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 ~~<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.

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_s</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.

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

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

{| class="wikitable"

|+

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

! colspan="3" |Intervals with hyper-generator <math>φ</math>

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

! colspan="3" |Intervals with hypo-generator <math>φ^-1</math>

|-

!In terms of

!In terms of metallic ratios

metallic ratios

!In surd form

!Absolute cents

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| colspan="2" |1

|0

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

|<math>δ_s</math>

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

|<code><nowiki><math>\frac{1 + \sqrt{2}}{2}</math></nowiki></code>

|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 <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.
+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_s</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.
-== Untempered version (arranged in quasi-Pythagorean fashion) ==
+==Untempered version (arranged in quasi-Pythagorean fashion)==
 {| class="wikitable"
 |+
-! colspan="3" |Intervals with hyper-generator <nowiki><math>\varphi </math></nowiki>
+! colspan="3" |Intervals with hyper-generator <math>φ</math>
-! colspan="3" |Intervals with hypo-generator <nowiki><math>\varphi</nowiki><sup>-1</sup><nowiki></math></nowiki>
+! colspan="3" |Intervals with hypo-generator <math>φ^-1</math>
 |-
-!In terms of
+!In terms of metallic ratios
-metallic ratios
 !In surd form
 !Absolute cents
@@ Line 18: / Line 17: @@
 | colspan="2" |1
 |0
-|<nowiki><math>δ</nowiki><sub>s</sub><nowiki></math></nowiki>
+|<math>δ_s</math>
-|<nowiki><math>δ</nowiki><sub>s</sub><nowiki></math></nowiki>
+|<code><nowiki><math>\frac{1 + \sqrt{2}}{2}</math></nowiki></code>
 |1525.854
 |-