22edo/Unque's compositional approach: Difference between revisions

! JI Intervals

! As a generator

|-

| 0\22

|  

| C

|-

| 1\22

| [[Escapade]]

| D♭, A𝄪

|-

| 2\22

| [[11edo]]

| B♯, E𝄫

|-

| 3\22

| [[Porcupine]]

| C♯, F𝄫

|-

| 4\22

| [[Wizard]], [[Jubilic]]

| D

|-

| 5\22

| [[Orwell]]

| E♭, B𝄪

|-

| 6\22

| [[Doublewide]]

| F♭, C𝄪

|-

| 7\22

| [[Magic]]

| D♯, G𝄫

|-

| 8\22

| [[Sensamagic]]

| E

|-

| 9\22

| [[Superpyth]]

| F

|-

| 10\22

| [[Joan]]

| G♭, D𝄪

|-

| 11\22

| [[2edo]]; period for several temps

| E♯, A𝄫

|-

| 12\22

| Joan

| F♯

|-

| 13\22

| Superpyth

| G

|-

| 14\22

| Sensamagic

| A♭, E𝄪

|-

| 15\22

| Magic

| B𝄫, F𝄪

|-

| 16\22

| Doublewide

| G♯, C𝄫

|-

| 17\22

| Orwell

| A

|-

| 18\22

| Wizard, Jubilic

| B♭

|-

| 19\22

| Porcupine

| C♭, G𝄪

|-

| 20\22

| 11edo

| A♯, D𝄫

|-

| 21\22

| Escapade

| B

|-

| 22\22

|  

| C

|}

=== The thirds of 22edo ===

!Gens Up

!Step Pattern

!Name

|-

!Gens Up

!Step Pattern

! Name

!Notes

=== 3L 2M 2s ===

The 5-limit harmony of this scale is much more reminiscent of the familiar harmony used in common-practice music, so popular music translated into this scale will be much more faithful to the harmony of the original piece than it would be using 5L 2s.

!Gens Up

!Step pattern

!Name

! Notes

! Gens Up

!Step pattern

! Name

!Notes

|}

===5L 2m 3s===

{| class="wikitable sortable"

|+ style="font-size: 105%;" |Modes of 5L 2m 3s (Grave)

!Gens Up

!Step pattern

!Name

!Notes

|LmLsLmLsLs

|C - C♯ - E♭ - E - F - F# - A♭ - A - B♭ - B - C

|Aeolian

|-

|3

|LmLsLsLmLs

|C - C♯ - E♭ - E - F - F# - G - G♯ - B♭ - B - C

| Dorian

|-

|2

|LsLmLsLmLs

|C - C♯ - D - D♯ - F - F# - G - G♯ - B♭ - B - C

| Mixolydian

|-

|1

|LsLmLsLsLm

|C - C♯ - D - D♯ - F - F# - G - G♯ - A - A♯ - C

| Ionian

|-

|0

|LsLsLmLsLm

|C - C♯ - D - D♯ - E - E♯ - G - G♯ - A - A♯ - C

|Lydian

|}

! Gens Up

!Step pattern

! Name

! Notes

|mLsLmLsLsL

|C - E𝄫 - E♭ - F♭ - F - A𝄫 - A♭ - B𝄫 - B♭ - C♭ - C

|Locrian

|-

| 3

| mLsLsLmLsL

| C - E𝄫 - E♭ - F♭ - F - G♭ - G - B𝄫 - B♭ - C♭ - C

| Phrygian

|-

| 2

|sLmLsLmLsL

|C - D♭ - D - F♭ - F - G♭ - G - B𝄫 - B♭ - C♭ - C

|Aeolian

|-

| 1

|sLmLsLsLmL

|C - D♭ - D - F♭ - F - G♭ - G - A♭ - A - C♭ - C

| Dorian

|-

| 0

|sLsLmLsLmL

|C - D♭ - D - E♭ - E - G♭ - G - A♭ - A - C♭ - C

|Mixolydian

|}

===2L 8s===

{| class="wikitable sortable"

|+ style="font-size: 105%;" |Modes of 2L 8s

!Gens Up

! Step pattern

!Name

! Notes

|8

| LssssLssss

|-

|6

| sLssssLsss

|Dynamic Major

|Dual thirds are subminor and major

|4

| ssLssssLss

| Static Major

|Laterally symmetrical

| 2

| sssLssssLs

|Static Minor

|Messiaen treated this rotation as the "default"

|0

|ssssLssssL

|Dynamic Minor

|Dual thirds are minor and supermajor

===4L 5s===

The [[4L 5s]] scale is another quite useful scale available in 22edo, closely associated with [[Orwell]] temperament, and as such is best utilized alongside Orwell Chords for functional harmony (see below).

{| class="wikitable sortable"

! Gens Up

!Step Pattern

!Notes

|-

|8

|LsLsLsLss

|^F♯ is actually the Wolf Fifth in this context, and F♯ is the desirable interval!

|-

|7

| LsLsLssLs

|-

|6

|LsLssLsLs

|

|-

| 5

|LssLsLsLs

|-

|4

|sLsLsLsLs

|-

|3

| sLsLsLssL

|

|-

|2

|sLsLssLsL

|-

|1

| sLssLsLsL

|vG♭ is actually the Wolf Fourth in this context, and G♭ is the desirable interval!

|-

|0

|ssLsLsLsL

|Subminor third above the root is unavailable in this mode.

|}

===3L 4s===

The [[3L 4s]] scale is a distant deviation from common-practice harmony.  The harmony in this scale is based primarily on Marvel triads (see below) rather than the typical major and minor triads that the other scales were quite generously accustomed to.  It is closely related to [[Magic]] temperament, and may be thought of as the functional opposite of the 4L 5s due to their nature as leaning into augmented and diminished harmony respectively as their primary concordances.  The modes of 3L 4s are given names by [[Andrew Heathwaite]].

{| class="wikitable sortable"

|+ style="font-size: 105%;" |Modes of 3L 4s

! Gens Up

! Step Pattern

!Name

!Notes

=== 3L 7s ===

Since the 3L 4s scale can be created by continually stacking Major Thirds, this structure can be extended quite easily into a larger scale that has more options available for harmonic content.  This pattern gives us the scale 3L 7s, which was discussed at length in the paper [https://ia904601.us.archive.org/18/items/TractatumDeModiSephiratorum/ModiSephiratorum.pdf Tractatum de Modi Sephiratorum] by Komorsky.  In addition to the scale itself, Komorsky provides unique names for all ten rotations of the scale, named for the ten Sefirot of the Kabbalah school of thought; if desired, however, one can also consider the modes to be Grave and Acute extensions of the 3L 4s modes, making the relationships between the two scales clearer.

{| class="wikitable sortable"

|+ style="font-size: 105%;" |Modes of 3L 7s

!Gens Up

!Step Pattern

!Name (Komorsky)

!Name (Heathwaite)

! Notes

|LssLssLsss

|C - vC𝄪 - vD♯ - vE - ^E♯ - ^F♯ - ^G - G𝄪 - A♯ - B - C

|Like Dril, contains no functional fourths

|-

| LssLsssLss

|C - vC𝄪 - vD♯ - vE - ^E♯ - ^F♯ - ^G - ^A♭ - A♯ - B - C

|Grave Gil

|Like Gil, contains no functional fourths

| LsssLssLss

|C - vC𝄪 - vD♯ - vE - vF - ^F♯ - ^G - ^A♭ - A♯ - B - C

|Grave Kleeth

|

|sLssLssLss

|C - D♭ - vD♯ - vE - vF - ^F♯ - ^G - ^A♭ - A♯ - B - C

|Also accounts for Acute Dril

|-

|sLssLsssLs

|C - D♭ - vD♯ - vE - vF - ^F♯ - ^G - ^A♭ - ^B𝄫 - B - C

|Grave Fish

|Also accounts for Acute Gil

| sLsssLssLs

|C - D♭ - vD♯ - vE - vF - vG♭ - ^G - ^A♭ - ^B𝄫 - B - C

|Acute Kleeth

| Also accounts for Grave Jwl

|ssLssLssLs

|C - D♭ - E𝄫 - vE - vF - vG♭ - ^G - ^A♭ - ^B𝄫 - B - C

|Acute Bish

|Also accounts for Grave Led

|ssLssLsssL

|C - D♭ - E𝄫 - vE - vF - vG♭ - ^G - ^A♭ - ^B𝄫 - ^C𝄫 - C

|

|-

|ssLsssLssL

|C - D♭ - E𝄫 - vE - vF - vG♭ - vA𝄫 - ^A♭ - ^B𝄫 - ^C𝄫 - C

|Like Jwl, contains no functional fifths

|-

|sssLssLssL

|C - D♭ - E𝄫 - F𝄫 - vF - vG♭ - vA𝄫 - ^A♭ - ^B𝄫 - ^C𝄫 - C

|Acute Led

|Like Led, contains no functional fifths

Additionally, there are four distinct types of diminished triads that can be formed using the two types of minor thirds; due to the [[225/224|Marvel comma]] being tempered out in 22edo, however, there are only two distinct types of augmented triads that can be formed using the two types of major thirds, as 7 + 7 + 8 = 22.

{| class="wikitable sortable"

! Name

!Symbol

!Formula

!Otonal

!Utonal

|-

|Major

|C maj

|C - vE - G

|7\22 + 6\22

|4:5:6

|1/(15:12:10)

|-

|Minor

|c min

|C - ^E♭ - G

|6\22 + 7\22

|10:12:15

|1/(6:5:4)

|-

|Supermajor

|C saj

|C - E - G

|8\22 + 5\22

|14:18:21

|1/(9:7:6)

|-

|Subminor

|c sin

|C - E♭ - G

|5\22 + 8\22

|6:7:9

| 1/(21:18:14)

|-

|Orwell Dim.

| c^ow

|C - E♭ - G♭

|5\22 + 5\22

|24:28:33

|1/(33:28:24)

|-

|Utonal Dim.

|c^ut

|C - E♭ - ^G♭

|5\22 + 6\22

| 30:35:42

| 1/(7:6:5)

|-

|Otonal Dim.

|c^ot

|C - ^E♭ - ^G♭

|6\22 + 5\22

|5:6:7

| 1/(42:35:30)

|-

|Orgone Dim.

|c^og

|C - ^E♭ - vG

|6\22 + 6\22

|25:30:36

|1/(36:30:25)

|-

|Minor Wolf

| c sv

|C - E♭ - vG

|5\22 + 7\22

|24:28:35

|1/(35:30:24)

|-

|Major Wolf

|C v

| C - E - vG

|7\22 + 5\22

|24:30:35

| 1/(35:28:24)

|-

|Marvel

|C+

| C - vE - ^G

|7\22 + 7\22

|16:20:25

|1/(25:20:16)

|-

|Marvel (1st inv.)

|vG♯+/C

|C - vE - vG♯

|7\22 + 8\22

|20:25:32

|1/(40:32:25)

|-

|Marvel (2nd inv.)

| E+/C

|C - E - vG♯

|8\22 + 7\22

|25:32:40

|1/(32:25:20)

|-

|Sensamagic

|C×

|C - E - G♯

|8\22 + 8\22

| 11:14:18

|1/(18:14:11)

|-

|Sensa (1st inv.)

|^G×/C

|C - E - ^G

|8\22 + 6\22

|7:9:11

|1/(14:11:9)

|-

|Sensa (2nd inv.)

|6\22 + 8\22

|9:11:14

|1/(11:9:7)

|}

! Gens Up

!Symbol

! Formula

!3-limit JI

|C⁴

| C - F - B♭

|9\22 + 9\22

|9:12:16

|Csus4

|C - F - G

|9\22 + 4\22

|6:8:9

|Csus2

|C - D - G

|4\22 + 9\22

|8:9:12