Modeless interchange: Difference between revisions

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'''Modeless interchange''', is a technique or a chord progression that consists of crossing over the [[~~Triad~~]] present in ~~the~~ 7-note [[MOS scale]]. In particular, an [[EDO]] in which all six types of 7-note ~~MOSs are possible~~ is called '''~~Interchangable~~''', and an EDO in which all ~~triad~~ 0-2-4 on all those 7-note MOSes are [[~~Delta~~-rational ~~chord~~]]s is called '''~~Perfectly Interchangable~~'''.

'''Modeless interchange''' is a technique, commonly used in the form of a chord progression, that consists of crossing over the [[triad]] present in a 7-note [[MOS scale]]. In particular, an [[EDO]] in which all six types of 7-note MOSes can be realized is called '''interchangable''', and an EDO in which all 0-2-4 triads on all those 7-note MOSes are [[delta-rational]] is called '''perfectly interchangable'''.

== Theory ==

~~As you know, there~~ are six different 7-tone MOS scales, [[1L 6s]], [[2L 5s]], [[3L 4s]], [[4L 3s]], [[5L 2s]] and [[6L 1s]]. ~~Of course~~, all of ~~which are based on different group of EDOs~~. However, as mentioned above, there are EDOs in which all of these scales are simultaneously valid. Taking [[19edo]] as an example~~, there is a [[subset notation~~|~~subset]] of this scale:~~ 6L 1s (L:s=3:1~~), 4L 3s (L~~:s=4:1~~), 3L 4s (L:s=~~5:1~~), 2L 5s (L:s=~~7:1~~), and 1L 6s (L:s=~~7:2). Naturally, a further subset of these scales could be the 0-2-4 triad, but not all of them sound beautiful. More specifically, it is currently assumed as that the simply ratio of the frequency difference of the triad is the [[Just Intonation]] ratio, i.e., that the triad is a [[Delta-rational]].

There are six different 7-tone MOS scales, [[1L 6s]], [[2L 5s]], [[3L 4s]], [[4L 3s]], [[5L 2s]] and [[6L 1s]]. Each MOS is realized by a different set of EDOs, and not all EDOs can realize all of these MOSes. However, as mentioned above, there are EDOs in which all of these scales are simultaneously valid. Taking [[19edo]] as an example:

{| class="wikitable"

|+ 7-note MOSes in 19edo

|-

! MOS

! 6L 1s

! 5L 2s

! 4L 3s

! 3L 4s

! 2L 5s

! 1L 6s

|-

| L:s

| 3:1

| 3:2

| 4:1

| 5:1

| 7:1

| 7:2

|}

Thankfully, since [[generator]]s are known to produce many ~~Delta~~-rational Chords when tuned close to the stock ratio, and since the [[5/4]] (major third, generator of 3L 4s) and [[6/5]] (minor third, generator of 4L 3s) approximations in 19EDO mean are as close to the JI ratio as possible, we can expect at least two modeless interchanges to be possible for the 4L 3s and 3L 4s. If you wish to use other averages, the following table will be helpful:

Naturally, the 0-2-4 scale step pattern of these scales could be the fundamental triad, but not all of them sound beautiful. Therefore, it is currently assumed as that the frequency differences of the two consecutive intervals in the triad form a simple integer ratio, i.e., that the triad is [[delta-rational]], since these chords tend to sound consonant.

Thankfully, since [[generator]]s are known to produce many delta-rational Chords when tuned close to the stock ratio, and since the [[5/4]] (major third, generator of 3L 4s) and [[6/5]] (minor third, generator of 4L 3s) approximations in 19EDO mean are as close to the JI ratio as possible, we can expect at least two modeless interchanges to be possible for the 4L 3s and 3L 4s. If you wish to use other averages, the following table will be helpful:

@@ Line 1: / Line 1: @@
-{{stub}}
+{{Novelty}}
-'''Modeless interchange''', is a technique or a chord progression that consists of crossing over the [[Triad]] present in the 7-note [[MOS scale]]. In particular, an [[EDO]] in which all six types of 7-note MOSs are possible is called '''Interchangable''', and an EDO in which all triad 0-2-4 on all those 7-note MOSes are [[Delta-rational chord]]s is called '''Perfectly Interchangable'''.
+'''Modeless interchange''' is a technique, commonly used in the form of a chord progression, that consists of crossing over the [[triad]] present in a 7-note [[MOS scale]]. In particular, an [[EDO]] in which all six types of 7-note MOSes can be realized is called '''interchangable''', and an EDO in which all 0-2-4 triads on all those 7-note MOSes are [[delta-rational]] is called '''perfectly interchangable'''.
 == Theory ==
-As you know, there are six different 7-tone MOS scales, [[1L 6s]], [[2L 5s]], [[3L 4s]], [[4L 3s]], [[5L 2s]] and [[6L 1s]]. Of course, all of which are based on different group of EDOs. However, as mentioned above, there are EDOs in which all of these scales are simultaneously valid. Taking [[19edo]] as an example, there is a [[subset notation|subset]] of this scale: 6L 1s (L:s=3:1), 4L 3s (L:s=4:1), 3L 4s (L:s=5:1), 2L 5s (L:s=7:1), and 1L 6s (L:s=7:2). Naturally, a further subset of these scales could be the 0-2-4 triad, but not all of them sound beautiful. More specifically, it is currently assumed as that the simply ratio of the frequency difference of the triad is the [[Just Intonation]] ratio, i.e., that the triad is a [[Delta-rational]].
+There are six different 7-tone MOS scales, [[1L 6s]], [[2L 5s]], [[3L 4s]], [[4L 3s]], [[5L 2s]] and [[6L 1s]]. Each MOS is realized by a different set of EDOs, and not all EDOs can realize all of these MOSes. However, as mentioned above, there are EDOs in which all of these scales are simultaneously valid. Taking [[19edo]] as an example:
+{| class="wikitable"
+|+ 7-note MOSes in 19edo
+|-
+! MOS
+! 6L 1s
+! 5L 2s
+! 4L 3s
+! 3L 4s
+! 2L 5s
+! 1L 6s
+|-
+| L:s
+| 3:1
+| 3:2
+| 4:1
+| 5:1
+| 7:1
+| 7:2
+|}
-Thankfully, since [[generator]]s are known to produce many Delta-rational Chords when tuned close to the stock ratio, and since the [[5/4]] (major third, generator of 3L 4s) and [[6/5]] (minor third, generator of 4L 3s) approximations in 19EDO mean are as close to the JI ratio as possible, we can expect at least two modeless interchanges to be possible for the 4L 3s and 3L 4s. If you wish to use other averages, the following table will be helpful:
+Naturally, the 0-2-4 scale step pattern of these scales could be the fundamental triad, but not all of them sound beautiful. Therefore, it is currently assumed as that the frequency differences of the two consecutive intervals in the triad form a simple integer ratio, i.e., that the triad is [[delta-rational]], since these chords tend to sound consonant.
+Thankfully, since [[generator]]s are known to produce many delta-rational Chords when tuned close to the stock ratio, and since the [[5/4]] (major third, generator of 3L 4s) and [[6/5]] (minor third, generator of 4L 3s) approximations in 19EDO mean are as close to the JI ratio as possible, we can expect at least two modeless interchanges to be possible for the 4L 3s and 3L 4s. If you wish to use other averages, the following table will be helpful: