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== Notation ==
== Notation ==
The notation used in this article is LssLsLssLss = ABCDEFGHJKL unless specified otherwise. Chromas are represented by regular sharps and flats.
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.
Thus the 15edo gamut is as follows:
Thus the 15edo gamut is as follows:
'''A''' A#/Bb '''B C D''' D#/Eb '''E F''' F#/Gb '''G H K''' K#Lb '''K L A'''
'''А҃''' А҃#/В҃b '''В҃ Г҃ Д҃''' Д҃#/Е҃b '''Е҃ Ѕ҃''' Ѕ҃#/З҃b '''З҃ И҃ Ѳ҃''' Ѳ҃#/І҃b '''І҃ Ѫ҃ А҃'''
 
==== Letter names ====
The letters can be named in English as such: Az, Vede, Glagol, Dobro, Yest, Dzelo, Zemlya, Izhe, Thita, I(ee), Yus.


== Intervals ==
== Intervals ==
U/C
{| class="wikitable center-all"
|-
! Generators
! Notation (1/1 = А҃)
! Interval category name
! Generators
! 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):
|-
| 0
| А҃
| perfect unison
| 0
| А҃
| dodecave (same as octave)
|-
| 1
| Д҃
| perfect myfourth (minor third)
| -1
| Ѳ҃
| perfect myninth (major sixth)
|-
| 2
| З҃b
| minor myseventh
| -2
| Ѕ҃
| major mysixth
|-
| 3
| І҃b
| minor mytenth
| -3
| Г҃
| major mythird
|-
| 4
| В҃b
| minor mysecond
| -4
| Ѫ҃
| major myeleventh
|-
| 5
| Е҃b
| minor myfifth
| -5
| И҃҃
| 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 ==
== Tuning ranges ==
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=== Hypohard ===
=== 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¢.
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 of the harmonic entropy minimums, where 6 generators make a just diatonic fifth ([[3/2]]), an octave above.
This range represents one of the harmonic entropy minimums, where 6 generators make a just diatonic fifth ([[3/2]]), an octave above.


=== 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 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¢.
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 ===
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¢.
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.
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 ==
== Modes ==
To be arranged ("Super-" versions of smitonic modes, with additions)
The names are based on smitonic modes, modified with the "super-" prefix, with thematic additions as there are an extra 4 modes available.


* 10|0 Supernerevarine
{| class="wikitable center-all"
* 9|1 Supervivecan
|-
* 8|2 Supernumidian
! Mode
* 7|3 Superlorkhanic
! [[Modal UDP Notation|UDP]]
* 6|4 Superbaardauan
! Name
* 5|5 Supersothic
|-
* 4|6 Supervvardenic
| LsLssLssLss
* 3|7 Superkagrenacan
| <nowiki>10|0</nowiki>
* 2|8 Supernecromic
| Supernerevarine
* 1|9 Superalmalexian
|-
* 0|10 Superdagothic
| LssLsLssLss
| <nowiki>9|1</nowiki>
| Supervivecan
|-
| LssLssLsLss
| <nowiki>8|2</nowiki>
| Supernumidian
|-
| LssLssLssLs
| <nowiki>7|3</nowiki>
| Superlorkhanic
|-
| sLsLssLssLs
| <nowiki>6|4</nowiki>
| Superbaardauan
|-
| sLssLsLssLs
| <nowiki>5|5</nowiki>
| Supersothic
|-
| sLssLssLsLs
| <nowiki>4|6</nowiki>
| Supervvardenic
|-
| 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 ==
Retrieved from "https://en.xen.wiki/w/4L_7s"