@@ Line 1: / Line 1: @@
-<span style="display: block; text-align: right;">
 __FORCETOC__
-[[:de:übermässige_Temperaturen|Deutsch]]</span>
+The 5-limit parent comma for the '''augmented family''' is 128/125, the [[128/125|diesis]]. Its [[monzo]] is {{Monzo| 7 0 -3 }}, and flipping that yields &lt;&lt;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.
-The 5-limit parent comma for the '''augmented family''' is 128/125, the [[128/125|diesis]]. Its [[monzo|monzo]] is |7 0 -3&gt;, and flipping that yields &lt;&lt;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.
+== Seven limit children ==
+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.
-=Seven limit children=
+== August ==
-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.
+[[Comma]]s: 36/35, 128/125
-=August=
+[[POTE tuning|POTE generator]]: 696.011
-[[Comma|Comma]]s: 36/35, 128/125
-[[POTE_tuning|POTE generator]]: 696.011
+[[Map]]: [&lt;3 0 7 -1|, &lt;0 1 0 2|]
-[[Map|Map]]: [&lt;3 0 7 -1|, &lt;0 1 0 2|]
+[[Wedgie]]: &lt;&lt;3 0 6 -7 1 14||
-[[wedgie|Wedgie]]: &lt;&lt;3 0 6 -7 1 14||
 [[EDO|EDOs]]: [[9edo|9]], [[12edo|12]], [[45edo|45cd]], [[57edo|57cd]], [[69edo|69cd]]
-[[Badness|Badness]]: 0.0265
+[[Badness]]: 0.0265
-==11-limit==
+=== 11-limit ===
 Commas: 36/35, 45/44, 56/55
@@ Line 32: / Line 29: @@
 Badness: 0.0202
-==13-limit==
+=== 13-limit ===
 Commas: 27/26, 36/35, 45/44, 56/55
@@ Line 43: / Line 40: @@
 Badness: 0.0184
-==Augustus==
+=== Augustus ===
 Commas: 26/25, 36/35, 45/44, 56/55
@@ Line 54: / Line 51: @@
 Badness: 0.0222
-=Augene=
+== Augene ==
 Commas: 64/63, 126/125
@@ Line 67: / Line 64: @@
 Badness: 0.0248
-==11-limit==
+=== 11-limit ===
 Commas: 56/55, 64/63, 100/99
@@ Line 78: / Line 75: @@
 Badness: 0.0196
-===13-limit===
+=== 13-limit ===
 Commas: 40/39, 56/55, 64/63, 66/65
@@ Line 89: / Line 86: @@
 Badness: 0.0208
-===Ogene===
+=== Ogene ===
 Commas: 56/55, 64/63, 91/90, 100/99
@@ Line 100: / Line 97: @@
 Badness: 0.0229
-===Agene===
+=== Agene ===
 Commas: 56/55, 64/63, 78/77, 100/99
@@ Line 111: / Line 108: @@
 Badness: 0.0231
-==Eugene==
+=== Eugene ===
 Commas: 55/54, 64/63, 77/75
@@ Line 122: / Line 119: @@
 Badness: 0.0356
-[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]
+* [http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of27sonatina.mp3 Galticeran Sonatina] by [http://soundcloud.com/joelgranttaylor/galticeran_sonatina Joel Taylor]
-=Inflated=
+== Inflated ==
 Commas: 28/27, 128/125
@@ Line 139: / Line 136: @@
 Badness: 0.0547
-==11-limit==
+=== 11-limit ===
 Commas: 28/27, 55/54, 128/125
@@ Line 150: / Line 147: @@
 Badness: 0.0312
-=Deflated=
+== Deflated ==
 Commas: 21/20, 128/125
@@ Line 163: / Line 160: @@
 Badness: 0.0591
-=Hexe=
+== Hexe ==
 Commas: 50/49, 128/125
@@ Line 176: / Line 173: @@
 Badness: 0.0577
-==11-limit==
+=== 11-limit ===
 Commas: 50/49, 56/55, 125/121
@@ Line 187: / Line 184: @@
 Badness: 0.0384
-==13-limit==
+=== 13-limit ===
 Commas: 50/49, 56/55, 66/65, 105/104
@@ Line 198: / Line 195: @@
 Badness: 0.0359
-=Hemiaug=
+== Hemiaug ==
 Commas: 128/125, 245/243
@@ Line 211: / Line 208: @@
 Badness: 0.0705
-==11-limit==
+=== 11-limit ===
 Commas: 56/55, 128/125, 245/243
@@ Line 222: / Line 219: @@
 Badness: 0.0382
-==13-limit==
+=== 13-limit ===
 Commas: 56/55, 91/90, 128/125, 245/243
@@ Line 233: / Line 230: @@
 Badness: 0.0302
-=Triforce=
+== Triforce ==
 Commas: 49/48, 128/125
@@ Line 248: / Line 245: @@
 [[File:triforce9.jpg|alt=triforce9.jpg|triforce9.jpg]]
-==11-limit==
+=== 11-limit ===
 Commas: 56/55, 77/75, 128/125
@@ Line 259: / Line 256: @@
 Badness: 0.0262
-===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
@@ Line 275: / Line 272: @@
 [[triphi|Triforce(9) with L:s = phi]]
-==Semitriforce==
+=== Semitriforce ===
 Commas: 49/48, 56/55, 77/75, 507/500
@@ Line 286: / Line 283: @@
 Badness: 0.0592
-=== ===
-=Hemiug=
+== Hemiug ==
 Commas: 128/125, 1323/1250
@@ Line 301: / Line 297: @@
 Badness: 0.1378
-==11-limit==
+=== 11-limit ===
 Commas: 56/55, 128/125, 1323/1250
@@ Line 312: / Line 308: @@
 Badness: 0.0681
-==13-limit==
+=== 13-limit ===
 Commas: 56/55, 66/65, 105/104, 507/500
@@ Line 323: / Line 319: @@
 Badness: 0.0423
-=Trug=
+== Trug ==
 Commas: 128/125, 360/343
@@ Line 334: / Line 330: @@
 Badness: 0.1383
-=Oodako=
+== Oodako ==
 Commas: 128/125, 2401/2400
@@ Line 347: / Line 343: @@
 Badness: 0.1132
-==11-limit==
+=== 11-limit ===
 Commas: 56/55, 128/125, 3773/3750
@@ Line 358: / Line 354: @@
 Badness: 0.0592
-==13-limit==
+=== 13-limit ===
 Commas: 56/55, 78/77, 128/125, 507/500
@@ Line 369: / Line 365: @@
 Badness: 0.0423
-=Hemisemiaug=
+== Hemisemiaug ==
 Commas: 128/125, 12005/11664
@@ Line 382: / Line 378: @@
 Badness: 0.2110
-==11-limit==
+=== 11-limit ===
 Commas: 56/55, 128/125, 3773/3645
@@ Line 393: / Line 389: @@
 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.
@@ Line 408: / Line 404: @@
 Badness: 0.0672
-==11-limit==
+=== 11-limit ===
 Commas: 56/55, 128/125, 540/539
@@ Line 419: / Line 415: @@
 Badness: 0.0349
-==13-limit==
+=== 13-limit ===
 Commas: 56/55, 78/77, 91/90, 128/125
@@ Line 430: / Line 426: @@
 Badness: 0.0241
-==Music==
+== Music ==
-[https://www.prismnet.com/~hmiller/music/temp-augmented.html Herman Miller's page about augmented temperament]      [[Category:augmented]]
+* [https://www.prismnet.com/~hmiller/music/temp-augmented.html Herman Miller's page about augmented temperament]
+[[Category:augmented]]
 [[Category:family]]
 [[Category:theory]]
+<!-- interwiki links -->
+[[de:Übermässige Temperaturen]]

Augmented family: Difference between revisions