# Help figuring out how to use twelve-tone technique with fibonacci numbers

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I am trying to create a tonerow using the first 300 fibonacci numbers, but I need help figuring out an equation or formula to decide what tone the number would be. What I mean is:

The twelve tones would obviously be:

C-----C#-----D-----D#-----E-----F-----F#-----G-----G#-----A-----A#-----B

and I am trying to find how many times the fibonacci number would go into 12 (representing the twelve tones) EX. :

(fibonacci #s)

1) 8

C-----C#-----D-----D#-----E-----F-----F#-----G-----G#-----A-----A#-----B
*------*--------*------*-------*------*------*-------(*)

-So the fibonacci number is eight so it stops at the eighth tone which means that it is a G natural.

2) 55

C-----C#-----D-----D#-----E-----F-----F#-----G-----G#-----A-----A#-----B
*------*--------*------*-------*------*------*--------*-------*-------*-------*-------*
*------*--------*------*-------*------*------*--------*-------*-------*-------*-------*
*------*--------*------*-------*------*------*--------*-------*-------*-------*-------*
*------*--------*------*-------*------*------*--------*-------*-------*-------*-------*
*------*--------*------*-------*------*-----(*)

-So the fibonacci number is 55 so it stops at the 55th tone which in the 12 tones, is really the 7th tone, which means that it is an F sharp.

I was able to figure out the first 10 fibonacci numbers (1, 1, 2, 3, 5, 8, 13, 21, 34, 55) by just counting it out, but how do I find out higher number fibonacci numbers like:
89, 144, 233, 377, 610, 987, 1597, 17167680177565, or 222232244629420445529739893461909967206666939096499764990979600?

I am extremely appreciative of any help I can get. Thanks.
Gear:
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-Fender 70s Reissue 60th anniversary Stratocaster
-Line 6 Flextone III
-Crate RFX30 RetroFex
-Line 6 Tone Port UX1
-Roland Digital Piano HP-4500
-(other stuff)
This might sound incredibly stupid, and I'd like to point out that math was never my strong suit, but couldn't you just take that number and divide it by 12, and then that's the number of octaves up that note would be, multiply that by 12 and subtract the product by your original Fibonacci number, and then count up that many intervals from whatever note you started on (A for example)?

Edit: I guess you'd also have to divide using remainder and not decimal points for that idea to work, and I'm too lazy to check it, so apologies if I'm wrong.
Last edited by J.T.W at Feb 18, 2008,
write a formula out or count the hard way...
Quote by J.T.W
This might sound incredibly stupid, and I'd like to point out that math was never my strong suit, but couldn't you just take that number and divide it by 12, and then that's the number of octaves up that note would be, multiply that by 12 and subtract the product by your original Fibonacci number, and then count up that many intervals from whatever note you started on (A for example)?

yes, he can just divide by 12 and note the octave
Quote by kirbyrocknroll
Maybe I'm misunderstanding, but why would you multiply by 12 after determining how many octaves up the next tone is? If you divide by 12, multiply by 12, then subtract the product by the Fibonacci number you're using, wouldn't that just be 0?

All I can think of is dividing by 12 repeatedly until the quotient is 12 of less, but I haven't reached this level of math yet (the whole Fibonacci number thing). I'm just curious.

From my Grade 10 level (halfway completed) understanding, that would work, because you'd have gone that many octaves up, and therefore remain at your original note, just higher octaved. And then I actually think you'd just take your remainder and count that many tones up, in hindsight, I'm not sure why I said remultiply it, apologies for the confusion.
Quote by J.T.W
From my Grade 10 level (halfway completed) understanding, that would work, because you'd have gone that many octaves up, and therefore remain at your original note, just higher octaved. And then I actually think you'd just take your remainder and count that many tones up, in hindsight, I'm not sure why I said remultiply it, apologies for the confusion.

Ah, I misunderstood.

So for like 55. 55/12 ≈ 4.583. 4 x 12 = 48. 55 - 48 = 7. Count 7 tones in.

?
Quote by kirbyrocknroll
Ah, I misunderstood.

So for like 55. 55/12 ≈ 4.583. 4 x 12 = 48. 55 - 48 = 7. Count 7 tones in.

?

Ahh Yes! There you go! You just made me understand my own logic, far as I can tell in the middle of the night, that's correct, and you've got the gist of it.
Edit: I just checked it and unless I'm horribly misguided (in which case, someone PLEASE step in before I convince someone of something that's wrong) that's correct.

Also, I know it's probably somewhere, but as long as you're here and I'm curious, why is there orange instead of black for your name?
^ um yes, something like that
Alrite, I did the math...
1. Divide number by 12...
2. Round the quotient down to the nearest whole number
3. Write out the division and find the remainder
4. From your first note, go up a note for each remainder you have.

Take 233.
Divide by 12 = 19.4167...
Round down = 19
233/12 = 19 r5
Since your tonerow thing starts from C, go up 5 steps.
Fibonacci # 233 = F natural

In short: find the remainder and go up however many notes the remainder happens to be.

This however does not work on any fibonacci number under 12.
Last edited by Arkhimedes at Feb 18, 2008,
Quote by J.T.W
Ahh Yes! There you go! You just made me understand my own logic, far as I can tell in the middle of the night, that's correct, and you've got the gist of it.
Edit: I just checked it and unless I'm horribly misguided (in which case, someone PLEASE step in before I convince someone of something that's wrong) that's correct.

Also, I know it's probably somewhere, but as long as you're here and I'm curious, why is there orange instead of black for your name?

Oh, thanks

It's orange because I delete spam in the comments sections in articles. Known as Column Cleaners/ Column Fags/ Shit Shovelers, etc.

http://ultimate-guitar.com/forum/showgroups.php?
Quote by kirbyrocknroll
Oh, thanks

It's orange because I delete spam in the comments sections in articles. Known as Column Cleaners/ Column Fags/ Shit Shovelers, etc.

http://ultimate-guitar.com/forum/showgroups.php?

I see, thanks for explaining that to me .
Just don't even call them Column Cleaners, pick on of the other names he suggested.
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I would recommend stopping the sequence shorter and repeating it if you're actually using this for a song. It could be a pretty cool sounding riff...though I wouldn't know without trying it...which I think I will later today.
Quote by Arkhimedes
Alrite, I did the math...
1. Divide number by 12...
2. Round the quotient down to the nearest whole number
3. Write out the division and find the remainder
4. From your first note, go up a note for each remainder you have.

Take 233.
Divide by 12 = 19.4167...
Round down = 19
233/12 = 19 r5
Since your tonerow thing starts from C, go up 5 steps.
Fibonacci # 233 = F natural

In short: find the remainder and go up however many notes the remainder happens to be.

This however does not work on any fibonacci number under 12.

I forgot waht a remainder is....
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-Roland Digital Piano HP-4500
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Quote by LoneWanderer13
I would recommend stopping the sequence shorter and repeating it if you're actually using this for a song. It could be a pretty cool sounding riff...though I wouldn't know without trying it...which I think I will later today.

lol, no its not going to be a "riff", it is atonal music, it's a contemporary classical composition.
http://en.wikipedia.org/wiki/Atonality
http://en.wikipedia.org/wiki/Tone_row
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Quote by fas11030
I forgot waht a remainder is....

A remainder would be how mnay you have left over if your number doesn't go cleanly into the other one. For example, if I was dividing 25 by 12 I would have a remainder of 1 since 12 would go into it twice (24) and I'd still have one left over to get to 25.
Quote by J.T.W
A remainder would be how mnay you have left over if your number doesn't go cleanly into the other one. For example, if I was dividing 25 by 12 I would have a remainder of 1 since 12 would go into it twice (24) and I'd still have one left over to get to 25.

I still dont get what you mean, so 25/12=2.0833333333333333... , so where do you get the 1 from??? _lol sorry, i'm really stupid when it comes to math...
Gear:
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-Fender 70s Reissue 60th anniversary Stratocaster
-Line 6 Flextone III
-Crate RFX30 RetroFex
-Line 6 Tone Port UX1
-Roland Digital Piano HP-4500
-(other stuff)
25/12 = 2.xxx
You multiply the 12 by the 2, and see what comes out of there (24)
You take 25 and substract the 24.
You get 1.
You could also multiply everything besides the whole number (so the 0.08333 in this case) by 12.
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yea, theres an entire function devoted to giving the remainder in this way, modulo. so
14 mod 12 = 2 12 mod 12 = 0 (could be taken as 12). wiki modulo or something, basically its just the remainder when dividing by 12
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can anyone explain what this means? I just read the first post and it's incredibly confusing.
Quote by Spamwise
can anyone explain what this means? I just read the first post and it's incredibly confusing.

The twelve-tone technique is a way of writing atonal music. It attempts to avoid creating any tonal center or key whatsoever.
Someones knowledge of guitar companies spelling determines what amps you can own. Really smart people can own things like Framus because they sound like they might be spelled with a "y" but they aren't.
Quote by Archeo Avis
The twelve-tone technique is a way of writing atonal music. It attempts to avoid creating any tonal center or key whatsoever.

wouldn't that sound utterly horrible??
Quote by linfield44
wouldn't that sound utterly horrible??

Used tastefully, there's no reason it would have to sound terrible. Though in most situations, I'd agree with you.
Someones knowledge of guitar companies spelling determines what amps you can own. Really smart people can own things like Framus because they sound like they might be spelled with a "y" but they aren't.
Quote by Archeo Avis
Used tastefully, there's no reason it would have to sound terrible. Though in most situations, I'd agree with you.

how does it work? i tried understanding the responses to the thread, but i don't understand how it's used, or how it works, or even what it is.
Quote by linfield44
how does it work? i tried understanding the responses to the thread, but i don't understand how it's used, or how it works, or even what it is.

I'll let someone else answer that. I'm not entirely familiar with the system.
Someones knowledge of guitar companies spelling determines what amps you can own. Really smart people can own things like Framus because they sound like they might be spelled with a "y" but they aren't.
Quote by linfield44
wouldn't that sound utterly horrible??

you need to be able to understand it and it takes a lot to reach a frame of mind where you can really appreciate what it is. It is very complicated and it would be easier to get if you study primarily classical and contemporary classical composition. I think that a lot of atonal music sounds good, but a lot of it is pretty bad as well, but in tonal music, there is a lot that sounds good, but there sure is a ton of it that sounds like crap. When dealing with atonal music, you need to reach a certain way of thinking which is very difficult to achive and sometimes it takes many years to reach this point. And also, just because a peice of music sounds "bad", it does not mean that it is a "bad" composition, and vise versa.
Gear:
-Brownsville BMAG3 (acoustic)
-Fender 70s Reissue 60th anniversary Stratocaster
-Line 6 Flextone III
-Crate RFX30 RetroFex
-Line 6 Tone Port UX1
-Roland Digital Piano HP-4500
-(other stuff)
Quote by fas11030
you need to be able to understand it and it takes a lot to reach a frame of mind where you can really appreciate what it is. It is very complicated and it would be easier to get if you study primarily classical and contemporary classical composition. I think that a lot of atonal music sounds good, but a lot of it is pretty bad as well, but in tonal music, there is a lot that sounds good, but there sure is a ton of it that sounds like crap. When dealing with atonal music, you need to reach a certain way of thinking which is very difficult to achive and sometimes it takes many years to reach this point. And also, just because a peice of music sounds "bad", it does not mean that it is a "bad" composition, and vise versa.

Any specific pieces you could recommend? I'd really like to incorporate this into a composition somehow.
Someones knowledge of guitar companies spelling determines what amps you can own. Really smart people can own things like Framus because they sound like they might be spelled with a "y" but they aren't.
Quote by Archeo Avis
Any specific pieces you could recommend? I'd really like to incorporate this into a composition somehow.

Arnold Schoenberg was the first person to use this technique, so any of his later works you should look at, anton webern is a follower of schoenberg, so you should take a look at some of his music, some igor stravinsky, karlheinz stockhausen, some bela bartok.
Gear:
-Brownsville BMAG3 (acoustic)
-Fender 70s Reissue 60th anniversary Stratocaster
-Line 6 Flextone III
-Crate RFX30 RetroFex
-Line 6 Tone Port UX1
-Roland Digital Piano HP-4500
-(other stuff)
anyway, sorry, I hate to be like this but I still don't understand how to do this calculation and everything with the remainder, etc. to find out what I'm looking for...
Gear:
-Brownsville BMAG3 (acoustic)
-Fender 70s Reissue 60th anniversary Stratocaster
-Line 6 Flextone III
-Crate RFX30 RetroFex
-Line 6 Tone Port UX1
-Roland Digital Piano HP-4500
-(other stuff)
Quote by fas11030
anyway, sorry, I hate to be like this but I still don't understand how to do this calculation and everything with the remainder, etc. to find out what I'm looking for...

Ok, so let's 1597 as an example. Divide that by 12. You get 133.0833333333. Round that down to 133 and multiply that by 12. You get 1596 subtract that from 1597 and you get 1, so you have one semi-tone left over. Assuming you started at A you are now at an a 1597 octaves up, and one semi tone higher, and an A#.
So, if X=the origional fibonacci number and Y=the number tone (of the twelve) in the chromatic scale, then to find out what tone it is, the formula/equation would be:

(round(X/12))12-X=Y

is that right?
Gear:
-Brownsville BMAG3 (acoustic)
-Fender 70s Reissue 60th anniversary Stratocaster
-Line 6 Flextone III
-Crate RFX30 RetroFex
-Line 6 Tone Port UX1
-Roland Digital Piano HP-4500
-(other stuff)
Well, if you did it that way, you'd get the negative number of steps into the chromatic scale. It's the original Fibonacci number (x) minus the (12 times the rounded number).

x - [x/12 (round)]12 = number of tones in.

55 - [55/12 (round)]12

55 - [4]12

= 55-48

=7. Count seven steps in.
EDIT: This is to answer spamwise's question

The Fibinocci sequence is a system of counting where you add each number to the one preceding it. Like this

1 1 2 3 5 8 12 21

1 + 1 = 2
2+ 1 = 3
3+ 2 = 5
5 + 3 = 8

et cetera.

What this character is attempting to do is to create an arbitrary mathematical basis for a melody, similar to the works of Iannis Xenakis.

Actually, @ TS:

Check your local (or university) library for a copy of "Formalized Music' by Iannis Xenakis. He was a 20th century Greek composer with all kinds of crazy ideas like this. He may have actually done something with Fibinocci numbers, but I don't really remember.
No worries, though. If he did, it was probably done with harmonic frequencies rather than tones, so I think you're in little danger of being reduntant.
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Last edited by Rebelw/outaCord at Feb 18, 2008,
Quote by kirbyrocknroll
Well, if you did it that way, you'd get the negative number of steps into the chromatic scale. It's the original Fibonacci number (x) minus the (12 times the rounded number).

x - [x/12 (round)]12 = number of tones in.

55 - [55/12 (round)]12

55 - [4]12

= 55-48

=7. Count seven steps in.

So, if X=the origional fibonacci number and Y=the number tone (of the twelve) in the chromatic scale, then to find out what tone it is, the formula/equation would be:

X-(round(X/12))12=Y

is that right?
Gear:
-Brownsville BMAG3 (acoustic)
-Fender 70s Reissue 60th anniversary Stratocaster
-Line 6 Flextone III
-Crate RFX30 RetroFex
-Line 6 Tone Port UX1
-Roland Digital Piano HP-4500
-(other stuff)
Quote by fas11030
So, if X=the origional fibonacci number and Y=the number tone (of the twelve) in the chromatic scale, then to find out what tone it is, the formula/equation would be:

X-(round(X/12))12=Y

is that right?

Well, since no one has corrected me, I'll go ahead and say yes. I don't know if "[round(X/12)]" is the proper notation though
Quote by kirbyrocknroll
Well, since no one has corrected me, I'll go ahead and say yes. I don't know if "[round(X/12)]" is the proper notation though

by this equation,
(fibonacci #)=(# tone in chromatic scale)
1=1
2=12
3=12
13=1
21=-3
55=-5

and that is all wrong except for 1 and 13.
Gear:
-Brownsville BMAG3 (acoustic)
-Fender 70s Reissue 60th anniversary Stratocaster
-Line 6 Flextone III
-Crate RFX30 RetroFex
-Line 6 Tone Port UX1
-Roland Digital Piano HP-4500
-(other stuff)
Try this:

X= an interger > 12
y= fib. number you need to find a tone for
z= actual pitch

z= y - (y/x, rounded down)(x)

so to find the pitch for 34, we'd divide 34 by 12. Answer rounds down to 2. 2 x 12 = 24. 34 - 24 = 10. Pitch is 10.

For 55:
55 / 12 rounded down = 4
12 x 4 =48
55 - 48 = 7
pitch = 7
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I suggest not screwing with the UGer with the best name on the site.

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Quote by fas11030
by this equation,
(fibonacci #)=(# tone in chromatic scale)
1=1
2=12
3=12
13=1
21=-3
55=-5

and that is all wrong except for 1 and 13.

55 - (55/12)12

55 - (4.583)12

55 - (4)12

55 - 48 = 7. How'd you get -5? And yeah, doesn't work for x<12.
Arnold Schoenberg was the first person to use this technique, so any of his later works you should look at, anton webern is a follower of schoenberg, so you should take a look at some of his music, some igor stravinsky, karlheinz stockhausen, some bela bartok.

Shoenberg actually wasn't the first to use serialistic composition methods. Alexander Scriabin, the post-romantic composer who's output was about 5orchestral works and over 200 piano pieces, including 10 sonatas and a number of popular tone poems, was the first. In fact, Scriabin is named "the father of the modern musician" (much like Schoenberg is called "the father of modern music" because of his pioneering in harmony and atonality, to which he preceded everyone else by some 5 to 10 years. In Schoenberg's defense though, Scriabin's serliaistic works were not dodecaphonic and Schoenberg was the first to create a system that eliminates melodic and harmonic pull. As far as I know, Stravinsky never composed using Schoenberg's twelve tone row system, the same goes for Bela Bartok, who composed a number of atonal pieces, but if I remember correctly none were dodecaphonic.

Any specific pieces you could recommend?

The majority of Schoenberg's output in the beginning of his compositional career are an extension of Wagner's chromatic innovations, but after that he went off the dodecaphonic deep-end and stayed there almost to the end. Apparently, and though I have never heard them, a few of his last works are not dodecaphonic and revert back to what is closer to his earlier style. So search the middle period. His acolytes all followed similar developments in there lives (As previous mentioned, Anton Webern, but also Alban Berg.)

Here is a piece by Anton Webern, a set of piano variations.

I must admit though, I am no fan of dodecaphony and find it very hard not to laugh while I listen to that recording.
Last edited by Erc at Feb 18, 2008,
Quote by Rebelw/outaCord
Try this:

X= an interger > 12
y= fib. number you need to find a tone for
z= actual pitch

z= y - (y/x, rounded down)(x)

so to find the pitch for 34, we'd divide 34 by 12. Answer rounds down to 2. 2 x 12 = 24. 34 - 24 = 10. Pitch is 10.

For 55:
55 / 12 rounded down = 4
12 x 4 =48
55 - 48 = 7
pitch = 7

wait, do you round down, or do you round to the nearest whole number?
Gear:
-Brownsville BMAG3 (acoustic)
-Fender 70s Reissue 60th anniversary Stratocaster
-Line 6 Flextone III
-Crate RFX30 RetroFex
-Line 6 Tone Port UX1
-Roland Digital Piano HP-4500
-(other stuff)