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:107 --><!-- ws:start:WikiTextTocRule:108: --><div style="margin-left: 1em;"><a href="#Trug">Trug</a></div>
| |
| <!-- ws:end:WikiTextTocRule:108 --><!-- ws:start:WikiTextTocRule:109: --><div style="margin-left: 1em;"><a href="#Oodako">Oodako</a></div>
| |
| <!-- ws:end:WikiTextTocRule:109 --><!-- ws:start:WikiTextTocRule:110: --><div style="margin-left: 2em;"><a href="#Oodako-11-limit">11-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:110 --><!-- ws:start:WikiTextTocRule:111: --><div style="margin-left: 2em;"><a href="#Oodako-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:111 --><!-- ws:start:WikiTextTocRule:112: --><div style="margin-left: 1em;"><a href="#Hemisemiaug">Hemisemiaug</a></div>
| |
| <!-- ws:end:WikiTextTocRule:112 --><!-- ws:start:WikiTextTocRule:113: --><div style="margin-left: 2em;"><a href="#Hemisemiaug-11-limit">11-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:113 --><!-- ws:start:WikiTextTocRule:114: --><div style="margin-left: 1em;"><a href="#Niner">Niner</a></div>
| |
| <!-- ws:end:WikiTextTocRule:114 --><!-- ws:start:WikiTextTocRule:115: --><div style="margin-left: 2em;"><a href="#Niner-11-limit">11-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:115 --><!-- ws:start:WikiTextTocRule:116: --><div style="margin-left: 2em;"><a href="#Niner-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:116 --><!-- ws:start:WikiTextTocRule:117: --><div style="margin-left: 2em;"><a href="#Niner-Music">Music</a></div>
| |
| <!-- ws:end:WikiTextTocRule:117 --><!-- ws:start:WikiTextTocRule:118: --></div>
| |
| <!-- ws:end:WikiTextTocRule:118 --><br />
| |
| <a class="wiki_link" href="http://xenharmonie.wikispaces.com/%C3%BCberm%C3%A4ssige%20Temperaturen">Deutsch</a><br />
| |
| </span><br />
| |
| The 5-limit parent comma for the <strong>augmented family</strong> is 128/125, the <a class="wiki_link" href="/128_125">diesis</a>. Its <a class="wiki_link" href="/monzo">monzo</a> is |7 0 -3&gt;, and flipping that yields &lt;&lt;3 0 -7|| for the <a class="wiki_link" href="/wedgie">wedgie</a>. Hence the period is 1/3 octave, and this is what is used for a major third. The <a class="wiki_link" href="/generator">generator</a> can be taken as a fifth or a semitone, and <a class="wiki_link" href="/12edo">12edo</a>, with its excellent fifth, is an obvious tuning for <a class="wiki_link" href="/5-limit">5-limit</a> augmented, though a sharper fifth might be preferred to go with the sharp third.<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Seven limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->Seven limit children</h1>
| |
| The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which <a class="wiki_link" href="/7-limit">7-limit</a> family member we are looking at. August adds 36/35, augene 64/63, hexe 256/245, hemiaug 245/243, and hemis 49/48. Hexe splits the period to 1/6 octave, and hemiaug the generator, giving quarter-tones instead of semitones.<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="August"></a><!-- ws:end:WikiTextHeadingRule:2 -->August</h1>
| |
| <a class="wiki_link" href="/Comma">Comma</a>s: 36/35, 128/125<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 696.011<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Map">Map</a>: [&lt;3 0 7 -1|, &lt;0 1 0 2|]<br />
| |
| <a class="wiki_link" href="/Wedgie">Wedgie</a>: &lt;&lt;3 0 6 -7 1 14||<br />
| |
| <a class="wiki_link" href="/edo">EDOs</a>: <a class="wiki_link" href="/9edo">9</a>, <a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/45edo">45cd</a>, <a class="wiki_link" href="/57edo">57cd</a>, <a class="wiki_link" href="/69edo">69cd</a><br />
| |
| <a class="wiki_link" href="/Badness">Badness</a>: 0.0265<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="August-11-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->11-limit</h2>
| |
| Commas: 36/35, 45/44, 56/55<br />
| |
| <br />
| |
| POTE generator: ~3/2 = 692.514<br />
| |
| <br />
| |
| Map: [&lt;3 0 7 -1 1|, &lt;0 1 0 2 2|]<br />
| |
| EDOs: 9, 12, <a class="wiki_link" href="/21edo">21</a>, <a class="wiki_link" href="/33edo">33e</a>, <a class="wiki_link" href="/45edo">45cde</a><br />
| |
| Badness: 0.0202<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="August-13-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-limit</h2>
| |
| Commas: 27/26, 36/35, 45/44, 56/55<br />
| |
| <br />
| |
| POTE generator: ~3/2 = 688.783<br />
| |
| <br />
| |
| Map: [&lt;3 0 7 -1 1 -3|, &lt;0 1 0 2 2 3|]<br />
| |
| EDOs: 9, 12, <a class="wiki_link" href="/21edo">21</a>, <a class="wiki_link" href="/33edo">33ef</a>, <a class="wiki_link" href="/54edo">54bcef</a><br />
| |
| Badness: 0.0184<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="August-Augustus"></a><!-- ws:end:WikiTextHeadingRule:8 -->Augustus</h2>
| |
| Commas: 26/25, 36/35, 45/44, 56/55<br />
| |
| <br />
| |
| POTE generator: ~3/2 = 685.356<br />
| |
| <br />
| |
| Map: [&lt;3 0 7 -1 1 11|, &lt;0 1 0 2 2 0|]<br />
| |
| EDOs: 9, 12, 21f<br />
| |
| Badness: 0.0222<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Augene"></a><!-- ws:end:WikiTextHeadingRule:10 -->Augene</h1>
| |
| Commas: 64/63, 126/125<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 709.257<br />
| |
| <br />
| |
| Map: [&lt;3 0 7 18|, &lt;0 1 0 -2|]<br />
| |
| Wedgie: &lt;&lt;3 0 -6 -7 -18 -14||<br />
| |
| EDOs: <a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/27edo">27</a>, <a class="wiki_link" href="/39edo">39d</a>, <a class="wiki_link" href="/66edo">66cd</a><br />
| |
| Badness: 0.0248<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Augene-11-limit"></a><!-- ws:end:WikiTextHeadingRule:12 -->11-limit</h2>
| |
| Commas: 56/55, 64/63, 100/99<br />
| |
| <br />
| |
| POTE generator: ~3/2 = 711.177<br />
| |
| <br />
| |
| Map: [&lt;3 0 7 18 20|, &lt;0 1 0 -2 -2|]<br />
| |
| EDOs: 12, 15, 27e<br />
| |
| Badness: 0.0196<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:14:&lt;h3&gt; --><h3 id="toc7"><a name="Augene-11-limit-13-limit"></a><!-- ws:end:WikiTextHeadingRule:14 -->13-limit</h3>
| |
| Commas: 40/39, 56/55, 64/63, 66/65<br />
| |
| <br />
| |
| POTE generator: ~3/2 = 712.013<br />
| |
| <br />
| |
| Map: [&lt;3 0 7 18 20 16|, &lt;0 1 0 -2 -2 -1|]<br />
| |
| EDOs: 12f, 15, 27ef<br />
| |
| Badness: 0.0208<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:16:&lt;h3&gt; --><h3 id="toc8"><a name="Augene-11-limit-Ogene"></a><!-- ws:end:WikiTextHeadingRule:16 -->Ogene</h3>
| |
| Commas: 56/55, 64/63, 91/90, 100/99<br />
| |
| <br />
| |
| POTE generator: ~3/2 = 712.609<br />
| |
| <br />
| |
| Map: [&lt;3 0 7 18 20 -8|, &lt;0 1 0 -2 -2 4|]<br />
| |
| EDOs: 12, 15, 27e, 69bcef<br />
| |
| Badness: 0.0229<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:18:&lt;h3&gt; --><h3 id="toc9"><a name="Augene-11-limit-Agene"></a><!-- ws:end:WikiTextHeadingRule:18 -->Agene</h3>
| |
| Commas: 56/55, 64/63, 78/77, 100/99<br />
| |
| <br />
| |
| POTE generator: ~3/2 = 709.677<br />
| |
| <br />
| |
| Map: [&lt;3 0 7 18 20 35|, &lt;0 1 0 -2 -2 -5|]<br />
| |
| EDOs: 12f, 27e<br />
| |
| Badness: 0.0231<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Augene-Eugene"></a><!-- ws:end:WikiTextHeadingRule:20 -->Eugene</h2>
| |
| Commas: 55/54, 64/63, 77/75<br />
| |
| <br />
| |
| POTE generator: ~3/2 = 714.150<br />
| |
| <br />
| |
| Map: [&lt;3 0 7 18 -4|, &lt;0 1 0 -2 3|]<br />
| |
| EDOs: 15, 27, 42<br />
| |
| Badness: 0.0356<br />
| |
| <br />
| |
| <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Sad%20Like%20Winter%20Leaves.mp3" rel="nofollow">Sad Like Winter Leaves</a> by <a class="wiki_link_ext" href="http://soundcloud.com/cityoftheasleep/sad-like-winter-trees" rel="nofollow">Igliashon Jones</a><br />
| |
| <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of27sonatina.mp3" rel="nofollow">Galticeran Sonatina</a> by <a class="wiki_link_ext" href="http://soundcloud.com/joelgranttaylor/galticeran_sonatina" rel="nofollow">Joel Taylor</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="Inflated"></a><!-- ws:end:WikiTextHeadingRule:22 -->Inflated</h1>
| |
| Commas: 28/27, 128/125<br />
| |
| <br />
| |
| POTE generator: ~3/2 = 722.719<br />
| |
| <br />
| |
| Map: [&lt;3 0 7 -6|, &lt;0 1 0 3|]<br />
| |
| Wedgie: &lt;&lt;3 0 9 -7 6 21||<br />
| |
| EDOs: 15, 48bc, 63bc, 78bc<br />
| |
| Badness: 0.0547<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="Inflated-11-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->11-limit</h2>
| |
| Commas: 28/27, 55/54, 128/125<br />
| |
| <br />
| |
| POTE generator: ~3/2 = 722.663<br />
| |
| <br />
| |
| Map: [&lt;3 0 7 -6|, &lt;0 1 0 3|]<br />
| |
| EDOs: 15, 48bce, 63bce, 78bce<br />
| |
| Badness: 0.0312<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc13"><a name="Deflated"></a><!-- ws:end:WikiTextHeadingRule:26 -->Deflated</h1>
| |
| Commas: 21/20, 128/125<br />
| |
| <br />
| |
| POTE generator: ~3/2 = 681.629<br />
| |
| <br />
| |
| Map: [&lt;3 0 7 13|, &lt;0 1 0 -1|]<br />
| |
| Wedgie: &lt;&lt;3 0 -3 -7 -13 -7||<br />
| |
| EDOs: 3, 9, 18bd, 21d, 30bd<br />
| |
| Badness: 0.0591<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:28:&lt;h1&gt; --><h1 id="toc14"><a name="Hexe"></a><!-- ws:end:WikiTextHeadingRule:28 -->Hexe</h1>
| |
| Commas: 50/49, 128/125<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 710.963<br />
| |
| <br />
| |
| Map: [&lt;6 0 14 17|, &lt;0 1 0 0|]<br />
| |
| Wedgie: &lt;&lt;6 0 0 -14 -17 0||<br />
| |
| EDOs: <a class="wiki_link" href="/6edo">6</a>, <a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/30edo">30d</a>, [<a class="wiki_link" href="/42edo">42d</a>, <a class="wiki_link" href="/54edo">54cd</a><br />
| |
| Badness: 0.0577<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:30:&lt;h2&gt; --><h2 id="toc15"><a name="Hexe-11-limit"></a><!-- ws:end:WikiTextHeadingRule:30 -->11-limit</h2>
| |
| Commas: 50/49, 56/55, 125/121<br />
| |
| <br />
| |
| POTE generator: ~3/2 = 714.304<br />
| |
| <br />
| |
| Map: [&lt;6 0 14 17 21|, &lt;0 1 0 0 0|]<br />
| |
| EDOs: 6, 12, 30de<br />
| |
| Badness: 0.0384<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="Hexe-13-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->13-limit</h2>
| |
| Commas: 50/49, 56/55, 66/65, 105/104<br />
| |
| <br />
| |
| POTE generator: ~3/2 = 710.005<br />
| |
| <br />
| |
| Map: [&lt;6 0 14 17 21 13|, &lt;0 1 0 0 0 1|]<br />
| |
| EDOs: 12f<br />
| |
| Badness: 0.0359<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:34:&lt;h1&gt; --><h1 id="toc17"><a name="Hemiaug"></a><!-- ws:end:WikiTextHeadingRule:34 -->Hemiaug</h1>
| |
| Commas: 128/125, 245/243<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~28/27 = 45.118<br />
| |
| <br />
| |
| Map: [&lt;3 1 7 -1|, &lt;0 2 0 5|]<br />
| |
| Wedgie: &lt;&lt;6 0 15 -14 7 35||<br />
| |
| EDOs: <a class="wiki_link" href="/24edo">24</a>, <a class="wiki_link" href="/27edo">27</a>, <a class="wiki_link" href="/105edo">105bc</a><br />
| |
| Badness: 0.0705<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Hemiaug-11-limit"></a><!-- ws:end:WikiTextHeadingRule:36 -->11-limit</h2>
| |
| Commas: 56/55, 128/125, 245/243<br />
| |
| <br />
| |
| POTE generator: ~28/27 = 45.788<br />
| |
| <br />
| |
| Map: [&lt;3 1 7 -1 1|, &lt;0 2 0 5 5|]<br />
| |
| EDOs: 24, 27e, 51ce, 78ce<br />
| |
| Badness: 0.0382<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="Hemiaug-13-limit"></a><!-- ws:end:WikiTextHeadingRule:38 -->13-limit</h2>
| |
| Commas: 56/55, 91/90, 128/125, 245/243<br />
| |
| <br />
| |
| POTE generator: ~28/27 = 46.250<br />
| |
| <br />
| |
| Map: [&lt;3 1 7 -1 1 13|, &lt;0 2 0 5 5 -1|]<br />
| |
| EDOs: 24, 27e, 51ce, 78ce<br />
| |
| Badness: 0.0302<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:40:&lt;h1&gt; --><h1 id="toc20"><a name="Triforce"></a><!-- ws:end:WikiTextHeadingRule:40 -->Triforce</h1>
| |
| Commas: 49/48, 128/125<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~7/6 = 247.049<br />
| |
| <br />
| |
| Map: [&lt;3 0 7 6|, &lt;0 2 0 1|]<br />
| |
| Wedgie: &lt;&lt;6 0 3 -14 -12 7||<br />
| |
| EDOs: 6, 9, <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/24edo">24</a>, <a class="wiki_link" href="/39edo">39</a>, <a class="wiki_link" href="/63edo">63cd</a>, <a class="wiki_link" href="/102edo">102cd</a><br />
| |
| Badness: 0.0202<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:119:&lt;img src=&quot;/file/view/triforce9.jpg/271381934/triforce9.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/triforce9.jpg/271381934/triforce9.jpg" alt="triforce9.jpg" title="triforce9.jpg" /><!-- ws:end:WikiTextLocalImageRule:119 --><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:42:&lt;h2&gt; --><h2 id="toc21"><a name="Triforce-11-limit"></a><!-- ws:end:WikiTextHeadingRule:42 -->11-limit</h2>
| |
| Commas: 56/55, 77/75, 128/125<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~7/6 = 247.068<br />
| |
| <br />
| |
| Map: [&lt;3 0 7 6 8|, &lt;0 2 0 1 1|]<br />
| |
| EDOs: 6, 9, 15, 24, 39, <a class="wiki_link" href="/63edo">63cd</a>, <a class="wiki_link" href="/102edo">102cd</a><br />
| |
| Badness: 0.0262<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:44:&lt;h3&gt; --><h3 id="toc22"><a name="Triforce-11-limit-Musical example:"></a><!-- ws:end:WikiTextHeadingRule:44 -->Musical example:</h3>
| |
| <a class="wiki_link_ext" href="http://soundcloud.com/cityoftheasleep/the-triforce-of-courage15" rel="nofollow">The Triforce of Courage (tuned in 15edo)</a> by Igliashon Jones<br />
| |
| <!-- ws:start:WikiTextHeadingRule:46:&lt;h2&gt; --><h2 id="toc23"><a name="Triforce-13-limit"></a><!-- ws:end:WikiTextHeadingRule:46 -->13-limit</h2>
| |
| Commas: 49/48, 56/55, 66/65, 77/75<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~7/6 = 248.313<br />
| |
| <br />
| |
| Map: [&lt;3 0 7 6 8 4|, &lt;0 2 0 1 1 3|]<br />
| |
| EDOs: 6, 9, 15, 24, <a class="wiki_link" href="/63edo">63cdf</a>, <a class="wiki_link" href="/87edo">87cdf</a><br />
| |
| Badness: 0.0202<br />
| |
| <br />
| |
| <a class="wiki_link" href="/triphi">Triforce(9) with L:s = phi</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:48:&lt;h2&gt; --><h2 id="toc24"><a name="Triforce-Semitriforce"></a><!-- ws:end:WikiTextHeadingRule:48 -->Semitriforce</h2>
| |
| Commas: 49/48, 56/55, 77/75, 507/500<br />
| |
| <br />
| |
| POTE generator: ~7/6 = 246.642<br />
| |
| <br />
| |
| Map: [&lt;6 0 14 12 16 27|, &lt;0 2 0 1 1 -1|]<br />
| |
| EDOs: 6, 24, 54cd, 78cd, 102cdf<br />
| |
| Badness: 0.0592<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:50:&lt;h3&gt; --><h3 id="toc25"><!-- ws:end:WikiTextHeadingRule:50 --> </h3>
| |
| <!-- ws:start:WikiTextHeadingRule:52:&lt;h1&gt; --><h1 id="toc26"><a name="Hemiug"></a><!-- ws:end:WikiTextHeadingRule:52 -->Hemiug</h1>
| |
| Commas: 128/125, 1323/1250<br />
| |
| <br />
| |
| POTE generator: ~21/20 = 52.093<br />
| |
| <br />
| |
| Map: [&lt;3 1 7 14|, &lt;0 2 0 -3|]<br />
| |
| Wedgie: &lt;&lt;6 0 -9 -14 -31 -21||<br />
| |
| EDOs: 21, 24, 45c, 69cd<br />
| |
| Badness: 0.1378<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:54:&lt;h2&gt; --><h2 id="toc27"><a name="Hemiug-11-limit"></a><!-- ws:end:WikiTextHeadingRule:54 -->11-limit</h2>
| |
| Commas: 56/55, 128/125, 1323/1250<br />
| |
| <br />
| |
| POTE generator: ~21/20 = 51.655<br />
| |
| <br />
| |
| Map: [&lt;3 1 7 14 16|, &lt;0 2 0 -3 -3|]<br />
| |
| EDOs: 21, 24, 69cd, 93cd<br />
| |
| Badness: 0.0681<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:56:&lt;h2&gt; --><h2 id="toc28"><a name="Hemiug-13-limit"></a><!-- ws:end:WikiTextHeadingRule:56 -->13-limit</h2>
| |
| Commas: 56/55, 66/65, 105/104, 507/500<br />
| |
| <br />
| |
| POTE generator: ~21/20 = 51.548<br />
| |
| <br />
| |
| Map: [&lt;3 1 7 14 16 13|, &lt;0 2 0 -3 -3 -1|]<br />
| |
| EDOs: 21, 24, 69cdf, 93cdf<br />
| |
| Badness: 0.0423<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:58:&lt;h1&gt; --><h1 id="toc29"><a name="Trug"></a><!-- ws:end:WikiTextHeadingRule:58 -->Trug</h1>
| |
| Commas: 128/125, 360/343<br />
| |
| <br />
| |
| POTE generator: ~48/35 = 501.980<br />
| |
| <br />
| |
| Map: [&lt;3 1 7 6|, &lt;0 3 0 2|]<br />
| |
| EDOs: 9bd, 12<br />
| |
| Badness: 0.1383<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:60:&lt;h1&gt; --><h1 id="toc30"><a name="Oodako"></a><!-- ws:end:WikiTextHeadingRule:60 -->Oodako</h1>
| |
| Commas: 128/125, 2401/2400<br />
| |
| <br />
| |
| POTE generator: ~8/7 = 223.3540873874507317<br />
| |
| <br />
| |
| Map: [&lt;3 3 7 8|, &lt;0 4 0 1|]<br />
| |
| Wedgie: &lt;&lt;12 0 3 -28 -29 7||<br />
| |
| EDOs: 6, 21, 27, 75c, 102cd, 129bcd<br />
| |
| Badness: 0.1132<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:62:&lt;h2&gt; --><h2 id="toc31"><a name="Oodako-11-limit"></a><!-- ws:end:WikiTextHeadingRule:62 -->11-limit</h2>
| |
| Commas: 56/55, 128/125, 3773/3750<br />
| |
| <br />
| |
| POTE generator: ~8/7 = 223.019<br />
| |
| <br />
| |
| Map: [&lt;3 3 7 8 10|, &lt;0 4 0 1 1|]<br />
| |
| EDOs: 6, 21, 27e<br />
| |
| Badness: 0.0592<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:64:&lt;h2&gt; --><h2 id="toc32"><a name="Oodako-13-limit"></a><!-- ws:end:WikiTextHeadingRule:64 -->13-limit</h2>
| |
| Commas: 56/55, 78/77, 128/125, 507/500<br />
| |
| <br />
| |
| POTE generator: ~8/7 = 223.449<br />
| |
| <br />
| |
| Map: [&lt;3 3 7 8 10 12|, &lt;0 4 0 1 1 -2|]<br />
| |
| EDOs: 6, 21, 27e<br />
| |
| Badness: 0.0423<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:66:&lt;h1&gt; --><h1 id="toc33"><a name="Hemisemiaug"></a><!-- ws:end:WikiTextHeadingRule:66 -->Hemisemiaug</h1>
| |
| Commas: 128/125, 12005/11664<br />
| |
| <br />
| |
| POTE generator: ~15/14 = 144.515<br />
| |
| <br />
| |
| Map: [&lt;6 1 14 4|, &lt;0 2 0 3|]<br />
| |
| Wedgie: &lt;&lt;12 0 18 -28 -5 42||<br />
| |
| Edos: 18, 24, 42, 66c, 108bc<br />
| |
| Badness: 0.2110<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:68:&lt;h2&gt; --><h2 id="toc34"><a name="Hemisemiaug-11-limit"></a><!-- ws:end:WikiTextHeadingRule:68 -->11-limit</h2>
| |
| Commas: 56/55, 128/125, 3773/3645<br />
| |
| <br />
| |
| POTE generator: ~15/14 = 144.780<br />
| |
| <br />
| |
| Map: [&lt;6 1 14 4 8|, &lt;0 2 0 3 3|]<br />
| |
| EDOs: 24, 42e, 66ce, 108bce<br />
| |
| Badness: 0.0807<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:70:&lt;h1&gt; --><h1 id="toc35"><a name="Niner"></a><!-- ws:end:WikiTextHeadingRule:70 -->Niner</h1>
| |
| Niner gives 9 as the complexity of an otonal tetrad, tying it with augene as a temperament supported by 27edo. Niner[18], therefore, has nine such tetrads.<br />
| |
| <br />
| |
| Commas: 128/125, 686/675<br />
| |
| <br />
| |
| POTE generator: ~3/2 = 707.167<br />
| |
| <br />
| |
| Map: [&lt;9 0 21 11|, &lt;0 1 0 1|]<br />
| |
| Wedgie: &lt;&lt;9 0 9 -21 -11 21||<br />
| |
| EDOs: 9, 18, 27, 63c, 90c<br />
| |
| Badness: 0.0672<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:72:&lt;h2&gt; --><h2 id="toc36"><a name="Niner-11-limit"></a><!-- ws:end:WikiTextHeadingRule:72 -->11-limit</h2>
| |
| Commas: 56/55, 128/125, 540/539<br />
| |
| <br />
| |
| POTE generator: ~3/2 = 706.726<br />
| |
| <br />
| |
| Map: [&lt;9 0 21 11 17|, &lt;0 1 0 1 1|]<br />
| |
| EDOs: 9, 27e, 36, 63ce<br />
| |
| Badness: 0.0349<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:74:&lt;h2&gt; --><h2 id="toc37"><a name="Niner-13-limit"></a><!-- ws:end:WikiTextHeadingRule:74 -->13-limit</h2>
| |
| Commas: 56/55, 78/77, 91/90, 128/125<br />
| |
| <br />
| |
| POTE generator: ~3/2 = 706.889<br />
| |
| <br />
| |
| Map: [&lt;9 0 21 11 17 19|, &lt;0 1 0 1 1 1|]<br />
| |
| EDOs: 9, 27e, 36, 63ce<br />
| |
| Badness: 0.0241<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:76:&lt;h2&gt; --><h2 id="toc38"><a name="Niner-Music"></a><!-- ws:end:WikiTextHeadingRule:76 -->Music</h2>
| |
| <a class="wiki_link_ext" href="https://www.prismnet.com/~hmiller/music/temp-augmented.html" rel="nofollow">Herman Miller's page about augmented temperament</a></body></html></pre></div>
| |