User:Rperlner: Difference between revisions

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we find that while we have two different versions of a number of 9-limit consonant chords that appear in the 12-edo version, both versions are consonant in the 9-limit also in the partially de-tempered version. For example, a dominant 7th chord might either be 4:5:6:7 or 1/9:1/7:1/6:1/5. Likewise, if we treat the half octave as representing 17/12 in addition to 10/7 and 7/5, we can always render some inversion of any diminished 7th chord as 10:12:14:17. The melodic structure is also only moderately more complex than the 12-edo version, featuring a small (s) semitone, and medium (M) and large (L) wholetones in a sMsLsMsL pattern.

Here is an Octatonic jazz piece based on a shorter theme I wrote for piano in three different Jubilismic tunings that distinguish between 6/5 and 7/6 minor thirds. Ranging from narrowest to widest perfect fifths, they are 26 EDO, 48 EDO, and 22 EDO:

<tr>

<td>[[File:Octatonic Groove 26 edo.mp3|thumb|none|Octatonic Groove in 26 EDO]]</td>

<td>[[File:Octatonic Groove 48edo.mp3|thumb|none|Octatonic Groove in 48 EDO]]</td>

<td>[[File:Octatonic Groove 22 edo.mp3|thumb|none|Octatonic Groove in 22 EDO]]</td>

</tr>

</table>

For contrast, here is the same piece in 12 EDO:

[[File:Octatonic Groove 12 edo.mp3|thumb|none|Octatonic Groove in 12 EDO]]

The 12 EDO version is pleasant enough to listen to, but I find it less interesting, and at times, less harmonious than some of the nonstandard tunings. (I especially like 26 and 48 EDO here.)

@@ Line 27: / Line 27: @@
 we find that while we have two different versions of a number of 9-limit consonant chords that appear in the 12-edo version, both versions are consonant in the 9-limit also in the partially de-tempered version. For example, a dominant 7th chord might either be 4:5:6:7 or 1/9:1/7:1/6:1/5. Likewise, if we treat the half octave as representing 17/12 in addition to 10/7 and 7/5, we can always render some inversion of any diminished 7th chord as 10:12:14:17. The melodic structure is also only moderately more complex than the 12-edo version, featuring a small (s) semitone, and medium (M) and large (L) wholetones in a sMsLsMsL pattern.
+Here is an Octatonic jazz piece based on a shorter theme I wrote for piano in three different Jubilismic tunings that distinguish between 6/5 and 7/6 minor thirds. Ranging from narrowest to widest perfect fifths, they are 26 EDO, 48 EDO, and 22 EDO:
+<table style="width:100%">
+  <tr>
+    <td>[[File:Octatonic Groove 26 edo.mp3|thumb|none|Octatonic Groove in 26 EDO]]</td>
+    <td>[[File:Octatonic Groove 48edo.mp3|thumb|none|Octatonic Groove in 48 EDO]]</td>
+    <td>[[File:Octatonic Groove 22 edo.mp3|thumb|none|Octatonic Groove in 22 EDO]]</td>
+  </tr>
+</table>
+For contrast, here is the same piece in 12 EDO:
+[[File:Octatonic Groove 12 edo.mp3|thumb|none|Octatonic Groove in 12 EDO]]
+The 12 EDO version is pleasant enough to listen to, but I find it less interesting, and at times, less harmonious than some of the nonstandard tunings. (I especially like 26 and 48 EDO here.)