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4L 7s: Difference between revisions

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TAMNAMS formerly used the name ''kleistonic'' for the name of this scale (prefix ''klei-''). Other names include '''p-chro smitonic''' or '''smipechromic'''.
TAMNAMS formerly used the name ''kleistonic'' for the name of this scale (prefix ''klei-''). Other names include '''p-chro smitonic''' or '''smipechromic'''.


== Intervals ==
== Scale properties ==
{{TAMNAMS use}}{{MOS intervals}}
{{TAMNAMS use}}


===Genchain===
=== Intervals ===
{| class="wikitable center-all"
{{MOS intervals}}
|-
 
! Generators
=== Generator chain ===
| -11||-10||-9|| -8||-7 ||-6||-5||-4||-3|| -2||-1||0||+1 ||+2||+3||+4 ||+5||+6||+7||+8||+9|| +10|| +11
{{MOS genchain}}
|-
 
!Interval quality
=== Modes ===
|d11md|| d8md ||m5md|| m2md||m10md||m7md|| m4md||m1md||m9md||m6md||P3md||P0md||P8md||M5md||M2md||M10md|| M7md||M4md||M1md||M9md||M6md||A3md||A0md
{{MOS mode degrees}}
|}
 
==Tuning ranges==
== Tuning ranges==
===Soft range===
=== Soft range ===
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¢.
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.
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 36: Line 36:
|-
|-
!
!
![[15edo]] (basic)
! [[15edo]] (basic)
![[26edo]] (soft)
! [[26edo]] (soft)
!Some JI approximations
! Some JI approximations
|-
|-
|generator (g)
| generator (g)
|4\15, 320.00
| 4\15, 320.00
| 7\26, 323.08
| 7\26, 323.08
|77/64, 6/5
| 77/64, 6/5
|-
|-
| L (octave - 3g)
| L (octave - 3g)
|2\15, 160.00
| 2\15, 160.00
|3\26, 138.46
| 3\26, 138.46
|12/11, 13/12
| 12/11, 13/12
|-
|-
|s (4g - octave)
| s (4g - octave)
|1\15, 80.00
| 1\15, 80.00
|2\19, 92.31
| 2\19, 92.31
|21/20, 22/21, 20/19
| 21/20, 22/21, 20/19
|}
|}


===Hypohard===
=== Hypohard ===
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¢.
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.
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]].
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:  
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"
{| class="wikitable right-2 right-3 right-4"
|-
|-
!
!
![[15edo]] (basic)
! [[15edo]] (basic)
![[19edo]] (hard)
! [[19edo]] (hard)
![[34edo]] (semihard)
! [[34edo]] (semihard)
!Some JI approximations
! Some JI approximations
|-
|-
|generator (g)
| generator (g)
|4\15, 320.00
| 4\15, 320.00
|5\19, 315.79
| 5\19, 315.79
|9\34, 317.65
| 9\34, 317.65
|6/5
| 6/5
|-
|-
|L (octave - 3g)
| L ({{nowrap|octave − 3g}})
|2\15, 160.00
| 2\15, 160.00
|3\19, 189.47
| 3\19, 189.47
|5\34, 176.47
| 5\34, 176.47
|10/9, 11/10 (in 15edo)
| 10/9, 11/10 (in 15edo)
|-
|-
|s (4g - octave)
| s ({{nowrap|4g − octave}})
|1\15, 80.00
| 1\15, 80.00
|1\19, 63.16
| 1\19, 63.16
|2\34, 70.59
| 2\34, 70.59
|25/24, 26/25 (in better kleismic tunings)
| 25/24, 26/25 (in better kleismic tunings)
|}
|}


===Parahard===
=== 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¢.
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¢.


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|-
|-
!
!
![[19edo]] (hard)
! [[19edo]] (hard)
![[23edo]] (superhard)
! [[23edo]] (superhard)
![[42edo]] (parahard)
! [[42edo]] (parahard)
!Some JI approximations
! Some JI approximations
|-
|-
| generator (g)
| generator (g)
|5\19, 315.79
| 5\19, 315.79
|6\23, 313.04
| 6\23, 313.04
|11\42, 314.29
| 11\42, 314.29
| 6/5
| 6/5
|-
|-
|L (octave - 3g)
| L ({{nowrap|octave − 3g}})
|3\19, 189.47
| 3\19, 189.47
|4\23, 208.70
| 4\23, 208.70
|7\42, 200.00
| 7\42, 200.00
| 10/9, 9/8
| 10/9, 9/8
|-
|-
|s (4g - octave)
| s ({{nowrap|4g − octave}})
|1\19, 63.16
| 1\19, 63.16
|1\23, 52.17
| 1\23, 52.17
|2\42, 57.14
| 2\42, 57.14
| 28/27, 33/32
| 28/27, 33/32
|}
|}
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|-
|-
!
!
![[23edo]] (superhard)
! [[23edo]] (superhard)
![[31edo]] (extrahard)
! [[31edo]] (extrahard)
![[27edo]] (pentahard)
! [[27edo]] (pentahard)
!Some JI approximations
! Some JI approximations
|-
|-
|generator (g)
| generator (g)
|6\23, 313.04
| 6\23, 313.04
|8\31, 309.68
| 8\31, 309.68
|7\27, 311.11
| 7\27, 311.11
|6/5
| 6/5
|-
|-
|L (octave - 3g)
| L ({{nowrap|octave − 3g}})
|4\23, 208.70
| 4\23, 208.70
|6\31, 232.26
| 6\31, 232.26
|5\27, 222.22
| 5\27, 222.22
|8/7, 9/8
| 8/7, 9/8
|-
|-
|s (4g - octave)
| s ({{nowrap|4g − octave}})
|1\23, 52.17
| 1\23, 52.17
|1\31, 38.71
| 1\31, 38.71
|1\27, 44.44
| 1\27, 44.44
|36/35, 45/44
| 36/35, 45/44
|}
|}


==Modes==
== Temperaments ==
{{MOS mode degrees}}
== Scales ==
==Temperaments ==
* [[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]]
}}


==Scales==
== Gallery ==
*[[Oregon11]]
[[File:19EDO_Kleistonic_cheat_sheet.png|825x825px|thumb|Cheat sheet for 19EDO, a hard tuning for 4L 7s (or kleistonic).|alt=|left]]
*[[Orgone11]]
*[[Magicaltet11]]
*[[Cata11]]
*[[Starlingtet11]]
*[[Myna11]]


==Scale tree==
{{Scale tree|Comments=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;
10/3: Parakleismic;
9/2: Oolong;
5/1: Starlingtet;
6/1: Myna}}
[[Category:11-tone scales]]
[[Category:11-tone scales]]
[[Category:Kleistonic]] <!-- main article -->
[[Category:Kleistonic]] <!-- main article -->
==Gallery==
[[File:19EDO_Kleistonic_cheat_sheet.png|825x825px|thumb|Cheat sheet for 19EDO, a hard tuning for 4L 7s (or kleistonic).|alt=|left]]
Retrieved from "https://en.xen.wiki/w/4L_7s"