8edo: Difference between revisions

Line 8:

| Prime factorization = 2<sup>3</sup>

| Step size = 150¢

Relative Radian = 23.87324¢

| Fifth = 5\8 = 750¢

| Major 2nd = 2\8 = 300¢

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Line 21:

8edo 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 8edo 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 12edo 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 8edo 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 12edo 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.

== Notation ==

@@ Line 8: / Line 8: @@
 | Prime factorization = 2<sup>3</sup>
 | Step size = 150¢
+Relative Radian = 23.87324¢
 | Fifth = 5\8 = 750¢
 | Major 2nd = 2\8 = 300¢
@@ Line 20: / Line 21: @@
 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 8edo 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 12edo 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 8edo 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 12edo 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.
 == Notation ==