User:Lhearne/Extra-Diatonic Intervals: Difference between revisions

Line 283:

wherein we can see that it supports Diminished temperament.

Mavila[23]11|11 can be written as:

P1 d1 A2 M2 m2 A3 M3 m3 d3 A4 P4 d4 A5 P5 d5 A6 M6 m6 d6 M7 m7 d7 A8 P8

The primary interval names for 23edo are the same but for the inclusion of intermediates:

P1 d1 1-2 M2 m2 2-3 M3 m3 3-4 A4 P4 d4 A5 P5 d5 5-6 M6 m6 6-7 M7 m7 7-8 A8 P8

=== Father ===

Line 387:

Line 395:

The primary interval names for the remaining trivial edos are trivially derived and are given along with all those described so far in the section below.

== Lists of ~~described~~ edos and MOS scales ==

=== 28edo ===

We encounter a new problem with 28edo. 28edo's best fifth is that of 7edo. It's primary intervals names are as such:

P1 sA1 1-2 Sm2 N2 sM2 2-3 Sm3 N3 sM3 3-4 S4 P4 sA4 4-5 Sd5 P5 s5 5-6 Sm6 N6 sM6 6-7 Sm7 N7 sM7 7-8 Sd8 P8

in 28edo 81/80 is represented by -1 steps. We en-devour to maintain as best we can in our primary interval names the original premise behind the notation - that the prefix 's' takes an interval down a single step of the edo and 'S' a single step up. In our primary interval names for 28edo we have S4 below P4 and d5 above P5. We can avoid this confusion however by using the secondary interval names for P4 and P5 in 28edo - N4 and N5. In our list of edos below this change is made. We made realise from this situation that P4 really is a m4, and P5 a M5. An alternative scheme is developed on this premise, which leads to N4 and N5 as the primary interval names for these intervals, and avoids any initial confusion, detailed after the lists immediately below. In the primary interval names for all edos listed our original premise, that 'S' and 's' correspond to alterations of 1 step of the edo up and down respectively.

== Lists of edos and MOS scales ==

=== Primary interval names for edos ===

Line 427:

Line 442:

22edo: P1 m2 Sm2 sM2 M2 m3 Sm3 sM3 M3 P4 S4 4-5 s5 P5 m6 Sm6 sM6 M6 m7 Sm7 sM7 M7 P8

23edo: P1 d1 1-2 M2 m2 2-3 M3 m3 3-4 A4 P4 d4 A5 P5 d5 5-6 M6 m6 6-7 M7 m7 7-8 A8 P8

24edo: P1 1-2 m2 N2 M2 2-3 m3 N3 M3 3-4 P4 N4 4-5 N5 P5 5-6 m6 N6 M6 6-7 m7 N7 M7 7-8 P8

Line 433:

Line 450:

27edo: P1 m2 Sm2 N2 sM2 M2 m3 Sm3 N3 sM3 M3 P4 N4 d6 A3 N5 P5 m6 Sm6 N6 sM6 M6 m7 Sm7 N7 sM7 M7 P8

28edo: P1 sA1 1-2 Sm2 N2 sM2 2-3 Sm3 N3 sM3 3-4 S4 N4 sA4 4-5 Sd5 N5 s5 5-6 Sm6 N6 sM6 6-7 Sm7 N7 sM7 7-8 Sd8 P8

29edo: P1 1-2 m2 Sm2 sM2 M2 2-3 m3 Sm3 sM3 M3 3-4 P4 S4 d5 A4 s5 P5 5-6 m6 Sm6 sM6 M6 6-7 m7 Sm7 sM7 M7 7-8 P8

@@ Line 283: / Line 283: @@
 wherein we can see that it supports Diminished temperament.
+Mavila[23]11|11 can be written as:
+P1 d1 A2 M2 m2 A3 M3 m3 d3 A4 P4 d4 A5 P5 d5 A6 M6 m6 d6 M7 m7 d7 A8 P8
+The primary interval names for 23edo are the same but for the inclusion of intermediates:
+P1 d1 1-2 M2 m2 2-3 M3 m3 3-4 A4 P4 d4 A5 P5 d5 5-6 M6 m6 6-7 M7 m7 7-8 A8 P8
 === Father ===
@@ Line 387: / Line 395: @@
 The primary interval names for the remaining trivial edos are trivially derived and are given along with all those described so far in the section below.
-== Lists of described edos and MOS scales ==
+=== 28edo ===
+We encounter a new problem with 28edo. 28edo's best fifth is that of 7edo. It's primary intervals names are as such:
+P1 sA1 1-2 Sm2 N2 sM2 2-3 Sm3 N3 sM3 3-4 S4 P4 sA4 4-5 Sd5 P5 s5 5-6 Sm6 N6 sM6 6-7 Sm7 N7 sM7 7-8 Sd8 P8
+in 28edo 81/80 is represented by -1 steps. We en-devour to maintain as best we can in our primary interval names the original premise behind the notation - that the prefix 's' takes an interval down a single step of the edo and 'S' a single step up. In our primary interval names for 28edo we have S4 below P4 and d5 above P5. We can avoid this confusion however by using the secondary interval names for P4 and P5 in 28edo - N4 and N5. In our list of edos below this change is made. We made realise from this situation that P4 really is a m4, and P5 a M5. An alternative scheme is developed on this premise, which leads to N4 and N5 as the primary interval names for these intervals, and avoids any initial confusion, detailed after the lists immediately below. In the primary interval names for all edos listed our original premise, that 'S' and 's' correspond to alterations of 1 step of the edo up and down respectively.
+== Lists of edos and MOS scales ==
 === Primary interval names for edos ===
@@ Line 427: / Line 442: @@
 edo: P1 m2 Sm2 sM2 M2 m3 Sm3 sM3 M3 P4 S4 4-5 s5 P5 m6 Sm6 sM6 M6 m7 Sm7 sM7 M7 P8
+edo: P1 d1 1-2 M2 m2 2-3 M3 m3 3-4 A4 P4 d4 A5 P5 d5 5-6 M6 m6 6-7 M7 m7 7-8 A8 P8
 edo: P1 1-2 m2 N2 M2 2-3 m3 N3 M3 3-4 P4 N4 4-5 N5 P5 5-6 m6 N6 M6 6-7 m7 N7 M7 7-8 P8
@@ Line 433: / Line 450: @@
 edo: P1 m2 Sm2 N2 sM2 M2 m3 Sm3 N3 sM3 M3 P4 N4 d6 A3 N5 P5 m6 Sm6 N6 sM6 M6 m7 Sm7 N7 sM7 M7 P8
+edo: P1 sA1 1-2 Sm2 N2 sM2 2-3 Sm3 N3 sM3 3-4 S4 N4 sA4 4-5 Sd5 N5 s5 5-6 Sm6 N6 sM6 6-7 Sm7 N7 sM7 7-8 Sd8 P8
 edo: P1 1-2 m2 Sm2 sM2 M2 2-3 m3 Sm3 sM3 M3 3-4 P4 S4 d5 A4 s5 P5 5-6 m6 Sm6 sM6 M6 6-7 m7 Sm7 sM7 M7 7-8 P8