User:TromboneBoi9/Approaches to weird EDOs: Difference between revisions

Line 304:

23edo is technically [[dual-fifth]] like [[13edo]], the fifths being 13\23 and 14\23. [[2L 5s|Antidiatonic]] seems more natural here, especially since the minor fifth is recognizable as a perfect fifth (the major fifth is far too sharp), but this means that the 3\23 neutral seconds get the role of major seconds rather than the very good [[9/8]] approximation, 4\23. Atonally, [[46edo]] subset notation will work best.

===Listen for yourself===

That being said, here are some audio demonstrations of the various split prime approximations so you can make a decision yourself as to which version is better.

'''Make sure your volume is set to about 50%, otherwise these may sound quite loud.''' You can alternatively listen to these comparisons in series on [https://luphoria.com/xenpaper/#%7B23edo%7D(osc%3Atriangle)(bpm%3A50)%0A%7Br220Hz%7D%0A%5B0_13%5D--._%5B0_14%5D--._%23_3%2F2_perfect_fifths%0A..%0A%5B0_7%5D--._%5B0_8%5D--._%23_5%2F4_major_thirds%0A..%0A%5B0_18%5D--._%5B0_19%5D--._%23_7%2F4_harmonic_sevenths%0A..%0A%5B0_'10%5D--._%5B0_'11%5D--._%23_11%2F4_harmonic_elevenths Xenpaper].

{|

| 5/4 || major third || 7\23 || A-vvC&sharp; || 8\23 || A-C&sharp; || [[File:Comparison-23edo-thirds.mp3]]

|-

| 3/2 || perfect fifth || 13\23 || A-vE || 14\23 || A-^E || [[File:Comparison-23edo-fifths.mp3]]

|-

| 7/4 || harmonic seventh || 18\23 || A-vvG || 19\23 || A-G || [[File:Comparison-23edo-sevenths.mp3]]

|-

| 11/4 || harmonic eleventh || 33\23 || A-^D || 34\23 || A-E&flat; || [[File:Comparison-23edo-elevenths.mp3]]

|}

My preferences lie in 0,7,13,18\23 for a 4:5:6:7, and is think either 33\23 or 34\23 could work for an 11/4. Both sound to me equally consonant, but the higher one has less beating when octave reduced (to 11\23). I personally prefer 33\23 (10\23) since I feel 34\23 (11\23) is too close to the tritone interval region; if there's any reason 11\23 has less beating, it's because it's actually a [[7/5]].

===Seconds===

Line 337:

Line 355:

|}

This system is ~~alike~~ to the 6L1s ~~system shown~~ earlier ~~for 13edo but with the step sizes swapped~~: B-C is ~~now~~ the only ''large'' step. 1L6s might work well if you find yourself preferring the 14\23 major fifth rather than the 13\23 minor fifth, since it features as the fifth in this scale.

This system is similar to antidiatonic in the same way that 6L1s from earlier is similar to diatonic: B-C is the only ''large'' step here rather than it being the only small step. This 1L6s system might work well if you find yourself preferring the 14\23 major fifth rather than the 13\23 minor fifth, since it features as the fifth in this scale.

@@ Line 304: / Line 304: @@
 edo is technically [[dual-fifth]] like [[13edo]], the fifths being 13\23 and 14\23. [[2L 5s|Antidiatonic]] seems more natural here, especially since the minor fifth is recognizable as a perfect fifth (the major fifth is far too sharp), but this means that the 3\23 neutral seconds get the role of major seconds rather than the very good [[9/8]] approximation, 4\23. Atonally, [[46edo]] subset notation will work best.
+===Listen for yourself===
+That being said, here are some audio demonstrations of the various split prime approximations so you can make a decision yourself as to which version is better.
+'''Make sure your volume is set to about 50%, otherwise these may sound quite loud.''' You can alternatively listen to these comparisons in series on [https://luphoria.com/xenpaper/#%7B23edo%7D(osc%3Atriangle)(bpm%3A50)%0A%7Br220Hz%7D%0A%5B0_13%5D--._%5B0_14%5D--._%23_3%2F2_perfect_fifths%0A..%0A%5B0_7%5D--._%5B0_8%5D--._%23_5%2F4_major_thirds%0A..%0A%5B0_18%5D--._%5B0_19%5D--._%23_7%2F4_harmonic_sevenths%0A..%0A%5B0_'10%5D--._%5B0_'11%5D--._%23_11%2F4_harmonic_elevenths Xenpaper].
+{|
+| 5/4 || major third || 7\23 || A-vvC&sharp; || 8\23 || A-C&sharp; || [[File:Comparison-23edo-thirds.mp3]]
+|-
+| 3/2 || perfect fifth || 13\23 || A-vE || 14\23 || A-^E || [[File:Comparison-23edo-fifths.mp3]]
+|-
+| 7/4 || harmonic seventh || 18\23 || A-vvG || 19\23 || A-G || [[File:Comparison-23edo-sevenths.mp3]]
+|-
+| 11/4 || harmonic eleventh || 33\23 || A-^D || 34\23 || A-E&flat; || [[File:Comparison-23edo-elevenths.mp3]]
+|}
+My preferences lie in 0,7,13,18\23 for a 4:5:6:7, and is think either 33\23 or 34\23 could work for an 11/4. Both sound to me equally consonant, but the higher one has less beating when octave reduced (to 11\23). I personally prefer 33\23 (10\23) since I feel 34\23 (11\23) is too close to the tritone interval region; if there's any reason 11\23 has less beating, it's because it's actually a [[7/5]].
 ===Seconds===
@@ Line 337: / Line 355: @@
 |}
-This system is alike to the 6L1s system shown earlier for 13edo but with the step sizes swapped: B-C is now the only ''large'' step. 1L6s might work well if you find yourself preferring the 14\23 major fifth rather than the 13\23 minor fifth, since it features as the fifth in this scale.
+This system is similar to antidiatonic in the same way that 6L1s from earlier is similar to diatonic: B-C is the only ''large'' step here rather than it being the only small step. This 1L6s system might work well if you find yourself preferring the 14\23 major fifth rather than the 13\23 minor fifth, since it features as the fifth in this scale.
 <!-- Next write a section about all the split primes WITH AUDIO DEMONSTRATIONS -->