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Mathematics and Art - Final Thoughts

Finally, the long chronicle that was the Mathematics and Art chapter that dominated much of my second semester was closing the curtains on its final moments. My knowledge in both departments separately, and together had developed swiftly during this time as I now document the last pieces of this chapter. Overall, this experience has taught me to keep my mind open to the many possibilities present in our world, through first sight, or hidden in the shadows divisible by the eye. I learned concepts of Mathematics and Art that I would never initially comprehend or accept and learned to truly appreciate the contribution that these two areas have imparted within our lives. Technological, historical and on astronomical standards that determined the path that the world has taken and will take. Although it has a been a hard subject to truly grasp and understand, and although my knowledge of this topic is far from mastered.. It has been a rewarding experience to understand foundations of subjects that I have already had knowledge and participated in once before but only on the surface. When I see Mathematics or Art lying before my eyes, I now know to appreciate every aspect, the symmetry, the beauty, the geometry, the atmosphere, the intentions behind artworks and equations. I developed a second sight, a second pair of eyes of the world that I live within and it is something that I can now cherish because I now have this second sight.
Mathematics and Art to me, has become another way to live the life I once lived in greater light.

Mathematics and Art - Finale

At last, I had finally reached the last day that I would have to adopt any time into doing anymore work for Mathematics and Art. I had already determined what I needed to do and tested the theory to ensure that it was plausible and could truly work over the past three days. Using the knowledge gained from the past few weeks and the last week of actual preparation and experimentation I now had all the tools necessary to actual play my water xylophone scale. Of course, because I had decided to draw lines to determine the water volume of each bottle for each respective note it didn't take long to fill bottles to their corresponding levels. With that done, I sat down in my conservatory and closed to door for a maximum effect as sound was best heard in this room.

I decided to play during night time as it would be the quietest time of the entire day without the natural sounds of the normal day so once the time came, I had planned what compositions to play in my head and had an arrangement positioned for optimum playing position. This position in my opinion was necessary so I could play without knocking over any bottles and tap the side of each bottle perfectly in the same place as the bottles all faced with the Fibonacci Symbol and Note of each bottle facing the camera. And so it was decided that 'Low C' would be in front, 'D' in the back, 'E' in front, 'F' in the back and so forth. Therefore I of course needed two metal chopsticks to play this the way I described and so I did just that and I of course played it in that way.

Below are the videos of each respective composition that I had planned with short descriptions underneath portraying the reasoning behind each chosen composition.

A scale is played here to demonstrate the notes in play in this octave. It shows what each note sounds like to the ear and will be utilized in a variety of ways as you progress through the videos below.

These are the Fibonacci Notes present in this particular scale that starts from root note 'Low C' so that everyone can identify which are the Fibonacci Notes in the octave.

These are the Non Fibonacci Notes present in this particular scale that starts from root note 'Low C' so that everyone can identify which are the Non Fibonacci Notes in the octave.

These are the possible Fibonacci chords that can be produced with this particular scale that starts from root note 'Low C'. I chose to show the possible combination of scales to demonstrate the strength of a harmony that is produced by a Fibonacci chord and the type of feeling that follows. Also, the first chord, C, E, G demonstrates the strongest Fibonacci bond. 'C' is the '1st' number and root note, 'E' is the '3rd' note in a scale and 'G' is the '5th' note in a scale, all which are of Fibonacci status which is something I was determined to portray. Therefore chords are a quick demonstration of Fibonacci in music.

An Arpeggio is a famous training method adopted by pianists to improve their finger and playing skills. In this case, the one we are looking at is the 'C Arpeggio.' This certain Arpeggio is considered to be playing only Fibonacci Notes as our root Note is of course 'Low C'. With that being our root note the only notes being played are 'Low C, E, G, and High C.' Therefore, the only notes being played are Fibonacci notes in this 'C Arpeggio.'

Mary Had A Little Lamb is a classic and famous song known by all ages and all races. So this became the perfect choice as it only uses Fibonacci notes when we follow note 'Low C' as being the root note. This composition uses only notes E, D, C, G which is a clear demonstration of Fibonacci notes in this particular case.

Mathematics and Art - Replicate (Day 2)

Having created and performed shortly on the created water xylophones the day before, I was now sure that it worked and I simply had to replicate and repeat the process until everything was the same as before. So, using the measuring cup and jug, I had now managed to reach the same point I was at before. However, this time deciding to create something that was more physically pleasing to the eye I got creative with masking tape. Firstly I taped the side of each bottle at the respective water levels and drew a line with pen to dictate where the water level had to be for each specific note and bottle. Therefore, should I choose to repeat this experiment I no longer have any need for measuring cups or jugs, but I simply just have to fill the bottle to the drawn line.
Realizing that this still had to follow my idea of Fibonacci Notes and the Golden Ratio, I used the tape to stick on the symbol for Phi on the neck of each bottle that was considered a Fibonacci note using the 'C' note as the root note.
And to ensure that everyone knew which bottle was which note, I stuck one small tape on the bottom of the bottle and wrote on it with pen, labeling it with what note it was ranging from 'Low C' to 'High C' on the piano scale.
Also, to ensure that it was obvious to plain sight what each bottle was from afar, I creatively used the type to spell out what note each bottle was. While for 'Low C,' I used the tape to spell 'C-' and for 'High C,' I used the tape to spell 'C+'.
So I now had all measurements perfected, and everything was labeled accordingly for future reference so no future mistakes could possibly be made. Ready as I was all that was left was to perform, and record. And that would be the task for me tomorrow on Monday.

Mathematics and Art - Determining Values (Day 1)

Today I awoke later than planned however, with the knowledge and equipment now at hand I was confident that this wouldn't be an issue in the long run.

So I finally had the gear and knowledge needed to really start the project. Following the recommendations of the site I started with 1/16 of the total volume of the bottle, moving into 1/8, then 1/4 and finally ending with 7/8. So I had the right amount of volumes needed in each bottle, and played a short melody to test if it worked properly or not and to my amazement it almost managed to completely mimic a proper scale. So with a smile on my face for a job well done, I found myself getting a goodnight sleep. Unfortunately I of course had to pour the water our and down into the drain seeing as the water level may not retain the same levels the next day but I was now aware of what needed to be accomplished tomorrow utili the 40 ml increment measuring cup and the large measuring jug for accuracy, it was a tedious job but ensured that there would be no real errors.

Mathematcis and Art - Gathering

So obviously today I didn't have much time, with it being D-Day for the Aural Terrains every moment I had was focused on the sound project. But of course out of today I did manage to come up with one positive. I didn't have any real physical medium to produce my idea until today. After the live performance I headed home early only to find out that I had a gathering that day with friends and family. On my mum's recommendation I came out because she reassured me that if I did I would be able to find the bottles that I was so desperate to locate. As per usual my friends and family would enjoy the occasional drinks and so with that I manage to obtain 9 identical beer bottles for my project. Of course I only needed 8, but 9 was just to be safe just in case anything happened to one bottle. So with this the day had unfortunately already ended for me, but of course I had Saturday to finally begin on my practical project for real.

Mathematics and Art - Experimentation for Accuracy

So now, with another session free for experimentation with my mum out of the kitchen and watching tv, I set out to move fast and quick. this time, I used to same measuring jug, but also got out 8 of the same glass cups. They weren't too small and they weren't too big so I guess it was just right in my opinion. So I decided to work at this myself before using the sources I researched earlier to see if I could do it myself.



So working in 40 ml increments I had one large jug to hold the water with a smaller measuring cup that measured 40 ml, 80 ml, 120 ml, and 160 ml. So of course, working in 40 ml increments was the smartest choice. I filled up to 40 and poured into the large jug. Then from the large jug into the glass cup for greater accuracy as the jug also had measurements present. Accounting for the fact that every time I swapped jugs or cups some water would remain in the previous cup or jug so I was always fill the water a bit past the 40 ml mark. So with this I had 8 cups in 40 ml increments. 40, 80, 120, 160, 200, 240, 280 and 320. I played these in order to notice that there was indeed a change.

But it didn't seem to match the scale that I had hoped for but with this I had confirmed that the size of the container would play a part so my next idea was to play this with fractions. So each glass container would hold water equivalent the a designated fraction of the entire container as recommended on one of my read sources below.
http://www.ehow.com/how_5104489_make-music-water-glasses.html

Mathematics and Art - Tampering for Confirmation

So with a idea in mind and what to do I set out some time apart today for Mathematics and Art. Finding time for my mum out of the kitchen I went in and did a little experimenting. Looking around I found my glass measuring jug so I could determine exact values for the volumes of water. Next I grabbed a metallic chopstick for maximum vibration sounds and effect and basically started with no water in the jug and tapped the side with the chopstick. Now I was certain I could create different notes with this idea but unfortunately I now had to wait for tomorrow to confirm more results as my mum needed the kitchen back for dinner. So it was a definite that the more water I had the lower the note. And the smaller amount of water in the container the higher the note.

Mathematics and Art - Extra Research

At this point, I had to of course ensure that I could either create a composition or find a famous composition that could appropriately gauge the presence of mathematics in art which was music in this case. At this point, I spent my efforts locating a song that employed the mathematical properties discussed in my essay. And I managed to find one that has been with our lives for many a year since childhood. So this was the composition that I aimed to play along with the various other demonstrations of mathematics that I wanted to portray, 'Mary had a little Lamb.'The piece only that I played of course only followed the top bars of every line with the notes already listed on, where these notes only employed notes considered to be Fibonacci Notes when 'Low C' is treated as a the root note.

Now, despite the fact that I lacked the actual material to represent my idea I also was aware of the fact that I lacked a little bit more research to ensure that my idea would actually properly and genuinely work. It was now up to me to find out the volume of water needed in each glass or bottle so I could properly mimic, a real piano scale for each separate note. Going through sites I located a variety of sites that each determined a different method to replicating a piano scale which made it difficult. So it was now my job to take up some spare time to find any normal glass and play around with it by tampering with water levels and comparing it with my piano to ensure that everything was right. So having done the research and saving it all in separate bookmarks for future reference when necessary.

Mathematics and Art - Idea created

As demonstrated in my Mathematics and Art Practical Project Essay in the link below I have chosen a medium to represent the ideas of mathematics and art.
http://robtey.blogspot.com/p/mathematics-and-art-practical-project.html

For maximum effect of this, I decided to directly represent a piano scale, or octave with a set of 8 bottles in the form of a water xylophone. So now every bottle would be designated with a letter in a scale on the piano. Low C, D, E, F, G, A, B, High C respectively. Now it was my job to find a good set of 8 bottles or glasses to represent this scale.

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