Modal Jam Theory
When the plain symmetry of the tritone interval is intentionally avoided... the spiral symmetry of the golden ratio (and its reciprocal) is revealed as the catalyst for modulation.
The following articles will attempt to demonstrate that harmony is a consequence of melody... and not the other way around.
It is precisely because the tone 'Fa' cannot be found (anywhere) in the harmonic overtone series that awards it - the profound catalyst... the melodic tone of greatest influence over any (and all) movement in natural harmony.
So far - in our study of Modal Jam Theory - we have been looking at this model of the Circle Of Fifths:
For a moment - let's revisit the guts of this thing... laid out flat. These are the 12 Major Scales (15 Major Key Signatures) represented using the solfege syllables of 'C' Major (only). Notice the column of 'Fa' (in the center of the 'grid'). As we look up the column (clockwise in the circle) - we see flatted tones.... and as we look down the column (counter-clockwise in the circle) we see (mostly) the diatonic tones in the Key of 'C.'
As we stay focused on this "column" of 'Fa' (above) --- follow this table:
Have we missed one (other than Locrian)? I count only 5 Modes. Yes - we are missing the Lydian Mode. It turns out that 'C' Lydian is the only 'C' Mode that reenforces the key of the Dominant with a raised 'Fa' (F#) - also known as '#11' or 'Fi'. It is the mode that claims 'Fa' as its root - and the only mode that does not have any 'Fa' of it's own. I call it the 'Harmonic Mode' because all its tones match the harmonic overtone series.
When we are playing a tune - we know when we've 'landed' in the Lydian mode... as all its tones 'work' with the harmony and everything feels like a 'bright' harmonic soup --- but eventually - as most tunes go - 'Fi' is flatted to become 'Fa' (in the melody) and the harmony responds with it. For me - this very common change feels like adding a shade of 'blue.'
The following table adds the true 'Fa' of Lydian into the scenario of 'melodic' modes. The true 'Fa' of Lydian is 'Do.'
The tonal relationship of 'Fa' (in relation to its fundamental) does not exist in the natural harmonic overtone series.
The intention of these articles (The Color Of 'Fa') is to demonstrate that there is a difference between melody and harmony. This difference is subtle and profound.
The 'F#' ('Fi') in the mode of 'C' Lydian is 'produced' in the natural harmonic overtone series by the single thump of the bass player's 'C' note. The 'F' ('Fa') in the Major Scale ('C' Ionian) is not heard (with this 'C' note) unless it is (physically) struck. When 'Fa' is (physically) struck with/against this 'C' note -- it is heard as a 'flatted tone' against the harmony.
The following is a general statement that can have a profound impact on the development of the musical ear:
Though - an experienced musician may hear the tone 'Fi' as an integral tone in the harmonic overtone series -- the average western ear is only 'practiced' in listening to melody [those tones that are (physically) struck or sung]. As I refrain from speculating about the details of music history -- let's just say that after thousands of years of singing tunes that sound a lot like 'Happy Birthday' --- the western ear just loves the way 'Fa' feels. The 'balanced' melodic palette we have come to know (and love) as the 'Dia-tonic' Scale (Ionian) is here to stay... as an integral part of our intricate and complex muse.
... but what happens when our (Fa' conditioned) melodic ear hears the tone 'F#' ('Fi') - (physically) struck in the melody - against the root of 'C'? The answer to this question is somewhat fascinating: First - it can hear this sharped tone 'Fi' - as 'Ti' -- then uses the uniqueness of the tri-tone interval to 'locate' a new 'Fa.' [In this particular case -- the new 'Fa' happens to be the root of 'C' Lydian (in the 'Key Of The Dominant' ('G' Major - Ionian).]