8edo: Difference between revisions

Line 71:

8-edo forms an odd and even pitch set of two diminished seventh chords, which when used in combination yield dissonance. The system has been described as a "barbaric" harmonic system; even so, it does a good job representing the [[just intonation subgroup]]s 2.11/3.13/5, with good intervals of [[13/10]] and an excellent version of [[11/6]].

Another way of looking at 8-EDO is to treat a chord of 0-1-2-3-4 degrees (0-150-300-450-600 cents) as approximating harmonics 10:11:12:13:14 (~0-165-316-454-583 cents), which is not too implausible if you can buy that 12-EDO is a 5-limit temperament. This interpretation would imply that 121/120, 144/143, 169/168, and hence also 36/35 and 66/65, are tempered out.

Another way of looking at 8-EDO is to treat a chord of 0-1-2-3-4 degrees ([[Tel:0-150-300-450-600|0-150-300-450-600]] cents) as approximating harmonics 10:11:12:13:14 (~0-165-316-454-583 cents), which is not too implausible if you can buy that 12-EDO is a 5-limit temperament. This interpretation would imply that 121/120, 144/143, 169/168, and hence also 36/35 and 66/65, are tempered out.

=== Differences between distributionally-even scales and smaller edos ===

{| class="wikitable"

|+

!N

!L-Nedo

!s-Nedo

|-

|3

|50¢

| -100¢

|-

|5

|60¢

| -90¢

|-

|6

|100¢

| -50¢

|-

|7

|128.571¢

| -21.429¢

|}

=Notation=

@@ Line 71: / Line 71: @@
 -edo forms an odd and even pitch set of two diminished seventh chords, which when used in combination yield dissonance. The system has been described as a "barbaric" harmonic system; even so, it does a good job representing the [[just intonation subgroup]]s 2.11/3.13/5, with good intervals of [[13/10]] and an excellent version of [[11/6]].
-Another way of looking at 8-EDO is to treat a chord of 0-1-2-3-4 degrees (0-150-300-450-600 cents) as approximating harmonics 10:11:12:13:14 (~0-165-316-454-583 cents), which is not too implausible if you can buy that 12-EDO is a 5-limit temperament. This interpretation would imply that 121/120, 144/143, 169/168, and hence also 36/35 and 66/65, are tempered out.
+Another way of looking at 8-EDO is to treat a chord of 0-1-2-3-4 degrees ([[Tel:0-150-300-450-600|0-150-300-450-600]] cents) as approximating harmonics 10:11:12:13:14 (~0-165-316-454-583 cents), which is not too implausible if you can buy that 12-EDO is a 5-limit temperament. This interpretation would imply that 121/120, 144/143, 169/168, and hence also 36/35 and 66/65, are tempered out.
+=== Differences between distributionally-even scales and smaller edos ===
+{| class="wikitable"
+|+
+!N
+!L-Nedo
+!s-Nedo
+|-
+|3
+|50¢
+| -100¢
+|-
+|5
+|60¢
+| -90¢
+|-
+|6
+|100¢
+| -50¢
+|-
+|7
+|128.571¢
+| -21.429¢
+|}
 =Notation=