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I have been trying to learn some music theory and have come across the amazing thing that is the circle of fifths.

It is such a beautiful construction and makes such intuitive sense, that it makes the way that music theory around building scales has been written feel a bit arbitrary and purely based around the fact that we like sequences of letters that go in order, rather than any kind of intuitive pattern.

To build a major scale using the traditional method, you have to transpose the pattern TTSTTTS (where T is a tone and S is a semitone) starting at the root note of whatever scale you are working with. Now, without a keyboard in front of you, or a fretted instrument, it's not intuitively apparent which incidentals should be included in each of the scales. To work that out, you need to consult the circle of fifths, so why not just use the circle of fifths to generate the scales in the first place?

It feels like it is so much more intuitive to play the scales using the circle of fifths. Much in the same way as this image suggests:

enter image description here

Here, we have a geometric representation for the scale, where CMaj contains the notes FCGDAEB, and it makes a lot more sense. In order to get the rest of the scales, this shape is rotated about the circle and it all works amazingly.

I guess my question is: why do we jump through so many hoops and make life so much harder for ourselves just to make our scales go up sequentially letters-wise? The notes are rarely ever played this way in practice (maybe during practice, but not really in practice, hehe). Is there actually some benefit to the way that we do it (ie. CMaj = CDEFGAB)? or is is really just because "this is the way we have always done it and it's too late to change anything now"?

I guess a logical extension of this idea would be that the Ionian mode shouldn't be the main mode and it would make sense for the Lydian mode to be considered the "major" mode. If that was the case, then learning the scales would be so much easier, because you would only have to remember the one sequence of notes, and then each scale of 7 notes would be a sub-sequence, that is "slid" along the main sequence, like this:

enter image description here

So I guess a sub-question for this is: is there a particular reason the Ionian mode is the main mode? or is that another arbitrary construction that is just "tradition"?

I am reminded of the debate about replacing the mathematical constant Pi with the proposed constant Tau (2*Pi). It would make everything make so much more sense, and it would be so much more elegant, if the circle constant we used was based on its radius as opposed to diameter; but Pi has just been used for so long that it would be too hard to change it now. And it kind of feels this way with this stuff.

Having said all of that, I am still definitely just learning all of this, and I am sure that there are a number of considerations that I haven't taken into account. I am not seriously proposing that music theory should be changed; I am just wondering if there is a proper reason that we do it the way we do, rather than this way, which feels more intuitive.

closed as unclear what you're asking by Carl Witthoft, Stinkfoot, Todd Wilcox, Dave, Richard Mar 3 '18 at 16:42

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    Regarding tau and pi, I think people advocating tau are underestimating how often we would have to write tau/2 instead of just pi. Regarding your question, i don’t think I understand what you mean by “building” a scale. Are you asking why the notes C and F aren’t right next to each other on the piano keyboard? – Todd Wilcox Mar 2 '18 at 15:30
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    You may be interested in this. George Russell took the fifth to be fundamental, noted that the Lydian mode could be built by stacking fifths, and developed a theory around this idea. – David Bowling Mar 2 '18 at 15:46
  • I suspect part of the reason why you see constructing scales with the circle of fifths as an option is that 12 perfect fifths come this close to spanning 7 octaves exactly. Seems like too many parts happy coincidence, though. – Dekkadeci Mar 2 '18 at 15:55
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    I don't see the problem. There are two views of the same object. One is more practical than the other in some situations, but both are equally valid. – Dave Mar 2 '18 at 18:28
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    @badjohn, agreed. Which is why i am not seriously proposing this new system of scales, just suggesting that it might be more intuitive. Well do i understand the inertia and practicalities around these things. Doesn't mean its not fun (and important to progress) to run little thought experiments every now and then! – guskenny83 Mar 3 '18 at 2:20
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I disagree with the premise. Scales are built from the cycle of fifths. However, they are arranged in order of pitch. At least this is how the medieval and a few other math-music-theory guys see things. Of course, one may just start by cutting holes in a pipe and see what happens.

Melodies do tend to follow scale patterns at least as much as they follow harmonic patterns. Naming (not necessarily constructing) scales in pitch-order is useful for melody-oriented operations (like singing.)

  • I'd like to add that the Greeks seemingly started with partial scales (overlapping tetrachords) and developed things from there. My explanation is only relevant for later times where the people thought they were returning to Greek ideals. – ttw Mar 2 '18 at 20:00
  • I guess my question was more about why we "double-handle" scales by building them from the cycle of fifths, and then arrange them in the order of pitch, because leaving them in the cycle of fifths seems more intuitive and makes it much easier to work out (just bisect the circle and play in order). It just seems arbitrary and a lot of extra work for not much reward. I understand that it was probably just developed that way, and there is a lot of inertia around changing it, but was asking if there was another reason, and if melodies tend to follow scale patterns then that seems like a good one.. – guskenny83 Mar 2 '18 at 22:50
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the way that music theory around building scales has been written feel a bit arbitrary and purely based around the fact that we like sequences of letters that go in order, rather than any kind of intuitive pattern.

How exactly are sequences of letters not intuitive? Everyone learns the alphabet when they're very young, and most of us use it everyday in some form for organizing all sorts of data, from financial reports and customer history, to the albums list in our phones music player. Everyone knows that 'A' is first followed by 'B', 'C', 'D', 'E', 'F', and finally 'G'. In music we add 5 notes in between these 7 natural notes, with only two being half steps apart (B to C and E to F). That's it, that's all there is. The black keys may have two names, but in the end there are only 12 notes, 7 white and 5 black.

To build a major scale using the traditional method, you have to transpose the pattern TTSTTTS (where T is a tone and S is a semitone) starting at the root note of whatever scale you are working with.

Counting notes is part of learning and memorizing where they all are, yes. It's like when you were in grade school and learned how to count from 1 to 10. Then they asked you to count from 2 to 10 but skip every other number (aka name the even numbers). It's not really intuitive when you first learn it, but over time it becomes second nature. You can think of C as 1, C# as 2, D as 3, etc, and count the same.

Here, we have a geometric representation for the scale, where CMaj contains the notes FCGDAEB, and it makes a lot more sense. In order to get the rest of the scales, this shape is rotated about the circle and it all works amazingly.

It may list all the tones that are present in the scale, but the ordering of the fifths is still something you have to learn and memorize to begin with. All fifths are 7 notes from each other (for instance, C0, C#1, D2, D#3, E4, F5, F#6, G7). Once you learn what these fifths are it becomes easier, but you still have to know how to count between them. Reordering the notes doesn't help because you still need to know the numbers. In contrast, building a scale from one tone with whole and half steps only involves counting up one or two notes, rather than 7 every time. Your method also ignores which notes are counted as flat or sharp.

Concering your last picture you'll notice that the pattern between all of the notes stays the same. FCGDAEB or 4152637. (You also misidentify each scale as major when really they are Lydian, and all of the notes are sharps which messes with flat keys by having both natural and sharp notes with the same letters.) That pattern of numbers will always be present in your method and will work for a variety of situations. You still have to know the order of these notes. Memorizing them only in fifths order won't help you when playing because being able to play in the normal order is just as, if not more important when actually playing. Being able to build scales from whole/half steps as well as from the circle of fifths is important, but being able to find and know why which notes are modified is arguably more important. You should know that when you add a flat you are flatting the 7th scale degree of the last scale, and it in turn becomes the 4th scale degree of your new scale. Conversely, when you add a sharp you are sharping the 4th degree of the previous scale and it becomes the new 7th degree. Notice how 4 and 7 are both ends of our 4152637 pattern?

circle of fifths Here's a chart I made that demonstrates this idea. You can also use your idea, simply flip the pattern around using 1 as the axis. For example, to find the Eb scale take Eb as one, Ab would be 4, Bb would be 5, F would be 2, etc.

In short, building the scales from the circle of fifths is a shortcut that doesn't help you understand why scales are built the way they are completely. It gives you an easy way to tell which notes are to be played, but it obscures why those particlar notes are chosen. Knowing all the intervals of the major scale, from every degree to every other degree, is something that has to be memorized at some point, and ordering the scale in fifths order does nothing to help this, it's simply another pattern that has to be parsed.

So I guess a sub-question for this is: is there a particular reason the Ionian mode is the main mode? or is that another arbitrary construction that is just "tradition"?

It sounds the best. No more, no less. Music theory is a means of describing what people already play, not telling them what they should play. Lydian is not used as much so there's no reason it should be considered the main mode. Modes themselves aren't even a mainstream idea, most people only think in terms of major and minor, and everything else is a deviation or modification of those two scales. Also, the only reason you want Lydian to be the main mode is because you want F natural to be the first scale and the first note of that scale, which is arbitrary.

  • I believe that OP understood that these are Lydian scales, but was wondering if we should consider Lydian scales more fundamental than Ionian. – David Bowling Mar 3 '18 at 2:45
  • @guskenny83 -- if this way of thinking provides you with a mnemonic, I would encourage it. In the end you need to know both the interval patterns and the spellings of the scales, though. It takes way to long to reference something like the circle of fifths and to work through the mental gymnastics needed to derive a scale. You need to just know them, and you will if you keep at it. – David Bowling Mar 3 '18 at 2:51
  • @guskenny83 -- But the observation about constructing the Lydian scale from fifths is a sharp one, and the Lydian Chromatic Concept that I linked to earlier was an influential development in jazz theory, supposedly influencing Bill Evans, Miles Davis, Coltrane, and others. This was heavy stuff. – David Bowling Mar 3 '18 at 2:53
  • Ah, I just read your link. What I don't understand is why does the first note you start on HAVE to be the tonic? Starting from 4 doesn't seem any harder to me and makes sense considering the vast body of work in major. The 4 to 7 tritone dissonance is also the very thing that makes Dominant 7th chords work so well, after all. – Tama Mar 3 '18 at 3:00
  • The reason that the first note is the tonic, is because if you are playing something in the key of Emaj (Amaj in my representation, sorry i should have used and asterisk or something!), in order to work out what notes to include in your scale, you only need to remember the one sequence of 12 notes, and take your scale as the 7 notes in that sequence (in a modular fashion) starting from E, if that makes sense? – guskenny83 Mar 3 '18 at 3:09
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Quite like this idea. Al the notes from a particular scale are lumped together, albeit in the wrong order!

The Ionian mode has been thought of as the datum point for a long time now, possibly because the majority of Western music seems to favour that set of notes with the root making it sound major. Especially in the widely used 12edo (Equal temperament).

It doesn't actually work, though. Bisect the circle C> Gb (or F#). 12>6. Key C has no F#. Bisect 9>3: key A has only 3#, not 4. Or, as shown here, b.

Or am I missing the point somehow?

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    I don't think there's a point to be missed . The OP is waxing philosophical. – Carl Witthoft Mar 2 '18 at 15:55
  • It does work if you take Cmaj to be C Lydian, rather than Ionian though. In this new interpretation, Cmaj would be CGDAEBF#, which is a permutation of the traditional, C Lydian CDEF#GAB... @CarlWitthoft is right though, there is no serious suggestion here; I am just curious if there is anything that I have missed that makes the traditional way better than the circle of fifths way, other than simply "tradition".. – guskenny83 Mar 2 '18 at 16:07
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    @CarlWitthoft - maybe. Plato and Aristotle came up with good stuff... And I leave waxing to the missus! – Tim Mar 2 '18 at 16:51
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I have been trying to learn some music theory and have come across the amazing thing that is the circle of fifths. It is such a beautiful construction and makes such intuitive sense...

It certainly is a beautiful construction. I'm not totally sure how intuitive it is though - although it looks very logical, a closed (genuinely cyclical) circle of fifths that could be used to generate scales in the sense you suggest only happens when using 12 equal divisions of the octave - which doesn't agree with the just intervals that people would intuitively arrive at. It's actually a clever compromise, rather than a secret of musical fundamentals.

To build a major scale using the traditional method, you have to transpose the pattern TTSTTTS (where T is a tone and S is a semitone) starting at the root note of whatever scale you are working with. Now, without a keyboard in front of you, or a fretted instrument, it's not intuitively apparent which [accidentals] should be included in each of the scales. To work that out, you need to consult the circle of fifths, so why not just use the circle of fifths to generate the scales in the first place?

It's certainly possible that if equal temperament had been 'standardised' on much earlier, we'd think about things differently - but we might think about them very differently to the way we do now, much more than you imagine. We might not even be thinking primarily in terms of the diatonic scale, or in terms of sharps and flats at all.

I guess my question is: why do we jump through so many hoops and make life so much harder for ourselves just to make our scales go up sequentially letters-wise?

I'm not sure people do, really! I think in most situations, people think of the set of notes in a scale as a set, rather than particularly a sequence.

Is there actually some benefit to the way that we do it (ie. CMaj = CDEFGAB)? or is is really just because "this is the way we have always done it and it's too late to change anything now"?

Western music theory being built around C Major is something of an accident of history. The Major scale is quite stable though, with notes that agree quite well with pitches in the harmonic series.

I guess a logical extension of this idea would be that the Ionian mode shouldn't be the main mode and it would make sense for the Lydian mode to be considered the "major" mode.

(from comment) @topomorto, because F Lydian contains the notes FCGDAEB, the same collection of notes as C Ionian, except with F as its "base". So, in this new encoding that i have (somewhat tongue-in-cheekly) suggested, "Fmaj" would be a permutation of F Lydian, not Ionian.

I can't see the sense in that really - It sounds to me like your logic there is based on the fact that F is the first note around the circle that is a 'natural' note (not sharp or flat). (Edit) - I was misunderstanding there, but it still seems a bit arbitrary to see the first one of the sequence as the root. From the point of view of harmonic stability, you might see D as the obvious 'home' note, as it's the fewest fifths away (on average) from every other note in the scale, which would make Dorian the home mode... but I'm sure it's possible to come up with alternative ideas. For example, one reason that Ionian became the 'main' mode is the leading tone a semitone below the root - the use of that leading tone is quite fashionable in much western music.

So I guess a sub-question for this is: is there a particular reason the Ionian mode is the main mode? or is that another arbitrary construction that is just "tradition"?

Absolutely a tradition - but one that's quite understandable, given its tonal stability.

I am not seriously proposing that music theory should be changed

Well, you should :) . The common way of naming notes in western music theory is only one way of looking at things, and people have invented various other ways - why not join them?

  • Thank you for your in-depth and considered response! I guess when i say intuitive, i meant, intuitive within the confines of western music theory as it has been developed; with 12 equal divisions of the octave; but i suppose that you are right that if we are tearing everything down and starting from scratch, why not go further and redesign the whole kit-and-kaboodle! I am coming at it as someone who is trying to come to grips with learning this stuff, and it just seemed like such a more efficient, and elegant way of deriving (and playing) the scales than having to rote learn everything.. – guskenny83 Mar 3 '18 at 2:32
  • One thing I did want to add tho, is that I was just using the example of F in this representation, because it translates to Cmaj, but it works for others as well.. F#maj in this representation would be F#C#G#G#D#A#FC, which is equivalent to: DbEbFGbAbBbC, Db Ionian or Gb(F#) Lydian in a different permutation. So it works for any other key. The reason the root note is what it is, is you need a reference point to start counting around the circle from. Anyway, it was a fun thought experiment, and i know that it won't change anything, but it is certainly the way that i will use to memorise scales! – guskenny83 Mar 3 '18 at 2:41
  • @guskenny83 I think it was a bit late when I replied and I wasn't reading clearly - have edited my musing about the Lydian mode. – topo morto Mar 3 '18 at 8:43
  • Ah, thats really interesting! I didnt know that about the leading note and its influence on the choice of ionian. Thats good to know and finding stuff like that out is exactly the reason i posted this in the first place! Also, i have to admit that i was thinking about the root as purely a convenient naming convention for the collection of notes and wasnt considering its role in harmonic stability.. Thanks again for your informative reply! – guskenny83 Mar 3 '18 at 10:22
  • @guskenny83 the important thing about the root is that it's the point the a piece of music 'revolves around' or 'wants to go back to' in the context of a given tonality. If we say that a piece is in C major, one of the things we're saying there is that the tonal feel of the piece is oriented around C. – topo morto Mar 3 '18 at 10:50
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Because circle of fifths doesn't allow for enharmonics creating all kinds of problems to tune instruments like guitars and keyboards. Suppose you have a keyboard and you want to play a piece on F major using fifths. You will probably set up the black key between the A and B to Bb (tune it to 2/3 against the F and you are done). Nice. Then you take this very same keyboard but you want to play something on B major. oops! Now you have a problem because the key is set to Bb and you will need this very same key to be tuned to A# (which is a comma higher than Bb). Not good. Or you might end up having at least 12 keyboards one tuned for each key. This is not practical. Ergo, tempered tuning.

  • Sorry, im not sure I follow you. I am not suggesting any different tunings. Just not forcing scales to be in order of pitch. In order for this to work and a scale to have a "root" note, it would have to be changed so that the Lydian mode is the primary mode, so that Fmaj would be FCGDAEB - but you can still use the same keyboard as we have today, you just have to "crab walk" up the keyboard when playing a scale, rather than playing the keys in order of pitch. – guskenny83 Mar 2 '18 at 22:54
  • Well.... I kind of think I understand your question now. I see two problems: How often do you think you will be able to find people that will be able to sing a whole "cycle" (assuming that you use enharmonics, which don't exist on circle of fifths... but anyway) in order to reach your starting point)? 2nd.... even your explanation about how Fmaj is built is showing you exactly the problem with cyrcle of fiths. Fmaj has Bb and going by fifths starting from F you hit a B instead. You won't be able to find a Bb going up any time soon. – eftshift0 Mar 3 '18 at 16:39

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