Wednesday, November 02, 2005

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:
NoteSymbolDuration
(beats)
Semi-breve4
Minim2
Crotchet1
Quaver1/2
Semiquaver1/4
Demisemiquaver1/8
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.