13edo: Difference between revisions
m →26edo subset: Use x instead of ## for double sharp |
→Notations: more changes |
||
| Line 211: | Line 211: | ||
13edo can also be notated with ups and downs. If one uses the best fifth, 8\13, the minor 2nd becomes a descending interval! Thus a major 2nd is wider than a minor 3rd, a major 3rd is wider than a perfect 4th, etc. And B is above C, E is above F, A is above Bb, etc. However one can use ups and downs to avoid minor 2nds. Thus A C B D becomes A vB ^C D. | 13edo can also be notated with ups and downs. If one uses the best fifth, 8\13, the minor 2nd becomes a descending interval! Thus a major 2nd is wider than a minor 3rd, a major 3rd is wider than a perfect 4th, etc. And B is above C, E is above F, A is above Bb, etc. However one can use ups and downs to avoid minor 2nds. Thus A C B D becomes A vB ^C D. | ||
Enharmonic intervals: ^m2 | Enharmonic intervals: v⁴A1, ^m2 | ||
{| class="wikitable center-all right-2" | {| class="wikitable center-all right-2" | ||
| Line 447: | Line 447: | ||
|} | |} | ||
=== Pentatonic 5th-generated === | === Pentatonic 5th-generated (3L2s) === | ||
The degrees are named unison, subthird, fourthoid, fifthoid, subseventh and octoid. | The degrees are named unison, subthird, fourthoid, fifthoid, subseventh and octoid. | ||
Keyboard: '''D * * | Keyboard: '''D * F * * G * * A * C * * D''' (generator = wide 3/2 = 8\13 = perfect 5thoid) | ||
Enharmonic interval: dds3 | Enharmonic interval: dds3 | ||
| Line 472: | Line 472: | ||
|D | |D | ||
|D# | |D# | ||
Fb | |||
| | |F | ||
| | |F# | ||
Gb | |Gb | ||
|G | |G | ||
|G# | |G# | ||
| Line 529: | Line 529: | ||
|- | |- | ||
|... | |... | ||
| | |Fb | ||
|Cb | |Cb | ||
|Gb | |Gb | ||
|Db | |Db | ||
|Ab | |Ab | ||
| | |F | ||
|C | |C | ||
|G | |G | ||
|D | |D | ||
|A | |A | ||
| | |F# | ||
|C# | |C# | ||
|G# | |G# | ||
|D# | |D# | ||
|A# | |A# | ||
| | |Fx | ||
|Cx | |Cx | ||
|... | |... | ||
| Line 569: | Line 569: | ||
|} | |} | ||
=== Octatonic 5th-generated (oneirotonic) === | === Octatonic 5th-generated (5L3s or oneirotonic) === | ||
Keyboard: '''A * B C * D * E F * G H * A''' (generator = wide 3/2 = 8\13 = perfect 6th) | Keyboard: '''A * B C * D * E F * G H * A''' (generator = wide 3/2 = 8\13 = perfect 6th) | ||
| Line 690: | Line 690: | ||
|} | |} | ||
=== Heptatonic 2nd-generated (archaeotonic) === | === Heptatonic 2nd-generated (6L1s or archaeotonic) === | ||
Keyboard: '''D * E * F * G A * B * C * D''' (generator = 2\13 = perfect 2nd) | Keyboard: '''D * E * F * G A * B * C * D''' (generator = 2\13 = perfect 2nd) | ||
| Line 806: | Line 806: | ||
|} | |} | ||
=== Heptatonic 3rd-generated (mosh) === | === Heptatonic 3rd-generated (3L4s or mosh) === | ||
This notation requires ups and downs because 7 perfect thirds octave-reduces to 2 edosteps, not 1. | This notation requires ups and downs because 7 perfect thirds octave-reduces to 2 edosteps, not 1. | ||
Keyboard: '''D E * * F G * * A B * * C D''' (generator = 4\13 = perfect 3rd) | Keyboard: '''D E * * F G * * A B * * C D''' (generator = 4\13 = perfect 3rd) | ||
Enharmonic intervals: vvA1, vm2 | Enharmonic intervals: vvA1, vm2 | ||
{| class="wikitable" | {| class="wikitable" | ||
|+notes/intervals in melodic order | |+notes/intervals in melodic order | ||