Music and math: The genius of Beethoven – Natalya St. Clair

Music and math: The genius of Beethoven - Natalya St. Clair



المترجم: Omar Aljubbah
المدقّق: Anwar Dafa-Alla قد يبدو الأمر متناقض أو مزحة سخيفة،
ولكن الأمر حقيقي بيتهوفن الذي ألّف بعض أفضل
المقطوعات الموسيقية في التاريخ، كان في الواقع أصمّا معظم حياته. إذا كيف استطاع تأليف هذه
المقطوعات الموسيقية التي لا تنسى؟ الإجابة تكمن في الأنماط المخفيّة
وراء تلك الأصوات الجميلة. لنلقي نظرة على مقطوعة ضوء القمر الشهيرة التي تبدأ بتيار مستقر و بطيء
للنوتات الموسيقية مجتمعة في ثلاثيات: واحد-اثنان-ثلاثة. ورغم أنها تبدو في غاية البساطة، إلّا أنّ كل ثلاثية تحتوي على
هيكلة لحن أنيقة، كاشفة العلاقة المذهلة
بين الموسيقى و الرياضيات. ذات يوم قال بيتهوفن: "تتشكّل لديّ صورة في ذهني
أثناء تأليف و عزف هذه الألحان." و بنفس الطريقة، نستطيع تخيّل قطعة موسيقية
عادية متكونة من 13 مفتاحا منفصلة عن بعضها بنصف فاصلة. السلم الصغير أو الكبير في العادة
يستعمل 8 من هذه المفاتيح مع 5 فاصلات كاملة مع نصفي فاصلة. و النصف الأول من الميزان 50، مثلاً، يتألف من 3 نوتات على مفتاح دو، مفصولاً بفواصل تسمى صول،
تلك القفزة عن النوتة التالية في الميزان. وبالنقر على الميزان الأول والثاني والخامس،
معاً، D و F حادة ، وA نحصل على النمط المتناسق
المعروف باسم الثلاثي ولكن هذه ليست مجرد ارقام سحرية
اعتباطية بل ، انها تعرض العلاقات الرياضية بين تردد الاشارات لنوتات مختلفة اذ بدأنا من النوتة A3 بتردد 220 هذه المتسلسلة يمكن ان يعبّر عنها
بهذه المعادلة حيث "n" تتوافق مع متتالية النوتات
على البيانو الD الاساسي الثلالثي في ضوء القمر
السونتا تستخدم 5 ، 9 و 12 وتربطها بتابع
نستطيع رسم المنحني لكل نوتة والذي يسمح لنا برؤية العلاقة الذي
رأاها بيتهوفن دون ان يسمعها عند رسم المنحيات الجيبية الثلاثة المنحنيات تتقاطع في نقطة ال0 وفي
نقطة ال 0.042 ضمن هذا المجال الD
تقوم بموجتين كاملتين F الحادة تقوم بموجتين ونصف بينما
الA تقوم بثلاث موجات هذا النمط هو التناغم الذي نشعر بأنه
بشكل طبيعي جذاب للاذن ولكن بنفس الوقت
بيتهوفن استخدم العشوائية انظر الى الاجراء 52 عن طريق 54 والتي تضم ثلاثية النوتات B و C كما يظهر المخطط الجيبي
الموجات ليست متناغمة التي تتطابق بشكل نادر . والتي تتكون متناقضة النوتات الشاذة مع الانسجام المتقدم لثلاثية D الشهيرة بيتهوفن اضاف العاطفة والابداع لنوتاته
بشكل لايمكن تفسيره في يقين الرياضيات بصنع ما وصفه "هيكتور بيرلوز" واحدة من الاشياء المذهلة التي لايمكن
للانسان ان يتمكن من تفسير آلية عملها إذن بالرغم من أن بإمكاننا تقصي الأنماط
الرياضية الكامنة في القطع الموسيقية، فإنه لم يكتشف بعد سبب أن
بعض الترنيمات لهذه الأنماط تؤثر في قلوب السامعين بطرق معينة. أما عبقرية بيتهوفن فتكمن في ليس فقط قدرته على رؤية الأنماط
دون الاصغاء إلى الموسيقى، و إنما بالشعور بتأثيرها. و كما كتب جيمس سيلفستر، "أليس ممكناً وصف الموسيقى
بأنها رياضيات الإحساس و الرياضيات بأنها موسيقى المنطق؟" إن الموسيقيّ يشعر بالرياضيات.
و عالم الرياضيات يفكر بالموسيقى. الموسيقى، هية الحلم.
الرياضيات، هية الحياة العملية.

46 Comments

  • Yoyo says:

    It's not only mathematics, there is a big deal of psychology in acoustics. Being gifted in maths is not a straightforward open door to be a composer.

  • Human first says:

    Nonsense

  • Reza M says:

    Those 32k people whole liked this, have 0 music knowledge.

  • Nakul Singh says:

    Was studying sounds wanted to take a break tripped over this exams sucks

  • riverstun says:

    So. Um. Why is the genius of Bach different? He didn't use dissonance? Um….

  • 은혜채널 says:

    뭔소리래여….월광에 싸인이라니….전 걍 들을께요…

  • bat flash says:

    Beethoven < Metal

  • Ludw1g V4n Beeth0ven says:

    Thank you for your nice comment I can see in the captions! By the way, fix your audio for the video.

  • Xela Pearl says:

    twoset violin should see this

  • Marián Mrázik says:

    Could be a great video. But I cannot comprehend the juxtaposition of Beethoven and maths. I think that this video could be much more interesting and meaningful if it would introduce Iannis Xenakis.
    In his music is the connection with maths the essential part. And if we go even further – the Meta art – which says that by using maths you can actually transcribe art to its another form. Xenakis was himself linking his architecture and music.
    And – as many others pointed out – now whats wrong with Beethoven in the video…
    There's a big difference between actual mathematical thinking and just feeling it. The other very important thing is to distinguish if Beethoven was dependent on mathematical and theoretical structures or could he use his intuition, memory and feeling. Because even though he was deaf… he could still HEAR…. It's the ability of musical audiation. And as a composer or musician it's a crucial skill of yours even if you're not deaf. When he was going deaf he was already experienced so he could rely on his imagination and inner hearing although not perceiving the physical sound. So… Still (not being able to hear) "ears" are the most important.
    The first thing (maths thinking vs. feeling it) should be the essence of this video (not the matter of deafness and Beethoven who "must" rely on maths). It would be terrible mistake however to say that composers only use their feeling and intuition. The aspect of mathematical thinking is so much important. (Again – you don't need deaf Beeth. It's part of composing in general). It would be very interesting to discuss this topic. The thing there is that composers have to imagine the whole piece – it's structure, developement – and even the smallest details like phrases and tiniest units of sound. They need to think rhythmically. There's whole universe of complex harmony. Also the polyphonic thinking and use of symetry or asymetry. Those aspect of composition are very closely related to maths. But… Was Beethoven really "doing the math" in his symphonies? Was Bach bothering himself with musical equations in his Art of Fugue? And further on – What about Messiaen's symetry and his modes? Ligeti's micropolyphony? And… Xenakis???
    It's discussion about 2 contrasting opposites. And everybody will find their own personal answer which may sound more like another question…

  • T R says:

    This is so misguided. Beethoven did so much study of other composers (especially Mozart) often copying out entire scores, that much of his grasp of stucture can be attributed to this. Of course he was a musical genius and was also driven to up the ante of proceeding music. But he was surely not thoughtful of the physics of sound as seems to be the point of this. Beethoven was educated in several areas. But ironically or maybe not, struggled with multiplication. I find that fascinating. But my point is that the premise of the video is ridiculous. Sometimes TED's attempts at being intelligent back-fires. I call shananagins.

  • bluestar musical says:

    bach's music in a beethoven video…
    wow

  • Variety of Everything says:

    Summarizing all the comments, I will say that it's not exclusively Beethoven that used the concepts of music to create beautiful pieces. Beethoven is simply one example out of many others; Mozart, Handel, Bach, etc. And it's not only classical music that uses this either. Even modern pop music relies on triads throughout chord progressions. I could go on, but long comments tend to go unread. You get my point.

  • Variety of Everything says:

    When you're a musician and you start getting existential about people who are music noobs

    Also hahah "fine"

  • Avran Abraham says:

    All composers do this it's not only Beethoven
    I just realized we got baited

  • Johnny James says:

    5th symphony: crunch crunch crunch crunch, dit dit dit dit. Drivel.

  • The Underrated Guy says:

    He was truly a genius!

  • TwinIceBear says:

    "The D major triplet from Moonlight Sonata"

    Yes I love how he chose a random chord in the middle of piece instead of the iconic C sharp minor opening. Bravo.

  • David Persson says:

    The genius of making a 4:20 long video

  • Zobdigi says:

    Why does Bach start playing at 3:30…

  • Duality says:

    this video is extremely misleading, and not at all what i expected it to be!

  • Duality says:

    well obviously he had practice and heard the music in his head.

  • Andre154 says:

    How to make a music video boring:

  • Bringel says:

    Não entendi, mas compreendo

  • Kate Ponystreet says:

    Why do you think Beethoven put his head to his piano? He could feel the vibration.

  • Joshua Langford says:

    2:00 says A3 writes A4 but plays D4

  • Sophia Perennis says:

    This video is a perfect case of "scientism", i.e., science seen more as a religion than the simple tool that it is supposed to be. Why was Beethoven a genius? Because science! Doesn't follow at all, but hey, we named dropped math so that gives us credibility. It's kinda embarrassing to be honest.

  • Fernanda Vasquez Sanchez says:

    As a musician and an aspiring mathematician this is awesome

  • Maestrorollo says:

    This is true of a natural (just) scale but not of the modern equal tempered scale.

  • Slim Essid says:

    noone, and i repeat NOONE will ever create a popular heart warming melody using math, you can probably try to explain it with math, but in order to create one you need emotion, and genius

  • Rich Wags says:

    This is a amazing video I am showing my students this.. Well done…

  • Naomi ! says:

    Im hoh and my dad tried to use mozart as a motivator for me to go back into music, and that motivation was much appreciate but unfortunately we both remembered that i have dyscalculia.

  • Kaya Malalgoda Weerakoon says:

    i would LOVE to have someone conducting like the conductor at the beginning…. XD XD XD

  • K P says:

    A3 or A4? 220 or 440? Which is it?

  • Applesauce says:

    I didn't get any of that.

  • GeorgiePentch2 says:

    3:42 This is really inspirational and I don't know why

  • M1cr0wav3 BEEP says:

    I thought Beethoven went deaf after performing his 9th symphony. And stop composing after.

    Did he have 10 symphonies?

  • Game Generation says:

    Beethoven: "Uh, yep, that's exactly what I was going for."

  • Miss Understood AngelaWalker says:

    I love this one ☝🏼 so very much ✌🏼💜😇☝🏼

  • LittlemissfeministXx says:

    What about one about Mozart?

  • Dam Jackass says:

    Dude is trying hard to make math so cool and interesting when really bethoven relied on music theory

  • hoang le says:

    after i watch this my head is bigger than normal

  • Mariska Brouwers says:

    Always asked about stuff like this in music class and my teachers were like no there two completely sepperate courses. art and sciense don't associate, ones exact the other isn't they said, leaving my curiocity unanswered. Now I have the satisfaction of knowing I unconsciously probably understood music better than they did. This has been my favorite compsistion by Beethoven since an early age. Thankyou TedX this was a truly clarifying and interressting video! ^^

  • HumanChalk says:

    1:13 êxćùšê mê hów đíď hê šâỷ òćťâvêś?

  • Ealdred Aruspex says:

    It's always cute when scientists try to explain the magic of music.

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