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{{Infobox MOS
{{Infobox MOS
| Name = kleistonic
| 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]].


'''4L 7s''' or '''kleistonic''' ''klyse-TON-ik'' /klaɪsˈtɒnɪk/ refers to the structure of MOS scales with generators ranging from 1\4edo (one degree of 4edo, 300¢) to 3\11edo (three degrees of 11edo, 327.<u>27</u>¢), representing approximate diatonic minor thirds ([[6/5]]). The name refers to the temperament that is one of the harmonic entropy minimums in this range ([[Kleismic family|Kleismic/Hanson]]), itself named after the interval known as the [[kleisma]].
== Name ==
TAMNAMS formerly used the name ''kleistonic'' for the name of this scale (prefix ''klei-''). Other names include '''p-chro smitonic''' or '''smipechromic'''.


4L 7s has a heptatonic subset, which is the [[hard]] end of the spectrum of the [[smitonic]] scale (4L 3s).
== Scale properties ==
{{TAMNAMS use}}


== Notation ==
=== Intervals ===
The notation used in this article is LssLsLssLss = А҃В҃Г҃Д҃Е҃Ѕ҃З҃И҃Ѳ҃І҃Ѫ҃А҃, based on old Cyrillic numerals 1-10 using the titlo as a numeric sign, and the addition of the big yus (Ѫ) for 11. Chromas are represented by regular sharps and flats.
{{MOS intervals}}
Thus the 15edo gamut is as follows:
'''А҃''' А҃#/В҃b '''В҃ Г҃ Д҃''' Д҃#/Е҃b '''Е҃ Ѕ҃''' Ѕ҃#/З҃b '''З҃ И҃ Ѳ҃''' Ѳ҃#/І҃b '''І҃ Ѫ҃ А҃'''


==== Letter names ====
=== Generator chain ===
The letters can be named in English as such: Az, Vede, Glagol, Dobro, Yest, Dzelo, Zemlya, Izhe, Thita, I(Ee), Yus. They can also be named as numbers 1-11.
{{MOS genchain}}


== Intervals ==
=== Modes ===
{| class="wikitable center-all"
{{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"
|-
|-
! Generators
!
! Notation (1/1 = А҃)
! [[15edo]] (basic)
! Interval category name
! [[26edo]] (soft)
! Generators
! Some JI approximations
! Notation of 2/1 inverse
! Interval category name
|-
|-
| colspan="6" style="text-align:left" | The 11-note MOS has the following intervals (from some root):
| generator (g)
| 4\15, 320.00
| 7\26, 323.08
| 77/64, 6/5
|-
|-
| 0
| L (octave - 3g)
| А҃
| 2\15, 160.00
| perfect unison
| 3\26, 138.46
| 0
| 12/11, 13/12
| А҃
| dodecave (same as octave)
|-
|-
| 1
| s (4g - octave)
| Д҃
| 1\15, 80.00
| perfect kleifourth (minor third)
| 2\19, 92.31
| -1
| 21/20, 22/21, 20/19
| Ѳ҃
| perfect kleininth (major sixth)
|-
| 2
| З҃b
| minor kleiseventh
| -2
| Ѕ҃
| major kleisixth
|-
| 3
| І҃b
| minor kleitenth
| -3
| Г҃
| major kleithird
|-
| 4
| В҃b
| minor kleisecond
| -4
| Ѫ҃
| major kleieleventh
|-
| 5
| Е҃b
| minor kleififth
| -5
| И҃
| major kleieight
|-
| 6
| И҃b
| minor kleieight
| -6
| Е҃
| major kleififth
|-
| 7
| Ѫ҃b
| minor kleieleventh
| -7
| В҃
| major kleisecond
|-
| 8
| Г҃b
| minor kleithird
| -8
| І҃
| major kleitenth
|-
| 9
| Ѕ҃b
| minor kleisixth
| -9
| З҃
| major kleiseventh
|-
| 10
| Ѳ҃b
| diminished kleininth
| -10
| Д҃#
| augmented kleithird
|-
| colspan="6" style="text-align:left" | The chromatic 15-note MOS (either [[4L 11s]], [[11L 4s]], or [[15edo]]) also has the following intervals (from some root):
|-
| 11
| А҃b
| diminished dodecave
| -11
| А҃#
| augmented unison (kleichroma, kleicomma)
|-
| 12
| Д҃b
| diminished kleifourth
| -12
| Ѳ҃#
| augmented kleininth
|-
| 13
| З҃bb
| diminished kleiseventh
| -13
| Ѕ҃#
| augmented kleisixth
|-
| 14
| І҃bb
| diminished kleitenth
| -14
| Г҃#
| augmented kleithird
|}
|}


== Genchain ==
=== Hypohard ===
The generator chain for this scale is as follows:
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}}}}.
{| class="wikitable center-all"
|-
| Д҃b
| А҃b
| Ѳ҃b
| Ѕ҃b
| Г҃b
| Ѫ҃b
| И҃b
| Е҃b
| В҃b
| І҃b
| З҃b
| Д҃
| А҃
| Ѳ҃
| Ѕ҃
| Г҃
| Ѫ҃
| И҃
| Е҃
| В҃
| І҃
| З҃
| Д҃#
| А҃#
| Ѳ҃#
| Ѕ҃#
| Г҃#
| Ѫ҃#
| И҃#
| Е҃#
| В҃#
| І҃#
| З҃#
|-
| d4
| d12
| d9
| m6
| m3
| m11
| m8
| m5
| m2
| m10
| m7
| P4
| P1
| P9
| M6
| M3
| M11
| M8
| M5
| M2
| M10
| M7
| A4
| A1
| A9
| A6
| A3
| A11
| A8
| A5
| A2
| A10
| A7
|}


== Tuning ranges ==
=== Soft range ===
The soft range for tunings of kleistonic 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]]].
=== Hypohard ===
Hypohard tunings of kleistonic 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 kleistonic edos include [[15edo]], [[19edo]], and [[34edo]].
Hypohard edos include [[15edo]], [[19edo]], and [[34edo]].
The sizes of the generator, large step and small step of kleistonic are as follows in various hypohard kleistonic tunings.
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"
{| class="wikitable right-2 right-3 right-4"
|-
|-
Line 239: Line 77:
| 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
Line 245: Line 83:
| 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
Line 253: Line 91:


=== Parahard ===
=== Parahard ===
Parahard tunings of kleistonic 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¢.
The minor third is at its purest here, but the resulting scales tend to result in intervals that employ a much higher limit harmony, especially in the case of the superhard 23edo.
 
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¢.


=== Hyperhard ===
Hyperhard tunings of kleistonic 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.
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 kleistonic edos include [[23edo]], [[31edo]], and 27edo.
Hyperhard edos include [[23edo]], [[31edo]], and [[27edo]].
The sizes of the generator, large step and small step of kleistonic are as follows in various hyperhard kleistonic tunings.
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"
{| class="wikitable right-2 right-3 right-4"
|-
|-
Line 277: Line 146:
| 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
Line 283: Line 152:
| 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
| 36/35, 45/44
|}
 
== Modes ==
The names are based on smitonic modes, modified with the "super-" prefix, with thematic additions, as there are an extra 4 modes available.
 
{| class="wikitable center-all"
|-
! Mode
! [[Modal UDP Notation|UDP]]
! Name
|-
| LsLssLssLss
| <nowiki>10|0</nowiki>
| Supernerevarine
|-
| LssLsLssLss
| <nowiki>9|1</nowiki>
| Supervivecan
|-
| LssLssLsLss
| <nowiki>8|2</nowiki>
| Superbaardauan
|-
| LssLssLssLs
| <nowiki>7|3</nowiki>
| Superlorkhanic
|-
| sLsLssLssLs
| <nowiki>6|4</nowiki>
| Supervvardenic
|-
| sLssLsLssLs
| <nowiki>5|5</nowiki>
| Supersothic
|-
| sLssLssLsLs
| <nowiki>4|6</nowiki>
| Supernumidian
|-
| sLssLssLssL
| <nowiki>3|7</nowiki>
| Superkagrenacan
|-
| ssLsLssLssL
| <nowiki>2|8</nowiki>
| Supernecromic
|-
| ssLssLsLssL
| <nowiki>1|9</nowiki>
| Superalmalexian
|-
| ssLssLssLsL
| <nowiki>0|10</nowiki>
| Superdagothic
|}
|}


== Temperaments ==
== Temperaments ==
== Scales ==
* [[Oregon11]]
* [[Orgone11]]
* [[Magicaltet11]]
* [[Cata11]]
* [[Starlingtet11]]
* [[Myna11]]


== Scale tree ==
== Scale tree ==
The spectrum looks like this:
{{MOS tuning spectrum
{| class="wikitable"
| 6/5 = [[Oregon]]
|-
| 10/7 = [[Orgone]]
| | 1\[[4edo|4]]
| 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]]
| | 300¢
| 9/2 = [[Oolong]]
| style="text-align:center;" |
| 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]]
| |
| |
| |
| | 10\[[39edo|39]]
| | 307.692
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 9\[[35edo|35]]
| |
| | 308.571
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| | 8\[[31edo|31]]
| |
| |
| | 309.677
| style="text-align:center;" | Myna
|-
| |
| |
| |
| |
| |
| |
| |
| | 23\[[89edo|89]]
| | 310.112
| style="text-align:center;" | Myna
|-
| |
| |
| |
| |
| |
| |
| | 15\[[58edo|58]]
| |
| | 310.345
| style="text-align:center;" | Myna
|-
| |
| |
| |
| |
| | 7\[[27edo|27]]
| |
| |
| |
| | 311.111
| style="text-align:center;" | Starlingtet
|-
| |
| |
| |
| | 6\[[23edo|23]]
| |
| |
| |
| |
| | 313.043
| style="text-align:center;" | Skateboard
|-
| |
| |
| |
| |
| |
| | 17\65
| |
| |
| | 313.846
| |
|-
| |
| |
| |
| |
| | 11\42
| |
| |
| |
| | 314.286
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| | 16\61
| |
| |
| | 314.754
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 21\80
| |
| | 315
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| | 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)
[[Category:11-tone scales]]
|-
[[Category:Kleistonic]] <!-- main article -->
| |
| |
| |
| |
| |
| |
| |
| |
| | 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
|-
| |
| |
| |
| |
| |
| | 16\59
| |
| |
| | 325.424
| style="text-align:center;" | Oregon
|-
| |
| |
| |
| |
| |
| |
| | 19\70
| |
| | 325.714
| style="text-align:center;" | Oregon
|-
| |
| |
| |
| |
| |
| |
| |
| | 22/81
| | 325.926
| style="text-align:center;" | Oregon
|-
| | 3\[[11edo|11]]
| |
| |
| |
| |
| |
| |
| |
| | 327.273
| style="text-align:center;" | Oregon
|}
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