The Octavarium theme.
(analysis of number symbolism by Jos Durkstra)
1985 the year Dream Theater began, Octavarium = album # 8, DT = 5 musicians
C A G F - C Ab G F - C A G F G - F G Ab Bb C Db
C A G F - C Ab G F - C A G F G - F G Ab Bb C Db (F (Octave higher)).
The theme consists of totally 8 motifs. The first 2 (closely related) motifs add up to 8 notes. The 3rd has 5 notes.The 4th has 6 but the 4th motif of the repeat has seven and 6 + 7 = 13: the 6th number in the Fibonacci-series. By the way: the scale degrees of the 4th motif (F G Ab Bb C Db) add up as follows: 1 + 2 + 3 + 4 + 5 + 6 = 21, the seventh number in the Fibonacci-series and the last to be used! Thus the 4th (last) motif which appears twice (2 x 4 = 8 ) stands for the 2 last Fibonacci-numbers used.
This is also interesting in the way that the 7th scale degree is the only one missing in the entire theme…..which spans 8 scale degrees (octave) 8 being the 5th number in the Fibonacci-series.
The first motif consists of the following scale-degrees: 5-3-2-1.
These represent the first four numbers of the Fibonacci-series: 1-2-3-5-8-13-21-etc. in which every number is the sum of the preceding two.
It appears 3 times (major, minor, major: thus emphasizing on the third degree) and these 3 appear 2 times because of the repeat.
All in all the motif is played 6 times but the sum of the numbers 3 (appearances) + 2 (repeats) equals 5.
The sums of the motif’s first three (!) notes' scale degrees equal:
8 (5+3) 5 (3+2) 3 (2+1)
So what about this 3?Could it stand for the third scale degree which totally appears 8 (!) times? It is also 8 – 5.
Let’s have a look at the number of appearances of every scale degree:
8 x F (1)10 x G (2) 4 x Ab (b3) 4 x A (3) 2 x Bb (4) 8 x C (5) 2 x Db (6) 1 x F 8va (8)
The 3rd scale degree appears 8 (4 major, 4 minor) times.
The 5th scale degree appears 8 times.
The 1st scale degree appears 8 times and the 8th scale degree appears 1 time which creates a kind of mirror image.
The degrees appearing 8 times are 1, 3, 5 and represent the triad of F, the key in which the album starts and ends: cycle complete.
21 is the highest number in the Fibonacci-series used. If I add up all numbers of the series including this highest number I get 1+2+3+5+8+13+21=53 of which the digits add up to 8 !
8 to the 5th power = 32768. 3+2=5 7+6=13 8+0=8 (duh): the additions of the digits not being 8 give me the two Fibonacci numbers surrounding 8 !
The theme also consists of 39 notes which has nothing to do with the Fibonacci-series whatsoever……..anyone? ;-) Now let’s look closer at Octane…..
Jos Durkstra 15 oktober 2006