Blackwood: Difference between revisions
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== Scales == | == Scales == | ||
[[File:blacksmith10.jpg|alt=blacksmith10.jpg|thumb|Lattice of Blackwood[10]]] | |||
[[File:BlackwoodMajor 15edo.mp3]] [[:File:BlackwoodMajor 15edo.mp3|Blackwood major scale in 15edo]] | [[File:BlackwoodMajor 15edo.mp3]] [[:File:BlackwoodMajor 15edo.mp3|Blackwood major scale in 15edo]] | ||
Revision as of 15:10, 23 April 2025
- This article is about the regular temperament. For the musician, see Easley Blackwood Jr.. For the scale structure sometimes associated with it, see 5L 5s.
Blackwood is a temperament that takes 5edo's circle of fifths for the 3-limit, but adds multiple copies to improve the tuning of the 5-limit. In the fundamental sense, it is the 5-limit temperament that tempers out the Pythagorean limma, and it extends to the 7-limit by recognizing that 4\5 is a good harmonic seventh, thus tempering out 28/27, 49/48, and 64/63, making it a member of trienstonic clan, semaphoresmic clan, and archytas clan.
The main interest in this temperament is in its mos scales, featuring pentawood (5L 5s). 15edo provides an excellent tuning for this temperament as well as for pentawood.
Blackwood was named in honor of Easley Blackwood Jr.
See Limmic temperaments #Blackwood for technical data.
Interval chain
In the following table, odd harmonics 1–9 are in bold.
| Period | Generator 0 | Generator 1 | ||
|---|---|---|---|---|
| Cents* | Approx. ratios | Cents* | Approx. ratios | |
| 0 | 0.0 | 1/1 | ||
| 1 | 240.0 | 7/6, 8/7, 9/8 | 151.1 | 10/9, 15/14 |
| 2 | 480.0 | 4/3 | 391.1 | 5/4 |
| 3 | 720.0 | 3/2 | 631.1 | 10/7 |
| 4 | 960.0 | 7/4, 12/7, 16/9 | 871.1 | 5/3 |
| 5 | 1200.0 | 2/1 | 1111.1 | 15/8, 40/21 |
* In 7-limit CWE tuning, octave reduced
Scales
Blackwood major scale in 15edo
Tunings
| Euclidean | |||
|---|---|---|---|
| Constrained | Constrained & skewed | Destretched | |
| Equilateral | CEE: ~5/4 = 386.3137 ¢ | CSEE: ~5/4 = 392.3287 ¢ | POEE: ~5/4 = 405.2729 ¢ |
| Tenney | CTE: ~5/4 = 386.3137 ¢ | CWE: ~5/4 = 395.1256 ¢ | POTE: ~5/4 = 399.5938 ¢ |
| Benedetti, Wilson |
CBE: ~5/4 = 386.3137 ¢ | CSBE: ~5/4 = 396.3386 ¢ | POBE: ~5/4 = 400.3211 ¢ |
| Euclidean | |||
|---|---|---|---|
| Constrained | Constrained & skewed | Destretched | |
| Equilateral | CEE: ~5/4 = 386.3137 ¢ | CSEE: ~5/4 = 388.6185 ¢ | POEE: ~5/4 = 387.1612 ¢ |
| Tenney | CTE: ~5/4 = 386.3137 ¢ | CWE: ~5/4 = 391.0976 ¢ | POTE: ~5/4 = 392.7675 ¢ |
| Benedetti, Wilson |
CBE: ~5/4 = 386.3137 ¢ | CSBE: ~5/4 = 392.2565 ¢ | POBE: ~5/4 = 395.3830 ¢ |