One more question about Russell Lydian theory. Russell uses as an example the Lydian C scale: C-D-E-F#-G-A-B-C comparing it with C maj scale, then he starts to explain his theory as if they belong to same key, otherwise why comparing C Lydian with C maj? This often happens with jazz theory, which confuses me as I was trained approaching harmony through keys (we actually use "tonality" as term - we gives key different meaning, such as bass key, baritone key, tenor key, etc). So, to me C Lydian belongs to the key of G (1 sharp). In fact, comparing the two modes, Lydian and Maj, he builds his theory on F of Cmaj and F# of Lydian (of course!). Sometimes I also find theories in which Cmaj is related to C- as parallel and I find it quite odd, as there is not a direct relationship, as far as I know. Of course in music everything could be related, mostly depends on the sound that comes out, even more on who plays it. Thanks to anybody who will be available to answer.
I think historical context is important in understanding Russell's rationale here.
At that time in music theory (and even up until the present day), everything was related to the major scale. Russell comes along and makes the claim that, no, everything isn't related to the major scale, but rather to the Lydian scale.
Thus his explanations often start with the major scale because that's what he knows his readers will understand the most. Furthermore, by relating C Lydian to C major, he's able to highlight the major difference between his theory and those prior: that his main starting point includes that F♯, whereas others don't.
But you're correct: the parent scale of C Lydian is G major, and in that sense G major is "closer" to C Lydian than C major is.
If I understand correctly, you are asking whether C Lydian "belongs" to G major or "belongs" to C major. I would say neither, or both, depending on what you mean by "belongs". C Lydian uses the same notes as G major but the same tonic as C major. Harmonically and melodically, though, it's different from both.
I think this is just a confusion about terminology.
The lydian scale is built on Fa (FaSoLaTiDoReMiFa=WWWHWWH). In the key of C this is F-G-A-BC-D-EF, in the key of G this is C-D-E-F#G-A-BC.
So, to me C Lydian belongs to the key of G (1 sharp). In fact, comparing the two modes, Lydian and Maj, he builds his theory on F of Cmaj and F# of Lydian (of course!).
You are correct:
Lydian C is the IV. mode of the G major scale but quite different (melodically and harmonically) from the key of G major or C maj.
Maybe this link will help you further:
To complete the confusion we could say (instead of saying C lydian is the mode of the 4th degree of the major scale=Ionian):
Each mode has its own row of halfsteps and wholesteps and its root tone is its 1st degree. This is historical more correct! But referring all modes to the major scale - as exemple preferring C major - is for students educated in the system of the western major/minor tonality as a pedagogical approach probably better understandable.
So we have to differentiate whether we think and discuss within the theory of Russell (where CDEF#GABC is mode I ("major") or try to explain it to someone who comes from the traditional Western theory (where Dorian C is mode IV of the G-key.)
"Finally, I realized that because of the first four tones of the C-major scale, the C major-scale could in no way be in unity with that C-major chord because of the Do, Re, Mi, and Fa, Fa itself was a Do. That doesn’t sound Do, a “C” Do, that sounds the Fa Do. But what led me to play the G-major scale was that the second tetra chord of C-major scale is G-A-B-C, and that does sound C. The following tetra chord in G is D-E-F#-G, and that at least resolves to a tone that is in the C-major chord. So it led me to say, “Well, let’s try the G-major scale.” As I said, I began to accept the G-major scale as actually sounding closer to the tonality of a C-major chord than the C-major scale. The problem, thinking practically, how can I tell musicians if you see a C-major chord, play a G-major scale? So then I began to understand that the first mode of the G-major scale, the Ionian, playing that with the chord presented this problem of having musi- cians playing a G-major scale. Then the Dorian, the same problem, kind of.
Then the Phrygian, finally the Lydian—C-D-E-F#-G-A-B. I said, “I don’t care what anybody says; this isn’t just the Lydian mode of the G-major scale, this is the C-Lydian scale, the closest scale to the C-major chord.”
Carr, interview with G. Russell, June 1992.
Source: George Russell: The Story of an American Composer (African American Cultural Theory and Heritage)
Series Editor: William C. Banfield
The confusion comes from the point that Do means the root tone of the Ionic scale DoReMi, but he pretends (or starts from Do) and says the Fa must be a sharpened IV = Fi ...
(mind that even some of his closest "followers" said, the LCC could be explained or described in the language of the traditional western music theory!)
What Russell wants to say is:
The root tone of his LCC is the Do of the lydian scale - in C this is C - (using the notes of "our well known" western G-major scale but this he explicitely denies: ths is not IV of G, it is I or Lydian C with the F#! Russell's approach is not a misconcpetion of the western theory: imho it is also a rebellish expression of the afro-american musician and composer against the dominance of western ("white") music culture but also a "traite" of an new (old) music theory - comparable with Debussy, Ravel, Schoenberg, Stravinsky, Bartok, Messiaen and others. One departing point is the development of the lydian scale from the circle of perfect fifths - another point is that (jazz) music is rooting in the African music.
The connection between
C minor, and
C lydian is they all have the same tonic of
C lydian and
G major share the
F# in their sets of tones, but they have different tonics. That matters, because relative to the two tonics you get differing chord types on the various scale tones. The big difference being the subdominant chord on the fourth scale degree. In
G major you have (natural)
^4 and its triad is major
IV. In lydian the subdominant is raised
#^4 and its triad is diminished
#ivo. So, while superficially the two sets of tones are the same, their tonal structures are different. And, of course, their tonic chords are different
C major and
G major. Simply put, they are not the same tonalities.
If you compare the parallel tonalities, the
C minor, and
C lydian, the ones that all have the same tonic, we will see some similarities. All three have a perfect fifth above their tonics, and a major triad can be built in all three, so all three have the same dominant chord of
V. And the tonic chords are the exact same between
C major and lydian:
I. The tonic chord in
C minor differs only in the third being minor, but the tonic and dominant scale degrees are the same as
C major and lydian. Those two scale degrees being tonal degrees means the main tonal foundation is largely the same. Not exactly the same, but there is significant overlap.
So, instead of just look at a set of tones, like
E F# G A B C D E, and then saying it's
G major, or
C lydian, or
E minor, or
A dorian, etc. etc. Look at the tonic, take note of what the tonal scale degrees are, and then note the modal scale degrees. Tonic, subdominant, and dominant scale degrees separated by perfect fourths/fifths is an essential tonal concept. That makes lydian and locrian modes the odd ones out, because they don't have all three of those tonal degrees.
As far as Russell is concerned, I haven't read his book, but I understand he gave significance to the raised fourth and lydian, because of the harmonic overtone series which contains that interval up high is the overtones. But you don't need that to explain the use of augmented fourths in jazz. They were used before Russell. The French augmented sixth chord features it and that chord is in the original song I Got Rhythm. Debussy used the augmented fourth, I think especially from the whole tone scale, and his music inspired jazz harmony. An augmented fourth can be enharmonically spelled as a diminished fifth, a flat fifth, and that's famously used in Take the A Train. Russell didn't invent or discover something new. The tritone has been used for a long time in different styles.
His idea that "lydian mode" is a more natural tonality than major just adds confusion in my opinion. Most of what I see of lydian in jazz harmony is decorative, stuff like "play a lydian dominant scale over a dominant chord", meanwhile the song's chord changes may use roots of a natural subdominant, which means the song isn't actually in a lydian mode. If I actually saw songs with
#ivo chords, I would think differently about Russell's idea.