4L 5s (3/1-equivalent): Difference between revisions
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| Depth = 7 | | Depth = 7 | ||
| 2/1 = Equally-tempered [[Bohlen–Pierce scale]] | | 2/1 = Equally-tempered [[Bohlen–Pierce scale]] | ||
| 13/6 = [[ | | 13/6 = [[BPS]] (Bohlen–Pierce–Stearns) is in this region | ||
| 22/13 = Essentially just 7/3 | | 22/13 = Essentially just 7/3 | ||
}} | }} | ||
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Analogously to how the diatonic scale equalizes approaching [[7edo]] and its small steps collapse to 0 in [[5edo]], this scale equalizes approaching [[9edt]] and its small steps collapse in [[4edt]]; therefore, temperaments setting the 7/3 generator to precisely 7\9edt and to precisely 3\4edt are analogs of [[whitewood]] and [[blackwood]] respectively. However, unlike for the diatonic scale, the just point is not close to the center of the tuning range, but approximately 1/4 of the way between 9edt and 4edt, being closely approximated by 37\[[48edt]] and extremely closely approximated by 118\[[153edt]]. | Analogously to how the diatonic scale equalizes approaching [[7edo]] and its small steps collapse to 0 in [[5edo]], this scale equalizes approaching [[9edt]] and its small steps collapse in [[4edt]]; therefore, temperaments setting the 7/3 generator to precisely 7\9edt and to precisely 3\4edt are analogs of [[whitewood]] and [[blackwood]] respectively. However, unlike for the diatonic scale, the just point is not close to the center of the tuning range, but approximately 1/4 of the way between 9edt and 4edt, being closely approximated by 37\[[48edt]] and extremely closely approximated by 118\[[153edt]]. | ||
[[Category: | [[Category:Bohlen–Pierce]] | ||