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 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).]