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{{Infobox MOS
{{Infobox MOS
| Name = mynatonic
| 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 '''mynatonic''' ''my-na-TON-ik'' /maɪnəˈtɒnɪk/ 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 ([[Myna]]), as well as being a pun on "minor third".
== 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 = А҃Б҃Г҃Д҃Е҃Ѕ҃З҃И҃Ѳ҃І҃Ѫ҃А҃, 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.
{{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 myfourth (minor third)
| 2\19, 92.31
| -1
| 21/20, 22/21, 20/19
| Ѳ҃
|}
| perfect myninth (major sixth)
 
=== 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"
|-
|-
| 2
!
| З҃b
! [[15edo]] (basic)
| minor myseventh
! [[19edo]] (hard)
| -2
! [[34edo]] (semihard)
| Ѕ҃
! Some JI approximations
| major mysixth
|-
|-
| 3
| generator (g)
| І҃b
| 4\15, 320.00
| minor mytenth
| 5\19, 315.79
| -3
| 9\34, 317.65
| Г҃
| 6/5
| major mythird
|-
|-
| 4
| L ({{nowrap|octave − 3g}})
| В҃b
| 2\15, 160.00
| minor mysecond
| 3\19, 189.47
| -4
| 5\34, 176.47
| Ѫ҃
| 10/9, 11/10 (in 15edo)
| major myeleventh
|-
|-
| 5
| s ({{nowrap|4g − octave}})
| Е҃b
| 1\15, 80.00
| minor myfifth
| 1\19, 63.16
| -5
| 2\34, 70.59
| И҃҃
| 25/24, 26/25 (in better kleismic tunings)
| major myeight
|-
| 6
| И҃b
| minor myeight
| -6
| Е҃
| major myfifth
|-
| 7
| Ѫ҃b
| minor myeleventh
| -7
| В҃
| major mysecond
|-
| 8
| Г҃b
| minor mythird
| -8
| І҃
| major mytenth
|-
| 9
| Ѕ҃b
| minor mysixth
| -9
| З҃
| major myseventh
|-
| 10
| Ѳ҃b
| diminished myninth
| -10
| Д҃#
| augmented mythird
|-
| 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 (mychroma, mycomma)
|-
| 12
| Д҃b
| diminished myfourth
| -12
| Ѳ҃#
| augmented myninth
|-
| 13
| З҃bb
| diminished myseventh
| -13
| Ѕ҃#
| augmented mysixth
|-
| 14
| І҃bb
| diminished mytenth
| -14
| Г҃#
| augmented mythird
|}
|}
== Genchain ==
The generator chain for this scale is as follows:
{| 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 mynatonic 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 mynatonic 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 [[kleismic]] temperament (and its extensions).


=== Parahard ===
=== Parahard ===
Parahard tunings of mynatonic 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.
 
=== Hyperhard ===
Hyperhard tunings of mynatonic 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 eponymous temperament, Myna, 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 it's melodically difficult due to the extreme step size disparity.


== Modes ==
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.
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"
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"
|-
|-
! Mode
!
! [[Modal UDP Notation|UDP]]
! [[19edo]] (hard)
! Name
! [[23edo]] (superhard)
! [[42edo]] (parahard)
! Some JI approximations
|-
|-
| LsLssLssLss
| generator (g)
| <nowiki>10|0</nowiki>
| 5\19, 315.79
| Supernerevarine
| 6\23, 313.04
| 11\42, 314.29
| 6/5
|-
|-
| LssLsLssLss
| L ({{nowrap|octave − 3g}})
| <nowiki>9|1</nowiki>
| 3\19, 189.47
| Supervivecan
| 4\23, 208.70
| 7\42, 200.00
| 10/9, 9/8
|-
|-
| LssLssLsLss
| s ({{nowrap|4g − octave}})
| <nowiki>8|2</nowiki>
| 1\19, 63.16
| Supernumidian
| 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"
|-
|-
| LssLssLssLs
!
| <nowiki>7|3</nowiki>
! [[23edo]] (superhard)
| Superlorkhanic
! [[31edo]] (extrahard)
! [[27edo]] (pentahard)
! Some JI approximations
|-
|-
| sLsLssLssLs
| generator (g)
| <nowiki>6|4</nowiki>
| 6\23, 313.04
| Superbaardauan
| 8\31, 309.68
| 7\27, 311.11
| 6/5
|-
|-
| sLssLsLssLs
| L ({{nowrap|octave − 3g}})
| <nowiki>5|5</nowiki>
| 4\23, 208.70
| Supersothic
| 6\31, 232.26
| 5\27, 222.22
| 8/7, 9/8
|-
|-
| sLssLssLsLs
| s ({{nowrap|4g − octave}})
| <nowiki>4|6</nowiki>
| 1\23, 52.17
| Supervvardenic
| 1\31, 38.71
|-
| 1\27, 44.44
| sLssLssLssL
| 36/35, 45/44
| <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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