The following chart illustrates the Number System applied to a common I  VImin  IV  V  chord change.  It would obviously also apply to a I  IV  V  chord change which is the most common chord change in Euro-American Music.

The Number System Illustrated
The Number System Illustrated
(See the notes below for the reason I hinted at certain notes by hi-liting them in oragne).


This chart is written in the context of the common use of the I IV V chord change;  Which includes a 4 note in the IV scale, which is NOT harmonious as it would be were it a #4 and thereby properly complying with the harmony of a complete parent Ionian mode structure (IMaj7).  Notice that each one of the chords on this chart and each of their scales have the very same notes as C Maj 7 Scale, except for the IV chord.  V7 is commonly used because it's b7 does comply with (contained in) the harmonious Ionian structure, but most Musicians don't realize why the V7 accentuates harmony.   Knowledgeable Musicians will use a G7 (and/or it's 9/11/13 extensions) because it accentuates the I chord tonic's parent scale, the I chord / Ionian / parent mode structure of the chord change.  Although Musicians should know / learn that a 4 note in the IV scale SHOULD be sharpened to remain within the Lydian scale and therefore within the Ionian composition that a I IV V chord change is built upon, they rather commonly still play FMaj scale notes in their IV chord playing rather than the #4 note which is in the Lydian mode and is therefore harmonious to the parent Ionian.  Not to worry though since the common IV chords don't voice the 4 note ...and a Musician vamping or soloing will usually avoid the IV 4 note in the IV chord sections of the song, ...or will have changed it to #4 in his / her playing patterns not knowing why (such as the blues scale which is a I minor 7 scale that has the proper #4 for the IV chord), ...or they will contine to play that 4 note which stands out like a sore thumb.  But since there really is no such thing as bad notes in the abstract and in some quite popular forms of Music, the use of the 4 note in the IV scale is just a matter of being harmonious or not.   The point being that chords in a song are either voiced harmonically to the mode the song is written in, OR, in effect, if they're not, the chords are actually modulating key though not commonly thought of like that by the Musicians playing it.  You can prove this to your own brain by humming or playing the melody of a song ... finding what mode that melody is ... play the chord changes while paying attention to the melody, ... and then try to modulate that mode to the chords.  In other words, the melody of the song "Away in a Manger" is a IMaj7 Ionian mode / scale ... C scale in the key of C;  and as the chords change with that melody the scale remains the same.  But try singing, humming or playing F Major scale or G Major scale when those chords come around ... and you will hear that it sound like a Musician that solos by modulating their solo pattern to/with the chord changes of a song .... as opposed to finding the mode of the song and working around that scale throughout the song.  Another great demonstration of this is to play any minor blues song you want to in the key of A while your bass player plays walking bass with ANY NOTE COMBINATIONS up and down G Major scale.  The reason it works is because he is playing a parent Major scale for Amin7 ... and no matter where the chords go they are still relative to the Tonic minor which is derived from the Tonic's bVIIMaj7 scale.  He could also do the same thing by walking up and down CMaj7 scale, because CMaj7 scale is the parent of Amin7b6 the Aolean mode which is the pure minor mode.  Now here's where it gets really cool.  A Lap Steel or Spanish Guitar (aka standard guitar, aka electric guitar) player could also play those Maj7 substitution scales for their relative minors.  OR, especially in the case of Lap Steel, they could find the dominant 7 (Mixolydian) equivilents to the Maj7's which would be relative to the Tonic minor ... and play there.  As a matter of fact, realizing we can use each and every mode in proper substitution relationship ... finger positions for Spanish Guitarists, bar positions for Steel Guitarists ... opens the doors to the cosmos of music because each musicians favorite neck patterns applied via relative mode substitution gives 7 DIFFERENT VOICING INVERSIONS for any particular parent mode.  IT'S THE MODE SLIDE RULE THANG.
b6; VImin chord / scale
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