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| '''Blackwood''', or '''blackwood[10]''' in [[15edo|15edo]] refers to the 10-note symmetric 5L5s [[MOSScales|MOS]] scale in 15edo, which has two modes: 2 1 2 1 2 1 2 1 2 1 and 1 2 1 2 1 2 1 2 1 2. In 15edo it has a period of 240 cents (5 periods per octave) and a generator of 80 or 160 cents (though it is more commonly described as having a generator of 400 cents). | | '''Blackwood''', or '''blackwood[10]''' in [[15edo|15edo]] refers to the 10-note symmetric 5L5s [[MOSScales|MOS]] scale in 15edo, which has two modes: 2 1 2 1 2 1 2 1 2 1 and 1 2 1 2 1 2 1 2 1 2. In 15edo it has a period of 240 cents (5 periods per octave) and a generator of 80 or 160 cents (though it is more commonly described as having a generator of 400 cents). |
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| ==Important features of Blacksmith[10] in 15edo==
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| <ul><li>As an 11-limit temperament, Blacksmith is extremely simple and efficient, and while it does fairly high damage to many ratios of 3 and 9, it does a very acceptable job of approximating most ratios of 5, 7, and 11. 9/8, 7/6, 11/9, 4/3, and their octave inversions are the most heavily-damaged, but 6/5, 12/11, and their octave inversions are tuned with good to tolerable accuracy.</li><li>Blacksmith[10] has the most 5-odd-limit consonant triads it is possible to have in a 10-note 5-limit scale.</li><li>Because it is a 10-note scale with a period of 1/5 of an octave, any arbitrary harmony will occur either 5 or 10 times within the 10-note scale, and for otonal harmonies consisting of three or more notes, the utonal counterpart of the harmony will also occur either 5 or 10 times within the scale; this is a property that is only held by other scales with 5 periods per octave.</li><li>Blacksmith[10] is also a "mode of limited transposition" like the Diminished and Augmented scales in 12edo: since the scale is built by applying the generator only a single time within each period, the scale has only two modes.</li><li>Another way to think about Blacksmith[10] is as a superposition of seven 7-note 5-limit Fokker blocks, representing untempered variations of the diatonic modes, built on a single tonic (more on this below).</li></ul>
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| [[file:blacksmith_lattice_igs.png|frame|none|Blacksmith lattice]]
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| ==Interval Classes in Blacksmith[10]== | | ==Interval Classes in Blacksmith[10]== |