Template:Infobox ET: Difference between revisions

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<includeonly>{{#invoke:Infobox_ET|infobox_ET|tuning={{{1|{{PAGENAME}}}}}|Zeta={{{Zeta|}}}|Consistency={{{Consistency|}}}|Distinct consistency={{{Distinct consistency|}}}|debug={{{debug|}}} }}</includeonly><noinclude>

The template '''Infobox ET''' was built to help presenting basic information about [[equal tuning]]s in a unified form, to make them obvious by glance. Also the formatting of the wiki text itself is easier to read and improve when it is obviously structured by this template.

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| Adjacent ETs

|

| Links to the previous and the next ~~ETs~~ in the family.

| Links to the previous and the next equal temperaments in the family.

|-

| Prime factorization

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| Step size

|

| One step ~~(1200/edo)~~ of the equal temperament in cents (6 significant digits).

| One step of the equal temperament in cents (6 significant digits). (<code>step size = 1200/X</code>)

|-

| Octave

|

| The closest approximation of 2/1, the octave (P8), in edosteps and in cents. Hidden for ~~EDOs~~. (<code>P8 := round(~~size~~ / log2(~~equave~~))</code>)

| The closest approximation of 2/1, the octave (P8), in edosteps and in cents. Hidden for edos. (<code>P8 := round(X/log2(Y))</code>)

|-

| Twelfth

|

| The closest approximation of 3/1, the twelfth (P12), in edosteps and in cents. Hidden for edos and edts. (<code>P12 := round(X/log3(Y))</code>)

|-

| Fifth

|

| The closest approximation of 3/2, the perfect fifth (P5), in edosteps and in cents. ~~Hidden~~ for ~~EDFs~~. (<code>P5 := ~~round(size * log2(3/2) / log2(equave)~~)</code>)

| The closest approximation of 3/2, the perfect fifth (P5), in edosteps and in cents. Shown only for edos. (<code>P5 := P12 - P8)</code>)

|-

| Semitones

|

| Size of the augmented unison (A1) and minor second (m2) in edosteps and cents as generated by the fifth. <br>The A1 is the [[sharpness]] of the edo. (<code>A1 := 7 * P5 - 4 * P8; m2 := 3 * P8 - 5 * P5</code>)

| Size of the augmented unison (A1) and minor second (m2) in edosteps and cents as generated by the fifth. Shown only for edos. <br>The A1 is the [[sharpness]] of the edo. (<code>A1 := 7 * P12 - 11 * P8; m2 := 8 * P8 - 5 * P12</code>)

|-

| Dual sharp fifth

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| Consistency

| The limit diamond to which the ET is [[consistent]]. This template will stop trying to compute this if the value is at least 43. The following generalization is used for arbitrary equaves: for degree ''n'', all ratios of the form <math>~~\text{equave}~~^{\mathbb{Z}} \cdot ~~\frac{~~a}{b}, a, b \leq n</math>, are considered; when an increase of ''n'' does not add any new ratios, this degree is skipped.

| The limit diamond to which the tuning is [[consistent]]. This template will stop trying to compute this if the value is at least 43. The following generalization is used for arbitrary equaves: for degree ''n'', all ratios of the form <math>Y^{\mathbb{Z}} \cdot a/b, a, b \leq n</math>, are considered; when an increase of ''n'' does not add any new ratios, this degree is skipped.

|-

| Distinct consistency

| The limit diamond to which the ET is ~~distinctly~~ [[consistent]]. This template will stop trying to compute this if the value is at least 43.

| The limit diamond to which the tuning is [[consistency|distinctly consistent]]. This template will stop trying to compute this if the value is at least 43.

|-

| Special properties

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 <includeonly>{{#invoke:Infobox_ET|infobox_ET|tuning={{{1|{{PAGENAME}}}}}|Zeta={{{Zeta|}}}|Consistency={{{Consistency|}}}|Distinct consistency={{{Distinct consistency|}}}|debug={{{debug|}}} }}</includeonly><noinclude>
 The template '''Infobox ET''' was built to help presenting basic information about [[equal tuning]]s in a unified form, to make them obvious by glance. Also the formatting of the wiki text itself is easier to read and improve when it is obviously structured by this template.
@@ Line 16: / Line 15: @@
 | Adjacent ETs
 |
-| Links to the previous and the next ETs in the family.
+| Links to the previous and the next equal temperaments in the family.
 |-
 | Prime factorization
@@ Line 24: / Line 23: @@
 | Step size
 |
-| One step (1200/edo) of the equal temperament in cents (6 significant digits).
+| One step of the equal temperament in cents (6 significant digits). (<code>step size = 1200/X</code>)
 |-
 | Octave
 |
-| The closest approximation of 2/1, the octave (P8), in edosteps and in cents. Hidden for EDOs. (<code>P8 := round(size / log2(equave))</code>)
+| The closest approximation of 2/1, the octave (P8), in edosteps and in cents. Hidden for edos. (<code>P8 := round(X/log2(Y))</code>)
+|-
+| Twelfth
+|
+| The closest approximation of 3/1, the twelfth (P12), in edosteps and in cents. Hidden for edos and edts. (<code>P12 := round(X/log3(Y))</code>)
 |-
 | Fifth
 |
-| The closest approximation of 3/2, the perfect fifth (P5), in edosteps and in cents. Hidden for EDFs. (<code>P5 := round(size * log2(3/2) / log2(equave))</code>)
+| The closest approximation of 3/2, the perfect fifth (P5), in edosteps and in cents. Shown only for edos. (<code>P5 := P12 - P8)</code>)
 |-
 | Semitones
 |
-| Size of the augmented unison (A1) and minor second (m2) in edosteps and cents as generated by the fifth. <br>The A1 is the [[sharpness]] of the edo. (<code>A1 := 7 * P5 - 4 * P8; m2 := 3 * P8 - 5 * P5</code>)
+| Size of the augmented unison (A1) and minor second (m2) in edosteps and cents as generated by the fifth. Shown only for edos. <br>The A1 is the [[sharpness]] of the edo. (<code>A1 := 7 * P12 - 11 * P8; m2 := 8 * P8 - 5 * P12</code>)
 |-
 | Dual sharp fifth
@@ Line 52: / Line 55: @@
 | Consistency
 | Consistency
-| The limit diamond to which the ET is [[consistent]]. This template will stop trying to compute this if the value is at least 43. The following generalization is used for arbitrary equaves: for degree ''n'', all ratios of the form <math>\text{equave}^{\mathbb{Z}} \cdot \frac{a}{b}, a, b \leq n</math>, are considered; when an increase of ''n'' does not add any new ratios, this degree is skipped.
+| The limit diamond to which the tuning is [[consistent]]. This template will stop trying to compute this if the value is at least 43. The following generalization is used for arbitrary equaves: for degree ''n'', all ratios of the form <math>Y^{\mathbb{Z}} \cdot a/b, a, b \leq n</math>, are considered; when an increase of ''n'' does not add any new ratios, this degree is skipped.
 |-
 | Distinct consistency
 | Distinct consistency
-| The limit diamond to which the ET is distinctly [[consistent]]. This template will stop trying to compute this if the value is at least 43.
+| The limit diamond to which the tuning is [[consistency|distinctly consistent]]. This template will stop trying to compute this if the value is at least 43.
 |-
 | Special properties