5L 3s: Difference between revisions
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Note: N is close to standard C, since the reference pitch 360 Hz for J was chosen to be nearly a pure 11/8 above standard 12edo C. | Note: N is close to standard C, since the reference pitch 360 Hz for J was chosen to be nearly a pure 11/8 above standard 12edo C. | ||
== Intervals == | |||
{| class="wikitable center-all" | |||
|- | |||
! Generators | |||
! Notation (1/1 = J) | |||
! Octatonic interval category name | |||
! Generators | |||
! Notation of 2/1 inverse | |||
! Octatonic interval category name | |||
|- | |||
| colspan="6" style="text-align:left" | The 8-note MOS has the following intervals (from some root): | |||
|- | |||
| 0 | |||
| J | |||
| perfect unison | |||
| 0 | |||
| J | |||
| octave | |||
|- | |||
| 1 | |||
| M | |||
| perfect mosfourth | |||
| -1 | |||
| O | |||
| perfect mossixth | |||
|- | |||
| 2 | |||
| P | |||
| major mosseventh | |||
| -2 | |||
| L | |||
| minor mosthird | |||
|- | |||
| 3 | |||
| K | |||
| major mossecond | |||
| -3 | |||
| Q@ | |||
| minor moseighth | |||
|- | |||
| 4 | |||
| N | |||
| major mosfifth | |||
| -4 | |||
| N@ | |||
| minor mosfifth | |||
|- | |||
| 5 | |||
| Q | |||
| major moseighth | |||
| -5 | |||
| K@ | |||
| minor mossecond | |||
|- | |||
| 6 | |||
| L& | |||
| major mosthird | |||
| -6 | |||
| P@ | |||
| minor mosseventh | |||
|- | |||
| 7 | |||
| O& | |||
| augmented sixth | |||
| -7 | |||
| M@ | |||
| diminished fourth | |||
|- | |||
| colspan="6" style="text-align:left" | The chromatic 13-note MOS also has the following intervals (from some root): | |||
|- | |||
| 8 | |||
| J& | |||
| augmented unison | |||
| -8 | |||
| J@ | |||
| diminished octave | |||
|- | |||
| 9 | |||
| M& | |||
| augmented mosfourth | |||
| -9 | |||
| O@ | |||
| diminished mossixth | |||
|- | |||
| 10 | |||
| P& | |||
| augmented mosseventh | |||
| -10 | |||
| L@ | |||
| diminished mosthird | |||
|- | |||
| 11 | |||
| K& | |||
| augmented mossecond | |||
| -11 | |||
| Q@@ | |||
| diminished moseighth | |||
|- | |||
| 12 | |||
| N& | |||
| augmented mosfifth | |||
| -12 | |||
| N@@ | |||
| diminished mosfifth | |||
|} | |||
== Oneirotonic rank-2 temperaments == | == Oneirotonic rank-2 temperaments == | ||
The only notable harmonic entropy minimum is Vulture/[[Hemifamity_temperaments|Buzzard]], in which four generators make a 3/1 (and three generators approximate an octave plus 8/7). The rest of this region does not approximate low-complexity JI harmony well, but can be melodically interesting due to the distorted diatonic scale structure (see also [[oneirotonic]]). | The only notable harmonic entropy minimum is Vulture/[[Hemifamity_temperaments|Buzzard]], in which four generators make a 3/1 (and three generators approximate an octave plus 8/7). The rest of this region does not approximate low-complexity JI harmony well, but can be melodically interesting due to the distorted diatonic scale structure (see also [[oneirotonic]]). | ||