4L 7s: Difference between revisions
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Replace instances of kleistonic with the new name p-chro smitonic. |
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4L 7s has a heptatonic subset, which is the [[hard]] end of the spectrum of the [[smitonic]] scale (4L 3s). | 4L 7s has a heptatonic subset, which is the [[hard]] end of the spectrum of the [[smitonic]] scale (4L 3s). | ||
The [[TAMNAMS]] name for this scale is ''' | The [[TAMNAMS]] name for this scale used to be ''kleistonic'', but is now simply called '''p-chro smitonic''' in the latest [[TAMNAMS Extension|extension]] (the [[User:Frostburn/TAMNAMS_Extension|euphonic name]] being '''smipechromic'''). The prefix for mossteps is ''klei-'''. | ||
== Notation == | == Notation == | ||
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== Tuning ranges == | == Tuning ranges == | ||
=== Soft range === | === Soft range === | ||
The soft range for tunings of | The soft range for tunings of p-chro smitonic 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. | 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. | ||
Soft | Soft p-chro smitonic edos include [[15edo]] and [[26edo]]. | ||
The sizes of the generator, large step and small step of | The sizes of the generator, large step and small step of p-chro smitonic are as follows in various soft tunings: | ||
{| class="wikitable right-2 right-3 right-4" | {| class="wikitable right-2 right-3 right-4" | ||
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=== Hypohard === | === Hypohard === | ||
[[File:19EDO_Kleistonic_cheat_sheet.png|400px|thumb|right|Cheat sheet for 19EDO | [[File:19EDO_Kleistonic_cheat_sheet.png|400px|thumb|right|Cheat sheet for 19EDO p-chro smitonic, a hard p-chro smitonic tuning]] | ||
Hypohard tunings of | Hypohard tunings of p-chro smitonic 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. | 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. | ||
Hypohard | Hypohard p-chro smitonic edos include [[15edo]], [[19edo]], and [[34edo]]. | ||
The sizes of the generator, large step and small step of | The sizes of the generator, large step and small step of p-chro smitonic are as follows in various hypohard p-chro smitonic tunings: | ||
{| class="wikitable right-2 right-3 right-4" | {| class="wikitable right-2 right-3 right-4" | ||
|- | |- | ||
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=== Parahard === | === Parahard === | ||
Parahard tunings of | Parahard tunings of p-chro smitonic 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 approximate 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. | The minor third is at its purest here, but the resulting scales tend to approximate 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. | ||
Parahard | Parahard p-chro smitonic edos include [[19edo]], 23[[23edo|edo]], and [[42edo]]. | ||
The sizes of the generator, large step and small step of | The sizes of the generator, large step and small step of p-chro smitonic are as follows in various parahard p-chro smitonic tunings: | ||
{| class="wikitable right-2 right-3 right-4" | {| class="wikitable right-2 right-3 right-4" | ||
|- | |- | ||
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=== Hyperhard === | === Hyperhard === | ||
Hyperhard tunings of | Hyperhard tunings of p-chro smitonic 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, where the small step is generally flat of a quarter tone. | 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. | ||
Hyperhard | Hyperhard p-chro smitonic edos include [[23edo]], [[31edo]], and [[27edo]]. | ||
The sizes of the generator, large step and small step of | The sizes of the generator, large step and small step of p-chro smitonic are as follows in various hyperhard p-chro smitonic tunings: | ||
{| class="wikitable right-2 right-3 right-4" | {| class="wikitable right-2 right-3 right-4" | ||
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| || || || || || 52\71 || 878.873 || 321.127 || 9 || 5 || 1.800 || | | || || || || || 52\71 || 878.873 || 321.127 || 9 || 5 || 1.800 || | ||
|- | |- | ||
| || 11\15 || || || || || 880.000 || 320.000 || 2 || 1 || 2.000 || Basic | | || 11\15 || || || || || 880.000 || 320.000 || 2 || 1 || 2.000 || Basic p-chro smitonic<br>(Generators smaller than this are proper) | ||
|- | |- | ||
| || || || || || 47\64 || 881.250 || 318.750 || 9 || 4 || 2.250 || | | || || || || || 47\64 || 881.250 || 318.750 || 9 || 4 || 2.250 || | ||