SandBox: Difference between revisions
Jump to navigation
Jump to search
No edit summary |
No edit summary |
||
| Line 1: | Line 1: | ||
{{SandBox please edit after this line}} | {{SandBox please edit after this line}} | ||
The '''Electrum temperaments''' are a group of rank-2 temperaments proposed by Iwuqety, inspired by the idea of using the [[acoustic phi]] (golden ratio | 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" | {| class="wikitable" | ||
|+ | |+ | ||
! colspan="3" |Intervals with hyper-generator | ! colspan="3" |Intervals with hyper-generator <math>φ</math> | ||
! colspan="3" |Intervals with hypo-generator | ! colspan="3" |Intervals with hypo-generator <math>φ^-1</math> | ||
|- | |- | ||
!In terms of | !In terms of metallic ratios | ||
metallic ratios | |||
!In surd form | !In surd form | ||
!Absolute cents | !Absolute cents | ||
| Line 18: | Line 17: | ||
| colspan="2" |1 | | colspan="2" |1 | ||
|0 | |0 | ||
| | |<math>δ_s</math> | ||
|<code><nowiki><math>\frac{1 + \sqrt{2}}{2}</math></nowiki></code> | |||
|1525.854 | |1525.854 | ||
|- | |- | ||
Revision as of 07:35, 12 June 2021
This is the sandbox. To experiment with editing, click on the [Edit] tab.
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]\displaystyle{ φ }[/math]) and acoustic silver ratio [math]\displaystyle{ δ_s }[/math] as generators, respectively replacing the 3/2 perfect fifth and the 2/1 octave used in common practice music. Electrum refers to naturally-occurring alloy which is mainly made up of gold and silver.
Untempered version (arranged in quasi-Pythagorean fashion)
| Intervals with hyper-generator [math]\displaystyle{ φ }[/math] | Intervals with hypo-generator [math]\displaystyle{ φ^-1 }[/math] | ||||
|---|---|---|---|---|---|
| In terms of metallic ratios | In surd form | Absolute cents | In terms of metallic ratios | In surd form | Absolute cents |
| 1 | 0 | [math]\displaystyle{ δ_s }[/math] | <math>\frac{1 + \sqrt{2}}{2}</math>
|
1525.854 | |