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4L 7s: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox MOS
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| Periods = 1
: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2012-10-05 03:15:00 UTC</tt>.<br>
| nLargeSteps = 4
: The original revision id was <tt>370455938</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]].


|| 1\[[4edo|4]] ||  ||  ||  ||  ||  ||  ||  || 300¢ ||=   ||
== Name ==
||  ||  ||  ||  ||  ||  ||  || 10\[[39edo|39]] || 307.692 ||=  ||
TAMNAMS formerly used the name ''kleistonic'' for the name of this scale (prefix ''klei-''). Other names include '''p-chro smitonic''' or '''smipechromic'''.
||  ||  ||  ||  ||  ||  || 9\[[35edo|35]] ||  || 308.571 ||=  ||
||  ||  ||  ||  ||  || 8\[[31edo|31]] ||  ||  || 309.677 ||=  ||
||  ||  ||  ||  ||  ||  ||  || 23\[[89edo|89]] || 310.112 ||= Myna is around here ||
||  ||  ||  ||  ||  ||  || 15\[[58edo|58]] ||  || 310.345 ||=  ||
||  ||  ||  ||  || 7\[[27edo|27]] ||  ||  ||  || 311.111 ||=   ||
||  ||  ||  || 6\[[23edo|23]] ||  ||  ||  ||  || 313.043 ||=   ||
||  ||  || 5\[[19edo|19]] ||  ||  ||  ||  ||  || 315.789 ||=   ||
||  ||  ||  ||  ||  || 19\[[72edo|72]] ||  ||  || 316.667 ||= Keemun/Hanson/Catakleismic is around here ||
||  ||  ||  ||  || 14\[[53edo|53]] ||  ||  ||  || 316.981 ||=  ||
||  ||  ||  || 9\[[34edo|34]] ||  ||  ||  ||  || 317.647 ||=  ||
||  || 4\[[15edo|15]] ||  ||  ||  ||  ||  ||  || 320 ||= Boundary of propriety
(generators larger than this are proper) ||
||  ||  ||  || 11\[[41edo|41]] ||  ||  ||  ||  || 321.951 ||= Superkleismic is around here ||
||  ||  || 7\[[26edo|26]] ||  ||  ||  ||  ||  || 323.068 ||=  ||
||  ||  ||  || 10\37 ||  ||  ||  ||  || 324.324 ||= Orgone is around here ||
|| 3\[[11edo|11]] ||  ||  ||  ||  ||  ||  ||  || 327.273 ||=  ||</pre></div>
<h4>Original HTML content:</h4>
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;4L 7s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This MOS is generated by an approximate 6/5 minor third between 300 (1\&lt;a class="wiki_link" href="/4edo"&gt;4edo&lt;/a&gt;) and 327.&lt;u&gt;27&lt;/u&gt;¢ (3\&lt;a class="wiki_link" href="/11edo"&gt;11edo&lt;/a&gt;).&lt;br /&gt;
&lt;br /&gt;


== Scale properties ==
{{TAMNAMS use}}


&lt;table class="wiki_table"&gt;
=== Intervals ===
    &lt;tr&gt;
{{MOS intervals}}
        &lt;td&gt;1\&lt;a class="wiki_link" href="/4edo"&gt;4&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;300¢&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10\&lt;a class="wiki_link" href="/39edo"&gt;39&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;307.692&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9\&lt;a class="wiki_link" href="/35edo"&gt;35&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;308.571&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8\&lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;309.677&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;23\&lt;a class="wiki_link" href="/89edo"&gt;89&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;310.112&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Myna is around here&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15\&lt;a class="wiki_link" href="/58edo"&gt;58&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;310.345&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7\&lt;a class="wiki_link" href="/27edo"&gt;27&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;311.111&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6\&lt;a class="wiki_link" href="/23edo"&gt;23&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;313.043&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5\&lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;315.789&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;19\&lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;316.667&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Keemun/Hanson/Catakleismic is around here&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14\&lt;a class="wiki_link" href="/53edo"&gt;53&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;316.981&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9\&lt;a class="wiki_link" href="/34edo"&gt;34&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;317.647&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4\&lt;a class="wiki_link" href="/15edo"&gt;15&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;320&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Boundary of propriety&lt;br /&gt;
(generators larger than this are proper)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11\&lt;a class="wiki_link" href="/41edo"&gt;41&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;321.951&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Superkleismic is around here&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7\&lt;a class="wiki_link" href="/26edo"&gt;26&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;323.068&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10\37&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;324.324&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Orgone is around here&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3\&lt;a class="wiki_link" href="/11edo"&gt;11&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;327.273&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
=== Generator chain ===
{{MOS genchain}}
 
=== Modes ===
{{MOS mode degrees}}
 
== Tuning ranges==
=== Soft range ===
The soft range for tunings of 4L&nbsp;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&nbsp;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&nbsp;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&nbsp;7s (or kleistonic).|alt=|left]]
 
[[Category:11-tone scales]]
[[Category:Kleistonic]] <!-- main article -->
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