6edϕ: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
'''6 equal divisions of [[acoustic phi]]''' ('''6edϕ''') is the [[nonoctave]] [[tuning system]] derived by dividing [[acoustic phi]] into 6 equal steps of 138.8 [[cent]]s each, or the sixth root of the golden ratio | '''6 equal divisions of [[acoustic phi]]''' ('''6edϕ''') is the [[nonoctave]] [[tuning system]] derived by dividing [[acoustic phi]] into 6 equal steps of 138.8 [[cent]]s each, or the sixth root of the golden ratio. | ||
It serves as a basic tempered approximation for the [[metallic harmonic series]], and the associated [[metallic intonation]]. The first metallic harmonic (the golden ratio) is represented exactly by the sixth step, while the second and third metallic harmonics are represented by the 11th and 15th steps respectively. | It serves as a basic tempered approximation for the [[metallic harmonic series]], and the associated [[metallic intonation]]. The first metallic harmonic (the golden ratio) is represented exactly by the sixth step, while the second and third metallic harmonics are represented by the 11th and 15th steps respectively. | ||
== Interval table == | == Interval table == | ||
{{Interval table}} | {{Interval table}} | ||
Revision as of 07:43, 4 April 2024
| ← 5edϕ | 6edϕ | 7edϕ → |
6 equal divisions of acoustic phi (6edϕ) is the nonoctave tuning system derived by dividing acoustic phi into 6 equal steps of 138.8 cents each, or the sixth root of the golden ratio.
It serves as a basic tempered approximation for the metallic harmonic series, and the associated metallic intonation. The first metallic harmonic (the golden ratio) is represented exactly by the sixth step, while the second and third metallic harmonics are represented by the 11th and 15th steps respectively.
Interval table
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 138.8 | 10/9, 11/10, 14/13, 15/14, 20/19, 21/19 |
| 2 | 277.7 | 13/11, 15/13, 17/14 |
| 3 | 416.5 | 13/10, 14/11, 17/13, 19/15, 21/17 |
| 4 | 555.4 | 4/3, 7/5, 15/11, 19/14 |
| 5 | 694.2 | 3/2, 17/11, 19/13 |
| 6 | 833.1 | 5/3, 11/7, 21/13 |