5L 3s: Difference between revisions
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You may have heard how [[2L 5s]] can be viewed as diatonic ([[5L 2s]]) generated by a fifth flatter than [[7edo]], in which case the large and small steps flip sizes. Similar to that, 5L 3s can be viewed as diatonic generated by a fifth sharper than [[5edo]]. To understand how this works and how you suddenly get an extra small step, let's first start with fifths slightly flat of 5edo and 5edo's fifth itself. | You may have heard how [[2L 5s]] can be viewed as diatonic ([[5L 2s]]) generated by a fifth flatter than [[7edo]], in which case the large and small steps flip sizes. Similar to that, 5L 3s can be viewed as diatonic generated by a fifth sharper than [[5edo]]. To understand how this works and how you suddenly get an extra small step, let's first start with fifths slightly flat of 5edo and 5edo's fifth itself. | ||
In diatonic scales generated by fifths slightly flat of [[5edo]]'s fifth, the small step (found by 8 octaves - 5 fifths) becomes increasingly narrow, for example in [[27edo]] (which has a fifth of 711.1 cents) the diatonic small step is 44.4 cents, and in [[32edo]] (which has | In diatonic scales generated by fifths slightly flat of [[5edo]]'s fifth, the small step (found by 8 octaves - 5 fifths) becomes increasingly narrow, for example in [[27edo]] (which has a fifth of 711.1 cents) the diatonic small step is 44.4 cents, and in [[32edo]] (which has a fifth of 712.5 cents) the diatonic small step is even smaller at 37.5 cents. The fifth-generated major scale in 32edo in [[cent]]s is 225-450-487.5-712.5-937.5-1162.5-1200 – notice how the "major third" (450) and "perfect fourth" (487.5) are quite close to each other, as are the "major seventh" (1162.5) and octave (1200). As the fifth gets closer and closer to 5edo's fifth, the small step becomes more and more narrow. | ||
In [[5edo]] itself, if you attempt to generate a diatonic scale by stacking 5edo's 720-centfifth, the diatonic small step becomes 0 cents, which means two pairs of notes in the diatonic scale will be the same, collapsing it into a 5-note scale (this is why a 1:0 step ratio is known as "collapsed" in [[TAMNAMS]]). For example, attempting to create the major scale in 5edo results in (in cents 240-480-480-480-720-960-1200 – now the "major third" and "perfect fourth" are ''identical'', as are the "major seventh" and "octave". | In [[5edo]] itself, if you attempt to generate a diatonic scale by stacking 5edo's 720-centfifth, the diatonic small step becomes 0 cents, which means two pairs of notes in the diatonic scale will be the same, collapsing it into a 5-note scale (this is why a 1:0 step ratio is known as "collapsed" in [[TAMNAMS]]). For example, attempting to create the major scale in 5edo results in (in cents 240-480-480-480-720-960-1200 – now the "major third" and "perfect fourth" are ''identical'', as are the "major seventh" and "octave". | ||