The Twelve Tone Matrix Reloaded
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- čas přidán 27. 07. 2024
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Schoenberg walks into a bar and says to the bartender, " I'll have a gin, with no ....."
LMAO
The inversion method "12-x = Inversion" only works when the Prime form starts on 0 or 6. My theory IV students follow your content and recently brought this to my attention.
just realized the same thing!
Why *doesn't* it work if the prime row doesn't start with a multiple of 6?
@@wyattstevens8574The first number of the prime row must also be the first number of the inversion row. That’s why 0 works here because 0 inverts to 0 (6 could also work bc 6 inverts to 6). The 12-x method won’t work for other numbers simply bc it can’t be applied to the first note of the prime row, which will cause a duplicate number to appear in the inversion row. With 12-tone matrices, duplicates will additively ruin an entire matrix.
If it’s confusing (understandable), try building a matrix using his method with the prime row
4 5 11 9 10 6 2 0 1 8 3 7 and my point will become clear.
Omg, college all over again. I've been thinking this awhile, but this is the video that has convinced me to share this channel with my college music theory teacher. I was blessed to have the same one all four years. 🙂
Yes this does bring back memories
When I was in High School I invented a 12-tone concept I called "tone blocks". I used all 48 notes of the row and its inversions as a block and then upon repeating this block I was free to transpose it. I also created a concept I called "tone islands" where a very short musical statement contained all 12 notes, but the order was only loosely based on the row. These short statements could only last a split second. I also found ways to make my rows sound a bit tonal by having tonal-sounding chords with the non-tonal notes coming quickly in between as a kind of minor disruption. I composed a little piece "For the Love of B-a-c-h" where the contrapuntal lines each had minor 6ths and where there were dozens of uses of "B-a-c-h" in numerous transpositions and inversion.
"So, Mr. Schoenberg, how tonal is your music?"
Schoenberg: yes
No
A?!
Last night I came up with a tone row, and today I did the math and filled out my matrix. It is awesome! Thank you. :)
Thanks for mentioning the base-12 (duodecimal) nature of the chromatic scale; I've used this for decades in quickly jotting down melodies & chords, when not having staff paper available, which is 99% of the time ;-) - - - & aligned with tick marks for rhythm/timing. This correspondence reveals, seamlessly, a lot of relationships that might otherwise remain obscure.
And transpositions become almost trivial. It just takes some brain-training to read this system as easily as reading staffed notes (which took just as much brain-training to learn, after all!)
There are a few instruments whose "traditional" notation is just a number from 1-12 (or 0-11). I believe Appalachian dulcimer is one.
Enjoyed the first play around, with my friend Tim, creating a 12 bar melody using your serialism number matrix. The pattern we came up with sounded melodic to my ears. I have been exposed to a fair bit of jazz and it kind of floated somewhere between Giant Steps and free jazz. It took my friend Tim a few more listens to find it comfortable at all. We talked about chromatic chord tone scales based around the major scale and the Dim, aug, dom 7 and half dim chords that can be played between the usual chords in a major chord tone scale. It may lead to a tune creation. I hope it stimulates Tim to miss a few of those default blues pentatonic majors and minors in improv solos and find some things that are a bit more daring. A good evening of musical discussion. Thanks @Sideways440 for sending me back to watch this again and @12ToneMusic for stimulating knowledge and exploration. You are appreciated.
Thanks for the guest appearance yesterday. It made me smile. Thanks for this clip too. Music is fascinating.
Here's an easy way to fill in a 12-tone matrix: the first tone going down diagonally is always the same (2:07-2:10), so just figure out the intervallic difference in the square directly above and transpose accordingly. Of course, I used letters (C, C#, D, etc.) in my matrix instead of numbers, which I think makes it easier to transpose by intervals.
Hey guys, I love what you guys are doing. I started a few weeks ago knowing some of what you're saying, but ultimately most of it going over my head but know I'm getting most of it. So thanks for that. I would really like to see more videos that aren't about harmonies. Maybe some weird but cool scales, or just a bunch of oddities put together into a video would be really enjoyable as well. Thanks again and keep making more great things :)
+Will Thomas Thanks, that's great to hear! We're always down to talk about weird, cool scales so I'm sure there'll be another one of those soon. As for oddities, we'll see what we can come up with! Thanks for watching!
I just watched The Matrix Reloaded so I appreciate the reference. I guess both the movie and this concept twist my head.
Great video - really helping me with some analysis. Thank you!!! 👏🏻👏🏻👏🏻
There are 479,001,600 different twelve tone rows to be made
ThePi314Man kind of, except since we're using numbers, you have to account for transposed rows which will end up with the same matrix but shifted. Then you'd also have to remove retrograde rows and inverted, so 11!/4
@Emmy Husmann There's only 11!/576 unique matrices, too.
Great video! I've been looking for a decent explainer on this topic.
Omggg this helped me sooo much. I had to make a 12 tone matrix for homework and i couldn't attend that lesson so when i was trying to do it I didn't understand how it worked. You literally saved me! Thank you sooooo muchhh!!! (Sorry if i said something incorrectly but English is not my native language)
A very concise and lucid explanation
Seeing that title after not thinking about 12-tone matrices in almost a decade is a special kind of funny.
Hi! I just discovered this videos and I'm loving them. I have a question though, about the harmony of twelve tone composition. Would you please explain a little about the harmony within the twelve tone composition? I understand the melodic aspect, but the harmony has always been a problem to me. Thanks!
Good question! Generally, twelve-tone pieces are written as a form of counterpoint, which means they're just multiple melodies playing at once. The harmony arises from interactions between those melodies, not from any underlying chord progression. Of course, in traditional counterpoint you can write with an implied functional progression, but in twelve-tone writing that's difficult to do because you have to use your row all the time.
There are a couple ways to work in chords, though. First, since harmonies arise from multiple melodies interacting, you can choose your statements and transformations so that you line them up to make a chord. For instance, if one line is playing D while another is playing F, your listener may well hear that as an incomplete D minor. The other thing you can do is build chords into your row itself: You're allowed to play multiple notes from the row simultaneously, so if your row contains A, C#, and E consecutively, you can always play an A major triad. (And, through transposition, any other triad, as long as you're willing to set it up with the rest of the row.)
Basically, traditional ideas of harmony aren't really that important to twelve-tone writing, but you can still sneak some in if you're careful. And, honestly, you can always just write a chord progression underneath your melody if you want. It's not allowed by the strict rules of the Second Viennese School, but no one says you have to follow those to the letter. Hope that helped!
Thank you so much! I worked on a twelve-tone piece recently and my teachers were criticising my "lack" of harmony. Now I understand why. Thank you again for the explanation. It's really useful for future pieces.
you should talk about the whole tone scale, theres a song by the band dream theater called "the dance of eternity" and around 4:43, you can clearly hear an oddly timed augmented riff being played on the guitar, and even weirder is how there is a bassline under it that sounds coherent, which brings up a question i have, is it considered atonal, or do the bass and guitar imply micro chord changes?
+sourcegamer101 We actually talked about the Whole Tone briefly here: czcams.com/video/QFdVRj3AbuA/video.html But that was mostly just describing its existence, there's definitely a lot more to say about it. We're planning to talk about augmented chords in the near future, and they're pretty related to Whole Tone, so I'm sure we'll cover it more soon.
To your question, I'd have to look at the song to figure out what they're doing, but generally speaking, the whole tone scale can be used atonally, but it also has the necessary notes to be used as a dominant scale (one we forgot to mention in our video on dominant scales...) which means it can have a tonal use as well. In that context, it's kind of like Altered but with a normal 9. I haven't had a chance to listen to the song yet, but if it's only used briefly I would guess that's probably what they're doing. If it's longer, it may be a temporary foray into atonality, I wouldn't put that past Dream Theater either. Thanks for asking!
Thankyou, makes way more sense using the numbers. How do you make a prime row?
Charity Rose take all 12 different notes and arrange them in a (random) order
you can use it for other stuff too right, like diatonical composition?
Just wanted to make sure that the operation that you do, which is subtracting and adding from 12 (as opposite to counting the number of intervals and adding and subtracting from there) only works if your prime row starts from 0 (12), right? like if i start my prime row from 3, i can't just subtract 12 to get the inversion. Is that correct? maybe i am doing something wrong in here lol. Thanks in advance.
Can we transpose the chords using matrix one by one of chords?
1:47 changed mylife!!
This looks exactly like a game of sudoku! It'd be cool if someone wrote a song in 9-tet and used a finished sudoku board as a 9 tone matrix. :D
Or use Base-12 sudoku.
Hey lads. I'd love another video on twelve tone serialism, specifically on different types/subgroups of rows. I've heard something about this, however I can't find much literature on this. So while I could roll dice and generate a pseudo-random series of 12 tones, I can also construct chords, or divide the row in two hexachords, for example. Could you perhaps look into making a video on more of these kinds of divisions on tone rows?
We've been meaning to revisit serialism for a while now, but in the meantime, we actually did a video on some of the structures you can use to build rows here: czcams.com/video/edxGTE0Y8LQ/video.html Hopefully that helps!
Yeah I've seen that a while back. :) Didn't find it when revisiting it, though, so it does help. However, I'd indeed love some more from you guys! Thanks for all the videos so far, in any case, and keep it up! :D
How is the retrograde correct? I thought it was just the prime row backwards?
Great video thanks. I can't quite see where the prime row comes from... I can't see what the basis of that particular number sequence is. Why that, exactly? Can anyone inform me please? Cheers!
Oh, it's arbitrary. I used one that I've used in other pieces, but you can use any order you want. Designing your prime row is an important part of writing a 12-tone piece.
Many thanks buddy, it's all new to me. Exciting times ahead.
WTF - awesome!
Thanks!
I get the concept and I'm a fan of some atonal music, I don't get how people expect a sudoku puzzle to produce good music though.
Huh? How did you decide what numbers go in the prime row?? Then you say in the left column you "put your inversion"... Inversion is normally about reordering chords isn't it? What does subtracting the top from 12 have to do with anything? Im assuming this relates to some other aspects of music theory but I don't see it?
Someone said that "put the inversion in the left column" only applies if the top left number is 0, 6, or 12.
The inverse is the prime row, just with the contour initially note-for-note opposing it. Serialism doesn't care about the octave.
This has got to be the weirdest game of Sudoku ever.
finally unolcking that Tenuto feature 😂
is it possible to play drums in 12tone?
You could tune drums, but probably more helpful would be a total serialism approach that serializes the rhythms.
@@12tone That sounds interesting.
cool school!
Thanks!
Whew! A little bit too fast on the Matrix! Why did you speed up the video???
+Pebber Brown Well, my thinking was that the point being made is more about matrices in general than about this specific matrix for this one row I wrote, so people's attention is better spent focusing on the mechanics and outcomes of matrices than watching me fill in a bunch of boxes with numbers. I did make sure that once it was filled in it stayed on the screen for a while so that people could check it out, but it didn't seem worth the time to me to go through every box in detail once the basic process was laid out.
I think his pace was fine. he didn't want to make too long of a video. it's just like making a times table it isn't hard
+Pebber Brown for me it is. how long have you been studying music?
*insert Keanu Reeves "Whoah!"*
Why do I have to study this... why??
My brain hate serialism but my autism loves it
what is "0 4 3 2 5 8 9 6 7 10 1 11"? What is it meant to represent? Edit: OK they are meant to be numbers 0 to 11 picked randomly. Should have explained that rather than drawing rockets and elephants but then we could have just understood what you're talking about and that apparently isn't the point of this video.
oh wait you did lol
What the hell did I just watch? :
bruh