The Fundamental Principles of Harmony

After 'Les éléments essentiels de la musique', behold 'The Fundamental Principles of harmony" which completes and gives a résumé of my harmonics teaching practice - a legacy of my teacher Nadia Boulanger.
Throughout my long experience, I have asserted that the current 'on paper' harmonics teaching, with the four traditional keys, often is an obstacle to the majority of pupils that neither have a sufficient level of music reading nor the internal pitch, that would permit them to imagine the sounds. Should those pupils thus be excluded from the knowledge of harmonics, which would provide a better understanding of music and help them develop their sense of hearing Nadia Boulanger attached great importance to harmonics on the keyboard with the praxis of harmonic progressions and the 'Vidal basses', which I use to help pupils acquire and develop the reflexes, which connect hearing with musical thinking and its mental and digital formulation. I therefore dedicate the first chapter of this book of mine to the introduction to harmonics on the keyboard, before switching over to the laws that rule tonal writing by means of some simple principles, based on a particular concept of melody, as regards harmonics and their relatedness to intervals.