Music Theory Thread

GloopyJon

Distinguished Member
I had a look but he didn't really explain the theory. However, I then took a look at the Wikipedia page on the Circle of Fifths, which explains the theory, albeit with quite a lot of musical jargon and so anyone without at least some knowledge of theory is going to get lost.

To try to explain the basics, the Circle of Fifths is just a representation of all of the possible key signatures, showing the closest relationships between them. It's called the Circle of Fifths because (a) the interval between each note and the next is a perfect fifth (7 semitones, e.g. C to G), and (b) if you keep jumping by a fifth, you go through all 12 notes before you end back on your starting note (hence the circle).

So the full sequence is:
C - G - D - A - E - B - F# - C# - Ab - Eb - Bb - F - C (back to the original note)

The sharps or flats can be expressed differently, i.e. F# can be written as Gb, but what I used here is generally the most common notation.

You probably know that an octave represents a doubling of the frequency of the sound waves. Hence the classic A440 tuning uses 440 hertz as the base A note - that's the A above Middle C on a piano. The A an octave above that is therefore 880 Hz. A fifth is half way between the two, i.e. 150% of the frequency, so the D above that A is 660 Hz.

BUT.....that's not quite true. If you follow the circle right round to the original note again, going up a fifth each time, you end up 7 octaves higher. If you do this mathematically, starting from a note of 100 Hz and increasing by 50% 12 times, you reach 12,975 Hz. If you go up the octaves, doubling it seven times, you reach 12,800 Hz. So-called "true tempering" adjusts the intervals to resolve this problem. Note that this is also why it's so hard to tune a guitar by tuning to the string below - essentially, the maths doesn't quite work (don't ask me why!).

A key fact about moving up a fifth is that you only need to change one note in the scale to do that. To illustrate, here are the notes of a C Major scale:
C D E F G A B C................and now a G Major scale, which is next to it on the circle:
G A B C D E F# G
You can see that the only note that's different is the F#. This progression continues around the circle, adding a sharp each time - F#, C#, G#, D#, A#, etc. The notation switches to flats half way through, but that's only a convention of notation which is a consequence of the choice of C Major as the basic scale with no accidentals (sharps or flats).

This means that shifting a fifth is harmonically very easy, since only one note changes, and only by a semitone. The same is true when you go up a perfect 4th, but this time one of the notes is flattened (going from C to F is achieved by changing the B to a Bb). That's why these three chords (I, IV and V - upper case numerals indicating major chords) are the base of a lot of simple harmony.

I think that's covered the main points in language that is hopefully relatively understandable. I know that this raises a lot more questions but I need to go and play some guitar now! :laugh:
 

Goooner

Distinguished Member
It started off as English, but then it must've drifted into some other language as it lose me :laugh:

It'll take a few re-reads for me to get my head around it, but I'll give it a go :)
 

hyperfish

Distinguished Member
I've spent some time on it, and I could draw it out. While interesting, I just can't see that it's a "must have" to play guitar.

I've settled into thinking that if I stick my finger on a root and can quickly find the 3rd, 4th and 5th that's as much as most players need to know. Learning a scale and moving it about sorts that out.

Perhaps an over simplistic view?
 

GloopyJon

Distinguished Member
It's probably not really an issue unless you want to start composing songs, when I think that some knowledge of theory can help you to be aware of what you can do. If you're just playing songs, then no, I don't think you really need to know it.

Bernie Marsden said in his recent interview with Lee Anderton (well worth a watch BTW) that he can't read music.
 

AndrewH13

Distinguished Member
It started off as English, but then it must've drifted into some other language as it lose me :laugh:

It'll take a few re-reads for me to get my head around it, but I'll give it a go :)
Got lost on 3rd line:laugh:
'the interval between each note and the next is a perfect fifth (7 semitones, e.g. C to G)'

Why 7 semitones?
 

Goooner

Distinguished Member
But why is it a perfect fifth if there's seven of them? :)

Guessing it's something to do with there being no e# or something.
 

Christian 71

Distinguished Member
Way over my head there Jon, but a good effort at explaining something I wouldn't have tried. Learnt a few things :)

The GAK guys were talking about a 9 string guitar that had slanted frets, kind of makes sense why from your explanation of frequencies.

To me it's just another way to break the tedium of learning scales/chords and the fret board. Cycling through groups of chords seems to work well if you pick a pattern based on the notes in a scale.
 

GloopyJon

Distinguished Member
Got lost on 3rd line:laugh:
'the interval between each note and the next is a perfect fifth (7 semitones, e.g. C to G)'

Why 7 semitones?
I'll try to explain the relationship between the major scale and all of the notes. A scale is simply a collection of notes that sound pleasing to our ears in relation to one another. There are fixed mathematical relations between the notes, as I alluded to briefly before, but I won't go into that (and I don't know much about it either).

There are 12 different notes in an octave, with the octave note (e.g. the top C if you start from a lower C) being the 13th. Each of these notes is a semitone apart (semitone = 1 fret). So the full chromatic scale contains all of the notes like this:
C - C# - D - D# - E - F - F# - G - G# - A - A# - B - C
I used only sharp signs to avoid getting into the subject of sharps and flats. You don't normally see some of these, particularly A# for example which is usually written as Bb, but they are the same note.

Secondly, we have the major scale which contains a subset of these notes, 7 of them (8 with the top C again), which make a more pleasing set. These are:
C - D - E - F - G - A - B - C
To make this scale, we have dropped all of the sharp notes, which are the black notes on a piano.

Thirdly, we have a scale that is more familiar for guitarists, the pentatonic scale. Pentatonic means "five tones", and a pentatonic scale contains five notes out of the twelve (plus the octave). The most commonly used pentatonic scale on the guitar is a minor scale, not a major one, and this is the minor pentatonic scale in C:
C - D# - F - G - A# - C

Lastly, there are the infamous arpeggios, which form another scale with only three notes. The basic major arpeggio is as follows:
C - E - G - C

Arpeggios are where we make the link into chords. The three notes of an arpeggio are called a triad and these three notes make a major chord. If you play a C chord on the guitar (x-3-2-o-1-0) they are all Cs, Es and Gs (the corresponding notes are x-C-E-G-C-E). Therefore a major chord is simply a major arpeggio with all of the notes played together, and usually with one or more of them duplicated. Generally, the lowest pitched note in a chord should be the root note (i.e. the first note in the scale) - that's why we don't play the bottom E string in a C chord, even though E is one of the arpeggio notes. A triad with a different bottom note from the root is called an inversion.

As you may have spotted, there are many variations on these scales. The variants of the major scale are the modes which you may have heard of - Lydian, Aeolian, Phrygian etc. These modes are simply a different selection of notes that makes a different sounding scale. Similarly, there are the different pentatonic scales, although they all use the same notes (a major pentatonic is the same as a minor pentatonic, but the root note is the next one up, i.e. the C minor pentatonic earlier is the same as a D# major pentatonic). Similarly, there are variants on the arpeggios and chords, changing notes or adding extra notes in (such as a 7th). All of that gets very complicated, though, and I just wanted to cover the basics here.

Finally, to answer the question about "why is that a perfect fifth", the interval from C to G is a fifth because it spans five notes on the major scale (C-D-E-F-G), which is the scale of reference for intervals. Intervals are another topic, though, and this is already too long! :)
 

Goooner

Distinguished Member
Thanks Jon, I did actually understand some of that :)

I know the major scale goes Tone (2 frets), T, Semitone (1 fret), T, T, T, S and isn't the rule you can't have two notes with the same name, which is where sharps and flats come into play with keys?

Intervals is about as far as I seem to get with the Justinguitar theory book, not so much what they aware, but remember the names, perfect fourth, minor third or whatever.

Maybe we need a music theory for idiots thread :)
 

AndrewH13

Distinguished Member
Jon, going to print those off and save for a long bath soaking and digesting them!

Two quick questions though. Assuming you know this theory from your previous piano learning in a past life, you are the perfect person to ask what we all want to know:

Does this theory help you play guitar?

My new tutor says its mostly bull that some guitarists say that they never had any theory training. Many who say it actually are magicians at scales etc but just learnt without formal teachings and music college. He says its vital for writing music, but also most important for improvisation and picking up new songs even if you learn by ear or you-tube.

Secondly, why a perfect fifth as opposed to a perfect 7th or perfect 6th:D
 

AndrewH13

Distinguished Member
Maybe we need a music theory for idiots thread :)
Not a bad idea rather than clog up the RS2014 pages! Recommending Justin's guide then including these last two posts be a good start.
 

Goooner

Distinguished Member
Whenever I ask my tutor about teaching me theory, he always says only bother when you're actually applying it in a musical context, don't try to learn it on it's own as it's dull and complicated :)

So he just gives me bite size pieces that are relevant to whatever we happen to be doing at the time.

So I'm guessing it's not *that* important.

The way I see it, if you know certain things, like scale shapes or chord progression in certain keys, it might make things easier to remember.

If you know a solo is using the minor pentatonic, you know roughly what notes it could possible use, so it's slightly less random and easier to memorise.

A bit like it'd be easier to memorise a passage from a book in English, because you'd actually understand it, making it easier to remember than if you tried to memorise the same passage in German where you'd be trying to remember seemingly random words. That's my theory anyway, but then I could quite possibly be talking complete crap :)
 

Goooner

Distinguished Member
Not a bad idea rather than clog up the RS2014 pages! Recommending Justin's guide then including these last two posts be a good start.
Maybe we could get past page 11 :laugh:

I'm pretty sure it's available to those with access to the shared drive, so maybe we could do Theory of the Week/Month or something and try and work through it, with Jon around to explain all the stuff we don't understand :laugh:
 

AndrewH13

Distinguished Member
Maybe we could get past page 11 :laugh:
I did take in on holiday a year or so back to complete it:rotfl:.

Seems I ended at about page 14 with Chromatic intervals in C that would have helped me learn intervallic relationships between notes, but the Diminished and Augmented intervals finished me off.

I think I chucked it back in the suitcase and jumped in the pool!
 

GloopyJon

Distinguished Member
[I'll get to Andrew's questions shortly but I'd already started this message so I'll finish this one first!]
I must confess that while a lot of this is background knowledge that I've had for many years, from studying music as a kid, some of it I've been refreshing from other sources and some things I'm discovering today, particularly the stuff about tempered tunings which is very interesting.

I didn't realise before today that the scales are not actually consistent, which I've been reading about. In other words, the notes of the chromatic scale in C are not the same as the chromatic scale for A, for example. I will try to briefly explain this mathematically.

I already mentioned that an octave is a 2 to 1 ratio of frequencies, i.e. an octave above your root note is twice the frequency. If we take a base frequency of 100 Hz (about 1.5 octaves below middle C), an octave above that will be 200 Hz. Similarly, a perfect fifth is a ratio of 3:2, i.e. a fifth above our 100 Hz root note is 150 Hz. This, by extension, gives us the ratio for a perfect fourth, which is 4:3, i.e. 200 Hz to 150 Hz (going up from our fifth note to the octave note instead of down, i.e. G - C instead of C - G).

The next most common "pleasing" interval is a major third. Surprise surprise, this is also a very simple mathematical ratio - this time it's 5:4. Hence a major third above 100 Hz is 125 Hz.

All of the other notes on the chromatic scale have similar, relatively simple ratios. I won't go into all of them but I found this article which explains it well. I'll just mention a major sixth (C - A), which is a ratio of 5:3, and I'll explain why.

In the examples below, I'm going to pretend that 100 Hz is a C on the major scale. It's not, but I will do this to make the calculations easier and so that I can label the notes more easily!

Taking our 100 Hz "pretend C" root note, a major sixth above that (the A) will be 100 * 5 / 3, i.e. 166.7 Hz. A is also three notes along the circle of fifths - i.e. it's the fifth of the fifth of the fifth (the circle goes C - G - D - A etc with each note being the fifth of the previous one). But the maths breaks down.

Let's work out the notes in the circle of fifths using two methods. For the first 5th, G, we just apply the 3:2 ratio, so that's 150 Hz. That's easy, no problem.

The second note is D, a fifth above the G. If we calculate 150% of the G, that makes 225 Hz. A major second is a ratio of 9:8, so to calculate this D from our 100 Hz C, we do the following:
100 * 2 (an octave up) = 200 * 9/8 (the second) = 225 Hz.

Great, both of these agree. Let's go up another 5th to the A above that. Firstly, a fifth above the 225 Hz note is 225 * 150%, i.e. 337.5 Hz. But if we start from the C and use the major sixth ratio (5:3), we get the following:
100 * 2 (octave up) * 5 / 3 (major 6th) = 333.3 Hz

Oops!

This difference illustrates the problem of tempering of scales. It arises because the ratios between the notes on one scale don't give the same results as the ratios of the notes on another scale, i.e. some of the notes on a C scale are not actually the same as the notes on, for example, a scale in Eb. This is why there are different ways of tuning instruments like guitars or pianos to try to compensate. On some instruments, particularly brass instruments, this is simply not possible since they just a few valves and are tuned to a specific scale. This is also why the frets on a guitar are an approximation, and why we have seen a strange tempered fretboard on some guitars (the True Temperament system that someone noticed a while ago). Even that won't solve the problem, because it's just a different way of choosing your note tunings.
 

Goooner

Distinguished Member
Mixing music theory with maths! That's just about finished me off :laugh:
 

GloopyJon

Distinguished Member
Jon, going to print those off and save for a long bath soaking and digesting them!
I'd actually suggest reading them while sitting with a piano or other keyboard instrument, if you have one, because then you can play the notes and look at them physically which would help. If you have a piano next to your bath, that would be perfect (although possibly not good for the piano).

Does this theory help you play guitar?
I think Goooner already provided the perfect reply to this question in his post #6672 above.

Secondly, why a perfect fifth as opposed to a perfect 7th or perfect 6th:D
You've reached the limits of my knowledge so let me go off and check...

OK, a bit of reading reveals that the term "perfect" goes back to Pythagoras, and nobody really knows why he termed these intervals perfect, but the bare bones are as follows. Firstly, there are actually four "perfect" intervals - unison (two of the same note), fourth, fifth and octave. These are the simplest ratios - 1:1, 4:3, 3:2 and 2:1 respectively. A perfect fifth (C to G) is 150%, and a perfect fourth is its inversion (G to C, i.e. 150 to 200 in our "C=100" scale).

All other intervals, when inverted, switch from Major to Minor as follows:
Major 2nd - Minor 7th (C-D, D-C)
Major 3rd - Minor 6th (C-E, E-C)
Major 6th - Minor 3rd (C-A, A-C)
Major 7th - Minor 2nd (C-B, B-C)

Also, as in my previous message, the tunings of the other notes will tend to be approximations due to the fact that we want to play in different keys on the same instrument.
 

AndrewH13

Distinguished Member
I'd actually suggest reading them while sitting with a piano or other keyboard instrument, if you have one, because then you can play the notes and look at them physically which would help. If you have a piano next to your bath, that would be perfect (although possibly not good for the piano)
Our music bedroom is already crammed full with Guitars, Marshall Stack, Blackstar returned squeezed in, bass amp, Zoom. music stand and taking most room of all, a set of Yamaha drums. If you think I'm getting a piano to block the middle of the room off I wouldn't be able to see telly and play Rocksmith again:D. And it would be just like my garage that I cant get in!!
 

GloopyJon

Distinguished Member
I did say "if you have one"! :)

Do it with a guitar instead, then. It's just a bit less directly visual than a piano, where you can actually see the C Major scale on the white notes.

Funnily enough, as I have very little work on at the moment, I brought in a book that I bought some time ago called "Tonal Harmony" which apparently is a standard textbook on harmony. I started reading it a year or two ago, but didn't get very far, and so I thought I'd do the same again now. I haven't yet opened it for the stuff we've been discussing here but I'm sure that will all be covered.
 

Goooner

Distinguished Member
As an extension to the learning to play for real thread, to try and help those of us theoretically challenged, like myself :)

Rather than clog up the Rocksmith 2014 thread where there have been several interesting questions and posts over the last 24 hours and to keep it all in one place, where it'll hopefully be easier to refer back to.

I know myself and Andrew have both attempted to get some with the Justinguitar Practical Music Theory e-book, but gave up really early as it quickly got complicated :laugh:

I'm sure we have a few knowledgeable people on hand, which Jon has already shown with his highly detailed answers in the other thread.

If anyone can come up with a snappier title, please do and I'll change it :)
 

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