PIL Sauveur ÷ Nombre d’or

Produit Indice Logarithmique [ 0.301 ÷ 1.618 = 0.18603213844 ]


Un exemple avec [C2] 65.406 Hz

65.406 Hz [C2] * 0.18603213844 = 12.1676180468 [ constante (K) fréquentielle (Hz) du PIL ]

f substrat * 0.18603213844 = Kf


Formulation

(65.406 * 0.301) /1.618 + 65.406 = 77.573618047 Hz 


Échelle exponentielle dérivée

 

f° + ( Kf  * 1, 2, 3….., et ainsi…)

65.406 + (12.1676180468 * 1) = 77.5736180468 Hz ~ (1200 * log(77.5736180468 / 65.406)) / log(2) = 295 ∆ = cents

65.406 + (12.1676180468 * 2) = 89.7412360936 Hz ~ (1200 * log(89.7412360936 / 65.406)) / log(2) = 548

65.406 + (12.1676180468 * 3) = 101.90885414 Hz ~1200 * log(101.90885414 / 65.406)) / log(2) = 768

65.406 + (12.1676180468 * 4) = 114.076472187 Hz ~ (1200 * log(114.076472187 / 65.406)) / log(2) = 963  

65.406 + (12.1676180468 * 5) = 126.244090234 Hz ~ (1200 * log(126.244090234 / 65.406))/ log(2) = 1138

65.406 + (12.1676180468 * 6) = 138.411708281 Hz ~ (1200 * log(138.411708281 / 65.406)) / log(2) = 1298 ∆

65.406 + (12.1676180468 * 7) = 150.579326328 Hz ~ (1200 * log(150.579326328/65.406)) / log(2) = 1144 ∆

65.406 + (12.1676180468 * 8) = 162.746944374 Hz ~ (1200 * log(162.746944374 / 65.406)) / log(2) = 1578 ∆

65.406 + (12.1676180468 * 9) = 174.914562421 Hz ~ (1200 * log(174.914562421 / 65.406)) / log(2) =1703

65.406 + (12.1676180468 * 10) =187.082180468 Hz ~ (1200 * log(187.082180468 / 65.406)) / log(2) = 1819

65.406 + (12.1676180468 * 11) =199.249798515 Hz ~ (1200 * log(199.249798515 / 65.406)) / log(2) = 1929 ∆

65.406 + (12.1676180468 * 55) = 734.624992574 Hz ~ (1200 * log(734.624992574 / 65.406))/ log(2)

= 4187.41570383 ∆  [espace frontière flottante]

Réalité sonore

Audio

Déploiement résiduelle Fibonacci / Sauveur

Audio


Cents & Suite de Fibonacci

Audio

Et encore une autre formulation…


⇔ Anexo J. Sauveur


MuseScore