This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| Periods = 1
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-05-23 16:45:34 UTC</tt>.<br>
| nLargeSteps = 4
: The original revision id was <tt>551975266</tt>.<br>
| nSmallSteps = 7
: The revision comment was: <tt></tt><br>
| Equalized = 3
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| Collapsed = 1
<h4>Original Wikitext content:</h4>
| Pattern = LssLssLssLs
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">This MOS is generated by an approximate 6/5 minor third between 300 (1\[[4edo]]) and 327.__27__¢ (3\[[11edo]]).
}}
{{MOS intro}}
One of the [[harmonic entropy]] minimums in this range is [[Kleismic family|Kleismic/Hanson]].
TAMNAMS formerly used the name ''kleistonic'' for the name of this scale (prefix ''klei-''). Other names include '''p-chro smitonic''' or '''smipechromic'''.
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>4L 7s</title></head><body>This MOS is generated by an approximate 6/5 minor third between 300 (1\<a class="wiki_link" href="/4edo">4edo</a>) and 327.<u>27</u>¢ (3\<a class="wiki_link" href="/11edo">11edo</a>).<br />
The soft range for tunings of 4L 7s encompasses parasoft and hyposoft tunings. This implies step ratios smaller than 2/1, meaning a generator sharper than {{nowrap|4\15 {{=}} 320{{c}}}}.
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 edos include [[15edo]] and [[26edo]].
The sizes of the generator, large step and small step of 4L 7s are as follows in various soft tunings:
{| class="wikitable right-2 right-3 right-4"
|-
!
! [[15edo]] (basic)
! [[26edo]] (soft)
! Some JI approximations
|-
| generator (g)
| 4\15, 320.00
| 7\26, 323.08
| 77/64, 6/5
|-
| L (octave - 3g)
| 2\15, 160.00
| 3\26, 138.46
| 12/11, 13/12
|-
| s (4g - octave)
| 1\15, 80.00
| 2\19, 92.31
| 21/20, 22/21, 20/19
|}
=== Hypohard ===
Hypohard tunings of 4L 7s have step ratios between 2/1 and 3/1, implying a generator sharper than {{nowrap|5\19 {{=}} 315.79{{c}}}} and flatter than {{nowrap|4\15 {{=}} 320{{c}}}}.
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 edos include [[15edo]], [[19edo]], and [[34edo]].
The sizes of the generator, large step and small step of 4L 7s are as follows in various hypohard tunings:
{| class="wikitable right-2 right-3 right-4"
|-
!
! [[15edo]] (basic)
! [[19edo]] (hard)
! [[34edo]] (semihard)
! Some JI approximations
|-
| generator (g)
| 4\15, 320.00
| 5\19, 315.79
| 9\34, 317.65
| 6/5
|-
| L ({{nowrap|octave − 3g}})
| 2\15, 160.00
| 3\19, 189.47
| 5\34, 176.47
| 10/9, 11/10 (in 15edo)
|-
| s ({{nowrap|4g − octave}})
| 1\15, 80.00
| 1\19, 63.16
| 2\34, 70.59
| 25/24, 26/25 (in better kleismic tunings)
|}
=== Parahard ===
Parahard tunings of 4L 7s 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.
Parahard edos include [[19edo]], 23[[23edo|edo]], and [[42edo]].
The sizes of the generator, large step and small step of 4L 7s are as follows in various parahard tunings:
{| class="wikitable right-2 right-3 right-4"
|-
!
! [[19edo]] (hard)
! [[23edo]] (superhard)
! [[42edo]] (parahard)
! Some JI approximations
|-
| generator (g)
| 5\19, 315.79
| 6\23, 313.04
| 11\42, 314.29
| 6/5
|-
| L ({{nowrap|octave − 3g}})
| 3\19, 189.47
| 4\23, 208.70
| 7\42, 200.00
| 10/9, 9/8
|-
| s ({{nowrap|4g − octave}})
| 1\19, 63.16
| 1\23, 52.17
| 2\42, 57.14
| 28/27, 33/32
|}
=== Hyperhard===
Hyperhard tunings of 4L 7s 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.
Hyperhard edos include [[23edo]], [[31edo]], and [[27edo]].
The sizes of the generator, large step and small step of 4L 7s are as follows in various hyperhard tunings:
{| class="wikitable right-2 right-3 right-4"
|-
!
! [[23edo]] (superhard)
! [[31edo]] (extrahard)
! [[27edo]] (pentahard)
! Some JI approximations
|-
| generator (g)
| 6\23, 313.04
| 8\31, 309.68
| 7\27, 311.11
| 6/5
|-
| L ({{nowrap|octave − 3g}})
| 4\23, 208.70
| 6\31, 232.26
| 5\27, 222.22
| 8/7, 9/8
|-
| s ({{nowrap|4g − octave}})
| 1\23, 52.17
| 1\31, 38.71
| 1\27, 44.44
| 36/35, 45/44
|}
== Temperaments ==
== Scales ==
* [[Oregon11]]
* [[Orgone11]]
* [[Magicaltet11]]
* [[Cata11]]
* [[Starlingtet11]]
* [[Myna11]]
== Scale tree ==
{{MOS tuning spectrum
| 6/5 = [[Oregon]]
| 10/7 = [[Orgone]]
| 11/7 = [[Magicaltet]]
| 13/8 = Golden superklesimic
| 5/3 = [[Superkleismic]]
| 7/3 = [[Catalan]]
| 13/5 = [[Countercata]]
| 8/3 = [[Hanson]]/[[cata]]
| 11/4 = [[Catakleismic]]
| 10/3 = [[Parakleismic]]
| 9/2 = [[Oolong]]
| 5/1 = [[Starlingtet]]
| 6/1 = [[Myna]]
}}
== Gallery ==
[[File:19EDO_Kleistonic_cheat_sheet.png|825x825px|thumb|Cheat sheet for 19EDO, a hard tuning for 4L 7s (or kleistonic).|alt=|left]]
The soft range for tunings of 4L 7s 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[7]. The small step is recognizable as a near diatonic semitone, while the large step is in the ambiguous area of neutral seconds.
Soft edos include 15edo and 26edo.
The sizes of the generator, large step and small step of 4L 7s are as follows in various soft tunings:
Hypohard tunings of 4L 7s 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.
Hypohard edos include 15edo, 19edo, and 34edo.
The sizes of the generator, large step and small step of 4L 7s are as follows in various hypohard tunings:
Parahard tunings of 4L 7s 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.
Parahard edos include 19edo, 23edo, and 42edo.
The sizes of the generator, large step and small step of 4L 7s are as follows in various parahard tunings:
Hyperhard tunings of 4L 7s 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.
Hyperhard edos include 23edo, 31edo, and 27edo.
The sizes of the generator, large step and small step of 4L 7s are as follows in various hyperhard tunings:
