Modeless interchange: Difference between revisions

(10 intermediate revisions by 4 users not shown)

Line 1:

~~{{stub}}~~

'''Modeless interchange'''{{idiosyncratic}} is a technique used for chord progression, that consists of modulating over different types of 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'''.

'''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 ~~a mean rule~~ in which all ~~triad~~ 0-2-4 on all those 7-note MOSes are [[~~Delta~~-rational ~~chord~~]]s is called '''~~Perfect Interchangable~~'''.

== Theory ==

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

|}

~~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]].

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:

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 36:

Line 54:

| +5:9, +4+5, +1+1 (L:s≒3:1)

|}

{{Todo| ~~expand~~ | inline=1 | comment=expand and refactor this table}}

{{Todo| complete table | correct maths | inline=1 | comment=expand and refactor this table}}

== Usage ==

This technique is still in its infancy and information is drying up, but it should be used like a modal interchange.

== Generalizations ==

Modeless interchange can be applied to MOSes with any number of notes, not just heptatonic ones.

[[Category:~~Chords|~~ ]]

[[Category:Harmony]]

@@ Line 1: / Line 1: @@
-{{stub}}
+'''Modeless interchange'''{{idiosyncratic}} is a technique used for chord progression, that consists of modulating over different types of 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'''.
-'''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 a mean rule in which all triad 0-2-4 on all those 7-note MOSes are [[Delta-rational chord]]s is called '''Perfect Interchangable'''.
 == Theory ==
+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
+|}
-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]].
+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:
+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 36: / Line 54: @@
 | +5:9, +4+5, +1+1 (L:s≒3:1)
 |}
-{{Todo| expand | inline=1 | comment=expand and refactor this table}}
+{{Todo| complete table | correct maths | inline=1 | comment=expand and refactor this table}}
 == Usage ==
 This technique is still in its infancy and information is drying up, but it should be used like a modal interchange.
+{{Todo| complete section | inline=1}}
-{{Todo| expand | inline=1}}
+== Generalizations ==
+Modeless interchange can be applied to MOSes with any number of notes, not just heptatonic ones.
+{{Todo| complete section | inline=1}}
-[[Category:Chords| ]]
+[[Category:Harmony]]