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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_s</math> as generators, 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.
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| ==Untempered version (arranged in quasi-Pythagorean fashion)==
| | ~~<noinclude />~~ |
| {| class="wikitable"
| | |
| |+
| | 833.090{{c}} |
| Period = <math>δ_s</math>
| |
| ! colspan="3" |Intervals with hyper-generator <math>φ</math>
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| ! colspan="3" |Intervals with hypo-generator <math>φ^{-1}</math>
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| |-
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| !In terms of metallic ratios
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| !In surd form
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| !Absolute cents
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| !In terms of metallic ratios
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| !In surd form
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| !Absolute cents
| |
| |-
| |
| | colspan="2" |1
| |
| |0
| |
| |<math>δ_s</math>
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| |<math>1 + \sqrt{2}</math>
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| |1525.864
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| |-
| |
| |<math>φ</math>
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| |<math>\frac{1 + \sqrt{5}}{2}</math>
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| |833.090
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| |<math>{δ_s} {φ^{-1}}</math>
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| |<math>\frac{(1 + \sqrt{2})(\sqrt{5} - 1)}{2}</math>
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| |692.774
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| |-
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| |<math>{δ_s^{-1}} {φ^2}</math>
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| |<math>\frac{(3 + \sqrt{5})(\sqrt{2} - 1)}{2}</math>
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| |140.317
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| |<math>{δ_s^{2}} {φ^{-2}}</math>
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| |<math>\frac{(3 + 2 \sqrt{2})(3 - \sqrt{5})}{2}</math>
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| |1385.547
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| |-
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| |<math>{δ_s^{-1}} {φ^3}</math>
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| |<math>(2 + \sqrt{5})(\sqrt{2} - 1)</math>
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| |973.407
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| |<math>{δ_s^{2}} {φ^{-3}}</math>
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| |<math>\frac{(3 + 2 \sqrt{2})(3 - \sqrt{5})}{2}</math>
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| |552.457
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| |-
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| |<math>{δ_s^{-2}} {φ^4}</math>
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| |<math>\frac{(1 + \sqrt{5})^4 (3 -2\sqrt{2})}{2}</math>
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| |280.633
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| |<math>{δ_s^{3}} {φ^{-4}}</math>
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| |<math>\frac{16(7 + 5 \sqrt{2})}{(1 + \sqrt{5})^4}</math>
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| |1245.231
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| |}
| |
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833.090 ¢