4L 7s: Difference between revisions

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== Notation ==

The notation used in this article is LssLsLssLss = А҃В҃Г҃Д҃Е҃Ѕ҃З҃И҃Ѳ҃І҃Ѫ҃А҃, based on old Cyrillic numerals 1-10 using the titlo as a numeric sign, and the addition of the big yus (Ѫ) for 11. Chromas are represented by regular sharps and flats.

Thus the 15edo gamut is as follows:

'''А҃''' А҃#/В҃b '''В҃ Г҃ Д҃''' Д҃#/Е҃b '''Е҃ Ѕ҃''' Ѕ҃#/З҃b '''З҃ И҃ Ѳ҃''' Ѳ҃#/І҃b '''І҃ Ѫ҃ А҃'''

Thus the 15edo gamut is as follows: '''А҃''' А҃#/В҃b '''В҃ Г҃ Д҃''' Д҃#/Е҃b '''Е҃ Ѕ҃''' Ѕ҃#/З҃b '''З҃ И҃ Ѳ҃''' Ѳ҃#/І҃b '''І҃ Ѫ҃ А҃'''

==== Letter names ====

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=== Soft range ===

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]]]. The small step is recognizable as a near diatonic semitone, while the large step is in the ambiguous area of neutral seconds.

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=== Hypohard ===

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 (aka [[Hanson]]) temperament and its extensions.

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=== Parahard ===

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. However, the large step is recognizable as a regular diatonic whole step, approximating both 10/9 and 9/8, while the small step is a slightly sharp of a quarter tone.

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=== Hyperhard ===

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.

These scales are stacked with simple intervals, but are melodically difficult due to the extreme step size disparity, where the small step is generally flat of a quarter tone.

@@ Line 15: / Line 15: @@
 == Notation ==
 The notation used in this article is LssLsLssLss = А҃В҃Г҃Д҃Е҃Ѕ҃З҃И҃Ѳ҃І҃Ѫ҃А҃, based on old Cyrillic numerals 1-10 using the titlo as a numeric sign, and the addition of the big yus (Ѫ) for 11. Chromas are represented by regular sharps and flats.
-Thus the 15edo gamut is as follows:
-'''А҃''' А҃#/В҃b '''В҃ Г҃ Д҃''' Д҃#/Е҃b '''Е҃ Ѕ҃''' Ѕ҃#/З҃b '''З҃ И҃ Ѳ҃''' Ѳ҃#/І҃b '''І҃ Ѫ҃ А҃'''
+Thus the 15edo gamut is as follows: '''А҃''' А҃#/В҃b '''В҃ Г҃ Д҃''' Д҃#/Е҃b '''Е҃ Ѕ҃''' Ѕ҃#/З҃b '''З҃ И҃ Ѳ҃''' Ѳ҃#/І҃b '''І҃ Ѫ҃ А҃'''
 ==== Letter names ====
@@ Line 217: / Line 217: @@
 === Soft range ===
 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]]]. The small step is recognizable as a near diatonic semitone, while the large step is in the ambiguous area of neutral seconds.
@@ Line 246: / Line 247: @@
 === Hypohard ===
 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 (aka [[Hanson]]) temperament and its extensions.
@@ Line 279: / Line 281: @@
 === Parahard ===
 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. However, the large step is recognizable as a regular diatonic whole step, approximating both 10/9 and 9/8, while the small step is a slightly sharp of a quarter tone.
@@ Line 312: / Line 315: @@
 === Hyperhard ===
 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.
 These scales are stacked with simple intervals, but are melodically difficult due to the extreme step size disparity, where the small step is generally flat of a quarter tone.