User:BudjarnLambeth/Breuddwyd scale: Difference between revisions
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| [[:Category:57-tone scales|57 tones]] [[Category:57-tone scales]] | | [[:Category:57-tone scales|57 tones]] [[Category:57-tone scales]] | ||
| 57/octave | | 57/octave | ||
| Polymicrotonal scale of [[5afdo]], [[11afdo]], [[13afdo]] and [[31afdo]] | | <small>Polymicrotonal scale of [[5afdo]], [[11afdo]], [[13afdo]] and [[31afdo]]</small> | ||
| The scale of all [[rational interval]]s with 5, 11, 13 or 31 in the denominator | | <small>The scale of all [[rational interval]]s with 5, 11, 13 or 31 in the denominator</small> | ||
| [[22165afdo]] | | [[22165afdo]] | ||
| 7/6, 6/5, 5/4, 4/3 (weak), 7/5, 3/2 (weak), 5/3, 7/4, 2/1, 7/3, 5/2, 3/1 (weak), 7/2, 4/1, 5/1, 6/1 (weak), 7/1 | | <small>7/6, 6/5, 5/4, 4/3 (weak), 7/5, 3/2 (weak), 5/3, 7/4, 2/1, 7/3, 5/2, 3/1 (weak), 7/2, 4/1, 5/1, 6/1 (weak), 7/1</small> | ||
|- | |- | ||
| 5&11&13&31ifdo <br>(''Breuddwyd inverse'') | | 5&11&13&31ifdo <br>(''Breuddwyd inverse'') | ||
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| 57 tones | | 57 tones | ||
| 57/octave | | 57/octave | ||
| Polymicrotonal scale of [[5ifdo]], [[11ifdo]], [[13ifdo]] and [[31ifdo]] | | <small>Polymicrotonal scale of [[5ifdo]], [[11ifdo]], [[13ifdo]] and [[31ifdo]]</small> | ||
| The scale of all [[rational interval]]s with 5, 11, 13 or 31, or any of their octave multiples (e.g. 10, 22, 26, 62 or 20, 44, 52, 124 or so on) in the numerator | | <small>The scale of all [[rational interval]]s with 5, 11, 13 or 31, or any of their octave multiples (e.g. 10, 22, 26, 62 or 20, 44, 52, 124 or so on) in the numerator</small> | ||
| [[22165ifdo]] | | [[22165ifdo]] | ||
| 7/6, 6/5, 5/4, 4/3 (weak), 7/5, 3/2 (weak), 5/3, 7/4, 2/1, 7/3, 5/2, 3/1 (weak), 7/2, 4/1, 5/1, 6/1 (weak), 7/1 | | <small>7/6, 6/5, 5/4, 4/3 (weak), 7/5, 3/2 (weak), 5/3, 7/4, 2/1, 7/3, 5/2, 3/1 (weak), 7/2, 4/1, 5/1, 6/1 (weak), 7/1</small> | ||
|- | |- | ||
| 5&11&13&31edo <br>(''Breuddwyd-2'') | | 5&11&13&31edo <br>(''Breuddwyd-2'') | ||
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| 57 tones | | 57 tones | ||
| 57/octave | | 57/octave | ||
| Polymicrotonal scale of [[5edo]], [[11edo]], [[13edo]] and [[31edo]] | | <small>Polymicrotonal scale of [[5edo]], [[11edo]], [[13edo]] and [[31edo]]</small> | ||
| | | | ||
| [[22165edo]] | | [[22165edo]] | ||
| 7/6, 6/5, 5/4, 4/3, 7/5, 3/2, 5/3, 7/4, 2/1, 7/3, 5/2, 3/1, 7/2, 4/1, 5/1, 6/1, 7/1 | | <small>7/6, 6/5, 5/4, 4/3, 7/5, 3/2, 5/3, 7/4, 2/1, 7/3, 5/2, 3/1, 7/2, 4/1, 5/1, 6/1, 7/1</small> | ||
|- | |- | ||
| 5&11&13&31edt <br>(''Breuddwyd-3'') | | 5&11&13&31edt <br>(''Breuddwyd-3'') | ||
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| 57 tones | | 57 tones | ||
| ~36/octave | | ~36/octave | ||
| Polymicrotonal scale of [[5edt]], [[11edt]], [[13edt]] and [[31edt]] | | <small>Polymicrotonal scale of [[5edt]], [[11edt]], [[13edt]] and [[31edt]]</small> | ||
| | | | ||
| [[22165edt]] | | [[22165edt]] | ||
| 7/6, 6/5, 5/4, 4/3, 7/5, 3/2, 5/3, 7/4, 2/1, 7/3, 5/2, 3/1, 7/2, 4/1, 5/1, 6/1, 7/1 | | <small>7/6, 6/5, 5/4, 4/3, 7/5, 3/2, 5/3, 7/4, 2/1, 7/3, 5/2, 3/1, 7/2, 4/1, 5/1, 6/1, 7/1</small> | ||
|- | |- | ||
| 5&11&13&31ed4 <br>(''Breuddwyd-4'') | | 5&11&13&31ed4 <br>(''Breuddwyd-4'') | ||
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| 57 tones | | 57 tones | ||
| ~29/octave | | ~29/octave | ||
| Polymicrotonal scale of [[5ed4]], [[11ed4]], [[13ed4]] and [[31ed4]] | | <small>Polymicrotonal scale of [[5ed4]], [[11ed4]], [[13ed4]] and [[31ed4]]</small> | ||
| | | | ||
| [[22165ed4]] | | [[22165ed4]] | ||
| 6/5, 5/4, 4/3 (weak), 3/2, 5/3, 7/4, 7/3, 3/1 (weak), 7/2, 4/1, 5/1, 6/1, 7/1 | | <small>6/5, 5/4, 4/3 (weak), 3/2, 5/3, 7/4, 7/3, 3/1 (weak), 7/2, 4/1, 5/1, 6/1, 7/1</small> | ||
|- | |- | ||
| 5&11&13&31ed5 <br>(''Breuddwyd-5'') | | 5&11&13&31ed5 <br>(''Breuddwyd-5'') | ||
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| 57 tones | | 57 tones | ||
| ~25/octave | | ~25/octave | ||
| Polymicrotonal scale of [[5ed5]], [[11ed5]], [[13ed5]] and [[31ed5]] | | <small>Polymicrotonal scale of [[5ed5]], [[11ed5]], [[13ed5]] and [[31ed5]]</small> | ||
| | | | ||
| [[22165ed5]] | | [[22165ed5]] | ||
| 7/6, 4/3, 3/2 (weak), 5/3, 7/4, 7/2, 5/1, 7/1 (weak) | | <small>7/6, 4/3, 3/2 (weak), 5/3, 7/4, 7/2, 5/1, 7/1 (weak)</small> | ||
|- | |- | ||
| 5&11&13&31ed6 <br>(''Breuddwyd-6'') | | 5&11&13&31ed6 <br>(''Breuddwyd-6'') | ||
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| 57 tones | | 57 tones | ||
| ~19/octave | | ~19/octave | ||
| Polymicrotonal scale of [[5ed6]], [[11ed6]], [[13ed6]] and [[31ed6]] | | <small>Polymicrotonal scale of [[5ed6]], [[11ed6]], [[13ed6]] and [[31ed6]]</small> | ||
| | | | ||
| [[22165ed6]] | | [[22165ed6]] | ||
| 7/6, 6/5, 5/4, 4/3, 7/5, 3/2, 5/3, 7/4, 2/1, 5/2, 3/1, 4/1, 5/1, 6/1, 7/1 | | <small>7/6, 6/5, 5/4, 4/3, 7/5, 3/2, 5/3, 7/4, 2/1, 5/2, 3/1, 4/1, 5/1, 6/1, 7/1</small> | ||
|- | |- | ||
| 5&11&13&31ed14/3 <br>(''Breuddwyd-14/3'') | | 5&11&13&31ed14/3 <br>(''Breuddwyd-14/3'') | ||
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| 57 tones | | 57 tones | ||
| ~26/octave | | ~26/octave | ||
| Polymicrotonal scale of [[5ed14/3]], [[11ed14/3]], [[13ed14/3]] and [[31ed14/3]] | | <small>Polymicrotonal scale of [[5ed14/3]], [[11ed14/3]], [[13ed14/3]] and [[31ed14/3]]</small> | ||
| | | | ||
| [[22165ed14/3]] | | [[22165ed14/3]] | ||
| 7/6, 4/3 (weak), 7/5, 3/2 (weak), 5/3 (weak), 7/4, 2/1, 7/3, 5/2, 3/1 (weak), 7/2, 4/1, 6/1, 7/1 | | <small>7/6, 4/3 (weak), 7/5, 3/2 (weak), 5/3 (weak), 7/4, 2/1, 7/3, 5/2, 3/1 (weak), 7/2, 4/1, 6/1, 7/1</small> | ||
|} | |} | ||
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| [[hexatonic|6 tones]] | | [[hexatonic|6 tones]] | ||
| 6/octave | | 6/octave | ||
| The [[hexany]] generated by 5/1, 11/1, 13/1 and 31/1 | | <small>The [[hexany]] generated by 5/1, 11/1, 13/1 and 31/1</small> | ||
| The octave-repeating harmonic series subset 220:260:286:310:341:403:440 | | <small>The octave-repeating harmonic series subset 220:260:286:310:341:403:440</small> | ||
| [[220afdo]] | | [[220afdo]] | ||
| (allowing rotations) 7/6, 6/5, 7/5, 5/3, 2/1, 7/3, 4/1 | | <small>(allowing rotations) 7/6, 6/5, 7/5, 5/3, 2/1, 7/3, 4/1</small> | ||
|} | |} | ||
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{| class="wikitable sortable mw-collapsible"}} | {| class="wikitable sortable mw-collapsible"}} | ||
|+ Tempered sonhar tunings | |+ <small>Tempered sonhar tunings</small> | ||
|- | |- | ||
! Systematic name <br>(& idiosyncratic common name) | ! <small>Systematic name <br>(& idiosyncratic common name)</small> | ||
! Equave | ! <small>Equave</small> | ||
! Equal temp mapping | ! <small>Equal temp mapping</small> | ||
! Reduced mapping | ! <sup>Reduced mapping</sup> | ||
! TE generator tunings (¢) | ! <small>TE generator tunings (¢)</small> | ||
! TE step tunings (¢) | ! <small>TE step tunings (¢)</small> | ||
! TE tuning map (¢) | ! <small>TE tuning map (¢)</small> | ||
! TE mistunings (¢) | ! <small>TE mistunings (¢)</small> | ||
! Complexity, <br>adjusted error, <br>TE error | ! <small>Complexity, <br>adjusted error, <br>TE error</small> | ||
! Unison vectors | ! <small>Unison vectors</small> | ||
! Recommended ETs | ! <small>Recommended ETs</small> | ||
! (x31 notation) | ! <small>(x31 notation)</small> | ||
|- | |- | ||
| c2 & c37 <br>(''Sonhar A'') | | <small>c2 & c37 <br>(''Sonhar A'')</small> | ||
| [[5/1]] | | <small>[[5/1]]</small> | ||
| 5,11,13,31 <br>[<2,3,3,4] <br> <37,55,59,79]> | | <small>5,11,13,31 <br>[<2,3,3,4] <br> <37,55,59,79]></small> | ||
| 5,11,13,31 <br>[<1,2,-2,-3] <br> <0,-1,7,10]> | | <small>5,11,13,31 <br>[<1,2,-2,-3] <br> <0,-1,7,10]></small> | ||
| 2789.3304, 1431.2645 | | <small>2789.3304, 1431.2645</small> | ||
| 40.49033, 73.19864 | | <small>40.49033, 73.19864</small> | ||
| 2789.330, 4147.396, 4440.191, 5944.654 | | <small>2789.330, 4147.396, 4440.191, 5944.654</small> | ||
| 3.017, -3.922, -0.337, -0.382 | | <small>3.017, -3.922, -0.337, -0.382</small> | ||
| 0.454182, <br>4.281341, <br>0.864185 | | <small>0.454182, <br>4.281341, <br>0.864185</small> | ||
| [-2,1,3,-2>, [-5,3,-1,1>, [-7,4,2,-1>, [-3,2,-4,3> | | <small>[-2,1,3,-2>, [-5,3,-1,1>, [-7,4,2,-1>, [-3,2,-4,3></small> | ||
| [[39ed5]], [[37ed5]], [[41ed5]], [[35ed5]], [[76ed5]], [[78ed5]], [[74ed5]], [[43ed5]](fk) | | <small>[[39ed5]], [[37ed5]], [[41ed5]], [[35ed5]], [[76ed5]], [[78ed5]], [[74ed5]], [[43ed5]](fk)</small> | ||
| c39, c37, c41, c35, c76, c78, c74, c43fk | | <small>c39, c37, c41, c35, c76, c78, c74, c43fk</small> | ||
|} | |} | ||
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! 7 integer limit intervals approximated within 15¢ | ! 7 integer limit intervals approximated within 15¢ | ||
|- | |- | ||
| PolyMOS 5\31(up2down2) 11\31(up0down2) 13\31(up1down1) | | PolyMOS <5\31(up2down2), 11\31(up0down2), 13\31(up1down1)> | ||
| [[31edo]] | | [[31edo]] | ||
| [[:Category:9-tone scales|9 tones]] per 31\31 [[Category:9-tone scales]] | | [[:Category:9-tone scales|9 tones]] per 31\31 [[Category:9-tone scales]] | ||
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| 5, 3, 3 | | 5, 3, 3 | ||
| 2:2, <br>0:2, <br>1:1 | | 2:2, <br>0:2, <br>1:1 | ||
| 5/4, 4/3, 3/2, 2/1, 5/2, 3/1, 4/1, 5/1, 6/1 | | <small>5/4, 4/3, 3/2, 2/1, 5/2, 3/1, 4/1, 5/1, 6/1</small> | ||
|} | |} | ||
[[Category:Scales by family]] | [[Category:Scales by family]] | ||