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Jone Apraiz

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How do you think mathematics are related to music?

This question is open to all persons who have ever been interested in mathematics and music. The idea is to create a space where people commenting on the relationship between these two areas and how they feel when they hear or play music, or read or work with math.

Topics: Mathematics
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    Mar 3 2011: There's an interesting cross-cultural pointer showing maths and music are related - but on a very basic level: in very many cultures, children are thought how to count by listening to rythmic songs. I work in Congo, and there's a popular game for girls here, played by almost all small girls: two girls face each other, jump according to a particular pattern and sing a tune that goes with it, while counting. The figures of the dance count as "points". The girl who falls out of pattern loses points and is replaced. The patterns are quite complex, and grow in complexity as the score goes up and finalists face each other. But this is mainly rythm-based, less harmony or melody based.
    We know many cultures "divide" and "position" (mathematical operations) a huge range of objects, qualities and persons according to patterns that are reflected in their music. We've discovered fractals in African architecture and music. So on these basic levels, music and math are closely related.

    Johannes Kepler thought the cosmos was "composed" on the basis of musical patterns - he wrote about the "harmony of the spheres". Many scientists have come to similar parallels. Some have begun to produce music from the patterns they discover in mathematical or biological processes (a few days ago some published the beautiful sound of yeast cell division...).

    On another note: after seeing Bobby McFerrin's brain experiment here at TED (which resembles the Congolese game a bit), I'm convinced both music and maths draw on innate capacities, shared universally by mankind.
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    Feb 22 2011: There is actually an extremely strong connection between mathematics and music, and the most simple way to look at this is to think of a guitar. Each fret on a guitar fretboard raises the pitch of the string by one semi-tone, but why does this work in every instance? Because there is a mathematical realation ship between the original length of the string, the amount by which it was shortened, and the resulting rise in pitch; it has an awful lot to do with ratios (in fact, the golden ratio produces the harmonics that can be played on a guitar).

    But to think of music as merely a colletiong of carefully worked out ratios and frequencies all jumbled together on in between five horizontal lines is extremely simplistic. Music is pure creativity, the very essense of artistic talent and expression; whereas mathematics is pure science, an example of what we can achieve when we listen to our best and brightest. They are as exclusive as they are mutual; as independent from each other as they rely on each other. Personally, when I listen to brilliant artists doing amazing things with their talents, I am in no way reminded of a mathematical equation.
    • Feb 22 2011: Thank you very much for your comment. I am mathematician and I love music, I always feel a huge emotion when I listen to a music I like a lot, I repeat the same song I like to listen again the moment where a change of chord is. Experiencing these moments is wonderful !!

      In the same way, when I realize about which is the way to solve a math problem, I feel like I saw the light, It is like when there is a change of chords in a song. I think that a music composer is in some sense like a mathematician or a mathematician is like a music composer.
  • Mar 7 2011: Math is in itself a composition, a orchestra. It is a combination of different math signals(instruments) to get a singular end(I do not say result fo a question is not mearly fo it's ends), a composition
    • Mar 7 2011: Good description, Cheong, thanks!
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    Mar 6 2011: This is an interesting topic to me. Growing up, I was always into singing and playing instruments. When I was 6 or 7, my parents tried to get me to take piano lessons and I would play everything by ear. The teacher caught on to me because I was practicing pieces of music she gave me, and when I would perform them for her in class sometimes I would do so in a different key(while pretending to read the music). I would also "add" things that I thought made the songs more interesting - she was NOT cool with that!

    Fast-forward to today. A few years ago I finally went and had some testing done and I was diagnosed with Dyscalcula - it is a Math and primarily numbers learning disability. However, I'm a published singer-songwriter and producer. I play keyboard and began programming electronic instruments at an early age, as well as playing acoustic ones and singing. I've produced several records and I continue to work in the area of music.

    Obviously, without the technology we have had since the 70s and 80s(when I grew up, I was born in '70), I probably would not be a musician today. Even though I can't do even simple Math or remember my phone number, I "get" how music works in terms of tracks, sequencing and time.

    So - I say all that to say that from my perspective Music has more of a relationship with "time" than with Mathematics. I think humans have tried to box in music to certain Mathematical equations, but when you listen to music from all over the world, it doesn't always fit - and not just "time" or "tempo" but pitch scales also are arbitrary. I think even what I wrote earlier about relating music to time may be incorrect also, or at least it can't explain it fully.

    I did a paper in college about Music and Language which tried to see if Music or Singing could have been used by early humans even before speech. Think about how animals communicate and how babies utter their first "words",,, Another topic for another time perhaps?

    Great topic Jone!
    • Mar 6 2011: Thank you Shanon, interesting words.
      I think that time is very relevant in music and in our lives, of course. The meaning of actions (in lives) or notes (in songs) change completely them.....really interesting, awesome, for a next conversation....
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    Mar 5 2011: I believe they are certainly related because both of them have governed by pattern: one, music for the patterns of notes, and the other, math for the pattern of numbers
  • Mar 4 2011: There are the obvious math connections between frequencies and their relations to notes, harmonics, etc. But I really saw it when I heard an interview with a savant named Daniel Tammet. He's the guy who recited Pi to 22,514 digits, verbally, with nothing in front of him. He's conversational and has helped some researchers tremendously in understanding how he gets the answers in his mind.

    He said that each number he sees as a color in his mind. When faced with a math problem, he sees how the colors combine and knows the answer.


    Now, I'm no savant, but it struck me. I've been playing music since I was 11 (40 now). And when I play, especially when I'm improvising, if I close my eyes, I see colors and patters. Much like abstract art. And if I don't think about it, I start to play to those patterns and colors...shades and textures in the music (dynamics, rhythmic elements, voicings, etc). And it struck me how maybe the connection isn't in the numeric values you can assign music (Hz, dB, phase, delay, decay time, etc) but that the connection is in how the mind perceives the action or process.
    • Mar 4 2011: Hi Kyle,

      I really appreciate your comment and I have to say that I watched several times Daniel Tammet´s video some months ago, I liked it a lot!!


      I recommend to watch it if you haven´t done, I think you will like it.
      I always visualize some forms and patterns when I imagine mathematical concepts and when I play music; I started playing music when I was 11 too!!

      It´s a pleasure to have your comment here, thanks!!
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      Mar 6 2011: This is a beautiful comment on a great question. When I play music I often see scenes of warped space-time in which distance and velocity cannot be judged by conventional means. I ride on what I call giant ribbons of light who bank with texture changes, pitch with note changes, and change velocity with rhythm changes. There are many other objects that are in the space, but I move without boundary or guidance as I can leap from one ribbon to another at will. Objects are made of an incredible variety of shapes and sizes. Their movements are difficult for me to describe, but it is what I would think of as the early universe with great density and energy. It is a consistent experience that varies in intensity depending on properties of the song. It is most profound when I am playing the music myself, but also happens while only listening.

      Other than the mathematical modeling of sound, there is also math represented in the symmetry of music.
    • Mar 6 2011: It would be interesting to continue with this conversation. If you want, you can send me an email.
      Have a nice day.
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    Mar 4 2011: I am a musicologist.I often meet with some questions about temperement.for example ,how to understand Pythagorean's Comma or Meantone in Bach's time or Zhu zaiyu's Equal Temperament.

    Chinese music theorists in a book named Huai Nan Tzu from Han-dynasty already knew how to generateall the tones and half tones on a scale with 12 tones, by alternatingly multiplying with 2/3 and 4/3, i.e. the quint and the reversed forth. In Greek, the series of fifth on which Pythagorean tuning is based is extended to 12 or more members. This can be achieved by successively multiplying by 3 / 2.......

    If I was not able to work out their's ratios and frequencies,I wouldnot really undertand the history of music.

    Music need to be understood by math.but math neednot to be understood by music. This is truth.
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      Mar 4 2011: Liu:

      I've been working on a wikipedia page on this topic. Let me know what you think:

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        Mar 5 2011: Wonderful! .Thank you for your message.
        That looks like an interesting Clock in which dissonant chords are more beautiful than consonant chords.More consonant chords are,more ugly chords are.but it is great idea.
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        Mar 6 2011: Maybe dorian mode seems to be a person.But I can't get the real idea straight in the clock.To me,each mode I see as a range from low to high in my mind.When I faced with mode problem,I see how the ranges combine in the keyworad of a piano.
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    Mar 4 2011: As a person who plays 3 instruments, I can say firsthand that mathematics and music are very, very similar both philosophically and technically.
    Music is made of math. Playing the cello, as I do, has shown me that it requires not only a good pitch, but a perfect count. Keeping the beat takes a lot of skill, and you have to constantly process it. The beat itself is made out of numbers, which you have to adhere to.
    And think of jazz music; it revolves around using a select number of notes and patterns in order to make a song (pentatonic scales). Sounds a lot like permutations/combinations, no?
    Also, each note is made out of a frequency, vibrations labeled numerically.

    So, I would say that, indeed, mathematics and music are quite related!
  • Mar 4 2011: For some reason there is a so-called harmonic mean... Its name derives from the concept of overtones, or harmonics in music: the wavelengths of the overtones of a vibrating string are 1/2, 1/3, 1/4, etc., of the string's fundamental wavelength. Every term of the series after the first is the harmonic mean of the neighboring terms; the term harmonic mean likewise derives from music.
  • Mar 2 2011: I think music is exactly mathematics! you know, it's not my opinion and there are many books written about their relation. One of the titles were very exciting(!) : "Musimathics"
    Except the note's frequency or anything about the voices thats related to physics and numbers, I feel if you think of matht as "a set of ruls", you can see it anywhere and specially in music. The music that when you put you finger just 1mm displaced and further on the violins fingerboard, you play the false tune!
    I'm working on it as my school project and I'm afer sth new . Also I've read some littel things! But if you could help me with this, I'd be glad!
    • Mar 3 2011: Thank you for your comment, Leila. I didn´t know about "Musimathics", it seems interesting...
      I think the proportions or measures that are given to different things and how they are combined determine the lifetime of this universe.
      I think the same way as if to play an instrument and change the finger to another position comes a different sound, a plant having a little amount of light or live in a different environment will be a completely different plant to another . And just as each person are different depending on how we have grown and affection we have received from our immediate environment.
  • Mar 1 2011: You should hear what Bob Dylan says about math and music. Its really amazing. He talks about patterns of 3's and 5's and 7's. I can't remember where I read it... maybe in his "Chronicles" But it really blew me away. I couldn't make any sense out of it ... but maybe you can... if you can find it.
    • Mar 1 2011: Good recommendation, Daniel !!!
      I have gone quickly to find the article you tell about, the combination of Dylan and Mathematics is awesome, fantastic, great, wonderful !!!!
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    Feb 26 2011: Yes, the whole concept of music is multiplication and division.
    MY son is a brilliant mathematician, and a scientist (Zoologist (Imp)). I’ve seen him in the School laboratory running 5 or 6 experiments; all with different starting times, different additives and different procedures, he finds multi-tasking effortless.
    I spent a colossal amount of money on music lessons for him all to no avail. He is now 30 he can’t play a note, nor can he drive a car, failed 5 times, (he actually does not wish to drive). Apparently very few poets have a driving license.
    So is music mathematical? Yes. Are mathematicians musical? Not necessarily so.
    • Mar 2 2011: I am highly skilled at basic mathematical skills and found Geometry to be effortless. However, fractions and Algebra I still to this day cannot grasp. In music I took piano and flute - failing miserably at both. Coming from a family where my father was a self-taught piano player and my mother taught piano lessons...this was crushing. I could "read" music well - but could not translate it to my hands in real time. I had to memorize every piece of music one bar at a time. To this day when I sit at the piano - I have to close my eyes...then my "body" remembers spatially where to go and I play quite well. I think for me math and music ARE interconnected...but for me its all in the 3d and spatial sense. I couldn't learn in the way my teacher and parents thought I should - so I found a way around it. Maybe your son just needed a teacher who could help him look at music differently. :)
  • Mar 6 2011: This space is going to close in one day (It´s a pity!) and I want to say thanks to all, people!!
    I will continue writing things in these section and if someone wants to contact with me, you can send me an email.
    I´m mathematician and I love maths, music, animals, interesting boys...

    Good week
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    Mar 6 2011: As a side point to your conversation, music nurtures core ideals that we want to impart in our children. It helps with memory, for one, as musicians must memorize not only the melody of a piece but also the individual notes that constitute it. Music also teaches us how to get along with others. A band must play in balance or else it becomes cacophony. If the drummer bangs away too loudly, for instance, everything feels off kilter. A powerful and supporting group dynamic teaches the importance of choice, of listening, and of conversing. The group that works together achieves its goals. In this way, it also interlinks with mathematics, which to my mind (and I'm not a mathematician) always seemed in some abstract way to be about balance.
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    Mar 4 2011: melodies and harmonies are just manipulations of sound waves... playing music is similar to performing calculations... the end result is what triggers human emotion.. in essence, music is the mathematics of emotion :)
  • Mar 4 2011: I don't know about this but I guess our brain has a centre for music. This centre is probably arranged in a pattern that recognize some rhythms and tones as "musical" and doesn't care for things that doesn't sound musical. Maybe this centre has evolved to be formed similar to our centre for mathematics? And that would be the explanation for the connection between mathematics and music? I don't know, just trying to... perhaps invoke some thoughts.

    I don't think there is any deep connection between math and music. I think music could be similar/connected to intuitive math maybe. However I don't think there's a hidden pattern in all good music or something like that. What's good or bad in music is a matter of taste, maybe these differences in taste arise because of trying to adapt yourself culturally to your surrounding, or maybe they're just random. But I'm opposed to ideas of "mathematically perfected" music. Seems implausible to me.
  • Mar 4 2011: Music can be created using fractals. Using the Lorenz attractor, Diana S. Dabby, a graduate student in electrical engineering at the Massachusetts Institute of Technology, has created variations of musical themes. ("Bach to Chaos: Chaotic Variations on a Classical Theme", Science News, Dec. 24, 1994) By associating the musical notes of a piece of music like Bach's Prelude in C with the x coordinates of the Lorenz attractor, and running a computer program, she has created variations of the theme of the song. Most musicians who hear the new sounds believe that the variations are very musical and creative.
  • Mar 3 2011: They both affect our brain (mind).
    They can both affect each other (lol).
  • Mar 3 2011: maths and Music are not related
    • Mar 3 2011: Couldn't be more wrong. How do you think a guitars frets are spaced out? Bearing edges on drums are set to a specific angle to create resonance. Chord patterns can be mapped out mathematically. MIDI is the mathematical way of looking at music and frequency. Sounds are translated into numbers. Time signatures are 100% math. You couldn't use syncopation without math. I could go on forever.

      Music may not be directly derived from math but it certainly crosses over. If you understand the correlation it can vastly improve your playing. Math and Music are related in more ways then not.
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    Mar 2 2011: same way music relates to visual art. Mostly harmonics. Principles of composition are based on counting because of brain comparative nature. That's why arts are fruitful for creation of widely developed personality.

    Mind decides something beautiful when it's solid and easy to comprehend, in other words it likes formulas and counting. When mind can't formulate something it may become puzzling and obnoxious.
  • Mar 2 2011: Math and music have always been considered closely connected in many ways. It is widely believed that students who do well in music also excel in math. Sometime that is myth – but the same theory is not try on me. I am not so good at Math, but I am good at MUSIC. Some research shows that starting music lessons at a young age enhances math ability. Let’s take a look at some of the basic components of music such as rhythm, tone and pitch, and see what math has to do with them.
    Rhythm is the basis of music just as numbers are the basis of math. When you play a few different notes together or even repeat the same note on an instrument, you create something called rhythm. Some rhythms are soothing such as waves crashing onto shore, or crickets chirping in a calm summer night. These rhythms make you relax. On the other hand, some rhythms make you get up and dance. Over the years, written notations were developed to record music. These words and symbols developed into what is known today as music theory.
    Since rhythm measures time, "Measure" and "Time Signature" are used to set up the rules of rhythm for different pieces of music. "Measure" is the space between two bar lines on the staff that represents the division of time by which air and movement of music are regulated. It is a phrase of music that has the exact number of beats (or counts) given in the time signature at the beginning of the piece. A piece of music is divided into many measures, or bars. Each bar represents the same amount of time. Each measure (bar) is again split into equal portions called beats.

    Time signature is found at the beginning of the piece next to the key signature. It looks like a fraction without a dividing bar such as or . The number on the bottom tells what type of note (half, quarter, eighth, etc…) gets a single beat, or count. The upper number tells how many of those notes are in a measure.

    For example, a time signature of means there are three quarter notes per measure. It also
  • Mar 2 2011: Have you heard of a young "mathemusician", composer and researcher Vi Hart? Check out her wonderful work at http://vihart.com/everything/
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    Mar 1 2011: There is an alternative genre called math rock that it is known for experimenting with unusual meters and structures. http://en.wikipedia.org/wiki/Math_rock
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    Mar 1 2011: ı think , mathematic is a mental exercise and matter calling for attention . many people listen to music work with math. that distend sometimes because music is confertable . and also , we can bilk unnecessary factor at out
  • Mar 1 2011: Rhythm
  • Mar 1 2011: Its not the tones that are the music.... but the spaces in between the tones....
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    Feb 22 2011: All one and the same just received via different senses. Although the art of listening seems to engage ALL the senses.