71zpi: Difference between revisions

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== Intervals ==

The table ~~bellow~~ presents 32 integer-limit ratios by direct ~~mapping~~ to 71zpi steps, with an allowable error determined by the formula: abs (~~cents_error~~) < (1200 / (~~n * d~~)), where n/d represents the octave-reduced ratio. If you have an alternative or more effective formula, please feel free to suggest it.

The table below presents 32-integer-limit ratios by [[direct approximation]] to 71zpi steps, with an allowable error in cents determined by the formula: abs (error) < (1200 / (''nd'')), where ''n''/''d'' represents the octave-reduced ratio. If you have an alternative or more effective formula, please feel free to suggest it.

There are multiple ways to approach notation. The simplest method is to use the notations from [[20edo]]. However, this approach will not preserve octave compression when the audio is rendered by notation software. If maintaining accurate step compression in notation software is important, consider using the ups and downs notation from [[182edo]] at every 9-degree. With this method, the tonal difference will be less than 1 cent up to the 86th harmonic.

{{~~todo~~|complete table|inline=1|comment=Fill in the blank sections with the ups and downs notation from ~~20-EDO~~ and ~~182-EDO~~. Additionally, incorporate a new column adjacent to each notation to indicate the corresponding octave.}}

{{Todo|complete table|inline=1|comment=Fill in the blank sections with the ups and downs notation from 20edo and 182edo. Additionally, incorporate a new column adjacent to each notation to indicate the corresponding octave.}}

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

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! Cents

! Ratios

! colspan="3" | [[Ups and Downs Notation]] from [[20edo~~|20EDO~~]]

! colspan="3" | [[Ups and Downs Notation]] from [[20edo]]

! colspan="3" | [[Ups and Downs Notation]] from [[182edo~~|182EDO~~]]

! colspan="3" | [[Ups and Downs Notation]] from [[182edo]]

|-

| 0

@@ Line 46: / Line 46: @@
 == Intervals ==
-The table bellow presents 32 integer-limit ratios by direct mapping to 71zpi steps, with an allowable error determined by the formula: abs (cents_error) < (1200 / (n * d)), where n/d represents the octave-reduced ratio. If you have an alternative or more effective formula, please feel free to suggest it.
+The table below presents 32-integer-limit ratios by [[direct approximation]] to 71zpi steps, with an allowable error in cents determined by the formula: abs (error) < (1200 / (''nd'')), where ''n''/''d'' represents the octave-reduced ratio. If you have an alternative or more effective formula, please feel free to suggest it.
 There are multiple ways to approach notation. The simplest method is to use the notations from [[20edo]]. However, this approach will not preserve octave compression when the audio is rendered by notation software. If maintaining accurate step compression in notation software is important, consider using the ups and downs notation from [[182edo]] at every 9-degree. With this method, the tonal difference will be less than 1 cent up to the 86th harmonic.
-{{todo|complete table|inline=1|comment=Fill in the blank sections with the ups and downs notation from 20-EDO and 182-EDO. Additionally, incorporate a new column adjacent to each notation to indicate the corresponding octave.}}
+{{Todo|complete table|inline=1|comment=Fill in the blank sections with the ups and downs notation from 20edo and 182edo. Additionally, incorporate a new column adjacent to each notation to indicate the corresponding octave.}}
 {| class="wikitable center-all right-2 left-3"
@@ Line 57: / Line 57: @@
 ! Cents
 ! Ratios
-! colspan="3" | [[Ups and Downs Notation]] from [[20edo|20EDO]]
+! colspan="3" | [[Ups and Downs Notation]] from [[20edo]]
-! colspan="3" | [[Ups and Downs Notation]] from [[182edo|182EDO]]
+! colspan="3" | [[Ups and Downs Notation]] from [[182edo]]
 |-
 | 0