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[Ronny]

mikepecchio wrote on Thu, 01 December 2005 01:33

tweakman wrote on Tue, 29 November 2005 17:19 If you want to comply with Fibonacci it would be: where can we get some reverse-fibonacci taper pots? mike p

Mapleshades has some for sale.

[hmm...]

I am fascinated every time Fibonacci series comes up...but seems very different than music frequencies.

At first blush:

music frequencies beat...and repeat.  musically related frequencies are multiples of each other...so they, at some point, create energy at the same point in time.  

100 hz = vibrating 100 times per second.
200 hz = vibrating 200 times per second.

If my very basic understanding of music is correct:

Energy from the vibrations from these two sources will occur at same point in time on every other 'beat' of the vibration (of the 100 hz source).

Fibonacci...not repeating....not multiples of each other

Fibonacci will have to be applied in another way to help out our music...

Obviously Chowning found something else out...

[dcollins]

jimmyjazz wrote on Wed, 30 November 2005 20:30

I realize you're looking at composition, but the same might hold in music theory -- perhaps other ratios than those based on the Golden Mean might be more pleasing.  Likely 1/IV/V, as Fibes suggests!

I can't believe the discussion has gone this far without mention of the great marketing genius George Cardas.  His cables are all based on Phi, whether electricity cares, or not!

 http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1&Sec  t2=HITOFF&d=PALL&p=1&u=/netahtml/srchnum.htm& ;amp  ;r=1&f=G&l=50&s1=4628151.WKU.&OS=PN/4628151& amp; amp;RS=PN/4628151

DC

[Ronny]

hmm wrote on Fri, 02 December 2005 23:31

I am fascinated every time Fibonacci series comes up...but seems very different than music frequencies. At first blush: music frequencies beat...and repeat.  musically related frequencies are multiples of each other...so they, at some point, create energy at the same point in time.   100 hz = vibrating 100 times per second. 200 hz = vibrating 200 times per second. If my very basic understanding of music is correct: Energy from the vibrations from these two sources will occur at same point in time on every other 'beat' of the vibration (of the 100 hz source). Fibonacci...not repeating....not multiples of each other Fibonacci will have to be applied in another way to help out our music... Obviously Chowning found something else out...

Fibonacci deals with sequence, many scales see it repeat, especially some Asian scales that use 1/4 and 1/3 tones, as opposed to western scales. This isn't voodoo science, it's just mathematics, same as hertz sequences that are harmonically consonant. For example your 100Hz to 200Hz, is a perfect octave. The next octave isn't 300Hz, it's another doubling to 400Hz, than again to 800Hz, 1600Hz etc. It's merely a ratio that applies to many things in nature.

Here's a basic article that will help you understand, but keep in mind that there are many more scales than the typical western scales that we deal with, used in other countries, that aren't based solely on half/whole 12 tone chromatic scale.

http://www.bikexprt.com/tunings/fibonaci.htm  

[dcollins]

Ronny wrote on Fri, 02 December 2005 22:22

Fibonacci deals with sequence, many scales see it repeat, especially some Asian scales that use 1/4 and 1/3 tones, as opposed to western scales.

Hi Ronny,
 
The Fibonacci "sequence" has nothing to do with musical intervals or scales.

It just means you add the last two values to get the next.

1, 1, 2, 3, 5, 8, 13 a bazzilion, etc.

Nature seems to like it, but no real connection to music.

Look to 2^12 for westerners.

DC

[Jerry Tubb]

Been watching this thread for a few days and here's my 2 cents.

Years ago when I was in graduate school, we studied the Golden Ratio, Section, Mean, etc. as relating to music.

In Formal considerations of some classical music (Sonata Allegro?), the recapitulation to the Main Theme would often occur approximately at the Golden Section (.618), into the piece.

The obvious analogy in nature is the Nautilus shell (B&W?).

In visual art the Golden Section would often be the focal point of the scene.


Actually the Fibonacci Series does hold true in the lower part of the series (1, 2, 3, 5, 8 ), as relating to music.

1 = A 110Hz (1 x 110)

2 = A 220Hz (2 x 110)

3 = E 330 Hz  (3 x 110)

5 ~ C# 550 Hz  (5 x 110)

8 = A 880 Hz  (8 x 110)

Which is a big A Major chord, but the numbers relating to frequency and pitch get a little wiggly after that. Also could apply to the harmonic series.

For more info consult:  http://www.golden-section.de.vu/

How this would apply to Equalization Frequencies (combination tones...110+220=330, 220+330=550?) or Compression Ratios (1.618:1?) in mastering I dunno !

Cheers

[Bobro]

"Seems like there is something there besides the simple fundamental/harmonic relationship of sounds."

If you change that to something beyond the simple fundmental/harmonic relationships, you've got the foundation of most musics of the world right there in the first partials of the (harmonic) overtone series. 1:1 (tone center), 1:2 (octave, reinforces tonal center) 2:3 (perfect fifth, a hair sharp of the equal tempered fifth).

The fourth is at 3:4 but that's no longer in the Fibonnacci series- 3:5 (major sixth pretty far from equal temperament) would be the next Fibonnacci number, then 5:8 (the purest minor sixth), then 8:13, a neutral sixth, then 21/13 etc., it gets fairly piquant quickly (but still "pure", being integer relationships, not irrational proportions like equal temperament).

There's a tremendous amount of Fibonacci stuff done in music, from synthesized Golden Mean overtone series for wavetable synthsesis and scanning fractals in multiple dimensions for wave terrain synthesis to overall form based on the Golden Mean.

What's audible or actually pertinent on a "natural" level so to speak is a whole other question.

-Bobro

[Ronny]

dcollins wrote on Sat, 03 December 2005 01:55

Ronny wrote on Fri, 02 December 2005 22:22 Fibonacci deals with sequence, many scales see it repeat, especially some Asian scales that use 1/4 and 1/3 tones, as opposed to western scales. Hi Ronny,   The Fibonacci "sequence" has nothing to do with musical intervals or scales. It just means you add the last two values to get the next. 1, 1, 2, 3, 5, 8, 13 a bazzilion, etc. Nature seems to like it, but no real connection to music. Look to 2^12 for westerners. DC

I know a few conductors that would argue that point with you. The sequence does repeat in diatonic scale, but as I said earlier you'll see it more with non-western scales such as, older pre-Pythagorean Greek scales, Pelog and Selandro scales, some Japanese scales, the buzuki is one instrument that is scaled using quarter tones. The 12 tone chromatic scale doesn't have enough tones to make it extremely relative, although it is visible on the 5, 7, 12 in a diatonic scale, but a lot depends on the temprament and it doesn't stay accurate with equal temprament for long. Speaking of the buzuki, it does sound out of tune until you get used to it and took me over a year before I could even tolerate it, when I lived on Okinawa, but there is a whole nother world out there in non-western scales, that many people in the US don't hear or aren't aware of where the sequence is seen more.

As far as utilizing it for eq settings, I don't take much stock in it, as all material is different and wouldn't suggest that anyone would actually benefit by eq'ing on any sequence, but some processors utilize it as an option, such as Anatares AT 4, which allows 19, 24, 31 and 53 tone scales. There was a special  awhile back on the Discovery channel, where they related Greek and Roman architecture and the later Roman cathedrals, to the same sequence in harmonic scales, all defined by Fibonacci's sequence in the 13th century.    

[Ethan Winer]

Ronny,

> As far as utilizing it for eq settings, I don't take much stock in it, as all material is different and wouldn't suggest that anyone would actually benefit by eq'ing on any sequence <

I agree. To me the main uses for EQ (both mixing and mastering) are LF shelf cut thinning, HF shelf boost brightening, and parametric notch cutting to eliminate specific problematic resonances. The last one is very important, and depends entirely on the physical characteristics of the specific instrument. (And the room too if that's the cause of the resonances.)

--Ethan

[dcollins]

Ronny wrote on Sat, 03 December 2005 06:10

I know a few conductors that would argue that point with you. The sequence does repeat in diatonic scale, but as I said earlier you'll see it more with non-western scales such as, older pre-Pythagorean Greek scales, Pelog and Selandro scales,

As they say on Car Talk, I'm going to "officially distance" myself from my earlier claim.  I know there have been compositions that intentionally used the series, but this is kind of interesting:

http://www.bikexprt.com/tunings/fibonaci.htm

Nothing about music, but some very interesting stuff:

http://mathworld.wolfram.com/FibonacciNumber.html

WENSLEYDALE:
   Oh, I thought you were complaining about the bouzouki player.
MOUSEBENDER:
   Oh, heaven forbid. I am one who delights in all manifestations of the Terpsichorean muse.

DC

[Ronny]

dcollins wrote on Sat, 03 December 2005 19:31

Ronny wrote on Sat, 03 December 2005 06:10 I know a few conductors that would argue that point with you. The sequence does repeat in diatonic scale, but as I said earlier you'll see it more with non-western scales such as, older pre-Pythagorean Greek scales, Pelog and Selandro scales, As they say on Car Talk, I'm going to "officially distance" myself from my earlier claim.  I know there have been compositions that intentionally used the series, but this is kind of interesting: http://www.bikexprt.com/tunings/fibonaci.htm Nothing about music, but some very interesting stuff: http://mathworld.wolfram.com/FibonacciNumber.html WENSLEYDALE:    Oh, I thought you were complaining about the bouzouki player. MOUSEBENDER:    Oh, heaven forbid. I am one who delights in all manifestations of the Terpsichorean muse. DC

If you arrange your cd blanks in a Fibonacci rack when you bake them in your car, you'll get less C1's.