5L 3s: Difference between revisions
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== Intervals == | == Intervals == | ||
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. | 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. | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|- | |- | ||
! | ! # generators up | ||
! Notation (1/1 = J) | ! Notation (1/1 = J) | ||
! Octatonic interval category name | ! Octatonic interval category name | ||
! | ! Abbrev. | ||
! # generators up | |||
! Notation of 2/1 inverse | ! Notation of 2/1 inverse | ||
! Octatonic interval category name | ! Octatonic interval category name | ||
! Abbrev. | |||
|- | |- | ||
| colspan="6" style="text-align:left" | The 8-note MOS has the following intervals (from some root): | | colspan="6" style="text-align:left" | The 8-note MOS has the following intervals (from some root): | ||
| Line 51: | Line 53: | ||
| J | | J | ||
| perfect unison | | perfect unison | ||
| P1 | |||
| 0 | | 0 | ||
| J | | J | ||
| octave | | octave | ||
| Po9 | |||
|- | |- | ||
| 1 | | 1 | ||
| M | | M | ||
| perfect oneirofourth (aka minor fourth, falling fourth) | | perfect oneirofourth (aka minor fourth, falling fourth) | ||
| Po4 | |||
| -1 | | -1 | ||
| O | | O | ||
| perfect oneirosixth (aka major fifth, rising fifth) | | perfect oneirosixth (aka major fifth, rising fifth) | ||
| Po6 | |||
|- | |- | ||
| 2 | | 2 | ||
| P | | P | ||
| major oneiroseventh | | major oneiroseventh | ||
| Mo7 | |||
| -2 | | -2 | ||
| L | | L | ||
| minor oneirothird | | minor oneirothird | ||
| mo3 | |||
|- | |- | ||
| 3 | | 3 | ||
| Line 73: | Line 81: | ||
| major oneirosecond | | major oneirosecond | ||
| -3 | | -3 | ||
| Mo2 | |||
| Q | | Q | ||
| minor oneiroeighth | | minor oneiroeighth | ||
| mo8 | |||
|- | |- | ||
| 4 | | 4 | ||
| N | | N | ||
| major oneirofifth (aka minor fifth, falling fifth) | | major oneirofifth (aka minor fifth, falling fifth) | ||
| Mo5 | |||
| -4 | | -4 | ||
| N@ | | N@ | ||
| minor oneirofifth (aka major fourth, rising fourth) | | minor oneirofifth (aka major fourth, rising fourth) | ||
| mo4 | |||
|- | |- | ||
| 5 | | 5 | ||
| Q& | | Q& | ||
| major oneiroeighth | | major oneiroeighth | ||
| Mo8 | |||
| -5 | | -5 | ||
| K@ | | K@ | ||
| minor oneirosecond | | minor oneirosecond | ||
| mo2 | |||
|- | |- | ||
| 6 | | 6 | ||
| L& | | L& | ||
| major oneirothird | | major oneirothird | ||
| Mo3 | |||
| -6 | | -6 | ||
| P@ | | P@ | ||
| minor oneiroseventh | | minor oneiroseventh | ||
| mo7 | |||
|- | |- | ||
| 7 | | 7 | ||
| O& | | O& | ||
| augmented oneirosixth | | augmented oneirosixth | ||
| Ao6 | |||
| -7 | | -7 | ||
| M@ | | M@ | ||
| diminished oneirofourth | | diminished oneirofourth | ||
| do4 | |||
|- | |- | ||
| colspan="6" style="text-align:left" | The chromatic 13-note MOS (either [[5L 8s]] | | colspan="6" style="text-align:left" | The chromatic 13-note MOS (either [[5L 8s]], [[8L 5s]], or [[13edo]]) also has the following intervals (from some root): | ||
|- | |- | ||
| 8 | | 8 | ||
| J& | | J& | ||
| augmented oneirounison (aka oneirochroma) | | augmented oneirounison (aka oneirochroma) | ||
| Ao1 | |||
| -8 | | -8 | ||
| J@ | | J@ | ||
| diminished oneirooctave (aka diminished oneironinth) | | diminished oneirooctave (aka diminished oneironinth) | ||
| do9 | |||
|- | |- | ||
| 9 | | 9 | ||
| M& | | M& | ||
| augmented oneirofourth | | augmented oneirofourth | ||
| Ao4 | |||
| -9 | | -9 | ||
| O@ | | O@ | ||
| diminished oneirosixth | | diminished oneirosixth | ||
| do6 | |||
|- | |- | ||
| 10 | | 10 | ||
| P& | | P& | ||
| augmented oneiroseventh | | augmented oneiroseventh | ||
| Ao7 | |||
| -10 | | -10 | ||
| L@ | | L@ | ||
| diminished oneirothird | | diminished oneirothird | ||
| do3 | |||
|- | |- | ||
| 11 | | 11 | ||
| K& | | K& | ||
| augmented oneirosecond | | augmented oneirosecond | ||
| Ao2 | |||
| -11 | | -11 | ||
| Q@ | | Q@ | ||
| diminished oneiroeighth | | diminished oneiroeighth | ||
| do8 | |||
|- | |- | ||
| 12 | | 12 | ||
| N& | | N& | ||
| augmented oneirofifth | | augmented oneirofifth | ||
| Ao5 | |||
| -12 | | -12 | ||
| N@@ | | N@@ | ||
| diminished oneirofifth | | diminished oneirofifth | ||
| do5 | |||
|} | |} | ||