5L 3s: Difference between revisions

The table of oneirotonic intervals below takes the flat fourth as the generator. Given the size of the subfourth generator ''g'', any oneirotonic interval can easily be found by noting what multiple of ''g'' it is, and multiplying the size by the number of generators it takes to reach the interval and reducing mod 1200 if necessary (The % sign can be used for the modulo operation on many search engines). For example, since the major oneirothird is reached by six subfourth generators, [[18edo]]'s major oneirothird is 6*466.67 mod 1200 = 2800 mod 1200 = 400¢, same as the [[12edo]] major third.

| major oneiroseventh

| Mo7

| minor oneirothird

| mo3

| major oneirosecond

| Mo2

| minor oneiroeighth

| mo8

| major oneirofifth (aka minor fifth, falling fifth)

| Mo5

| minor oneirofifth (aka major fourth, rising fourth)

| mo4

| major oneiroeighth

| Mo8

| minor oneirosecond

| mo2

| major oneirothird

| Mo3

| minor oneiroseventh

| mo7

* [[21edo]]'s P1-Mo2-Mo3-Mo5 approximates 9:10:11:13 better than the corresponding 13edo chord does. 21edo will serve those who like the combination of neogothic minor thirds (285.71¢) and Baroque diatonic semitones (114.29¢, close to quarter-comma meantone's 117.11¢).

The ''Oneiro Falling Suspended Pentatonic'', i.e. R-Mo2-Po4-Mo5-Mo7, is also an important subset in ana modes: it roughly implies the "least" tonality (In particular, it only implies ana-ness, not major or minor tonality), and it sounds floaty, and suspended, much like suspended and quartal chords do in diatonic contexts. The ''Oneiro Rising Suspended Pentatonic'' R-Mo2-Po4-Po6-Mo7 (J-K-M-O-P) can be used for similar effect.

# R-Mo2-Po4-Mo5-Mo7 Oneiro Falling Suspended Pentatonic

# R-Mo2-Po4-Po6-Mo7 Oneiro Rising Suspended Pentatonic

# R-mo3-Po4-Po6-Mo7 Oneiro Symmetrical Pentatonic

# R-mo3-Po4-Po6-mo8 Oneiro Expanding Quartal Pentatonic

# R-mo3-mo5-Po6-mo8 Oneiro Diminished Pentatonic

Another Western-classical-influenced approach to oneirotonic chord progressions is to let the harmony emerge from counterpoint. This would allow, for example, using the perfect oneirofourth and minor oneirofifth (instead of the major oneirothird and the perfect oneirofourth) as stand-ins for major thirds and fourths in neobaroque contexts (this adds some dissonance which might be what you want sometimes, e.g. in a chord that is supposed to resolve to a more consonant chord).

* R-Mo3-Mo5: Falling Major Triad; Squashed Major Triad

* R-mo3-Mo5: Falling Minor Triad; Squashed Minor Triad

* R-mo3-mo5: Squashed Dim Triad

* R-Mo3-Ao5: Squashed Aug Triad

* R-Mo3-Mo5-Ao6: Falling Major Triad Add6

* R-mo3-Mo5-Ao6: Falling Minor Triad Add6

* R-Mo3-Mo5-Mo7: Falling Major Tetrad

* R-mo3-Mo5-Mo7: Falling Minor Tetrad

* R-mo3-mo5-Mo7: Oneiro Half-Diminished Tetrad

* R-mo3-mo5-mo7: Orwell Tetrad, Oneiro Diminished Tetrad

* R-Mo3-Ao6: Squashed 1st Inversion Minor Triad; Sephiroth Triad (approximates 8:10:13 in 13edo and 31edo)

* R-Mo3-Ao6-Mo8: Sephiroth Triad Add7

* R-Mo3-Ao6-(Mo2)-(Po4): Sephiroth Tetrad Add9

* R-Mo3-Ao6-(mo2)-(Po4): Sephiroth Tetrad Addm9

* R-Mo3-Ao6-(Po4): Sephiroth Tetrad

* R-mo3-Po6: Rising Minor Triad; Squashed 1st Inversion Major Triad

* R-Mo3-Po6: Rising Major Triad

* R-mo3-Mo7: Minor add6 no5

* R-mo3-mo7: Minor addm6 no5

* R-mo5-Mo7: Falling no3 add6

* R-mo5-mo7: Falling no3 add6

* R-Mo3-Mo8: Major 7th no5

* R-mo3-Mo8: Minor Major 7th no5

* R-Mo3-Mo5-Mo8: Falling Major Seventh Tetrad

* R-mo3-Mo5-Mo8: Falling Minor Major Seventh Tetrad

* R-Mo3-Mo7-Mo8: no5 Major Seventh Add6

* R-mo3-Mo7-Mo8: no5 Minor Major Seventh Add6

* R-Mo3-Po6-Mo8: Rising Major Seventh

* R-mo3-Po6-Mo8: Rising Oneiro Minor Major Seventh

* R-Mo3-(Mo2): Oneiro Major Add9

* R-mo3-(Mo2): Oneiro Minor Add9

* R-Mo3-Mo5-(Mo2): Falling Major Triad Add9

* R-mo3-Mo5-(Mo2): Falling Minor Triad Add9

* R-Mo3-(Mo2)-(Po4): no5 Major Add9 Sub11

* R-mo3-(Mo2)-(Po4): no5 Minor Add9 sub11

* R-Mo2-Po4: Sus24 No5

* R-Mo2-Mo5: Falling Sus2 Triad

* R-Po4-Mo5: Falling Sus4 Triad

* R-Mo2-Po4-Mo5: Falling Sus24

* R-Po4-Mo7: Oneiro Quartal Triad

* R-Po4-Mo7-(Mo2): Oneiro Quartal Tetrad, Core Tetrad

* R-Po4-Mo7-(Mo2)-(Mo5): Oneiro Quartal Pentad, Core Pentad

* R-Po4-Mo7-(Mo2)-(Mo5)-(Mo8): Oneiro Quartal Hexad

* R-Po4-Mo7-Mo8: Oneiro Quartal Seventh Tetrad

* R-Po4-mo8: Expanding Quartal Triad

* R-Mo2-Po4-mo8: Expanding Quartal Triad add2

* R-mo3-Po4-mo8: Expanding Quartal Triad Addm3

* R-mo5-mo8: Contracting Quartal Triad

* R-mo5-mo7-mo8: Contracting Quartal Triad Addm7

* R-Mo3-Mo5-mo8: Falling Major Triad addm7

21edo has the [[Step ratio|soft]] [[oneirotonic]] (5L 3s) MOS with generator 8\21; in addition to the [[naiadic]]s (457.14¢) and extremely sharp fifths (742.85¢) that generate it, it has neutral thirds (instead of major thirds as in [[13edo]] oneirotonic), neogothic minor thirds, and meantone-like diatonic semitones. The oneirofifths (4-step intervals) are more tritone-like than fifth-like, unlike in 13edo, although they do have a consonant, even JI-like quality to them. In terms of JI, it mainly approximates 5:9:11:13 (R-mo8-Mo2-Po4) and 16:23:30 (R-Mo5-Mo8). Importantly, the sharp fifth is now harmonically much more fifth-like than the flat fifth, unlike in [[13edo]] and harder tunings. Rather than squashed tertian triads, it may be preferable to use triads with sharp fifths, quartal harmony, stacks of seconds and thirds, third+sixth and third+seventh chords, and using the JI approximations (subsets of 5:9:11:13 (R-mo8-Mo2-Po4), 9:10:11:13 (R-Mo2-Mo3-Mo5), and 8:15:23 (R-Mo7-Mo5)).