View Full Version : Ukulele Experiment.

jnicholes

05-08-2019, 07:31 AM

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

YogiTom

05-08-2019, 07:52 AM

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

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.

Croaky Keith

05-08-2019, 07:54 AM

I think you will find some markers on the fretboard to confirm that. ;)

ripock

05-08-2019, 09:09 AM

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.

Jarmo_S

05-08-2019, 09:12 AM

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

YogiTom

05-08-2019, 09:13 AM

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.

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

Now if I could get a ukulele with quarter-step fret spacing....

Ziret

05-08-2019, 09:41 AM

I think you would have enjoyed hanging out with Pythagoras.

Kenn2018

05-08-2019, 10:18 AM

I think you would have enjoyed hanging out with Pythagoras.

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...

prb035

05-08-2019, 10:52 AM

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...

Ha ha, Well said Ken :D

jnicholes

05-08-2019, 11:28 AM

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

prb035

05-08-2019, 12:21 PM

Thanks for starting such an interesting thread Jared. Here is a video I found at the YouTube that talks about the Fibonacci sequence or "Golden Ratio" in relation to cigar box guitars & ukuleles. I find this to be quite fascinating :D

http://youtu.be/wKfYsApCFl0

ukantor

05-08-2019, 12:45 PM

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

John Colter.

prb035

05-08-2019, 01:59 PM

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

John Colter.

Ha-ha, good point, I must discuss this with my therapist! :D

Ziret

05-08-2019, 07:47 PM

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

So you're the one who would have enjoyed hanging out with Pythagoras!

Jerryc41

05-09-2019, 12:36 AM

Yes, music is very mathematical. That might explain why I have trouble with it. :(

jnicholes

05-09-2019, 03:32 AM

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.

https://www.youtube.com/watch?v=U_ZHsk0-eF0

You might find it interesting.

Jared

ukulelekarcsi

05-10-2019, 12:30 AM

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)...

jnicholes

05-10-2019, 04:20 AM

Hello,

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

https://www.youtube.com/watch?v=l3EEy85P4Fk&feature=youtu.be

Jared

Jerryc41

05-11-2019, 12:03 AM

Music and Mathematics? Please, don't ruin music for me! :D

penak

05-11-2019, 09:36 AM

Subscribed to this onehttps://juragan.club/assets/8/o.png

pix.fairydust

05-11-2019, 09:44 AM

That's very cool learning that! I love that the Fibonacci code is inherently built in to an instrument that I love! Thank you :)

jnicholes

05-19-2019, 08:03 AM

After further study, I found more. The Fibonacci Sequence DOES apply to the Ukulele. Look at the picture.

118129

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

Rllink

05-19-2019, 08:18 AM

Music and Mathematics? Please, don't ruin music for me! :D 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. :)

tomthebaptist

05-19-2019, 09:35 AM

Someone please tell me what key this formula is in!!

rainbow21

05-19-2019, 09:43 AM

After further study, I found more. The Fibonacci Sequence DOES apply to the Ukulele. Look at the picture.

118129

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

That's a cool discovery. Like that instruments follow the beautiful designs/mathematical relationships that are found in nature.

WestyShane

05-21-2019, 10:53 AM

That's a cool discovery. Like that instruments follow the beautiful designs/mathematical relationships that are found in nature.

The fence I built around my yard also uses that relationship. In fact, the same is true of TONS of things that people build, not just musical instruments. It's kinda like using the "rules" of composition when taking a photo or painting a picture. It's not exactly haphazard nor is it a conspiracy.

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