Fibinacci Numbers

Musical Notation

If a crotchet is taken as lasting for one beat, then the semibreve is 4 beats , the minim 2, a quaver ¹/₂, a semiquaver ¹/₄ and demi-semiquaver is ¹/₈. They are written in musical notation as shown here:

Note	Symbol	Duration (beats)
Semi-breve		4
Minim		2
Crotchet		1
Quaver		1/2
Semiquaver		1/4
Demisemiquaver		1/8

A dot is placed after a note to add on one half of its value. So a dotted crotchet is a crotchet plus a quaver and has a duration of 1·5 time units; two dots after a crotchet give a duration of 1 + 1/2 + 1/4 = 1·75 units.

F.J Budden in An Introduction to Number Scales and Computers, Longmans, 1965, page 65, says he thinks the record number of dots is 4 in Verdi's Requiem in the Rex Tremenda. It is useful when a long note is followed by a quick note and the next note is "on the beat".

Binary fractions are written using column headings as follows:

   ... 8  4  2  1   ·  1/2  1/4  1/8 ...

So 1/4 = 0·01₂ and 3/8 = 0·011₂ since it is 1/4+1/8.

In binary, a dot after a crotchet adds a one in a fractional column:

crotchet = 1
crotchet dot = 1·1₂
crotchet dot dot = 1·11₂
crotchet dot dot dot = 1·111₂

and so on.