10th-octave temperaments: Difference between revisions
Jump to navigation
Jump to search
→Neon: explain what exactly makes this notable |
Review, switch to Sintel's badness, WE & CWE tunings |
||
| Line 6: | Line 6: | ||
== Neon == | == Neon == | ||
Neon tempers out {{monzo| 21 60 -50 }} in the 5-limit, equating [[3125/2916]] with one step of 10edo. Neon extensions discussed elsewhere include [[deca]], [[calcium]], and [[zinc]]. | Neon tempers out {{monzo| 21 60 -50 }} in the 5-limit, equating [[3125/2916]] with one step of 10edo. It was named by [[Eliora]] in 2023 after the 10th element. Neon extensions discussed elsewhere include [[deca]], [[calcium]], and [[zinc]]. | ||
[[Subgroup]]: 2.3.5 | [[Subgroup]]: 2.3.5 | ||
| Line 13: | Line 13: | ||
{{Mapping|legend=1| 10 4 9 | 0 5 6 }} | {{Mapping|legend=1| 10 4 9 | 0 5 6 }} | ||
: Mapping generators: ~3125/2916, {{monzo| 10 29 -24 }} | : Mapping generators: ~3125/2916, {{monzo| 10 29 -24 }} | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[WE]]: ~3125/2916 = 119.9999{{c}}, {{monzo| 10 29 -24 }} = 284.3890{{c}} | |||
: [[error map]]: {{val| -0.001 -0.011 +0.019 }} | |||
* [[CWE]]: ~3125/2916 = 120.0000{{c}}, {{monzo| 10 29 -24 }} = 284.3891{{c}} | |||
: error map: {{val| 0.000 -0.010 +0.021 }} | |||
{{Optimal ET sequence|legend=1| 80, 190, 270, 460, 730, 1730, 2460, 3190, 5650 }} | {{Optimal ET sequence|legend=1| 80, 190, 270, 460, 730, 1730, 2460, 3190, 5650 }} | ||
[[Badness]]: | [[Badness]] (Sintel): 4.85 | ||
{{Navbox fractional-octave}} | {{Navbox fractional-octave}} | ||
[[Category:10edo]] | [[Category:10edo]] | ||
Revision as of 07:34, 5 July 2026
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
10edo is notable for having close approximations of 15/14 to one step, and 13/8 to 7 steps. 10th-octave temperaments naturally occur between any equal divisions of the octave whose greatest common divisor is 10.
Temperaments discussed elsewhere include: decoid, deca, decile, decimetra, decistearn, decavish, and linus.
Neon
Neon tempers out [21 60 -50⟩ in the 5-limit, equating 3125/2916 with one step of 10edo. It was named by Eliora in 2023 after the 10th element. Neon extensions discussed elsewhere include deca, calcium, and zinc.
Subgroup: 2.3.5
Comma list: [21 60 -50⟩
Mapping: [⟨10 4 9], ⟨0 5 6]]
- Mapping generators: ~3125/2916, [10 29 -24⟩
- WE: ~3125/2916 = 119.9999 ¢, [10 29 -24⟩ = 284.3890 ¢
- error map: ⟨-0.001 -0.011 +0.019]
- CWE: ~3125/2916 = 120.0000 ¢, [10 29 -24⟩ = 284.3891 ¢
- error map: ⟨0.000 -0.010 +0.021]
Optimal ET sequence: 80, 190, 270, 460, 730, 1730, 2460, 3190, 5650
Badness (Sintel): 4.85