How Facebook Helped Solve A Musical Mystery
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How Facebook Helped Solve A Musical Mystery

hey, welcome to 12tone! has anyone ever thought
about how E is the only note that’s in the major scale of all seven white keys? that’s the beginning of a post made by Kieran
Ridge to a music theory facebook group early this year, and barring some extreme pedantry
about note names, it’s absolutely true. you can pretty easily double check that if
you’ve got a piano handy. I don’t know about you, though, but despite
having over a decade of piano experience, I had never noticed, and judging by the replies
to Ridge’s post, I’m not the only one. and on the surface it seems really weird: why
would this happen, and more importantly, what’s so special about E? well, let’s find out. (intro sequence) I think the first question we need to answer
is just, like, who cares? I mean, first of all, the major scale has
7 notes, which means every note’s gonna be in 7 different major scales. the 7 that E belongs to happen to be based
on the 7 white keys on a piano, but that layout is just for convenience: there’s no functional
difference between the white keys and the black keys except that the white keys never
recorded Little Black Submarines. it’s all just labels, and from a theory standpoint
those labels don’t really mean all that much, so any property that’s inherent to the white
keys has to just be a coincidence, right? well, no, not quite. it’s true that for the most part we can treat
white keys and black keys as identical, and as a music theorist I do that all the time,
but there is one thing that sets the white keys apart: they’re the notes of the C major
scale. (bang) this, again, rarely matters, because
the specific key you’re working in rarely matters, but in this particular case it means
we’re looking at a sort of scale-based fractal: we’re building major scales off all the notes
of the major scale, which means this property might not be quite so arbitrary after all. to demonstrate, let’s try it somewhere else. if we take D major (bang) and then build a
new major scale off each of these notes, they’ll all look pretty different, but every single
one will contain F#. again, you can pretty easily confirm that yourself. in fact, if you do this with any major scale,
you’ll find that the shared note between all the secondary majors you can build off it
will always be the third note of the parent scale, which lets us answer our initial question. why is E in every white key major scale? because
the white keys are the notes of C major, and E is the third note in that key. cool, episode over. bye! ok, maybe we’re not quite done yet. after all, this isn’t really an answer, it’s
just kicking the can down the road a bit, but at least now we’ve found a better question:
what’s so special about the third note? and this is where theorist Ian Ring picks
up the banner and runs with it. I’ve talked about Ring before on this channel:
he’s the guy who runs the database of scales that I use for my random scale challenge videos. he’s also in that facebook group that Ridge
posted to, and he decided to do a pretty thorough analysis of the concept, which he dubbed ridge
tones in honor of their discovererer. their discovererer. the person who discovered them. this gives us an even more precise question
to ask: why is the third note of the major scale a ridge tone? is it just a coincidence,
or is there something more meaningful going on here? well, I don’t believe in coincidences, at
least not in music theory, so let’s take a closer look. we said that, in D major, the ridge tone is
F#, but let’s confirm that by making a list of all the major scales that F# is a part
of. obviously, there’s F# major, where it’s the
root. then there’s E major, where it’s the major 2nd, D, where it’s the major 3rd, and
moving on, in C# it’s the perfect 4th, B the perfect 5th, A the major 6th, G the major
7th, and then we’re back to F# again. so what does this accomplish? well, if we take these notes and treat them
like a scale (bang) then suddenly we have what’s called F# phrygian, which is kind of
like F# minor but with a lowered 2nd. this tells us something pretty important: the list
of roots of all the major scales that contain a given note is the same thing as a phrygian
scale built off that note. the two groups are equivalent, which means
that any property of one is also a property of the other. now, we can compare like with like: major
and phrygian are both scales, so we can just do some scale theory to them. we don’t have to worry about those weird,
nesting pitch collections we were building earlier, we just have to look for connections
between major and phrygian, which lots of people have already done for us. we haven’t solved the problem yet, but we’ve
managed to move it into familiar terrain. so are there any connections between major
and phrygian? yeah. there’s a lot. they’re extremely related scales, but for
our purposes, we only actually care about two things. the first is that they’re what’s called inversions
of each other: phrygian is just a major scale turned upside-down. like, to build major, we start with a root,
then go up a whole step, whole step, half-step, whole step, whole step, whole step, half-step,
and if we wanted to build phrygian instead, we could start on a high root, then go down
a whole step, whole step, half-step, whole step, whole step, whole step, half-step. it’s the same interval pattern, the only difference
is which direction it’s going. and this makes sense in the context of our
problem: in order for F# to be in any given major key, it needs to be a major-scale interval
above that key’s root or, put another way, the root needs to be a major-scale interval
below F#. that leads us to a crucial observation: in order to find all the major scales a note
belongs in, we just have build an upside-down major scale descending from that note, and
as it turns out, upside-down major is right-side-up phrygian. but having an inversion isn’t enough to give
you a ridge tone: every scale has an inversion. that’s how inversions work. no, in order to fully explain what’s happening
here, we need to turn to our second connection: major and phrygian are modes. modes are scales that share all the same notes
but treat a different one as the root, so if we take D major (bang) and F# phrygian
(bang) we see they both have F#, they both have G, they both have A, and so on. the only difference is what note they start
on. this gives us the final piece of the puzzle:
we know that the roots of all the major scales that contain F# form the notes of F# phrygian,
and we know that the notes of F# phrygian are equivalent to the notes of D major, which
means that, by simple deductive reasoning, the roots of all the major scales that contain
F# form the notes of D major. and now we finally have a satisfying answer: the major scale
contains a ridge tone because its inversion is one of its modes, so E is in every white
key major scale because it’s the root of the phrygian, or upside-down major, scale that
shares all its notes with C major. and once we’ve got that, we can even apply
this to other scales. for instance, melodic minor (bang) inverts to a scale called dorian
flat 2 (bang) and it turns out that dorian flat 2 is the second mode of melodic minor,
which means that this scale also has a ridge tone: if you build a melodic minor scale off
any note from D melodic minor, for instance, you’ll always wind up with an E. but this is kinda hard to search for: you
have to invert the scale, then check it against each of the modes to see if you can find a
fit. fortunately, Ring found an easier way, but
to understand it, we’ll have to switch from staff notation to clock diagrams. Sideways did a video on these a while back,
which I’ll link in the description, but real quick, they work like this: you draw a circle
out of 12 little circles, each representing a different note in the scale. this top one is the root, then going clockwise
we have the minor 2nd, major 2nd, minor 3rd, major 3rd, and so on. next we just fill in all the circles that
represent the notes we’re using, and boom, we’ve got a scale. for example, major’s clock diagram looks like
this, and if I just draw a dotted line through it, connecting the major 2nd to the minor
6th, you may notice something interesting: the bottom half is a reflection of the top
half. all the same dots are filled in. the line is behaving as a sort of mirror,
which means that starting on the root and going clockwise is exactly the same as starting
on the reflection of the root and going counterclockwise. and, hey, would you look at where the root
reflects to in major? it’s our old pal, the 3rd. that’s right, being across this mirror
line from the root is the same thing as being a ridge tone, so instead of messing around
with inversions and modes we can just look for scales with reflection symmetry. this all follows pretty directly from the
stuff we’ve already talked about, but I’ll leave the full explanation as an exercise
for the viewer. or you can just read Ring’s article. and some scales even have multiple reflections,
which means multiple ridge tones. as an extreme example, take the whole tone scale: (bang)
here, every note is a whole step away from each of its neighbors, making it the same
pattern all the way through. thus, the whole tone scale inverts to the
whole tone scale, and every mode of the whole tone scale is also the whole tone scale, so
every note of the whole tone scale is a ridge tone in the whole tone scale, and I promise
this is the last time I’m gonna say whole tone scale. scales with multiple ridge tones are pretty
rare, though: heck, most of them don’t have any. only about 15% of 7-note scales have the necessary
symmetry, which makes this yet another on the long list of rare and exciting set theory
properties that major happens to possess. what a good scale. so where does that leave us? well, obviously, I’m excited about the property
itself, but what I really love about this is that it all came from some idle musing
about key signatures. Ridge noticed a silly little property and
shared it not because it was obviously groundbreaking, but because it seemed interesting. music theory doesn’t always have to be about
grand models that probe at the deepest levels of musical meaning: sometimes it can just
be fun. it turns out ridge tones are connected to
some pretty serious scale theory, but even if they weren’t, isn’t it just cool that E
is in all the white key major scales? I think it’s cool. everything else is just a bonus. anyway, that’s it, but before you go, you
may have noticed that this video doesn’t have a sponsor. that’s because I’m trying to cut back on how
many of those I do: I talked about this in my latest update video on my side channel,
but the short version is that if most of my income is coming from sponsors then my financial
incentive isn’t to make good music theory videos, it’s to sell you products. and they’re good products, I do genuinely
like the things my sponsors do, but I’m a music theorist, not a salesperson, and the
more I focus my energy there, the less I have to spend on the things I want to make. 12tone’s my full-time job, though, which means
to keep the lights on I do have to get that income from somewhere, so I figured I’d use
this opportunity to remind everyone how valuable Patreon support is. even 1 dollar a month helps, and you get to
help pick the songs we analyze. get ready for next week’s, by the way: it’s
gonna be a good one. plus I’ve set some goals over on Patreon to
let me reduce the number of sponsors I do per month in a sustainable way. so yeah, if you can afford it, there’s a link
to my patreon page in the description and I’d really appreciate your support, but as
always, if you can’t afford it or just don’t want to, that’s fine too. 12tone’s free on purpose. you don’t owe me your money. anyway, thanks for watching! normally I plug
my patreon here, but since I just did that, uh… here’s some links to my social media
accounts instead. follow me on twitter. you can also join our mailing list to find
out about new episodes, like, share, comment, subscribe, and above all, keep on rockin’.

100 thoughts on “How Facebook Helped Solve A Musical Mystery

  1. Some additional thoughts/corrections:

    1) Check out Kieran Ridge's music! It's really good!

    2) I forgot to link to the video on my side channel so for those of you who are curious, here it is:

    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.

  2. 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.

  3. I don't even see why this is a question. Orders of sharps (with the key in which they appear in brackets) is : F# (G) C# (D) G# (A) D# (E) A# (B). Now simply add the key of C (has no sharp) and the key of F (has a B flat) and there you have it, all 7 white notes keys. E# would appear in the key of F# major, more often notated Gb though (at least in jazz).
    The reason E is in all white key scales is because it's the last one of the sharps to appear.
    Same reason for B flat to be in all black key scales : it's the first flat to appear…

    The thing with the phrygian scale just seems to be a tautology. If every white key major scale has E in it, they are the notes of the C major scale and therefore, automatically, of the E phrygian scale. Nothing new…

    In short, this all seems to be a lot of overthinking for something that seems very simple. Thanks for the video though, the symmetry thing is still interesting to look up.

  4. This is just like math – except the "coincidences" are often snatched up by conspiracy people. I wish numerology was this easy to debunk

  5. If you sort every mode in order:
    Lydian (F)
    Ionian (C)
    Mixolydian (G)
    Dorian (D)
    Aeolian (A)
    Phrygian (E)
    Locrian (B)

    and pick two opposite modes (like ionian-phrygian or lydian-locrian) you'll find that for each construction of the first mode using only white keys, you'll also get the note from which the opposite mode is built. For instance:
    If you pick ionian (major, starting from C) your opposite mode (counting from bottom to top) will be phrygian (built from E). Every major scale starting on a white key will have an E.

    If you pick lydian (F), your opposite mode will be locrian (built from B). This way, every lydian scale starting from a white note will get a B.

    If you pick mixolydian, you'll find that every mixolydian scale built from a white key has an A (from the opposite mode, aeolian or minor)

    Dorian doesn't have any "opposite" mode because it falls right in the centre (i'm guessing it also has to do with the fact that it's symmetrical)

  6. 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!

  7. 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.

  8. 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!

  9. hey just checking if you still do music analysis. If you still do could you maybe breakdown a tool song their new album just dropped.

  10. Generalization to pentatonic fails if we assume certain things:
    CDE GA
    DEF# AB
    EF#G# BC#
    FGA CD
    GAB DE
    ABC# EF#

    Obviously this will "qualify" from a diatonic point of view – you ever get, say D# and E# or Eb and Fb simultaneously, since this basically reduces to dropping tones out of the major scales – E either "is there" or "drops out". However … let's "rename" these notes instead, such that we use arabic numbers for them. I think we shouldn't think of the pentatonic scale really as root-second-third-fifth-sixth, but rather as it's own set of "root-second-third-fourth-fifth" that mean different things than in the diatonic context.

    123 45
    23b4 5b1
    3b4b5 b1b2
    45b1 b2b3
    5b1b2 b3b4

    Conclusion: this is a property that is not universal to Moment of Symmetry-scales / Scales with Myhill's property, since the pentatonic scale is one of them, just as the diatonic is.

  11. Is this why very often in metal music the E note just seems to get thrown into everything All the time despite it not necessarily making a ton of sense?

  12. 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.

  13. 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

  14. 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

  15. Here's another "mystery" for you: If you take the 12 notes of the chromatic scale and remove all the notes belonging to a major scale, you're left with a major pentatonic a tritone apart.

  16. 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).

  17. Fellow leftie! You know what's great about being a left-handed pianist? You can transcribe chords with your left hand while you phrase them on the keys with your right hand. 🙂

  18. The 3rd thing, where you took the major 3 and made a scale and it became phrygian, yeah thats what i do for minor scales too, the 6th of any major scale will build your minor scale.

  19. Sooo… the Whole tone scale's inversion, call it the anti scale, is itself. So its a Majorana scale, then? 

    (Guess this could also be part of string theory???)

  20. You sir, are awesome. Came here for a Youtube 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!

  21. Best video in a while imo
    I like that thing about E because I play bass, so I'm always looking for a place to play that open E string. 😅

  22. Hi, question for 12tone. In episode 2F09, when Itchy plays Scratchy's skeleton like a xylophone, he strikes that same rib twice in succession yet he produces two clearly different tones. I mean, what are we, to believe that this is some sort of a, a magic xylophone or something? Boy, I really hope somebody got fired for that blunder.

  23. I can''t believe I only just now noticed you're left handed like me. Always wondered how you kept from smudging, never noticing that you go from right to left… hmm…

  24. My initial impression is that all of this has to do with the fact that in the fifths side of the circle of fifths, E is the last note to be altered. Wouldn't this just be a much simpler explanation, or am I missing something?

  25. Isn't the connection via circle of fiths much simpler? A major scale contains exactly the notes that you get when you stack up 6 fifths the changes you get from one scale to it's dominant is always the 4th note. And 6 fifths + a 4th are the same as okataves + a third

  26. Small question: In the section about the F# major scale (around 3:00), you talk about F# being the root, E the Major 2nd, D Major 3rd, but the C# is a Perfect 4th? And B the Perfect 5th? Then back to the major 6th and F# again..
    Could you (or anybody) enlighten why it's not a Major 4th and 5th in this scenario?

  27. How does a music theorist that doesn't believe in coincidences deal with polyphonic music where 2, or more notes, coincide? 🙂

  28. I'm wondering if there is any way to select a scale of 7 notes out of the 12 semitones where there isn't a note that is common to all of the scales of the parent scale?

  29. Had a crack at it before watching. (Bastard) algebra fits in text. (Bastard) geometry doesn't.
    C=1 etc
    Major scale covers -1,+5
    6-1= 5

    Petty, but can't give facebook a point

  30. Not watching the video. But if you have a system of only twelve, every one is bound to pop up everywhere isn't it?

  31. 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.

  32. All the modes of the diatonic scale has a ridge note. A neat thing about the modes of the diatonic scale is that the inversion of each scale is also a mode of that scale. To find the ridge note, take the inversion of the scale and find the scale degree which is the root of that mode.
    So the ridge notes are:
    Ionian: 3rd
    Dorian: 1st
    Phrygian: 6th (b6)
    Lydian: 4th (#4)
    Mixolydian: 2nd
    Aeolian: 7th (minor7)
    Locrian: 5th (b5)

    Now the tricky question is: What is the use of this? Are the ridge notes particularly important to the scale? For lydian and phrygian, the ridge notes are the unique scale degrees for those modes, but not for the others.

  33. 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.

  34. 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…

  35. 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.

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