186zpi: Difference between revisions
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It is important to note that [[124edo]] provides two possible [[3/2|fifths (3/2)]]. The closest one, from the [[val]] <124 197] (i.e. the [[patent val]]), is the [[3/2|fifth]] mapped to 73 steps of [[124edo]] with a [[relative error]] of +46.465%. The second closest, from the [[val]] <124 196] (i.e. the [[val]] 124b), is mapped to 72 steps of [[124edo]] with a [[relative error]] of -53.535%. This second [[3/2|fifth]], which appears in [[124ed8]], also corresponds to the [[3/2|fifth]] of [[31edo]]. Therefore, we choose to use the [[ups and downs notation]] of the 124b temperament, denoted as <124 196]. | It is important to note that [[124edo]] provides two possible [[3/2|fifths (3/2)]]. The closest one, from the [[val]] <124 197] (i.e. the [[patent val]]), is the [[3/2|fifth]] mapped to 73 steps of [[124edo]] with a [[relative error]] of +46.465%. The second closest, from the [[val]] <124 196] (i.e. the [[val]] 124b), is mapped to 72 steps of [[124edo]] with a [[relative error]] of -53.535%. This second [[3/2|fifth]], which appears in [[124ed8]], also corresponds to the [[3/2|fifth]] of [[31edo]]. Therefore, we choose to use the [[ups and downs notation]] of the 124b temperament, denoted as <124 196]. | ||
{| class="wikitable center-all | {| class="wikitable center-all center-1 right-2 left-3 center-4 center-5" | ||
|- | |- | ||
| colspan="3" | JI ratios are comprised of 32-integer limit ratios,<br>and are stylized as follows to indicate their accuracy: | | colspan="3" style="text-align:left;" | JI ratios are comprised of 32-integer limit ratios,<br>and are stylized as follows to indicate their accuracy: | ||
* '''<u>Bold Underlined:</u>''' relative error < 8.333 % | * '''<u>Bold Underlined:</u>''' relative error < 8.333 % | ||
* '''Bold:''' relative error < 16.667 % | * '''Bold:''' relative error < 16.667 % | ||
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* <small><small>Small Small:</small></small> relative error < 41.667 % | * <small><small>Small Small:</small></small> relative error < 41.667 % | ||
* <small><small><small>Small Small Small:</small></small></small> relative error < 50 % | * <small><small><small>Small Small Small:</small></small></small> relative error < 50 % | ||
| colspan="2" | <center>'''124b at every 3 steps'''</center><br>[[9/8|Whole tone]] = 20 steps<br>[[256/243|Limma]] = 12 steps<br>[[2187/2048|Apotome]] = 8 steps | | colspan="2" style="text-align:right;" | <center>'''124b at every 3 steps'''</center><br>[[9/8|Whole tone]] = 20 steps<br>[[256/243|Limma]] = 12 steps<br>[[2187/2048|Apotome]] = 8 steps | ||
|- | |- | ||
! Degree | ! Degree | ||