186zpi: Difference between revisions

Line 107:

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 left-1 right-2 left-3 center-4 ~~right~~-5"

{| class="wikitable center-all left-1 right-2 left-3 center-4 left-5"

|-

|colspan="3"|

| colspan="3" | JI ratios are comprised of 32-integer limit ratios, and are stylized as follows to indicate their accuracy:

JI ratios are comprised of 32-integer limit ratios,

and are stylized as follows to indicate their accuracy:

* '''Bold Underlined:''' relative error < 8.333 %

* '''Bold:''' relative error < 16.667 %

Line 118:

Line 116:

* Small Small: relative error < 41.667 %

* Small Small Small: relative error < 50 %

|colspan="2"|

| colspan="2" | 124b at every 3-degree step Pythagorean limma = 12 steps whole tone = 20 steps

124b at every 3-degree

Pythagorean limma = 12 steps

whole tone = 20 steps~~ ~~

|-

!~~Step~~

! Degree

!Cents

! Cents

!Ratios

! Ratios

!Ups and Downs Notation

! Ups and Downs Notation

!Step

! Step

|-

| 0

@@ Line 107: / Line 107: @@
 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 left-1 right-2 left-3 center-4 right-5"
+{| class="wikitable center-all left-1 right-2 left-3 center-4 left-5"
 |-
-|colspan="3"|
+| colspan="3" | JI ratios are comprised of 32-integer limit ratios,<br>and are stylized as follows to indicate their accuracy:
-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 %
 * '''Bold:''' relative error < 16.667 %
@@ Line 118: / Line 116: @@
 * <small><small>Small Small:</small></small> relative error < 41.667 %
 * <small><small><small>Small Small Small:</small></small></small> relative error < 50 %
-|colspan="2"|
+| colspan="2" | 124b at every 3-degree step<br>Pythagorean limma = 12 steps<br>whole tone = 20 steps
-b at every 3-degree<br>
-Pythagorean limma = 12 steps<br>
-whole tone = 20 steps<br>
 |-
-!Step
+! Degree
-!Cents
+! Cents
-!Ratios
+! Ratios
-!Ups and Downs Notation
+! Ups and Downs Notation
-!Step
+! Step
 |-
 | 0