Pisano Periods:

The core repetitive cycles found in Fibonacci & Lucas number progressions when numbers are reduced to modulo values


Pisano Periods are explored as musical notation

ANAHATA: A=432Hz; mod9



The melodies are composed using mod9 values of Fibonacci & Lucas 24 point cycles as notes. [ cycles are transposed as loops ] The composition is taken from a construction procedure of the 24 point cycle using only one circle unit.  (diagram)

The 24 point cycle is the mod9 Pisano period of the Lucas series - from which all the remaining note values are derived.

Triangles are drawn from the 3, 6 & 9-0 values, which are used for the track's framework melody (9=0=silence)

MOD6 UK LOTTERY DRAW HISTORY(Pt2)- concept track; A=450Hz          

24mins 24secs


Tuning A=450Hz  (accommodates harmonic values & 7.5Hz earth's magnetic frequency):

mod6 pentatonic scale; F,G,A,Bb,C: numbers as notes - played in the order the numbers were drawn: Wed & Sat draws as separate tracks:

End date: Sat 10 Oct 2015 - after this date more balls were added to the draw

Start date (Pt2) Sat 29 Jan 2011 [ Pt2 track time 24min 24secs ] [ calendar time 4yrs 36wks ]

[ Pt1 Start date Sat 19 Nov 1994 ] [ Wed draw starts 1 Feb 1997 ]

[ Pt1 track time 1hr 24min 24secs ] [ calendar time 16yrs 12wks ]

LUCAS SERIES: binaural theta 7.5Hz: A=457Hz: mod 8

17min 46secs


Melody: Lucas A & Lucas B cycles (alternate values of the Lucas series; Phi ratio rising, Phi ratio falling).

Lucas Series values: Transposing to Mod 8 produces a standard scale.

The binaural 7.5Hz is the frequency of the Earth's magnetic field.

Tuning at 457Hz accommodates the OM frequency in the scale.

6 composite all

Lucas Mod9 Pisano Period: 24

Simplest method of constructing a 24 point cycle using one circle radius & six dissector lines.

One circle radius produces 12 points (A)

Six dissector lines produce 12 ALTERNATE points (B)

The original 'construct' is not discarded but retained. Using the process of alternate addition (Fibonacci - to - Lucas)  (Anahata petals?)  all Mod9 values are computed.

Extension of concept: Using Modulo 6 to compute random data

selection of AUDIO: click to play

lucas framework cycle anahata

Notice how this basic geometric figure is also the base figure for an ancient vedic symbol 'ANAHATA'. The two trikonas isolate numbers 2 & 7.

This is pertinent since the Lucas cycle is a 2-7 Fibonacci series.

TUNING MODULO 6 RETURN lucas trikonas mod9

A thorough reading of the array of trikornas within Lucas & Fibonacci reveals interesting patterns: ['Solfeggio' trikornas & Doubling - Reverse Doubling]; [Reflected & Reciprocal Arrays]

fin1-8 trikonas mod9