SandBox: Difference between revisions

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The '''Electrum temperaments''' are a group of rank-2 temperaments proposed by Iwuqety, inspired by the idea of using the [[acoustic phi]] (golden ratio [math~~]φ[~~/math]) and acoustic silver ratio [math]δs[/math] as generators, respectively replacing the [[3/2]] perfect fifth and the [[2/1]] octave used in common practice music. [[wikipedia:Electrum|Electrum]] refers to naturally-occurring alloy which is mainly made up of gold and silver.

The '''Electrum temperaments''' are a group of rank-2 temperaments proposed by Iwuqety, inspired by the idea of using the [[acoustic phi]] (golden ratio <nowiki><math>\varphi</math></nowiki>) and acoustic silver ratio <nowiki><math>δ</nowiki>s<nowiki></math></nowiki> as generators, respectively replacing the [[3/2]] perfect fifth and the [[2/1]] octave used in common practice music. [[wikipedia:Electrum|Electrum]] refers to naturally-occurring alloy which is mainly made up of gold and silver.

== Untempered version (arranged in quasi-Pythagorean fashion) ==

{| class="wikitable"

|+

! colspan="3" |

! colspan="3" |Intervals with hyper-generator <nowiki><math>\varphi </math></nowiki>

! colspan="3" |

! colspan="3" |Intervals with hypo-generator <nowiki><math>\varphi</nowiki>-1<nowiki></math></nowiki>

|-

!In terms of

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| colspan="2" |1

|0

|[math]δs[/math]

|<nowiki><math>δ</nowiki>s<nowiki></math></nowiki>

|<nowiki>[math~~]\frac {1 + \sqrt{2}}{2}[~~/math]</nowiki>

|<nowiki><math>δ</nowiki>s<nowiki></math></nowiki>

|1525.854

|-

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-The '''Electrum temperaments''' are a group of rank-2 temperaments proposed by Iwuqety, inspired by the idea of using the [[acoustic phi]] (golden ratio [math]φ[/math]) and acoustic silver ratio [math]δ<sub>s</sub>[/math] as generators, respectively replacing the [[3/2]] perfect fifth and the [[2/1]] octave used in common practice music. [[wikipedia:Electrum|Electrum]] refers to naturally-occurring alloy which is mainly made up of gold and silver.
+The '''Electrum temperaments''' are a group of rank-2 temperaments proposed by Iwuqety, inspired by the idea of using the [[acoustic phi]] (golden ratio <nowiki><math>\varphi</math></nowiki>) and acoustic silver ratio <nowiki><math>δ</nowiki><sub>s</sub><nowiki></math></nowiki> as generators, respectively replacing the [[3/2]] perfect fifth and the [[2/1]] octave used in common practice music. [[wikipedia:Electrum|Electrum]] refers to naturally-occurring alloy which is mainly made up of gold and silver.
 == Untempered version (arranged in quasi-Pythagorean fashion) ==
 {| class="wikitable"
 |+
-! colspan="3" |
+! colspan="3" |Intervals with hyper-generator <nowiki><math>\varphi </math></nowiki>
-! colspan="3" |
+! colspan="3" |Intervals with hypo-generator <nowiki><math>\varphi</nowiki><sup>-1</sup><nowiki></math></nowiki>
 |-
 !In terms of
@@ Line 18: / Line 18: @@
 | colspan="2" |1
 |0
-|[math]δ<sub>s</sub>[/math]
+|<nowiki><math>δ</nowiki><sub>s</sub><nowiki></math></nowiki>
-|<nowiki>[math]\frac {1 + \sqrt{2}}{2}[/math]</nowiki>
+|<nowiki><math>δ</nowiki><sub>s</sub><nowiki></math></nowiki>
 |1525.854
 |-