Ukulele Experiment.

J

jnicholes

Well-known member
Joined
Mar 18, 2019
Messages
261
Reaction score
6
Hello,

So, I learned something about the Ukulele today I wanted to share.

There is an interesting mathematical pattern with the frets on the Ukulele. Allow me to explain:

You have your A string, no fingers pressing down on it. Put a finger on the first fret, then the second fret, then the fourth fret, then the seventh, then finally the 12th fret. What happens? On the 12th fret, it is exactly one octave higher than when there is no finger on the A string.

This mathematical pattern is called the Fibonacci Sequence. It goes as 0+1, 1+1, 1+2, 2+3, 3+5. More appropriately 1,1,2,3,5,8. When you put the fingers on the frets in this sequence, you will end up one octave higher. This sequence somehow has to do with music as well as natural formations like nautilus shells, flowers, etc.

This teaches me that the Ukulele is not just a beautiful sounding instrument, it is also mathematically beautiful.

I hope you all found this interesting.

Happy playing,

Jared
 
jnicholes said:
Hello,

So, I learned something about the Ukulele today I wanted to share.

There is an interesting mathematical pattern with the frets on the Ukulele. Allow me to explain:

You have your A string, no fingers pressing down on it. Put a finger on the first fret, then the second fret, then the fourth fret, then the seventh, then finally the 12th fret. What happens? On the 12th fret, it is exactly one octave higher than when there is no finger on the A string.

This mathematical pattern is called the Fibonacci Sequence. It goes as 0+1, 1+1, 1+2, 2+3, 3+5. More appropriately 1,1,2,3,5,8. When you put the fingers on the frets in this sequence, you will end up one octave higher. This sequence somehow has to do with music as well as natural formations like nautilus shells, flowers, etc.

This teaches me that the Ukulele is not just a beautiful sounding instrument, it is also mathematically beautiful.

I hope you all found this interesting.

Happy playing,

Jared
Click to expand...

Makes sense to me. That sequence is everywhere in nature, and natural harmonics of a vibrating string getting shorter fits well within the natural order of the world as we know it. Thanks for sharing.

I wouldn’t be the least surprised to find out that a subjectively beautifully proportioned double bout ukulele design had things like the Golden Ratio, A+B is to A as A is to B, at play (another beautiful piece of mathematics derived from the Fibonacci Sequence), where the width of the upper bout width is B and lower bout width is A.
 
Jared, let me share two observations I have made about the fret board.

1. Take any note on the G string. For example, the E on the 9th fret. Move horizontally to the C string and then down one fret. Now we have the G# note on the 8th fret of the C string. Make the same movement now to the E string and we are on the B note on the 7th fret of the E string. Those three notes are the notes of the E major triad.

2. The fret markers aren't arbitrary. They indicate the minor pentatonic scale. Being from the United States as I am, this has an historical significance. It reminds me a quote from the poet Horace: Graecia capta ferum victorem cepit et artes intulit agresti Latio (Greece, after it had been defeated, captured its savage victor and introduced art to rural Italy). When the Greeks were brought to Italy, they brought their art with them and they suffused the culture of their masters with their art. Similarly the enslaved peoples brought their music with them when they were kidnapped to the United States. Now the pentatonic scale is the cornerstone of the American sound, underlying--as it does--rock and roll, R&B, soul, country and some jazz. And our sweet ukuleles give tribute to the nightmarish legacy of slavery with their pretty abalone dots.
 
Music and musical instruments have many mathematical properties. I do fail to see that Fibonacci connection and octave. I guess if you decrease Fibonacci number 13 by one you get the 12 :p
 
ripock said:
Jared, let me share two observations I have made about the fret board.

1. Take any note on the G string. For example, the E on the 9th fret. Move horizontally to the C string and then down one fret. Now we have the G# note on the 8th fret of the C string. Make the same movement now to the E string and we are on the B note on the 7th fret of the E string. Those three notes are the notes of the E major triad.

2. The fret markers aren't arbitrary. They indicate the minor pentatonic scale. Being from the United States as I am, this has an historical significance. It reminds me a quote from the poet Horace: Graecia capta ferum victorem cepit et artes intulit agresti Latio (Greece, after it had been defeated, captured its savage victor and introduced art to rural Italy). When the Greeks were brought to Italy, they brought their art with them and they suffused the culture of their masters with their art. Similarly the enslaved peoples brought their music with them when they were kidnapped to the United States. Now the pentatonic scale is the cornerstone of the American sound, underlying--as it does--rock and roll, R&B, soul, country and some jazz. And our sweet ukuleles give tribute to the nightmarish legacy of slavery with their pretty abalone dots.
Click to expand...

Well said, and thanks for calling out the history behind the music.

Now if I could get a ukulele with quarter-step fret spacing....
 
I think you would have enjoyed hanging out with Pythagoras.
 
Ziret said:
I think you would have enjoyed hanging out with Pythagoras.
Click to expand...

Nah! Geometry was part of a secret society. It was believed everything could be expressed by it. And revealing it's secrets would get you killed.

Fortunately, ukulele players aren't as strict. Most everything can be expressed by them. And they are happy to share the instruments' secrets. At least here...
 
thanks so much for the replies. I found what you guys said very interesting.

To be honest, one of my hobbies is actually geometry. Sometimes when I figure something out on my own, I say to myself as a joke, " Pythagoras would be proud of me."

I've learned a lot on my own about geometry. It's one of the area's I excel at.

back on the subject, it was very interesting to hear everybody's input on this. Thank you so much!

Jared
 
Seeing significance in things, where there is none, can be a very worrying sign.

John Colter.
 
jnicholes said:
thanks so much for the replies. I found what you guys said very interesting.

To be honest, one of my hobbies is actually geometry. Sometimes when I figure something out on my own, I say to myself as a joke, " Pythagoras would be proud of me."

I've learned a lot on my own about geometry. It's one of the area's I excel at.

back on the subject, it was very interesting to hear everybody's input on this. Thank you so much!

Jared
Click to expand...

So you're the one who would have enjoyed hanging out with Pythagoras!
 
Ok, since were on the subject of how mathematics applies to music, let me show you something. This video short was what got me interested in mathematics. The first 8 minutes talk about how it applies to music. It also talks about the golden ratio, which some people here have mentioned.



You might find it interesting.

Jared
 
Music is applied mathematics, or could be understood as such.

I'm not entirely convinced though by all that's said. The Fibonacci sequence and the golden ratio share links (especially through the Fibonacci spiral, which is essentially a pile of endless golden ratio-boxes), but they are not the same; fret markers are usually on 3-5-7-(9 or 10)-12 while the Fibonacci sequence is (0-1-1)-2-3-5-8-13 and thus not the same; a purely mathematical construction of pitches in a 12-note just intonation system following a logarhythm like you suggested (and first described by Pythagoros) has long been overtaken by a 12-note equal temperament system with fixed intervals (first described by Simon Stevin)...
 
Hello,

I just made this video about my discoveries about math and music.



Jared
 
Subscribed to this one
o.png
 
After further study, I found more. The Fibonacci Sequence DOES apply to the Ukulele. Look at the picture.

Fibonacci Ukulele.jpg

My Ukulele is 21 inches long, a Fibonacci number. Look what happened when I did the Fibonacci sequence on a picture of my Ukulele on Paint. (Sketch is a little rough.)

The end of the fret board, the hole, the string, its all the golden ratio!

So, it DOES apply to music!

Jared
 
Jerryc41 said:
Music and Mathematics? Please, don't ruin music for me! :D
Click to expand...
Mathematics has let me down too many times for me to let it into my music. Even counting four beats to a measure has let me down a few times. I don't trust it. Never will. :)
 
You must log in or register to reply here.

Similar threads

emba
Library Ukulele thought experiment
Replies
12
Views
614
emba
emba
W
An experiment in learning ukulele
Replies
11
Views
2K
Wayne Conrad
W
sequoia
The Thin Ukulele: An Experiment
Replies
10
Views
1K
J.F. Custom
J.F. Custom
kennymelodica
This needs you - the International Blues Experiment - check it out - ADD SOME UKULELE
Replies
0
Views
272
kennymelodica
kennymelodica
TommyG
Ukulele Orchestra of Great Britain
Replies
1
Views
70
frets alot
frets alot
Top Bottom