Blackwood
Blackwood is a regular temperament primarily supported by 15edo but in technicality by any EDO with 5edo's fifth (such as 25edo or 10edo) which takes 5edo as its 2.3.7, and treats 5 as an independent generator. Its 10-note scale (LsLsLsLsLs, pentawood) is unique among scales of its complexity for making a perfect fifth available on every note of the scale, at the cost of a ~18c detuned fifth. This means that every step of the scale has either a major or a minor triad built on it. Blackwood has Zarlino as a subset, specifically tunings wherein the difference between the large and medium steps is the same size as the small step. This overlaps with Porcupine tunings of zarlino only at 15edo.
There is also a 15-note, 20-note, etc. Blackwood scale, but these are much less common than the 10-note version which will be the main version discussed here.
Name
Blackwood is named after Easley Blackwood Jr., a microtonal composer and theorist who extensively used what we now know as the Blackwood[10] scale.
The 7-limit version of Blackwood was called "Blacksmith" originally; this name is almost obsolete.
Generator chain
The provided tuning is DR 4:5:6.
Cells highlighted in gray are intervals found in 5edo, which Blackwood expands. Yellow intervals are found in major blackwood[10], and green intervals in minor blackwood[10]. Blackwood[15] can thus be considered the "chromatic scale" of blackwood, and in any reasonable tuning closely approximates 15edo, which is the best edo tuning.
| Period 0 | Period 1 | Period 2 | Period 3 | Period 4 | ||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Generators | Cents | JI | Cents | JI | Cents | JI | Cents | JI | Cents | JI |
| -2 | 1034.4 | 50/27 | 74.4 | 25/24 | 314.4 | 25/21 | 554.4 | 25/18 | 794.4 | 100/63 |
| -1 | 1117.2 | 15/8, 40/21 | 157.2 | 10/9 | 397.2 | 5/4 | 637.2 | 10/7 | 877.2 | 5/3 |
| 0 | 0 | 1/1 | 240 | 8/7 | 480 | 4/3 | 720 | 3/2 | 960 | 7/4 |
| 1 | 82.8 | 21/20, 16/15 | 322.8 | 6/5 | 562.8 | 7/5 | 802.8 | 8/5 | 1042.8 | 10/9 |
| 2 | 165.6 | 27/25 | 405.6 | 63/50 | 645.6 | 36/25 | 885.6 | 42/25 | 1125.6 | 48/25 |
Blackwood[10] modes
Blackwood[10] has only two modes: major (LsLsLsLsLs) and minor (sLsLsLsLsL). The unilatus, fourth, fifth, and antilatus, under 10-form classification, are always perfect. The second, third, tritone, sixth, and seventh are all major in the major scale, and all minor in the minor scale.
| Mode | Step 0 | Step 1 | Step 2 | Step 3 | Step 4 | Step 5 | Step 6 | Step 7 | Step 8 | Step 9 | Step 10 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Major | 0c | 160c | 240c | 400c | 480c | 640c | 720c | 880c | 960c | 1120c | 1200c |
| Minor | 0c | 80c | 240c | 320c | 480c | 560c | 720c | 800c | 960c | 1040c | 1200c |
Blackwood tonality
Like in diatonic, the fourth and fifth may be considered stable tones; another consideration is consider the unilatus and antilatus, and thus all perfect intervals, also stable. However, note that the unilatus creates a tendency tone towards the minor third, much as the perfect fourth creates a tendency tone towards the major third. So they may be considered dissonant in that context. While the tritone of blackwood is not a perfect antitonic, the sharp tritone regardless leads up to the fifth, and the flat tritone down to the fourth. The flat tritone also resolves inward to a major third.
