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Maybe this is elementary - but I've always been fascinated with the fact that the musical ear can still distinguish any triad when it is inverted. The Ear Just Knows To illustrate the practical significance of the concept of reciprocity – here are a few exercises you can try using any harmonic instrument such as a piano or a guitar: Exercise 1 1) Strike a ‘C’ note and then the ‘G’ note above. You are now hearing a Perfect 5th interval. This should give the impression of some sort of ‘C’ Chord --- and all is right with the universe. ‘C’ is functioning as the generative fundamental tone – and everything indicates the ‘harmony’ of ‘C.’ 2) Now, strike a ‘G’ note and then the ‘C’ note above. You are now hearing the reciprocal of the Perfect 5th interval - which is a Perfect 4th. This should also give the impression of some sort of ‘C’ Chord -- but something is odd. The ‘G’ note is ‘serving’ as the generative fundamental tone of the harmonic structure, but your ear recognizes the ‘C’ note (the higher tone) as the root of the chord. This is the prime example of the ear naturally negotiating the reciprocity of the Perfect 5th. Now, let’s investigate the ear’s natural harmonic intelligence in discerning the Major 3rd with its interval of reciprocity – the Minor 6th: Exercise 2 1) Strike a ‘C’ note and then the ‘E’ note above. You are now hearing a Major 3rd interval. This should give the impression of some sort of ‘C’ Chord (with a definitive ‘major’ quality) - and all is right with the universe. ‘C’ is functioning as the generative fundamental tone – and everything indicates the ‘harmony’ of ‘C’ (major). 2) Now, strike an ‘E’ note and then the ‘C’ note above. You are now hearing the reciprocal of the Major 3rd Interval - which is a Minor 6th. This should also give the impression of some sort of ‘C’ Chord (with a definitive ‘major’ quality) -- but something is odd. The ‘E’ note is ‘serving’ as the generative fundamental tone of the harmonic structure, but your ear recognizes the ‘C’ note (the higher tone) as the root of the chord. This is the prime example of the ear naturally negotiating the reciprocity of the Major 3rd. Now, let’s investigate the ear’s natural harmonic intelligence in discerning the Minor 3rd with its interval of reciprocity – the Major 6th: Exercise 3 1) Strike a ‘C’ note and then the ‘Eb’ note above. You are now hearing a Minor 3rd interval. This should give the impression of some sort of ‘C’ Chord (with a definitive ‘minor’ quality) - and all is right with the universe. ‘C’ is functioning as the generative fundamental tone – and everything indicates the ‘harmony’ of ‘C’ (minor). 2) Now, strike an ‘Eb’ note and then the ‘C’ note above. You are now hearing the reciprocal of the Minor 3rd interval - which is a Major 6th. This should also give the impression of some sort of ‘C’ Chord (with a definitive ‘minor’ quality) -- but something is odd. The ‘Eb’ note is ‘serving’ as the generative fundamental tone of the harmonic structure, but your ear recognizes the “C’ note (the higher tone) as the root of the chord. This is the prime example of the ear naturally negotiating the reciprocity of the Minor 3rd. Subjectivity & Harmonic Impression At this point it is important to note that as we experiment with intervals (in this context) that are less prominent (audible) in the overtone series; our experience of the initial harmonic impressions become more and more subjective. I will close by describing my subjective impressions of the reciprocity between intervals other than the Perfect 5th and the Major 3rd. The Minor 3rd Interval The Minor 3rd interval - and its interval of reciprocity - the Major 6th - are still quite clear in harmonic definition (probably because of the relative modal implications we are so used to hearing in contemporary music). The Major 2nd Interval The Major 2nd interval – and its interval of reciprocity – the Minor 7th – give me the impression of being Non-Definitive. This means that the root of the harmony is not very clear. To add to the ambiguity of this situation – the character of their sound is Open and Suspended - without the feeling of ‘needing’ to be ‘resolved.’ I have found the exploration of this harmonic interval-pair fascinating over the years. In the key center of ‘C’ – the Major 2nd (‘D’) is the ‘So’ of ‘So’ ---- and the Minor 7th (‘Bb’) is the ‘Fa’ of ‘Fa.’ The Major 7th Interval The Major 7th interval – and its interval of reciprocity – the Minor 2nd – give me the impression of being Non-Definitive. This means that the root of the harmony – when either of these intervals are heard - by themselves – is not very clear. The character of their sound is Closed and Angular - with the feeling of ‘needing’ to be ‘resolved.' This suggests (to me) some form (or modality) of a Dominant Chord. In the key center of 'C' - the Major 7th ('B') is the 'tri-tone' of 'Fa' ---- and the Minor 2nd ('Db') is the 'tri-tone' of 'So.' Taken from the book: 'What Does This Have To Do With Music?' By Ben Higgins |