Harmonic Series and the Number 7

something interesting I discovered. It's probably not anything significant and I'm just reading into it too much... but take a look if you will.

The first 7 distinct iterations of the harmonic series (an octave and 6 consecutive perfect fifths), starting on F, are:
F - (F) - C - G - D - A - E - B
If you number then diatonically (in the Lydian mode)
you get
1 - (8) - 5 - 2 - 6 - 3 - 7 - 4

let's condense it.....18526374
remember that sequence...

Now let us take the first 100 multiples of 7 (7 + 7 + 7 etc....)
This gives us 100 sums, let us arrange them in a 10x10 pattern.

007, 014, 021, 028, 035, 042, 049, 056, 063, 070,
077, 084, 091, 098, 105, 112, 119, 126, 133, 140,
147, 154, 161, 168, 175, 182, 189, 196, 203, 210,
217, 224, 231, 238, 245, 252, 259, 266, 273, 280,
287, 294, 301, 308, 315, 322, 329, 336, 343, 350,
357, 364, 371, 378, 385, 392, 399, 406, 413, 420,
427, 434, 441, 448, 455, 462, 469, 476, 483, 490,
497, 504, 511, 518, 525, 532, 539, 546, 553, 560,
567, 574, 581, 588, 595, 602, 609, 616, 623, 630,
637, 644, 651, 658, 665, 672, 679, 686, 693, 700.

Notice anything?
All of the numbers in each column share the same number in the ones place that is unique to each column.
The first column is 7, then 4, then 1, 8, 5, 2, 9, 6, 3.
If we assign each number to it's diatonic equivalent in the F Lydian scale we get.
741852963 (this is the harmonic series,
bear in mind 8 = 1, and 9 = 2. 18526374) it just starts on the 7

Now look at the descending numbers in the tens column from left to right. The diatonically numbered sequence is approximately the harmonic series.

Here is the multiples chart with their numbers changed to musical notes. (1 and 8 both equal F, 2 = G, 3 = A, and so on...)
we are looking for FCGDAEB, think of it as a crossword puzzle.

,__E,__FB,__GF,__GF,__AC,__BG,__BG,__CD,__DA,__E_,
,_EE,__FB,__GF,__GF,_F_C,_FFG,_FFG,_FGD,_FAA,_FB_,
,FBE,_FCB,_FDF,_FDF,_FEC,_FFG,_FFG,_FGD,_G_A,_GF_,
,GFE,_GGB,_GAF,_GAF,_GBC,_GCG,_GCG,_GDD,_GEA,_GF_,
,GFE,_GGB,_A_F,_A_F,_AFC,_AGG,_AGG,_AAD,_ABA,_AC_,
,ACE,_ADB,_AEF,_AEF,_AFC,_AGG,_AGG,_B_D,_BFA,_BG_,
,BGE,_BAB,_BBF,_BBF,_BCC,_BDG,_BDG,_BED,_BFA,_BG_,
,BGE,_C_B,_CFF,_CFF,_CGC,_CAG,_CAG,_CBD,_CCA,_CD_,
,CDE,_CEB,_CFF,_CFF,_CGC,_D_G,_D_G,_DFD,_DGA,_DA_,
,DAE,_DBB,_DCF,_DCF,_DDC,_DEG,_DEG,_DFD,_DGA,_E__.
(copy and paste this into a text editor and change the font to "courier new")

The harmonic series is all over this. Please help me find out why!

Well, everyone knows that there is a definite connection between math and music.

Think simple, A = 440hz. We all know that. That is what a tuning fork is. No, it isn't just one number.

Every half tone, i.e. A to A# is the same. 12 √ 2. (That's something I just researched. ) So moving in semi tones, if you start at A, you have 440. A# would be 440 x (12 √ 2). B would be, 440(440(12 √ 2)). If you do that 12 times you'll get back to A, only an octave higher, 880.

That was just tuning your instrument. Take it a step further. Think scales. Why do they sound different? Intervals. We know that. What are intervals? They are ratios.

Take C Major:

C D E F G A B C







C D E F G A B C 

1 2 3 4 5 6 7 8

Obviously the numbers are degrees. Let's compare two scales in C Major:

C Ionian:



C D E F G A B C 



D Dorian



D E F G A B C D

C Ionian is C to D to E to F etc...

That's 1 to 2 to 3 etc...

D Dorian is D to E to F to G etc...

That's 2 to 3 to 4 to 5 etc...

Simple ratios. Even using the same numbers, you will have a different result. Take 1 and 2.

1:2 = 0.5 but 2:1 = 2.0

 C          D          E           F         . . .

1:1 = 1.0, 1:2 = 0.5, 1:3 = 0.33, 1:4 = 0.25 . . .

 D          E          F           G         . . .

2:1 = 2.0, 2:2 = 1.0, 2:3 = 0.66, 2:4 = 0.5  . . .

 E          F          G          A          . . .

3:1 = 3.0, 3:2 = 1.5, 3:3 = 1.0, 3:4 = 0.75  . . .

 F          G          A           B         . . .

4:1 = 4.0, 4:2 = 2.0, 4:3 = 1.33, 4:4 = 1.0  . . .

 G          A          B           C         . . .

5:1 = 5.0, 5:2 = 2.5, 5:3 = 1.66, 5:4 = 1.25 . . .

 A          B          C          D          . . .

6:1 = 6.0, 6:2 = 3.0, 6:3 = 2.0, 6:4 = 1.5   . . .

 B          C          D           E         . . .

7:1 = 7.0, 7:2 = 3.5, 7:3 = 2.33, 7:4 = 1.75 . . .

 C          D          E           F         . . .

1:1 = 1.0, 1:2 = 0.5, 1:3 = 0.33, 1:4 = 0.25 . . .

1:2 = 2:4. That doesn't need explaining.

As for the rest, you can clearly see the circular patterns that start. That explains why you don't need actual notes to explain modes. That also explains why every mode is the same in every key. The ratios within the intervals are the same.

But you see my point. The scales are different, because the ratios within the scales are different even though they contain the same notes/numbers.

Chords, needless to say, are the same as far as intervals.

Therefore, it doesn't surprise me at all, that you discovered this. Music operates via mathematical operatorations. If you break it down, it is really logical and common sense based.

I know I didn't really answer your question, but I hope you know see the connection with math and music and maybe you will discover the perfect equation for harmonics.

Rock on!

*KA-BOOM!!!!!!!*

@Venom,

Was that the sound of my head exploding?

@LA and GS,

While I don't fully understand what you guys are talking about I am extremeley impressed by both of you and your knowledge of theory. It was math that got me interested in theory to begin with.

Has either of you done any research on fractal theory applied to music? Or any other algorithmic applications? Very interesting stuff.

Never heard of Fractal Theory applied to music. However, Pythagorus, whom I am sure you've heard of was very much into fractions in music. Which is pretty much the whole ratio thing I mentioned above.

I love math and I love music. To me they seem to go hand in hand. I believe that if you can understand one you can understand the other and that you can use each one to better understand both.

Music emerges from physics. Physics is based on math.

Umm... 1+2... goddamit...