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{{Infobox MOS
{{Infobox MOS
| Name =
| Periods = 1
| Periods = 1
| nLargeSteps = 4
| nLargeSteps = 4
| nSmallSteps = 7
| nSmallSteps = 7
| Equalized = 3
| Equalized = 3
| Paucitonic = 1
| Collapsed = 1
| Pattern = LssLssLssLs
| Pattern = LssLssLssLs
}}
}}
{{MOS intro}}
One of the [[harmonic entropy]] minimums in this range is [[Kleismic family|Kleismic/Hanson]].


This MOS is generated by an approximate 6/5 minor third between 300 (1\[[4edo|4edo]]) and 327.<u>27</u>¢ (3\[[11edo|11edo]]).
== Name ==
TAMNAMS formerly used the name ''kleistonic'' for the name of this scale (prefix ''klei-''). Other names include '''p-chro smitonic''' or '''smipechromic'''.


{| class="wikitable"
== Scale properties ==
{{TAMNAMS use}}
 
=== Intervals ===
{{MOS intervals}}
 
=== 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"
|-
|-
| | 1\[[4edo|4]]
!
| |
! [[15edo]] (basic)
| |
! [[26edo]] (soft)
| |
! Some JI approximations
| |
| |
| |
| |
| | 300¢
| style="text-align:center;" |
|-
|-
| |
| generator (g)
| |
| 4\15, 320.00
| |
| 7\26, 323.08
| |
| 77/64, 6/5
| |
| |
| |
| | 10\[[39edo|39]]
| | 307.692
| style="text-align:center;" |
|-
|-
| |
| L (octave - 3g)
| |
| 2\15, 160.00
| |
| 3\26, 138.46
| |
| 12/11, 13/12
| |
| |
| | 9\[[35edo|35]]
| |
| | 308.571
| style="text-align:center;" |
|-
|-
| |  
| s (4g - octave)
| |  
| 1\15, 80.00
| |
| 2\19, 92.31
| |
| 21/20, 22/21, 20/19
| |
|}
| | 8\[[31edo|31]]
 
| |
=== 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}}}}.
| | 309.677
 
| style="text-align:center;" | Myna
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
| |
| |
| | 23\[[89edo|89]]
| | 310.112
| style="text-align:center;" | Myna
|-
|-
| |
| generator (g)
| |
| 4\15, 320.00
| |
| 5\19, 315.79
| |
| 9\34, 317.65
| |
| 6/5
| |
| | 15\[[58edo|58]]
| |
| | 310.345
| style="text-align:center;" | Myna
|-
|-
| |  
| L ({{nowrap|octave − 3g}})
| |
| 2\15, 160.00
| |
| 3\19, 189.47
| |
| 5\34, 176.47
| | 7\[[27edo|27]]
| 10/9, 11/10 (in 15edo)
| |
| |
| |
| | 311.111
| style="text-align:center;" | Starlingtet
|-
|-
| |  
| s ({{nowrap|4g − octave}})
| |  
| 1\15, 80.00
| |  
| 1\19, 63.16
| | 6\[[23edo|23]]
| 2\34, 70.59
| |
| 25/24, 26/25 (in better kleismic tunings)
| |
|}
| |
 
| |
=== Parahard ===
| | 313.043
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¢.
| style="text-align:center;" | Skateboard
 
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
| | 17\65
| |
| |
| | 313.846
| |
|-
|-
| |
| generator (g)
| |
| 5\19, 315.79
| |
| 6\23, 313.04
| |
| 11\42, 314.29
| | 11\42
| 6/5
| |
| |
| |
| | 314.286
| style="text-align:center;" |
|-
|-
| |  
| L ({{nowrap|octave − 3g}})
| |
| 3\19, 189.47
| |
| 4\23, 208.70
| |
| 7\42, 200.00
| |
| 10/9, 9/8
| | 16\61
| |
| |
| | 314.754
| style="text-align:center;" |
|-
|-
| |  
| s ({{nowrap|4g − octave}})
| |
| 1\19, 63.16
| |
| 1\23, 52.17
| |
| 2\42, 57.14
| |
| 28/27, 33/32
| |
|}
| | 21\80
 
| |
=== Hyperhard===
| | 315
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¢.
| style="text-align:center;" |
 
|-
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.
| |
| |
| |
| |
| |
| |
| | 26\99
| | 315.152
| style="text-align:center;" | Parakleismic
|-
| |
| |
| |
| |
| |
| |
| |
| |
| | 315.332
| |
|-
| |
| |
| | 5\[[19edo|19]]
| |
| |
| |
| |
| |
| | 315.789
| style="text-align:center;" | Keemun
|-
| |
| |
| |
| |
| |
| | 19\[[72edo|72]]
| |
| |
| | 316.667
| style="text-align:center;" | Catakleismic
|-
| |
| |
| |
| |
| |
| |
| |
| |
| | 316.785
| style="text-align:center;" |
|-
| |
| |
| |
| |
| | 14\[[53edo|53]]
| |
| |
| |
| | 316.981
| style="text-align:center;" | Hanson/Marveltwintri/Cata
|-
| |
| |
| |
| |
| |
| |
| |
| |
| | 317.17
| |
|-
| |
| |
| |
| |
| |
| | 23\[[87edo|87]]
| |
| |
| | 317.241
| style="text-align:center;" | Countercata
|-
| |
| |
| |
| | 9\[[34edo|34]]
| |
| |
| |
| |
| | 317.647
| style="text-align:center;" |
|-
| |
| | 4\[[15edo|15]]
| |
| |
| |
| |
| |
| |
| | 320
| style="text-align:center;" | Boundary of propriety


(generators larger than this are proper)
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"
| |
| |
| |
| |
| |
| |
| |
| | 321.539
| |
|-
| |
| |
| |
| | 11\[[41edo|41]]
| |
| |
| |
| |
| | 321.951
| style="text-align:center;" | Superkleismic
|-
| |
| |
| |
| |
| |
| |
| |
| |
| | 322.268
| |
|-
| |
| |
| |
| |
| | 18\67
| |
| |
| |
| | 322.388
| |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| | 322.585
| |
|-
| |
| |
| | 7\[[26edo|26]]
| |
| |
| |
| |
| |
| | 323.068
| style="text-align:center;" | Magicaltet/Orgone
|-
| |
| |
| |
| | 10\37
| |
| |
| |
| |
| | 324.324
| style="text-align:center;" | Orgone
|-
| |
| |
| |
| |
| | 13\48
| |
| |
| |
| | 325
| style="text-align:center;" | Oregon
|-
|-
| |
!
| |
! [[23edo]] (superhard)
| |
! [[31edo]] (extrahard)
| |
! [[27edo]] (pentahard)
| |
! Some JI approximations
| | 16\59
| |
| |
| | 325.424
| style="text-align:center;" | Oregon
|-
|-
| |
| generator (g)
| |
| 6\23, 313.04
| |
| 8\31, 309.68
| |
| 7\27, 311.11
| |
| 6/5
| |
| | 19\70
| |
| | 325.714
| style="text-align:center;" | Oregon
|-
|-
| |  
| L ({{nowrap|octave − 3g}})
| |
| 4\23, 208.70
| |
| 6\31, 232.26
| |
| 5\27, 222.22
| |
| 8/7, 9/8
| |
| |
| | 22/81
| | 325.926
| style="text-align:center;" | Oregon
|-
|-
| | 3\[[11edo|11]]
| s ({{nowrap|4g − octave}})
| |
| 1\23, 52.17
| |
| 1\31, 38.71
| |
| 1\27, 44.44
| |
| 36/35, 45/44
| |
| |
| |
| | 327.273
| style="text-align:center;" | Oregon
|}
|}
== 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 -->
Retrieved from "https://en.xen.wiki/w/4L_7s"