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This is like the equivalent of J.S Bach's prelude in C for minimalism in my opinion. The building of harmony through outlined chords with subtle changes. But i guess that sums up much of minimalism. That is just a connection i made as someone more familiar with 19th century and earlier. Cool to be back here, i last heard this in 2019 when a friend played it for me.

👍

This is amazing man. I've been learning this piece and you nailed the transcription! There's so many little details that add to this piece. Kudos to you!

現在は削除されているのですが、タイトルに関しては序破急と守破離を混ぜて序破離としていることを示すポストがケンカイヨシ氏のXに投稿されていたのでご参考程度に〜

Wow two pages is that all for this whole piece?

It’s incredible My eyes say math My mind says wow My ears can’t get enough My whole body screams Dance

v × w = (v ∧ w)i

geometric algebra has a much simpler generalization

Gracias por la partitura

This was short but surprisingly very cool

0:42 1:24

Thank you!

now i get it now i get why we use the determinant to calculate the cross product and now i get it why the vector perpendicular to a vector or a line is (-b,a) goshdayyum teachers dont teach us this kind of interesting stuff it seems like they care about finishing the curriculum fast and thats it thank you man💪

Muito obrigado

I read that you could only do the cross product for 3 and 7 dimensions

I was truly shocked, when I found out, that my most favorite version of "Eight Lines" was not performed by a real orchestra, but by the software "Sibelius 7". Compliments to the author. (Matekon?) To create such a beauty, probably takes a LOT of time, tweaks, skills, and musical taste. Very well done here! Thank you! I understand, how it basically works. You need the sheet music (score), on paper or as PDF. You need OMR-software (Optical Music Recognition) like in Sibelius 7. That will create a MIDI file or something, that shows the score in the program. Then add instruments to the various parts of the score. (All easier said, than done) Than edit everything, and save it as an audio file. This will not work with all music, but it certainly does with Steve Reich! And your version of Eight Lines shows, how important the rhythmic synchronisation of all instruments is here. All of a sudden, everything sounds coherent, dragging you into a universe of it's own. Normally I like 'breathing' rythms, that can stretch or compress, whatever the music needs. (variable, as life itself is.) I don't like MIDI-files, or recordings with ear clicks, for a lack of livelyness. But being a supporting bass gitarist, I have to listen very well, and am very sensitive to rhytms, and subtilities of timing and interpretation. And here I think: nothing can beat the MIDI versions here! Live performances can still be a challenge and enjoyable, but might never be that good. For me, it was a true adventure. I like Eight Lines. I also found Matekon's version, feeling it was the best. Then I found the "Small Dots" version with visualisations (Amazing!). But info on any orchestra called "Small Dots ensemble", could not be found. Then I realised, the visualisations could only come from a MIDI file. So for listening, I returned to the 'best live performance', uploaded by Matekon. Then I tried to find info on this 'teriffic orchestra' called "Sibelius", which resulted of course in absolutely nothing too. Then "Sibelius 7" in the title here, opened my eyes.. Thanks for this beauty! :-)

One of the best pieces, I have ever heard.. Blue image fit's very well.. Thanks!

I wonder what was the logic behind the claim that only 3 dimensions and 7 dimensions have analogs to the cross product. I suppose that was specifically for binary operations, and I thought it had something to do with quaternions and octonions, but your presentation reminds me that there's no such thing as a single line of all vectors orthogonal to just two vectors in 7D space.

Tu pourrais essayer avec Melodyne pour retuner chaque élément vers JI. ?

I love this music keep it up you're the best pianist I know I love it🤩🤩

Thanks for this explanation

I was the 69th like

amazing

If it's one thing Koji Kondo is really good at, it's the usage of sus4 chords. Nocturne of Shadow is by far my favorite one.

oh wow, damn! C'est encore plus stressant comme ça!

Oh, I'm so glad people are still doing arrangements of Lightning Returns tracks! This OST is so good !

i'm supposing if you take a 4x4 matrix with two columns, one using (e) elements, one using unknowns, and the other two using variables, it should be possible to get a function that represents the plane perpendicular to the two vectors in 4 dimensions, similarly a column of (e) and a column of (unknown) given a vector in 3d should return a polynomial representing the plane perpendicular to it, and finally in 2d the determinant of that simple matrix ends up being (y, -x) which if you vary the values x and y can give you the whole plane

Interesting, although a bit cumbersome imo. Still prefer exterior/wedge product as an generalization, it encapsulates more of the geometry :p

Many thanks indeed.

can provide references or authors used this

Is that the Stern-Brocot tree?

Just use geometric algebra

Typo in video title. it's VIII not XIII

cool videos man!!!!

Really cool, keep up the good work

bonne video 👍

Interesting generalization. I usually think of the cross product as representing the area of the parallelogram between the two vectors, as well as the plane that the parallelogram lives in. This leads to a very different kind of generalization commonly called the wedge product. Your generalization reminds me of the Hodge star operator, if you're familiar with it.

One nice thing is that these generalizations keep the notion that the absolute value of the cross product measures a kind of volume. The one in R^2 has an absolute value that is the lenght of the segment defined by the original vector and the one in R^4 has an absolute value that is the volume of the parallelepiped defined by the 3 vectors, just like the one in R^3 measures the area of the parallelogram the 2 vectors define.

Really interesting!!!

math + art sounds like something I would love to watch :o

Wow. I hadn't seen James Tenney's piece. This is very cool stuff. Have you seen Jacob Collier's favorite polyrhythm? ruclips.net/video/M2CJOb0_joU/видео.html math is music is rhythm :)

Very cool, in fact this is basically how a ring is defined. Btw another cool example is direct sum and tensor product of vector spaces.

Really cool! thank you!

I have a very rudimentary understanding of matrix products, and this video brought up a helpful way of thinking that helps to combat the confusion of seeing the "same" operations being used in different ways. I like the analogy that addition is like performing operations on like-objects, while multiplication is like operating on different objects.

So the answer is, a convention? Or do you mean some categorical notion?

Very informative. Thanks, I learned a new thing today

LET'S GOOOO VINCENT - SOIT REVEILLÉ POUR TON SHIFT CE SWARRRR

Thanks for providing the sheet music! I made a piano cover of this and provided your arrangement credit in the description!

that video is so mesmerizing

Agreed! The sheet music does not exist lol