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 <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) == | == Untempered version (arranged in quasi-Pythagorean fashion) == | ||
{| class="wikitable" | {| 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 | !In terms of | ||
| Line 18: | Line 18: | ||
| colspan="2" |1 | | colspan="2" |1 | ||
|0 | |0 | ||
| | |<nowiki><math>δ</nowiki><sub>s</sub><nowiki></math></nowiki> | ||
|<nowiki> | |<nowiki><math>δ</nowiki><sub>s</sub><nowiki></math></nowiki> | ||
|1525.854 | |1525.854 | ||
|- | |- | ||
Revision as of 07:27, 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>\varphi</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. 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>\varphi </math> | Intervals with hypo-generator <math>\varphi-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>δs</math> | <math>δs</math> | 1525.854 | |