How Facebook Helped Solve A Musical Mystery

[@12tone]

Some additional thoughts/corrections: 1) Check out Kieran Ridge's music! It's really good! kzbin.info/door/18Bx9_gOyZ3g5UCgpsmpZA 2) I forgot to link to the video on my side channel so for those of you who are curious, here it is: kzbin.info/www/bejne/qoTIn3yhmJWWiJI 3) One explanation I'm seeing pop up is that this is a result of the circle of fifths, and since E is the leading tone of F major, the flattest white-key major scale, you can just follow the circle of fifths and it'll be the last one sharped. This is true, but I feel like it misses out on some important details: Specifically, it fails to address the fact that most scales _don't_ have this property, and it doesn't really generalize to the other scales that do, since it only works because major is formed from 7 consecutive notes on the circle of 5ths (in fact, that's one definition of the major scale, or at least the diatonic set.) and other scales with ridge tones don't do that. So while it's certainly a true and valid observation, and one that, in retrospect, I wish I'd included in the video, I don't feel like it tells the whole story.

[@7177YT]

Absolutely beautiful reasoning on this one, pleasure to watch thx! (:

[@literal76]

Hi 12tone. Thanks for the videos. I have an elegant solution for this one. Can you PM me the Facebook group it was discussed in? It needs to be explained with diagrams.

[@commentfreely5443]

that's why spanish guitar works, Phrygian .

[@captainalex8003]

The Dorian b2 was more like Melodic Phrygian, because you played a D# instead of a D.

[@fredashay]

So you're saying that note "E" is a racist note?!?! And the C Major scale is a racist scale?!?!

[@spencerd6126]

All I saw was “why is e everywhere” and it took me a minute to realize this isn’t a math video

[@stefanalexanderlungu1503]

*E*

[@randfrazer814]

Funny, I had the same thing, but I was thinking it would be about the English language

[@stefanalexanderlungu1503]

I was thinking it was about the meme

[@DraGon72097]

I only realized it wasn't because it was capitalized, lol

[@bachpham6862]

@@DraGon72097 I still thought that this is going to be a math video since I saw him draw the Mandelbrot set so confused me had to roll down to the comment.

[@eleanorrigby7914]

I feel like I understood nothing yet everything at the same time

[@lillithyukiutacrow2532]

Hi welcome to the club... want candy, soda, cider? *pulls out several bags and bottles*

[@BrunoWiebelt]

this was confusing

[@lillithyukiutacrow2532]

@@eleanorrigby7914 shure *opens one bottle with another* I'll take a cookie *hands over bottle*

[@SoundsOfTheWildYT]

This video was more of a mathematical proof than anything explicitly to do with music. Unless you’re really desperate to write a piece in 7 different major keys that share a note, I don’t think there’s much of an application to this, but it was an basically a (very interesting) talk about properties of reflectively symmetric subsets of fixed size in an ordered 12 element set.

[@joshpohlner8716]

I thought you died in the church and were buried along with your name

[@sebasmusician736]

B was almost also a ridge tone but it fell flat

[@luigivercotti6410]

An interesting remark.

[@bfish89ryuhayabusa]

A does the same, but I don't have a sharp enough wit for a similar pun.

[@strongeststrike6737]

Sebas Musician F

[@ayyocam1917]

U guys are naturals

[@gabrielmahutasoit8953]

Yeah. B is the b7 of C# major scale, it sure feels flat. The other notes' major scale contains B as the main note of their scales, except C# major (it has B# tho, the B note brings us to the C# mixolydian -F# ionian-).

[@darleschickens7106]

2:58-3:11 ... descending F# Phrygian scale in major chords with an E pedal note? Why did that sound so incredibly awesome?! Damn....I wanna make some music with that!

[@kairo175]

I agree, that was nice

[@krcprc]

I was thinking the same! The first half sounds si like the andalusian cadence, maybe that's why it souds so familiar

[@danielhayun304]

Its in every jewish/israelian folk music

[@djvoid1]

Sort of like the end of 'I am the Walrus'

[@NanoMan737400]

Just a quick correction: it's F# pedal, not E. But I thought the exact same thing!

[@Caramelldanson]

This is remarkably similar to how high-level Mathematics is done. Many important results, and even the foundations of entire subfields, started with somebody pointing out some interesting little detail in something that appeared quite innocuous. From this point, one must clarify the question at hand, until one has a well-defined problem. Then one can set off in trying to create a rigorous proof (or disproof) of the stated problem. Often, from that point, it becomes clear that there is more information to be discovered from generalizing, or there is an obvious link to other mathematical works, or new patterns and interesting details emerge from the answered question. Probably the most famous example of this is that the solution of the riddle of the Seven Bridges of Königsberg laid out by Leonhard Euler led to the foundations of the fields of Graph Theory and Topology. Heck, there are innumerable silly little pen and paper games that are intimately linked with core results in Mathematics, and that is no coincidence. I've always heard that Music is closely related to Mathematics, and there are a lot of obvious surface-level connections between them, but this really gleans of a much richer interplay between the two fields. I suspect that the concept of Ridge Tones has an analogous counterpart in either Graph Theory, Set Theory, or Group Theory, and if no such property has yet been discovered, then the very proofs presented here in terms of Music Theory would be a very good launching point to finding it.

[@danielnewby2255]

This is easier to understand mathematically: kzbin.info/www/bejne/f5StlWmAq52sd6s&lc=UgwS_NbikM6TG1a48Ud4AaABAg

[@7177YT]

In mathematics though you'd be obliged to rigorously prove assertions about all scales or groups of scales, i.e. the 'general case' instead of demonstrating it for one particular scale and just state/assume it holds for all. ...small aside from a working mathematician (; ....the elegance of his reasoning reminded me of the way neat proofs in combinatorics or graph theory are set up, sure. and yah the rigorous side of music is combinatorics + graph theory + smidge of number theory I guess. (;

[@JacobBanerjee2821]

Music theory is surprisingly similar to mathematics

[@DerikHendric]

Adam Neely has this really awesome video about a talk he presented on Ableton where he demonstrates some mathematics applied on music, he starts with polyrhythms and how their ratios turns into pitch that we perceive as notes. From there he goes to analyze optics and how Newton described light frequencies with musical notes and turns out that given notes when you calculate their absurdedly high octaves, fall on visible light frequencies of given colours. He could extract music from a painting, is so interesting... Link to the full talk video here if anyone gets excited to see: kzbin.info/www/bejne/gJqxfJ-eqNWXgck

[@Torthrodhel]

Do you use the word "one" instead of "you", because mathematics? :) Just seemed funny to me. :D

[@DeflatingAtheism]

2:58 - That sequence of descending major chords is quite a handsome sound in itself.

[@arcioko2142]

it’s a descending F# phrygian scale with major chords with a pedal F#

[@jpob5]

For a practical use, a Ridge tone could be used to the change key on the fly. If you're improvising over one key and the song all of a sudden changes to another key, just play the E over the transition and it will still work (although it may sound bad or jazzy in F Major).

[@Gabriel-jx4or]

I love the "it may sound bad... or jazzy"

[@Pika915]

0:54 I was NOT expecting a Black Keys refference to one of my favorite songs of all time.

[@krozjr5009]

That descending line about half way through you did was wonderful! I loved that walk down the Phrygian scale with a F# Pedal; it inspired me slightly and I found myself a few weeks later making a short piano piece which revolved around a descending line and a recurring minor triad.

[@rtyuik7]

E is so special, it gets TWO strings tuned to it (on a Standard-Tuned, Standard 6-String guitar)

[@barackobama3264]

THREE strings are tuned to D in open g...

[@EnmaDarei]

This is something I noticed when I was in college and I mentioned it to one of my teachers and we spent the whole class (a one on one class) discussing and analyzing it.

[@lenaxo8260]

8:00 "what a good scale" is kinda rare and unreasonably cute thing to hear in a music theory video.

[@WhirligigStudios]

5:59 The sheet music shows D natural (the correct note), but the MIDI piano plays D sharp.

[@MrDemby1]

Whirligig Studios make sure the synth and the vocals are in the same key

[@FrantzesElzaurdia]

@@MrDemby1 pro tip

[@DuffyLONER64]

Actually, no it doesn't. However, the MIDI does play an E natural (the correct note), but the sheet music shows E flat.

[@Holobrine]

Both Eb and Bb are used by all black key major scales.

[@garfd2]

Eb/D# is the iii of B, and so Bb is to Gb. Eb and Bb are a 5th apart, so are B and F#/Gb.

[@zeke7209]

Also F

[@vaclavm4647]

You have only 5 black keys per whole chromatic scale so cant make proper full major diatonic scale without some white keys. Pentatonic maybe but full major scale no.

[@brennanlable]

you have no idea how excited this makes me (or maybe you do?) i was looking at negative harmony and by proxy dualism and inverting the major scale and found that by creating a point between all the notes in and out of a major scale we can find all the "negative" sort of modes. while the famous one that places the point between e and eb and inverting the major scale starting from G is the only one that really retains the important harmonic functions that relate back to c and gives you enharmonically c Aeolian explaining the relationships of modal mixture and parallel majors and minors within a single key. when i tried doing this for all the notes i wound up with basically major scales starting on all the notes and didnt really know what i was looking at however now it looks like theres even more little nuggets of stuff when we flip and invert scales! fun fact the major bebop scale adds the b6 scale degree which basically allows your modes to have 2 identities at a time and introduces the minor iv chord or the ii-7b5 which is basically the same as modal mixture from the parallel minor but it also introduces fully diminished and augmented chords which allows for some crazy symmetry and inverted madness.

[@TheArturoLig]

"let's take a closer look" *Polyphonic theme playing in my head*

[@whichgodofthousandsmeansno5306]

Understanding the math is probably easier then actually playing.

[@duncanw9901]

I'm a mathematician/physicist and absolutely everything in this screamed abstract algebra. Surely someone has analyzed scale relationships as a group under inversion or something? Can anyone point me to literature that does this or similar?

[@derikdavis567]

Dimitri Timozco(sp?) Geometry of Music

[@mrarmaggedon31415926]

I figured it out pretty soon after I started watching music theory vids. Maybe I'm strange, but I write out all the scale and mode tables obsessively, so it's pretty easy to spot. Also make a lot of sense. If you look at the circle of fifths it's easy to see it as two parallel processes of going up in tones: F G A B C# D# and C D E F# G# A# wedged in between. Since this also determines the order in which notes are sharpened or flattened as you go around the circle, E being located where it is, it makes sense for it to be in all the seven white-note scales. Its neighbours A and B exist in 6 of the white-note scales with A not appearing BM and B not appearing in FM, which themselves are the first and last of the white-note scales in the circle of fifths. The patterns are strong in music

[@TheNick1704]

Anyone notice that he actually sung the pitch F# while he said F# out loud? (5:13) Probably subconcious, but I love finding these patterns in human speech, it's pretty fascinating

[@jacobname4310]

Now I’m wondering if 12tone has perfect pitch lol

[@rlbaase3]

F sHaRp

[@wyattstevens8574]

@@jacobname4310 People have asked him, but no, he doesn't.

[@jacobname4310]

@@wyattstevens8574 thanks! 2 year wait was worth it XD

[@uzjwi859]

I think it's important to note that every mode has a ridge tone- Iodian (Major)- 3rd Dorian- 1rst Phrygian- 6th Lydian- 4th Mixolydian- 2nd Aeolian (Minor)- 7th Locrian- 5th In C: C-E D-D E-C F-B G-A A-G B-F I think somewhere in here is the key to why the Major scale is so perfectly balanced.

[@yoavshati]

I think the simpler explanation can come from the circle of fifths. C major has the notes from F to B in the circle of fifths, which means the major keys they are roots of have between 1 flat and 5 sharps. E is the second note to get flattened and the sixth to be sharpened, so our 7 major keys just barely fit in there If you wanted to do the same for natural minor keys, you're still going from F to B, but now it's 4 flats to 2 sharps, so the minor Ridge tone is G

[@mss11235]

Yup

[@EneldoSancocho]

In fact i think there should be music theory with scales and chords symmetries in math group theory, there are so many good examples

[@livi39]

Liked the shout-out to The Black Keys at 0:50!

I love diving into modal theory and tonality mirroring as patterns of steps, shapes and proportional symmetry. I enjoyed this episode. Well done!

[@karinacomposer]

You sir, are awesome. Came here for a KZbin recommendation and thought it would really be about Facebook solving a musical mystery, but ended up getting an uplifting enrichment of knowledge. So thank you!

[@korvette21]

I love these videos, and I know they're already kinda long, but slowing it down a smidge would keep me from having to pause it and go back to look at a previous screen. I kinda like to play this stuff as I go along.

[@shadowhenge7118]

Its funny. I noticed a pattern in the numbers with the third notes in the scales but you only see it when you plot the numbers (semitones between notes method) plotted out across all modes of a given scale. I love the mathematical structures of music.

[@marsegan8788]

I've always been fond of the symmetry of Dorian. It's interesting that it relates to this question. It's like it's own little retrograde inversion.

[@ilikeplayingffftonecluster851]

Mars Egan Come to Florida right now and you’ll learn more about Dorian than you could have ever imagined.

[@marsegan8788]

@@ilikeplayingffftonecluster851 oof

[@wege8409]

It's neat too that if you use the triangles of a tonnetz, dorian gets you a straight row of interlocking triangles if you consider the leftmost triangle to be the root. △▼△▼△▼

[@jakescheps8449]

As soon as you finished explaining the method of finding the mode which inverts the original, I wanted to check if it worked for another example and chose melodic minor; and of course it worked, because I unpause the video and that's exactly what you did next! I'm working through some other properties now; for instance in the major collection, every mode has a different ridge tone which essentially pairs modes which invert to each other. Since there are an odd number of notes in the collection, one of them must invert to itself, and dorian has the root as its ridge tone because dorian is its own inversion. Also, if you put the modes next to each other, and work out the ridge tone for each, the ridge tones spell out a mode in the opposite direction from how you laid out the modes; so ridge tone of D dorian is D, E phrygian is C, F lydian is B, and so on. I'll probably have to play with this more before it all makes intuitive sense. If you like this kind of thing, I've got another "piano layout" puzzle which I haven't seen elsewhere: all of the white keys make up a C major scale, and all of the black keys make up an F# major pentatonic scale. Why should the complement of a major scale be a pentatonic scale rooted a tritone away? I found thinking about this was a good way to get some insights into what's special about the composition of the heptatonic major scale collection, and how we choose to form our pentatonic collection as a subset of the heptatonic one.

[@mikahkilgore4972]

That progression at 2:58 where you list all the major keys with F# is amazing!!! It’s super simple, but I still love it! Also, I want my name to be attached to something. The Kilgore (incert term/phrase/other theoretical tool here). It’ll probably never happen, but it’s fun to think about.

[@DominicAirola]

2:58 that actually sounds really cool

[@abuzzedwhaler7949]

Love that you sketched out the Mandelbrot set :)

[@ivyssauro123]

this is both mind blowing and incredibly frivolous at the same time haha

[@zyaicob]

Welcome👏to👏music👏theory👏

[@khartian]

@4:50 12tone: Every scale has an inversion Dorian: I would like to have a word with you, sir

[@stijnvanloock3194]

Well technicly you can invert to yourself if you say you work mod 3 for example 2 inverts to itself

[@zornsllama]

@@stijnvanloock3194 or, like, 1

[@stijnvanloock3194]

@@zornsllama Or indeed like 1 in pretty much every monoid 😅

[@zornsllama]

@@stijnvanloock3194 in any group, monoids don't require a notion of inverses

[@stijnvanloock3194]

@@zornsllama No indeed they don't but since you have that 1*x=x with 1 the id of the monoid and x an element of the monoid so 1*1 = 1 wich can be a basic notion of inverse no? In a group you just demand that this notion can be extended to al elements wich doesn't mean we can't study invertable elements of monoids. But i agree that in case of groups it is more outspoken

[@misterguts]

2:40 Ha! Talks about a "Ridge tones", draws the Mid-Atlantic Ridge!

[@LunaBari]

Ridge joke, much?

[@dylanmeiler7082]

That galaxy on the second last slide near the end is freaking me out: soul gazing stuff. Great video!

[@plasterpenguin]

I was so relieved when this went deeper. Thanks for staying authentic!

[@xenontesla122]

I’m definitely going to try this in a musical context. Hearing the tonic of each key with F# as a pedal tone sounded really cool.

[@hiqwertyhi]

this is one of the most entertaining and intellectually stimulating music theory videos I've seen, right up there with the jacob collier/ june lee interviews. thanks for making this :)

[@nonewmsgs]

With this is mine I'm thinking of having an e as my low string and high string on guitar

[@relevantusername1575]

horsey not a knight you’re a revolutionary.

[@chicowonder8872]

WHY DID I NEVER THINK OF TUNING MY GUITAR THIS WAY?

[@ChristyAbbey]

I long wondered about why a guitar is tuned the way it is. Then I figured out that it's the only way you can play all major chords with three fingers (starting, of course, with E). While this is a true thing, I actually have no idea if that is the primary reason, or just a coincidence.

[@schall3603]

I think that's more down to the fact that, by having the strings a major 4th (5 semitones) apart, you can put a chord tone on each string without having to stretch your hand too wide. Some people do actually use an "all 4th" tuning (EADGCF), but the standard has become to have the top and bottom string be the same note, so a major 3rd (4 semitones) has to be put in somewhere. I've not looked into this myself, but I suspect that there isn't another place to put that smaller interval in a way that still has all the strings be tuned to white keys (which is probably a concession to making the guitar easier to teach).

[@ChristyAbbey]

@@schall3603 Likely. I didn't really wonder about it until I started experimenting with alternate tunings, something I'd never done until my kid wanted to learn how to play certain metal songs (mostly tuned to C#m, the complement to E). My twelve-string is also tuned to an open C, which makes non-barred chords a bit of a pain. I suspect one of the reasons for not even considering the length of hand aspect is because I have five fret stretch on a dreadnaught, so nothing is out of reach for me. Good points. Thank you.

[@noahmcgaffey797]

@@schall3603 the major third could be the c and high e strings (EADGCE) but then you have to handle the minor sixth on the open E major chord

[@aspirativemusicproduction2135]

I tuned my guitar to C( sixth string is C). It's still in standard tuning. I don't know what genius decided to tune guitars to E standard. There is no reason.

[@FelixFraenkel]

If I recall correctly, the tuning of the guitar is just compromise of being as symmetrical as possible (tuned in all 4ths except one major 3rd) while being able to barre chords - which you can shift around the whole neck, so it's kinda symmetrical again

[@oboemadness1995]

Man, this was an intense one. Whewwee

[@glebkuzmin8062]

"except the white keys never recorded Little Black Submarine" LOL

[@xerogh1821]

Great vid, you always find these interesting theory facts and break them down/present in a creative way that just makes sense. Keep them coming! But I will say that my brain hurts after this one... going to need to watch it again. Maybe I'll compose something using Major & Phrygian then switch keys a few times to see the parallels? I'll get it eventually... maybe...

[@tamsinlm]

Oh god I'm having flashbacks to Abstract Algebra!

[@crimfan]

Symmetries!

[@willcollings5681]

A good introduction to groups, normal subgroups, and generators as well, if you're coming at it from the modern algebra perspective. This is awesome!

[@gregonline6506]

So satisfying the gentle brain massage following your explanations does to my brain. Love it.

[@Huntracony]

I'm guessing the major scale has many, many exciting set theory properties, at least in part, because it's the scale that music theorists are most familiar in. If there was as much attention on any other scale, it would probably also stand out as having many exciting properties.

[@auxchar]

So you could use E as a pedal note/passing tone to modulate to every scale with a root in the scale of C major?

[@yitzharos]

Based on diatonic harmony and the layout of Major and minor based on the 12 tone octaves, I asked which Note is played the most, or always appears in each key. This note is F# which means most modal changes should center arpund the F# tonic chord structures and variants.

[@charper13126]

Anybody else catch the Polyphonic Easter egg there? Awesome video as always!

[@JakeDiToro]

Even as I was laughing to myself I could hear the intro music in my head.

[@eglathren]

I was looking for this comment

[@johnnymaddocks]

I love polyphonic but didn't catch it :( where was it

[@JakeDiToro]

@@johnnymaddocks 2:46

[@mementomori8930]

Hi i just discovered this site and loving it so much! I’ve been watching your video a lot to the point that even when i stopped, your voice kept ringing in my head lol

[@randomguy-tg7ok]

Well my answer to this is that it's because E is the second flat - which I where the black-key flat majors begin - and the sixth sharp - which is where the black-key sharp majors begin. Why E? Because reasons. G is in every white-key minor. B is in every white-key lydian.

[@abramthiessen8749]

In 31TET major still has the same ridge tone. I define a 31TET whole step as being 5 steps, and a half step as being 3 steps so major is 5,5,3,5,5,5,3 steps. In this way, all the common scales transfer over by just changing 12TET steps into 31TET steps. And because for the purposes of symmetry, only the sequence of steps matters regardless of the tuning, any tuning that has only one size for whole steps and half steps will also have the same ridge tones for the familiar 7-note scales. 53TET, on the other hand, has different sizes of whole steps (8 or 9) so such logic no longer holds. Major is 9,8,5,9,8,9,5 steps, which is based on 5-limit tuning major's steps of 9/8, 10/9, 16/15, 9/8, 10/9, 9/8, 16/15 pattern which I would describe as "true" major, and it completely lacks ridge tones because the 2nd isn't half-way between the root and the 3rd. I want to play with an alternative major and minor scale incorporating the harmonic 7th, but don't have a 31TET keyboard yet (I am working on the design and may never build it). Anyways it would be similar to Mixolydian for major and only change the 7th degree of the scale from 15/8 to 7/4. If you follow negative harmony, negative Mixolydian would have a 6th degree of minor at 21/16 from the root (8/7 from the 5th). These scales have even less symmetry as the 31TET version of this Mixolydian would be 5,5,3,5,5,2,6. Sorry for rambling about my idiocentric tunings again.

[@benjaminmarks8765]

Dear God, 53tet? Why?)😂

[@marktyler3381]

I'm confused, but it sounds fascinating. Are you talking about 53TET meaning breaking the octave into 53 steps?

[@ashtarbalynestjar8000]

This is because 31TET is still a meantone temperament, where four stacked fifths make a major third. A major scale is just a chain of 6 fifths, 5 above the root and 1 below; for example, C major is [F-C-G-D-A-E-B]. So let’s take a really long chain of fifths, and mark each major scale with a white-key root on it: F major: ...-E♭-[B♭-F-C-G-D-A-E]-B-F♯-C♯-G♯-D♯-A♯-E♯-... C major: ...-E♭-B♭-[F-C-G-D-A-E-B]-F♯-C♯-G♯-D♯-A♯-E♯-... G major: ...-E♭-B♭-F-[C-G-D-A-E-B-F♯]-C♯-G♯-D♯-A♯-E♯-... D major: ...-E♭-B♭-F-C-[G-D-A-E-B-F♯-C♯]-G♯-D♯-A♯-E♯-... A major: ...-E♭-B♭-F-C-G-[D-A-E-B-F♯-C♯-G♯]-D♯-A♯-E♯-... E major: ...-E♭-B♭-F-C-G-D-[A-E-B-F♯-C♯-G♯-D♯]-A♯-E♯-... B major: ...-E♭-B♭-F-C-G-D-A-[E-B-F♯-C♯-G♯-D♯-A♯]-E♯-... In 31TET the chain of fifths doesn't close as fast, but also you have the modes of the chromatic (12-tone) and enharmonic (19-tone) MOS scales to deal with. And because they’re also built on chains of fifths, they still have a ridge tone.

[@abramthiessen8749]

@@ashtarbalynestjar8000 The circle of 5ths is the basis of pythagorian tuning and is an alternative to 5-limit tuning, but I think that it ignores the importance of the major 3rd and minor 6th, which I believe comes from its place in the overtone series as the 5th harmonic shifted down by 2 octaves (the 5/4 ratio). This is a far simpler ratio to the 81/64 ratio that Pythagorian tuning suggests. For the purposes of 12-TET and 31-TET 81/64 is indistinguishable from 5/4, 53-TET is the first good tuning system that can distinguish them. And in fact my method for choosing 31TET and 53TET is due to their better approximations of the 5th, and 7th harmonics in the overtone series even compensating for the advantages they get from having smaller step sizes.

[@christophervaca7116]

You blew my mind. Great job.

[@Fempath]

This is awesome! I love finding a new way to think about the major scale, this is very informative 😊

[@Marijnzor]

Played around with this idea in a two-dimensional harmonic map a bit. The most concise and correct answer to this that I can give is "Because the natural major scale is constructed symmetrically across the major third axis." The scale consists of: Root note P5 down from root P5 up from root Two P5's up from root And then inverted for the major third Major third P5 up from major third P5 down from major third Two P5's down from major third (and yes, this means that the major scale technically has 8 notes and I will die on that hill) What's interesting as well is that you can construct a scale that is symmetrical across the perfect fifth axis, and then you build a scale where the fifth is the only note that exists in all of its children For example: Let's build a scale using the following notes: Root M3 up from root M3 down from root Two M3's down from root And then mirrored across the P5 axis: P5 M3 down from P5 M3 up from P5 Two M3's up from P5 The resulting scale would be C D# Eb E Fb G Ab B If we wanted to eliminate enharmonic equivalents and write it down in western notation that would be something along the lines of "Ionian #2 b6 no 4" Which is a scale that has G in all of its children. It also points out how limiting and out of touch with reality the western notation is, since we now find ourselves having to use a 6 note name for a scale that technically has 8 notes. Fun.

[@ndykman_pdx]

It has to be this way. Given a major scale, we can modify (flat or sharp) one note to get another major scale. If we repeat the process, we have to pick a different note or it wouldn't be a different major scale. We can do this six times before we get back to the same scale. But, we have seven notes, so there must be a note we did *not* change.

[@12tone]

That's an interesting way of looking at it! Major scales can smoothly transform into each other in ways that not every scale can, which makes a ridge tone an inevitability. However, unlike the symmetry explanation, this isn't generalizable: It doesn't work for other scales with ridge tones. for instance, melodic minor scales have a minimum change requirement of 2 notes to get to another melodic minor scale, and yet they still have a ridge tone. Still, another neat property of major scale, and another good perspective on the initial problem. Thanks for sharing!

[@ndykman_pdx]

@@12tone Symmetry is a stronger property for sure. I'll have to double, double check, but the ability to make the same scale at a different root by changing only one note (or two) might fall out of the symmetry property.

[@Ynherag]

2:39 you're looking for "découvreur" :-)

[@doim1676]

If you look at the circle of fifths youll see that you just add a sharp if you wanna go through all the major scales of the white keys. And e happens to be the last note getting a sharp, so it is in all major keys along the way

[@aaronmyers6686]

Why did that walkdown of all the major scales with F# in them sound so beautiful? It's not a walk down of a single scale, since all the chords are major. At least, I don't think - I mean, both Major and Phrygian have minor chords...

[@samlawman3365]

A much easier way of explaining it would have been to refer to the circle of fiths. Then you can have quickly concluded also B is the only commom note in lydian scales starting on a white key, A for mixolydian, D for dorian (should also have interesting symmetries), G for natural minor, C for phrygian, and F for locrian.

[@eruantien9932]

SO. I made a spreadsheet for just intonation based on A440 the other day. Basically I assumed JI for A440, and then calculated the frequencies that JI required for all other key-centers using the frequencies given by A440. And E was the only note that was *always* in tune.

[@francoisrd]

After about the 1 minute mark, I had a feeling set theory would make an appearance in the video. Glad my intuition was correct.

[@SoundsOfTheWildYT]

This video could be remade purely as a video about reflectively symmetric subsets of ordered sets, with the music part purely as a side note/corollary of the proven result.

[@zyaicob]

@@SoundsOfTheWildYT i don't have anything cool to add but i really love this comment

[@diegoromero4471]

then for example can i modulate in any major escale (and their subsecuent modes) whit a melodý tha contains the 3th grade form one especific root note? (sorry for my inglish)

[@Ngasii]

Super ready for next week's song🔥🔥🔥

[@mr88cet]

Admittedly, I haven’t listened to but the first minute or so of this. I paused it to think about it, and in hindsight it’s pretty obvious: What would you have in the scale if you didn’t have an E? Unless you’re getting into double-sharps, the only alternative would be Eb. An Eb is only going to be present in major keys Bb, Eb, Ab, ..., which obviously aren’t white-key majors. OK, listened to the rest of it. Good stuff!

[@mikegeld1280]

Really,wow,,,,had no idea,glad you guys informed me of this ,dont know if I could of continued with my music career without that information, cheers😏

[@ThisIsTeeKay]

F# Phrygian... was that used in Feist's "I Feel It All"

[@MuzikBike]

also every single Boom Kitty song

[@twistedgwazi5727]

@@MuzikBike Most of his music uses Phrygian Dominant, not Phrygian.

[@enricopersia4290]

You always put another file in my music theory mental library, thanks!

[@carlsong6438]

2:59 actually sounds rly good as a concept. Pedal the third, descending chords

[@11kravitzn]

This is super easy to see on a circle of fifths. Major scales consist of 7 consecutive perfect fifths, the root being the second of these. So scales with their root being one of these consecutive fifths will include the second-to-last of these fifths, which is a major third above the root of the original scale.

[@arastoomii4305]

There is actually a very easy way to understand this. If you start a cycle of 5ths on F to gather 7 tones ending on B, you will get C major, now since all major scales of C major (excluding F major) have sharp accidentals (and continue your cycle of 5ths process), you can simply have E and even B (last 2 tones of your initial cycle) in all of the major scales, except F which has B flat so that leaves you with only E.

[@Herfinnur]

Wait: you have a side channel and I don't know about it!? Thank you for making this video, it gave me lots of ideas and inspiration, and I have had neither for about a month!

[@dethronedemperor]

Really interesting! Maybe this is why guitar standard tuning is based on E

[@cognitivedissonance8406]

When you ran down the scale with F# ringing, it was basically the structure of the breakdown at the end of I Am the Walrus

[@anirudhsilai5790]

That's awesome! I never noticed that either but it makes great sense

[@columbus8myhw]

But _why_ does major have a line of symmetry? It's easier if you stop thinking of it as CDEFGAB (which has the uneven pattern of WWHWWWH), and start thinking of it as FCGDAEB (which has the very even pattern of 5555555).

[@BarryMagrew]

One explanation is that the scale is “well-formed.” If you generate notes with a single interval, like the 5s here, then rearrange the notes to fall within a single interval of periodicity (octave, say, or triave), then, whenever your scale has exactly two different sizes of steps, the scale is well-formed. If you try this with 5s, 5,, 55, 555, 5555, etc. the resulting scale will have either two different step sizes or three.(The exception, of course, is in equal temperament: if you generate the whole chromatic scale this way, you’ll end up with just one step size, which is also considered well-formed.) In general, the ones that have two step-sizes are the well-formed scales. A well-formed scale with an odd number of notes will have this symmetry. The black-key pentatonic is another well-formed scale, where the symmetrical mode is Ab Bb Db Eb Gb (Ab), 23232. Depending on tuning, some versions of the Bohlen-Pierce scale are well-formed.

[@HipsterShiningArmor]

The problem with that pattern is that because F is the first note I will always see it as F Lydian rather then C Major.

[@mss11235]

​@@HipsterShiningArmor Okay. Then just convert...

[@IanWagner94]

I've asked myself that yesterday, thank you

[@Aux1Dub]

The drawing was driving me crazy. I couldn’t take it.

[@wilh3lmmusic]

This applies to every mode: B in Lydian E in major A in mixolydian D in Dorian G in minor C in Phrygian F in locrian

[@garfd2]

My brain likes this. This is really easy to see with the circle of 5ths. Take it and highlight/shade in C Maj. Notice how D (Dorian) is in the middle of the 7 consecutive notes, then notice how C (Ionian) and E (Phyrigian) are equidistant from the middle. I keep referring back to this Dorian Brightness Quotient idea I got from Neely's "Why Is Major Happy?" videos 'cus it comes in handy with things like this.

[@Astronomater]

don't worry about having a sponsor for each video. make your ends any way you can.

[@danielnewby2255]

Music theory is funny... this is about the most difficult way to analyze something that is a fairly obvious mathematically. Essentially we're asking what series of numbers {a, a+k_1, ... a+k_6} mod 12 always contains an element congruent to some n (4, in the case of the major third). When looked at from this perspective it's curious, but it *is* entirely coincidental that the major scale inherently has that property: When you build the major scale as a cycle of fifths: C-G-D-A-E-B you're building that set in intervals of of 7 (semi-tones), and since 7 is coprime to 12 it fully covers the set of numbers mod 12, E just occurs relatively late in that sequence--the anomaly in the sequence is the 4th, which exists in place of the naturally occurring tone in that sequence, the tritone... and this explains E's presence in B. Two is not coprime to 12, which explains the recurring (and fully overlapping) pattern for the whole tone scale. Likewise, 3 is not, so you would see this behavior in the half-whole or whole-half scales as well.

[@nikitaustinov2864]

Love the Polyphonic reference

[@mebamme]

Next question: why does 2:59 sound so nice?

[@AlexKnauth]

Huh, you're right but I don't know why. In counterpoint it's called oblique motion when one line stays still and the other line goes toward or away from it, and oblique motion can create a feeling of independence and stability mixed together, but that doesn't explain all of it. The last two chords of that line also form a tritone-substitution resolution for a satisfying ending, and that doesn't explain all of it either. Any other ideas?

[@denogowli]

Haha yeah I also realized how nice of a chord progression that was with the F# always in the melody.

[@UODZU-P]

thats interesting, I came across the same geometric relationship there at work when converting polar coordinate systems. Reflecting the notes across that symmetry line has the same affect as rotating 45deg and reversing parity (ascending clockwise / counterclockwise) Edit: the artist had labeled some directional animation files with 0/360deg as North increasing clockwise and I was converting it to the traditional coords of 0/360 East increasing counter clockwise

[@Armakk]

They say talking about music is like dancing about architecture. This was like origami about be-bop in the finale of INTERSTELLAR on a tilt-a-whirl on acid.

[@freesk8]

Awesome video! Thanks!

[@je-pq3de]

pinging adam neely and david bruce to explore compositionally

[@dreistein]

Seems easier to understand just by listening. Most of the doodles were cute but not necessary - as far as I could make them out under the moving arm, wrist, hand and pen.

[@BlightVonDrake]

Me: Been trying to figure out music for years so I can eventually make my own. "Ok, I think I've figured it out. Scales are the most important thing to know how to work, because they carry the mood and set up tension and release in ways the ear can understand, which makes music." 12tone: "The specific key you're working in rarely matters." Me: *_Commence desk inversion._*

[@thebobthebobanite6287]

Key is different than scale. A key is a note, the scale is the internal pattern. The scale 100% matters, the key defines what register the song is in.

[@BlightVonDrake]

@@thebobthebobanite6287 Ohhhhh. I'd always thought they were the same thing. Thanks for letting me know!

[@Tabu11211]

Ian is the best!

[@joshpohlner8716]

Can someone help me get my head round this? What I'm getting from the video and comments is that if you use the circle of fifths and since there's 1 white key "flatter" than C and 5 that are "sharper" and Phrygian can go one note flatter before losing the root and 5 sharper before losing the root (both of these cases being E) then it's in 1 key flatter than C and 5 keys sharper than C? Or have I missed the point and I'm just pointing out another interesting property? Thanks in advance

[@lydiasteinebendiksen4269]

Like Ford Prefect (the beetlegeuise dude) thought "Isn't it enough to find a garden beutiful without tyinking there are fairies at the bottom of it too?"

[@celliot]

What’s with all the elephant doodles?

[@NunoTiagoMartins]

This sounds a lot like symmetry groups in physics/maths :)

[@mistershaf9648]

E is special because E is a perfect 5th above A, which is what we tune to an even frequency (A110, A220, A440…).

[@xatnu]

It's the leading note of F major, that's why, I think. The major seventh is the highest in the circle of fifths, and F is the lowest of the white keys in the circle of fifths. Start at F and go up the circle of fifths through all the white notes until you get to B. You always have enough room for the E to fit in. It's hard to explain without a picture. Now I'll watch the rest of the video and see what conclusion you came to.

[@RizalBudiLeksono]

I understand your reference. I thought the same too.