Tool, Lateralus - A Classical Musician’s In-Depth Analysis 

Please list here only your questions.

Finally somebody breaks down the 5-16 polyrhythm in the middle of this song. So many musicians review this song and all of them gloss right over it. In particular Danny’s 5 pattern with the bass drum quadruplets and open hi-hat accents on 1 and 3 is just filthy good and one of the most creative things I’ve ever heard in rock music. I’d love to hear you do a breakdown of Rosetta Stoned and analyze the polyrhythms in that song, and there are many.

I appreciate your explanation of poly rhythms. Tool didnt write this piece specifically with the fibonacci sequence in mind. It wasnt until the singer put the vocals to the track that that it was deliberately done. The music had been finished, and just happened come out with 9/8 8/8 7/8. Maynard has gone on record that his addition of the vocal syllables was him "poking fun" at the coincidence.

It's really fun to watch this analysis as Lateralus is playing in the background .

I think the band would appreciate your review. They are open minded and have fun with their criticism and don't take themselves too seriously. I enjoy their music and I appreciate your take on all music. Refreshing! Thanks for posting, I've been waiting for this one!

Saw Tool at a festival with 100,000 people, all nodding their head but no two people had the same rhythm! Everyone has their own personal experience. I think you ought to dig into the back catalogue of Opeth, rhythmically interesting and some of their chord structures and sequences are very special.

In rock music King Crimson's leader was obsessed with math-founding of each composition. I can hear the inspiration in Tool's work.

"Little stride, long stride" reminds me of watching car indicators at night while sitting at traffic lights, seeing them flash at different rates and matching up eventually , before going off on another cycle...

Please consider reviewing Pneuma by Tool. It has some unusual time signatures and syncopation that you might find particularly interesting.

Amy's explanation of time signature reminds me of an explanation of jazz I once heard: Four guys playing different songs at the same time.

if you are looking for Tool demonstrating more interesting ideas with melody , whilst still using cray rhythms, "Jambi" is a great demonstration of that and more melodically developed. If you are looking for more emotive connection in Tool tracks, the songs from the album "AEnima" are the best examples. "46&2" or "Jimmy" or "Push it" are more emotive some of their later tracks from a later album, " Wings for Marie/10'000 days is very emotive" Most of Tools music is not inspired directly by maths, but many have a lot of those elements in and they use poly rhythm a lot

Right hand snaps squares, left hand snaps triangles. Now add you left foot tapping octogons and the right foot stomping hexagons and you're Danny Carey! 😎👽🐙

I adored this breakdown of the Tool track, I have been into the band since 97/98 and as an 18 year old they blew my mind, quite a contrast to the Nirvana diet I was consuming. I agree regarding the melodic aspects, and its the one weakness of the track. Other tracks they do demonstrate their use of melody a lot better. Its also music that the more you listen the more your ears tune to their whole vibe and it grows on you.

I absolutely loved watching her classically trained mind shifting and moving to the rythem of Tool.

Tool set out, from the start, to explore rhythm as thoroughly as so many others have explored melody. when I try to imagine how a bunch of busy melody would sound over their rhythms, the results are comical and catastrophic XD

Rather than being about harmony, and counterpoint rock music tends to be about groove, timbre, impact, attitude and provoking physical reactions in the audience (kinestesia, maybe). This videos are so interesting to me because for someone who´s sensibility isn´t "calibrated" to find meaning and nuance within these popular music parameters you still find a lot of value digging for things you can relate to inside the music.

As I'm a child of that era, I can't listen to this song without thinking of Donald Duck In Mathmagic Land - particularly the part where it explains the Fibonacci sequence, it's relation to The Golden Spiral, and their relationship to music. I was a huge Tool fan before I heard this song and I wasn't surprised when I heard they used Fibonacci here. They're amazing individuals and an incredible team.

You pretty much nailed it from your opening statement on the “golden ratio” and how it already exists in music and, well, everything. Even the vocalist said he felt it was kind of juvenile to essentially point it out as they already exist in everything. There’s no need to point them out. It’s pointing out the obvious. Even so, it’s still a brilliant song.

I'd also recommend "Monomyth" by Animals As Leaders. They are an all instrumental band that focus almost exclusively on rhythm and mathematics for their song writing to great effect. You might enjoy it.

Been waiting for your analysis of this one since you started the channel.

if you're waiting for more melodic and harmonic complexity from Tool, you'll be waiting forever. I'm pretty sure all of their songs are written in the same key lol. Their focus has always been rhythm because they have one of the best drummers alive steering the ship. On top of that, most of the band is into mystical Kabbalah to some extent, so numbers play a key role in their creation of art. Puscifer is the name of Tool's vocalist's side project. It has a much greater focus on exploring melody and harmony, while still maintaining a rhythmic structure that goes against the grain of most popular music. Grand Canyon (Live), The Arsonist (Live), and Life of Brian (Live) from the album Billy D and the Hall of Feathered Serpents are all great places to start. Would love to see a breakdown of one of their live songs on your channel. Your content is excellent. You've earned a like and a sub.

May I suggest Breaking all illusions from the band Dream Theater? thanks!

Your explanation of polyrhythms was F*****G AMAZING!!! Theory and execution wise. I have never understood it better than after you explained it.

Listening to Lateralus in the order that it was placed in on the Lateralus album would give you a better feel of being drawn in AND carried along. Promise! I really enjoyed hearing about why TOOL is amazing, as always they are given their own spot in my all time there is no other that will be better (I saw them live in Nashville, it was soul cleansing), but Alice In Chains and Deftones are my favorite bands 😅 is it too audacious to think that they should be comparable to Beethoven, Mozart, Bach? I believe that they will live into history and be appreciated a few centuries down the line like their fellow musicians!

Metal is the new classical music. It's very technical

Great job Amy. You put in so much effort and care.

Thanks for this, absolute delight listening to someone else classically trained discuss one of my favourite artists. Lateralus, the LP as whole is thoughtful composition, it would be akin to me just giving a short part from the second movement of a concerto, and asking what you thought of the whole piece. There is also the 'Holy Gift Sequence' of this albulm where you listen to the songs in order to match the Fibonacci sequence.

You are the Carl Sagan of music. The explanation is marvelous and much interesting. Thanks for sharing your vast knowledge!

The source and ultimate example of dark, intense spiritual music: The Inner Mounting Flame(1971) by the Mahavishnu Orchestra - highly complex music by some of the best rock fusion players of all time such as John McLaughlin and Billy Cobham. All virtuosos.

I'm truly appreciating the comments. You people know so much more about this than i do. Blowing my mind, but also with laughs, and insight into the band, their intentions, and their awareness in creating it.. Their sense of humor.

As others have pointed out, the song wasn't really structured with the fibonacci sequence in mind and the theme was only added by Maynard when writing the lyrics. And the actual connections to the sequence are somewhat superficial. * The word grouping in the verse follows the sequence. But in a not very consistent way, and without much effect to the rhythm structure of the rest of instruments. * The time signatures in the chorus are 9/8 - 8/8 - 7/8. But that was mostly a coincidence and has a very naive relationship with 987. Because that relationship only exists with decimal notation, so it just relates to our base 10 representation of the number, not the number itself. For instance, 987 in octal notation would be 1733. A relationship that depends on a specific notation is not mathematically relevant. * Maynard starts singing after after 97 seconds, which divided by 1 minute (60 seconds), is a number somewhat close to the golden ratio. But the one minute mark is not super relevant to the song anyway and the ratio there doesn't really mean much. There are a few fun little references to the fibonacci sequence, but they are always a little tongue-in-cheek and not mathematically rigorous at all nor integral to the structure of the song. This is why in the chorus Maynard reminds the listener not to overthink it too much :). This song is very close to my heart and very emotional for me, and I would love seeing more analyses of it independent of its superficial relationship with the fibonacci sequence.

Their Pneuma explores musicality and harmony in much deeper fashion

While I thoroughly enjoy your video, all about it, the language, the sophistication, the expertise, down to the atom analysis, I'd like to just say, that you are decomposing A rock/metal song. Something which is of a niche today, maybe not as much as classical music, but still far less popular than e.g. crappy pop or hip-hop. I'd like people to appreciate the effort and thought put through by TOOL to create such piece of art, like with many other of their work. The fact that you spent 40 minutes in two videos on it, while not belittling it, is a testament of its quality. Thank you :) Tool fan...

I agree with another comment here. I’d love to see you listen to and break down pneuma by tool. There is a part of the song that just the drummer is holding a crazy polyrhythm and it’s very interesting to listen to.

You are such a talented presenter. Thank you for creating this videos please please make many many more

Yes! I would strongly recommend the next time you visit TOOL, watch the video of the Drum Cam for Pneuma. A wonderful expansion on their work with poly rhythms! 🤘🧙‍♂️🤘 Rich tAMB

I feel like a lot of people in your comments probably over-hyped this as far as the Fibonacci correlation. Yes, it's there. But it wasn't written with that concept in mind. The way Tool approaches the writing process is this: the band writes all the music together without the singer involved (this usually takes between 5 and 13 years per album lol). Once the music is complete and finished, Maynard (the singer) listens to what they have done, and writes the lyrics based on what he feels in the music. So once the band was done he happened to notice the Fib sequence in this music and applied lyrics that... sort of obviously point to it, while also making fun of it. He is quite the character... writing incredibly deep and profound lyrics while also making a joke out of everything at the same time. In this instance, "Look at this amazing math. Don't be an idiot by looking at this amazing coincidence of math and forget that you're listening to an amazing tribal rhythm"

On the Fear Inoculum album, Pneuma, the 7th song (not counting interstitial music) on their 7th album uses seven as the basis for the time signatures

Awesome. I think this might be the best breakdown of this song that I have heard. It also gave me more music to look in too. Thank you for the effort you put into all of your videos, they are always both interesting and educational 👍🏽👍🏽

Thank you for your analysis. It was very thoughtful and informative. Their live shows are expertly played, while accompanied by a visual art and light show that has few rivals. For composition, the three instrumentalists put the song together and the singer writes the lyrics that he feels fit the music, thus making his voice a fourth instrument, thus adding the melodic element to their music. If you have fifteen minutes to kill, watch a live version of this song. Almost always fan shot, but it gives you a sense of what a live experience is like. Cheers!

Like a lot of tool fans, my first introduction to Tool was the Sober video on MTV in the 90s. At the time I was living with a lady who was into R&B and hip hop and jazz. Needless to say, my musical tastes didn’t get much respect from her and her family. Once I got out of that relationship, I stumbled into a music store and started looking for the CD with Sober on it (Undertow, but I didn’t know it at the time). Fortunately or unfortunately, however you choose to view it, they didn’t have Undertow, but they did have Aenima, which I bought, got it home and played it. There were a couple tracks I liked, but generally…eh. But then I played it through a couple of times… the again…and again. And I got it.. Pretty much the same with Lateralus. My brother in law burned me a copy, which I barely listened to. Then, one night while working graveyard shift, the FM station in town had a nightly show called 10 O’Clock Tool. And I heard the Holy Trinity. From that point on, Tool is dominant on every play list I have, including classical playlists… Through that 10 O’clock Tool show I was also introduced to APC and Puscifer- it never stops amazing me the depth… the genius . There is a spiritual aspect to tool music I really don’t have the words to explain.

Also, the Fibonacci sequence in the vocal performance is in the syllables during the verse. Each word in each line builds upon the sequence. It goes up and then back down the sequence. Sound it out and count. It’s there!

Fabulous! Your analysis is insightful, well reasoned and described in detail yet intelligible to even a novice such as myself. I only recently became aware of Tool’s music and of course find it fascinating. When I was young (I am in my 60’s now) I worked with a company that developed high rise office buildings. We developed and built a 33 story building in Tampa FL that was designed by an architect named Harry Wolfe. It’s a very recognizable building on the Tampa skyline since it’s completely round. He was an award winning designer and had some interesting and unusual approaches to his work. The Tampa project was designed based on the Fibonacci sequence (FS). All of the dimensions from large to small were numbers found on the FS. For example, in most office buildings the structural floors are ~12 feet from floor to floor, but the floors in this building are 13 feet apart. This is only one example- there are many. Two cube shaped buildings stand adjacent to the round tower. They are attached to each other at the middle, and are each 78’x78’ X 78’ tall. Inside, the cubes are mostly hollow, they have 5 balcony levels. There are so many other details that there’s far too many to mention here, from the patterns of the stone used in the lobby floor and the detailed pattern that is reflected in the ceiling above it to the specific sizes of the windows in the building. It was the most fun I had in my years doing this kind of work (and being in Tampa made it all the more so- Tampa is a wonderful city!). It was a ridiculously expensive building to construct however. The necessity of keeping to the non-standard dimensions drove up the cost of materials in numerous instances and many specialty materials such as the French limestone exterior walls were called for by Harry Wolfe. The customer was a predecessor bank that later became Bank of America. Sadly, today the building has traded hands a number of time and I believe was last purchased out of a bankruptcy case. I don’t recall all the numbers anymore but if memory serves i think it cost more per square foot than it has ever been worth as an asset. I’m sure the amount of money that it’s owners have lost is a dollar figure that lies somewhere on the Fibonacci sequence😂!

Frank Zappa did a lot with mathematical principles. He used a lot of pitch-interval ratios in his melodies and harmonies and applied a similar method to his rhythms. (This is mostly in his orchestral work, but also in some of his rock stuff as well).

Holy smokes this was so good Lateralus is my favorite tool song by a good measure. And there is nothing I love watching more than experts in a craft discuss said craft I ate this video up like Candy. Thank you so much for your dedication and expertise!!!

WOW .. JUST WOW ! What a Break Down .. Thank You...

So much food for thought. Thank you for listening, researching, then creating this video!

Imagine watching a top notch hip hop dance routine, and then saying you couldn't like it because there weren't enough pirouettes. Rock and metal songs, in general, don't have complex melodic or harmonic development. I feel like Amy will be hard-pressed to like any rock song.

I thought it was over after the reaction, thank you for this!

Another very famous piece of classic rock….which is well known for the drums snd bass being at a different rhythm from the guitar in certain sections, is Black Dog by Zeppelin.

Vitamin String Quartet has some good TOOL covers.

On the danger to repeat me: If you are searching for a band and a song, which put as much or even more intensity into the melodic structure as into the rhythm, listen to "Close to the edge" or "Awaken" by Yes. You'll find everything there and in many of their musical artworks from the 70s aera, what you miss here and in other guitar shredding songs.

I always wondered what happened to Miss Hathaway from the Beverly Hillbillies.

Pythagoras "All is number" Music is such a pleasant expression of it. I don't know of a more intricate and hypnotic piece than this one though I am indeed, "attracted to this sort of exercise"! Peace

Another Tool piece you might enjoy that is very moving is Pneuma. I would love you to review it!

I love your interpretation and explanation using visuals that we all understand. I am a scientist and explaining this piece to somebody is just confusing. They understand your language.

I just found your channel today. I have watched a number of the video's and love both segments, 1st reaction and in depth analysis. I hope you are enjoying this and keep doing it.

I have no idea what your talking about, but find it very interesting and educational. Gives the music a totally different perspective and understanding. I love music but this is on a different level. You are obviously an educated person who really takes music to another level.

I recommend you listen to other tool songs if you liked the intricate though expressive style. They have many songs like this with varying themes and feelings you can attribute to it and it's really easy to spiral into

A sincere understanding breakdown. Thank you for your info.

You should check out Pneuma by Tool. There is a drum cam of Danny Carey that has millions of views. Or even listen to the studio version, but drum cam gives you a view of the genius of Danny. Each of these Band members are really top of their game.

Interesting that you didn’t feel drawn into the music! Maybe because you missed the 40 mins of music that preceded it. This album is a beautifully designed cohesive musical work, with varying degrees of melody and rhythm throughout. When I listen to the full album, I always feel like one song carries me into the next, and overall it really absorbs me and takes me somewhere. I think it would be jarring and less enjoyable to come in as you did 2/3 of the way through, at somewhat of the climax (just what you were talking about on the song scale in the first listen video!) And the song has a long intro that functions more as a palette cleanser from what came before (which was quite emotionally intense/draining 😉) than a super necessary part of a radio single-type song. I think I might have suggested starting it just where the vocals come in, to get a stronger first impression of just the one song. I guess the promise of a song built on the Fibonacci sequence set you up for some disappointment. I haven’t followed the band closely so I don’t know what they say about it, but to me it sounds like a kernel of an idea that they allowed to take on a life of its own (as the lyrics suggest) rather than the be-all end-all Fibonacci rock song 😂 When I first listened to it, all I heard were some cool rhythms that were unusual yet memorable and enjoyable.

Thank you Amy. This music has always struck me as cold and unengaging, and you perfectly explained why it makes me feel like that. It's rhythmically clever, but the melodies and harmonies to match the rhythms are insufficient. Brian Eno once commented that very complicated rhythms are capable of carrying a great deal of melody and it's a real shame that this is not done with this piece.

Tool has a song titled, '46&2'

I have seen Tool three times. And they are simply amazing. Mostly in Portland. I love Tool so much . Washington state as well. This was early. And I can tell you. They brought people together, regardless of any particular political ideology. LOVE ME some Tool. Carrey is a prodigy as well as Maynard. Adam, well yeah...a Rock GOD.

Do Tool Descending/ Pneuma analysis or reaction. Please !!!

If Amy is looking for more melody I’d strongly recommend looking into the Austin music scene. There are thousands(?) of world-class rock musicians there making a living playing onstage nightly, allowing them to hone their skills to the highest degree. There is truly something for everyone. I guess in other locations, musical talent that is more devoted to musicianship than appealing to the masses might die off (by having to get a day job), but in Austin it is able to thrive due to the supportive live music environment they’ve intentionally built. As for relevance to Rock History, they might not often take center stage, but Austin players are constantly just out of the spotlight playing supporting roles on the rock greats’ albums and tours.

Thank you very much for your in depth analysis. Learning a lot from your channel. I have never been a Tool fan, I tried. I felt like music I hade to like somehow. Even friends with a more mainstream music taste love Tool. It is to cold an feels too controlled for me I think. I'm a big advocate of Italian progressive rock, music can make me shed a tear and create a smile often in the same song. After watching your analysis, (and struggling with the snapping exercise) I'm more confident that it is just not my cup of tea. But I do appreciate the brains and musicianship of Tool even more now. Keep up your excellent work!

Not a Question, just Stunning. Well done.

Thanks for this analysis you really explained it all very well. Thank you I’m going to listen again

I strongly recommend that you become familiar with the band Dream Theater. Their use of both melody and rhythm in interesting and intricate ways might satisfy your wish for more melodic diversity as mentioned in this analysis. God bless!!

Just came across your channel. Love your videos. Subscribed! 🙂

I really enjoy your first impression and analysis of the song. I am not a musician in any way, but I do know that they can essentially replicate this song live, as they can all their other songs. If you listen to a band like The Mars Volta, which does a lot of what you want from Tool here, they have trouble replicating that same sound live. Tool does all this with three musicians and a singer. They may bring another musician along during some tours, but I don't think that is common.

When you recount the lyrics it becomes more poetic.

I very much enjoy the explanations and insights of a more learned mind in music. Thank you.

This video is a great example why I like to watch musicians reacting to Tool or other prog bands. :)

What a great way to explain that was heard. Just really well done. Listen to "The Golden Path".

I think your analysis is very good.I like how you try to educate the average listener and you did really well explaining concepts by using good and simple examples. As you already mentioned, the song does not offer much in terms of harmony and melody. Sadly, this is a general thing with Tool and it is the reason why i can not really connect with them. While their music is appealing in a certain way, it leaves me somehow cold and disconnected.

I´ve followed this channel for a while. I wish it could take a step back to the more basic kind of rock music, like The Troggs "Wild thing" or something. This Tool, Lateralus thing did make it to my playlist though.

Xenakis 🤘

@13:40 putting head and rubbing stomach. exactly. 😂

The sequence started because the time signature is 9/8 8/8 7/8 repeating and 987 is a fibanacci number

Please try the group Renaissance. The lead singer Annie Haslam has a 5 octave voice.

I always considered Megadeath as math rock too! Take a dive into some of their music some day, I will be there! A couple others I missed in a different comment elsewhere would be Polyphia and Yes. Both crazy good!!

Thank for the interesting dive into this song.

Thank you for another great analysis! I appreciate that what you seem to love most about music is melody and/or harmony. However, rock music is all about the rhythm. You will probably enjoy it more when you make peace with this. Anyway, keep up the excellent work!

Here is another in-depth analysis of Lateralus that may show you of just how much this song is rooted in the Fibonacci Sequence: How TOOL Used Math To Create Lateralus - ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-uOHkeH2VaE0.html

I’m so glad I discovered your channel, you’re a wonder!

Thank you for this. What a great analysis 👏

Please check tool schism, it has 48 time signature change!

You have to check out a Meshugah song. They are the kings of Math music and polyrythms.

Check out Earl Haig Symphonic Strings cover of lateralus! I wept through the whole video!

I don’t believe in coincidence. I also run and swim in time depending in speed or going up/down hill. Great channel.

Very interesting mathematical observations and insights Amy. Hopefully there won't be a pop quiz in the next video.😉

As a drummer, I remember the first time I heard the 5/4 polyrhythm and it clicked kinetically. It’s kinda like riding a bike now. It’s a groove you can’t unfeel.

Earl Haig secondary school symphonic strings. It's not too shaby

I can play poly rhythms on drums and guitar...but I cant do the square triangle thing hahaha I got my head around them by noticing that many basic poly cycles are actually partial phrasing in many fills and variations in 4/4, and they all connect in ways where you can move in and out of them.

Here is a cover of Lateralus I think you will enjoy.

The way I see the Fibonacci sequence is simply: Present plus the Past Equals the Future.

Tool checked. Now it is time for MESHUGGAH!