Blackwood temperament modal harmony (in 15edo): Difference between revisions

Mike Battaglia (talk | contribs)
m Mike Battaglia moved page Harmony in 15edo Blacksmith to Blacksmith Temperament Modal Harmony (in 15EDO): Changed name to match Porcupine Temperament Modal Harmony and Mavila Temperament Modal Harmony, so that if one searches for "Modal Harmony" this page is also there
Mike Battaglia (talk | contribs)
Added small note about much of this being also useful for Blacksmith in general, not just 15
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Blacksmith[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. It can be thought of as a 5-limit temperament tempering out 256/243 (the Pythagorean diatonic semitone), a 7-limit temperament tempering out 28/27 and 49/48, and an 11-limit temperament tempering out 28/27, 49/48, and 55/54 (though in 15edo 121/120 and 100/99 are both tempered out as well, making the tuning identical to Ferrier and the unnamed 5c&15 temperament). 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).
Blacksmith[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. It can be thought of as a 5-limit temperament tempering out 256/243 (the Pythagorean diatonic semitone), a 7-limit temperament tempering out 28/27 and 49/48, and an 11-limit temperament tempering out 28/27, 49/48, and 55/54 (though in 15edo 121/120 and 100/99 are both tempered out as well, making the tuning identical to Ferrier and the unnamed 5c&15 temperament). 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).
Most of this page focuses on [[15-EDO]], perhaps the canonical Blacksmith tuning (and near to the POTE tuning), but much of it is also useful for Blacksmith temperament in general, even if played in other Blacksmith-supported equal temperaments.


==Important features of Blacksmith[10] in 15edo==
==Important features of Blacksmith[10] in 15edo==