4L 7s: Difference between revisions
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== Tuning ranges == | == Tuning ranges == | ||
=== Soft range === | === Soft range === | ||
The soft range for tunings of | The soft range for tunings of kleistonic encompasses parasoft and hyposoft tunings. This implies step ratios smaller than 2/1, meaning a generator sharper than 4\15 = 320¢. | ||
This is the range associated with extensions of [[Orgone|Orgone[7]]]. | This is the range associated with extensions of [[Orgone|Orgone[7]]]. | ||
=== Hypohard === | === Hypohard === | ||
Hypohard tunings of | Hypohard tunings of kleistonic have step ratios between 2/1 and 3/1, implying a generator sharper than 5\19 = 315.79¢ and flatter than 4\15 = 320¢. | ||
This range represents one of the harmonic entropy minimums, where 6 generators make a just diatonic fifth ([[3/2]]), an octave above. This is the range associated with the eponymous Kleismic temperament and its extensions, such as the 5-limit [[Hanson]]. | This range represents one of the harmonic entropy minimums, where 6 generators make a just diatonic fifth ([[3/2]]), an octave above. This is the range associated with the eponymous Kleismic temperament and its extensions, such as the 5-limit [[Hanson]]. | ||
=== Parahard === | === Parahard === | ||
Parahard tunings of | Parahard tunings of kleistonic have step ratios between 3/1 and 4/1, implying a generator sharper than 6\23 = 313.04¢ and flatter than 5\19 = 315.79¢. | ||
The minor third is at its purest here, but the resulting scales tend to result in intervals that employ a much higher limit harmony, especially in the case of the superhard 23edo. | The minor third is at its purest here, but the resulting scales tend to result in intervals that employ a much higher limit harmony, especially in the case of the superhard 23edo. | ||
=== Hyperhard === | === Hyperhard === | ||
Hyperhard tunings of | Hyperhard tunings of kleistonic have step ratios between 4/1 and 6/1, implying a generator sharper than 8\31 = 309.68¢ and flatter than 6\23 = 313.04¢. | ||
The temperament known as Myna (a pun on "minor third") resides here, as this is the range where 10 generators make a just diatonic fifth (3/2), two octaves above. | The temperament known as Myna (a pun on "minor third") resides here, as this is the range where 10 generators make a just diatonic fifth (3/2), two octaves above. | ||
These scales are stacked with simple intervals, but are melodically difficult due to the extreme step size disparity. | These scales are stacked with simple intervals, but are melodically difficult due to the extreme step size disparity. | ||