Music Theory
 

I'm very new to music theory and I was just wondering if I understood this correctly...

Notes are specific sounds at specific frequencies and these are the 7 fundamental notes. After the 7 notes, they repeat, but at double the frequency and that switch to the double frequency after the 7 notes is a change of one octave?

there are 12 notes (you can see them as the white and black keys in a piano), the 7 fundamental notes are derived trough a formula called "the major scale".

So, A, B, C, D, E, F, G, Gm, Am, Bm, Dm, and Em?

Did I understand octaves correctly? They are simple those notes played at double, triple, etc. the frequency? So if F had a frequency of 21 Hz, a note played two octaves higher would be 63 Hz?

Basic Harmony 101
 

The cromatic scale goes like this, this is basically all the notes you have one after the other = C C# D D# E F F# G G# A A# B C

0= c 1= c# 2= D 3=D# 4= E 5= F 6= F# 7= G 8= G# 9= A 10= A# 11= B 12= C


(# is called sharp)

the numbers before the notes are called intervals, this is what the distance of the notes in relationship to the root is called.
here the root is "c" as an example, but any note can be the root.

0 = Unison 1= flat second 2= second 3= minor 3rd 4= Major 3rd 5= perfect 4th 6= Diminished 5th 7= perfect 5th 8= minor 6th 9= Major 6th 10= minor 7th 11= Major 7th 12= octave

you make the major scale by taking the unison, second, major third, perfect four, perfect fifth, major sixth, major seventh and octave.

and if you have c as the root it will look like= C D E F G A B C
but this formula can be applied to all the other notes and you come up with the other major scales.

G= G A B C D E F# G
D= D E F# G A B C# D

and so on...

after you have a scale you make up chords by using another formula and you get 7 chords from each scale.

in the C major scale you get=

C major, D minor, E minor, F major, G major, A minor and B diminished.


And i think you are correct about the frequencys in the octaves, but i cant tell you the info if you want to know it in Hzs... but you can google it.

So if my root was A, my major scale would = A B C# D E F# G# A?

I still have to learn the difference between sharp, flat, diminished, perfect, major and minor.

Thank you for the lesson :) I'm trying to learn it while learning guitar so I still have a long way to go before everything makes practical sense.

good times
 

learning that stuff is half the fun. i spent many hours going trough that info again and again, doing sheets of those scales until it all made sense..

now a day im thnkful that i did that, after your done you find out that this is basic stuff and theres more to come but you become more secure of yourself.

Dont presure yourself with anything, it will all grow with you.

lucky you that you have a forum where you can ask and people can teach you stuff just like that.. i had to go trough books and stuff.

Its all definetly worth while.
keep at it and find out where it will take you. : D

No. Octaves are always either doubling or halving the frequency. So an octave above 21 Hz is 42 Hz and two octaves is is 84 Hz and the next is 168 Hz and so on.

No. It would be A, A#, B, C, C#, D, D#, E, F, F#, G, G# and back to A again.

A# (A-sharp) is also Bb (B-flat). G# is also Ab. These are called enharmonic equivalents.

So, your scale could read as A, Bb, B, C, Db, D, E, Fb, F etc.

Now this is standard 12 TET (12-tone equal temperament). Other scales as quarter-tone have separate sharps and flats (i.e. A# is not the same note as Bb).

There is no sharp or flat note between B and C and also between E and F.

I just saw this on my mobile and had to jump on the computer.

There are historical reasons for most of this but just start with your C scale as a starting point (also easier because no sharps/flats).

The 7 tones you're referring to, that is a diatonic (dia = 7; tonic = tones). It is the most common scale pattern in Western music (also pentatonic, 5 tone scale, penta meaning 5).

Now in Western music, you have 12 total tonalities, each of which has an enharmonic equivalent (same note, different name; the name you use depends on the context).

C
C#/Db
D
D#/Eb
E
F
F#/GB
G/Fhttp://upload.wikimedia.org/wikipedi...oubleSharp.svg *
G#/Ab
A
A#/Bb
B
C

*(double sharp, rare to see this but goes back to historical technicalities)

Now scales are made up of how each of these tones relate to one another by interval degree.

C D E F G A B C
This is your C Major. The pattern of steps (one half step is two tones next to each other, C to C# for instance or E to F; whole step is two half steps) would be: w w h w w w h

The octave is the root. Now the scale patterns are useful but not as useful from a theoretic standpoint.

What we have then is intervals and their relationships. Of these, in Western music, diatonically based scales you have 4 perfect tones (1 4 5 8 [octave]) and 4 major tones (2 3 6 7). Lower case m = minor, upper case = Major, + = augmented, - = diminished (listed without enharmonic equivalents with the exception of augmented 4/diminished 5):
Root (P1)
2m
2M
3m
3M
P4
4+/5-
P5
6m
6M
7m
7M
Octave (P8)

The interval pattern is simply what it takes to map out, from the root, the major scale. P1, 2M, 3M, P4, P5, 6M, 7M, P8:
C (P1/Root)
C# (2m)
D (2M)
D# (3m)
E (3M)
F (P4)
F# (4+/5-)
G (P5)
G# (6m)
A (6M)
A# (7m)
B (7M)
C (P8)

Now the way intervals work is also what determines chord builds (must have root, third, fifth for a proper triad, typically [exceptions abound]).

Your sharps and flats essentially mean one half step up (for sharp) or down (for flat) from the given tone. So if you had to modulate, Writing an F note in the sheet music and flatting it would give you an E, but for theoretical purposes and playability via site reading and so on, you wouldn't write E, you'd write Fb (which also shows a modulation). Don't worry with modulations for now. Just explaining what sharp and flat means.

There are 12 fundamental tones in Western music which repeat. You don't really need to know much about frequency in most cases, just know that the frequency perfectly doubles when you go up one octave. If you place a C and then play the next octave of C (often written C' which is called C-prime), then the wavelengths perfect match to make them perfectly harmonious, though the C octave is twice as fast (perfectly twice as fast) and therefore is a higher pitch.

http://cnx.org/content/m10862/latest/octavewaves.png

Now back to intervals.

Your intervals can be major or minor and your chords can be major or minor (M/m); they can also be diminished or augmented.

However the NOTES in the scale are NOT individually major or minor. A note by itself can only be natural (♮), sharp (♯) or flat (♭). These are called Accidentals. You usually won't see a natural unless you need to alter a note that, according to the key signature or modulation, is usually sharp or flat, as being natural.

OK so for something simple and highly relevant, writing out a scale and the enharmonic equivalents.

A Major, since that was mentioned. You only use each tone (C D E F G A B C) ONCE. Never use the same tone twice, that's what accidentals and enharmonic equivalents are for.

Correct: A, B, C#, D, E, F#, G#, A
Wrong: A, B, Db, D, E, Gb, Ab, A

This goes back to readability on the staff (sheet music). If you're going to learn theory, being able to read sheet music at least moderately is a MUST. It will get more and more imperative as you advance in theory to be able to read sheet music.

Going back to C major, you may see it listed by Roman numeral. These indicate the triad chords on each degree. For the major scale (regardless of tonal key being C or D or whatever, this is ALWAYS the major scale):
I ii iii IV V vi vii°

Capital numeral is major, lower case is minor and a lower case with a ° is diminished.

So to make a proper triad, as I said before, you need root, third and fifth. This is based on the actual root of the chord, not the root of the scale so for C major... (root of chord in bold at bottom):
G A B C D E F G
E F G A B C D E
C D E F G A B C

Now look at the first chord, CM (I). You have your root C P1, (d = second, skip), your third which is a Major third interval above the C and then your G is your fifth above C and it is perfect, so you have a major triad (R, 3M, P5).

Look at the second chord. You have your root of D, then the F is a minor third above the D (F# would be a Major third), and then your A is a perfect 5th of D so you have a minor triad (R, 3m, P5).

The last chord is diminished, the B because you have over the B, a minor third and a diminished 5th. (R, 3m, 5-). Look at the list of intervals above and map it out from the B: B is your root, then you have C 2m, C# 2M, D 3m, D# 3M, E P4, E# 4+ but because we already have an E in the key (C Major), it must be F which makes it 5-.

Sure? "Dia-" means "across" to the best of my knowledge. Like diametric--"measure across".
Diatonic = "Across the tones"

I would also advise the OP to ear train BEFORE delving too deeply into theory and notation or he might get sidetracked. It's important to develop a good ear for music before doing anything else.

For engineers, yeah. But in music education it can be an abbreviation for diatonic. It depends on who your instructors are.

Depends on origin.

diatonic (adj.)
c.1600, from French diatonique, from Latin diatonicus, from Greek diatonikos, from diatonos "extending; pertaining to the diatonic scale," from dia- (see dia-) + teinein "to stretch" (see tenet).

In Greek, literally translates as "through the tones" but means, even in original context with DIATONIC, 7-tone scale (that's what they understood as being "through the tones"). Just like schizophrenia literally translates from Greek as "split mind" but that's not the understanding they had of it (they didn't at all believe it to be the mind being split in two or anything like that).

I don't know what the point is that you're making here. I'm saying that "dia-" doesn't mean "seven" but rather "across".

You're arguing semantics here.

It goes back to Pythagorean mathematics and theory, it means 7. It only means through in Latin contexts and is completely irrelevant, diatonic is ALWAYS a 7 tone scale, so it doesn't matter.

Dia also means "day" in Spanish. So the point I was making is that it is found in many languages and means something different in each. Regardless, to the ancient Greek Pythagoreans, it meant the 7 tone scale, regardless of literal translation.

It is not going to do anything but confuse somebody new to theory, like the OP, to debate a highly irrelevant point.

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Next, you'll be telling me "chromatic" means "12".

I'm not sure why you're so hung up on what these words actually mean. Accept that it's the standard terminology for music theory.

All right, now you're starting to get really annoying and stupid.

"Dia" as in diatonic from Greek roots means, regardless of literal translation or how much of an arse you want to be, SEVEN tone scale... PERIOD.

End of discussion. I told you the history and where the root comes from for the word diatonic and what it meant to the people who first used it.

And chromatic means "skin-like". So the chromatic scale means all the tones in the ancient Grecian sense.

I know this may be a hard concept for somebody so full of themselves to understand, but some words in other languages translate literally in a way far different than their actual understood meaning.

Now jog on before I get a mod in here.

I'm already in here haha

The Greek word "chroma" CAN mean skin but it means color. And the word chromatic as used in music refers to color not to skin. I'll leave it to you to puzzle out why.

And stop telling me that it's irrelevant. It's NOT irrelevant and it's NOT a matter semantics. It's a matter of correct translation--PERIOD! You're either propagating accurate information or you're spouting BS. It can't be both at the same time. It's either right or it's wrong. In your case, it's WRONG.

This conversation is going around in circles. Both of you are just arguing semantics here with each other, to be honest. It is what it is, can we leave it at that?

OH I'm not responding anymore, so it doesn't really matter.

Yes, each 7 set is an octave. A scale is 8 notes. To play a scale is 15 notes up and back.
I don't see where anyone answered your qstn about whether or not high notes vibrate to double or triple the frequency the higher a note gets.

:laughing: Some people still wouldn't hear you, if you hit them with it.

An octave is seven notes, eight pitches. C and C' are the same note played at different pitches. To play a scale up and back is still seven notes.

Yes, I did answer it. The frequencies of octaves can only be doubled or halved.

Ah, that's the word I'm looking for 'pitch'...

I was classically trained on double bass first in private with one of the finest instructors in this state and later at Wayne State University with another very fine instructor. I've played in both classical and jazz ensembles. All my instructors are now close friends of mine. I know a thing or two about music theory. If you let little inaccuracies creep in, eventually you're disseminating a bunch of BS and not true music theory anymore.

It's like that game we played in school where the teacher whispers something to a student and that student whispers it to another and so on. Then after 30 rounds, the last student goes up to the board and writes out the phrase and it is compared to the original and they are nothing alike. Usually, what the student writes on the board doesn't even make sense. That's what happens to music theory when it's being disseminated online by people who either don't have the background to be teaching it to anyone else or who think their inaccuracies are irrelevant. It gets passed on by others who don't realize it's wrong and they pass it on with further errors added in and so on until it is a useless mish-mash of errors and half-truths.

No wrong, all of that.

An octave is 12 notes higher not counting the first note.

A diatonic scale is seven tones within a given octave (and repeats exactly each octave).

However, chromatic (12 notes), whole tone (6 notes), pentatonic (5 notes) and 99% of all other scales regardless of the amount ot notes fall within an octave and restart on the next octave.

However an octave is NOT 7 notes.

From C in the major scale, there are 7 notes with that C to C' (12 notes not counting the octave) range that you use.

In other words, western diatonic scales span one octave but only play 7 notes (of the 12) within that octave, then repeats in the next octave.

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In college courses, you get marked down for confusing note and pitch in tests. They are real sticklers about it.

Not all of it is wrong... :p:

Yes, it is. If you want to learn music theory, go to college or a conservatory. I know you haven't because you don't know the difference between a note and pitch. Go to college and you definitely will learn it.

Actually, to say an octave is 7 or 8 tones IS dead wrong. You can span an octave in any number of notes up to 12.

Within those 12 notes that make an octave, 7 are played for a diatonic scale.

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That's an octave INTERVAL not an octave scale!

I do know and I have studied and played music for well over 12 years, to include university courses.

7 tones out of 12 notes is a diatonic.

And you are talking about spreading incorrect bs. Literally everyone here will correct you on that.

An octave is 12 tones, a diatonic scale is 7 specific interval-related tones within that octave.

If western music was based on the pentatonic rather than the diatonic, you could say it is 5. It is not always 8, it depends on the type of scale.

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Yeah why? lol
One is out to prove everyone wrong and no one is necessarily wrong.

EVERYBODY is a music critic these days... :cool:

My understanding of all of this, feel free to correct me if I'm wrong, I rarely deal with strict notation or form.

Note = The musical notes, all of them, ABCDEFG, and their respective sharps and Flats. If referring to a specific note in a specific octave, in isolation of musical context, the musical notes, by octave, become specified, IE Low C, Middle C, High C, or A1 A2 A3, where the numbers refer to the octaves of the notes (Each numbered octave usually being split at the C).
Tone= Tone or semitone - another term for intervals one note apart, or two notes apart. Also referred to as being one half step apart or one step apart.
Pitch = The specific Hz frequency of a sound, IE, instruments tuned to A440, are tuned to a 440Hz pitch.

You can use all 3 of these to refer to notes, and people will generally understand you, but its a little confusing in some situations. Honestly though, mostly semantics and preference as to whether someone says notes or tones, or even pitches, since there aren't a ton of real-life situations where the other person will be confused by using them interchangeably.

Interval = The distance between two notes played either simultaneously or next to each other.

For example, a note of A (note being defined as above), played with a note of E, is an interval of a perfect 5th. A note of A, played with a note of D, is a perfect 4th.

The names of the intervals is derived from their position within a traditional major/minor scale, where if starting on A, E is the 5th note you would play as you ascended the scale, and D the 4th. (Since this gap exists in both Major and minor scales, these intervals are known as "perfect". Intervals such as the 3rd, which is in a different place in a Major Scale or Minor Scale, are usually defined as major or minor 3rd.

If you are playing in a scale or context other than the basic major scale, intervals cease to be simply perfect 5ths or Perfect 4ths or Major/Minor 3rds and so on, and you get things like augmented or diminished intervals, the descriptions of which serve to denote how those intervals differ from the major/minor scale's standard arrangements.


Scale - A grouping of notes separated by specific intervals. (Notes as described above), repeated by octave. This can be any number of notes, for Example Pentatonic being 5, A traditional major or minor would contain 7 notes, a full chromatic scale would contain 12 notes. (A, B flat, B, C, D flat, D, E flat, E, F, G flat, G, and A flat).

Scales are odd in that they refer to the intervals between the notes, and not the notes themselves. A major scale starts at a given root note, and ascends in a given sequence of intervals. A major scale for example ascends by a tone, tone, semitone, tone, tone, tone, semitone. A minor scale ascends in a pattern of tone, semitone, tone, tone, semitone, tone, tone. They can both start on a note of A, and repeat across all octaves.

The actual notes within that sequence are defined by the root note, that which is defined as first in the scale. (Intervals, as we discussed before, are also discussed based on this, at least when using the major scale.) There *are* strange things that can be done with this, such as with the various modes, and with "outside" playing, but those are something of a multi-headed beast and can get relatively complicated very quickly.


Octave = A doubling of frequency. For example, a guitar is traditionally tuned to a note of A, A being defined as 440Hz. An octave above that note is another note of A, at 880Hz. Another octave above that, is A1760Hz.

An octave of a scale, is exactly the same. The same scale repeats, with the same notes, but all the frequencies are doubled and therefore the notes are all one octave higher. As before, the scale can realistically have any number of notes, as long as the intervals between them are the same leading up to the next octave. Commonly, 5 notes in a pentatonic scale, 7 in a traditional, diatonic, major or minor scale (And the modes thereof), and a chromatic scale would have 12. Other, more esoteric scales, might have more or less, such as blues scales, which have "6", and one of those is a fluid, which is why you often hear blues music use quarter tone bends and so on, which is a peculiarity of blues.

You can also get musical systems, such as indian music, which deal with microtones, and split the octave into more than the traditional 12 semitones, such as systems with as 19 or more possible notes, though I don't know how many notes these musical systems tend to use to define the scale.

Middle-Eastern music has a 24 tone system but they don't view the extras as micro-tones.

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Tell me why we have perfect intervals. Why can't a 5th, for example, be major or minor?

Scales are not laid out this way. It's customary, and far more useful, to use numbers to represent the scale degrees or positions:

1, 2, 3, 4, 5, 6, 7, 8

In a major scale, the two half-steps occur between 3 and 4 and also 7 and 8.
In a minor scale, the two half-steps occur between 2 and 3 and also 5 and 6.
For every major, there is a corresponding or relative minor. Both scales use the identical notes.

The term root note is used for the lowest note in a chord. It's customary to refer to the notes in a scale as:

1. Tonic
2. Super tonic
3. Mediant
4. Subdominant
5. Dominant
6. Submediant
7. Subtonic/Leading tone

We usually call a minor 7th the subtonic and the major 7th the leading tone. Each one of these positions has certain task to perform. The tonic is the foundation note of the scale. The subdominant and dominant are called that precisely because they are the dominant notes in the scale. They are also inverses of each other. They are the twin pillars holding the scale up. The submediant and mediant add color to the scale via major and minor intervals. The leading tone adds restlessness to the scale and wants to propel it back to the tonic again so that the scale can rest. We say that it wants to resolve. Likewise, the supertonic wants to lead way from the tonic.

Now you may wonder why the mediant at position 3 comes before the submediant at 6. It's because the straight-line scale we are accustomed to is misleading as hell. The tonic is really the note around which the others revolve so it is in the center. The dominant is a 5th above and the subdominant is a 5th below it. The closest notes to the tonic are the supertonic a step above and the leading tone a half-step below it. Both are restless and want to lead away from or back to the tonic. The mediant is a major 3rd above the tonic and the submediant is a minor 3rd below but since they are squeezed between the supertonic and leading tone and the dominant and subdominant, they are in the middle or median positions.

So a scale is like a solar system rather than a ladder (scale is derived from the Italian scala or ladder). The tonic is like the sun in the center, the supertonic and leading tone flank the tonic. Then the mediant and submediant flank the supertonic and leading otne and then the dominant and subdominant flank the mediant and submediant.

Hope that wasn't too confusing.

Scales are assembled using the Fibonacci Sequence. This sequence starts off with two numbers and the third is the sum of the first two. For example:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc. Notice how each number is the sum of the two before it? Scales follow this same sequence--5 (pentatonic), 7 (diatonic), 12 (chromatic). The next scale would be 19 notes and then 31 after that. They have built 19-tone keyboards but they are unruly. The cool thing about the Fibonacci Sequence is that the closer to infinity one gets, the more closer any two adjacent numbers in the sequence divide out to Phi or phi. Phi is 1.618 (it's actually irrational) and phi is 0.618 and is the reciprocal or Phi. The same is true of the scales, the closer to infinity they get, the closer any two adjacent scales will divided out to Phi or phi. It's a characteristic of the Fibonacci Sequence. You can look around the web for all the cool stuff there is about Phi and phi and the Golden Section and the Golden Mean and the Golden Spiral. It's really neat.

I did, read my post through and see if you can spot where.

I'm really not sure why you feel the need to explain all of this just because I defined a scale as a sequence of intervals and told everyone what those intervals were for the two most common scales. You're just repeating what I said in a different (much longer) way.

Its true that semantically the root is the lowest note of a given chord, but there's nothing wrong with referring to the first note of a scale as the root instead of the tonic.

All of this is true - (in the germanic tradition and those informed specifically by it), but you really need to stop phrasing all of this as if it is immutable fact. Music isn't about knowing the rules so you can abide by them, its about knowing the rules so that you can break them properly. When you go on forever about a note or scale degrees "function", always discuss it on the basis that this is a common, but not the only, way to deal with it.

What absolute ****. There's a significant difference between "Based on" and "Coincidentally resembles". The fibonacci sequence and the golden ratio crop up absolutely everywhere, and its very, very rare that the intent has ever been to apply it in advance - Its far more common to simply find that the way something has already been done, consciously or unconsciously resembles or takes advantage of the sequence, not the other way around. (Unless you're James Maynard Keenan and pals, in which case you just write songs around it to be flashy to math geeks).

Also, you'll note that the scales I noted specifically, only went up to 12. I stated, very clearly in the next paragraph, that those indian musical systems split the OCTAVE into 19 (Or more) notes, not that they necessarily use a 19 note scale. You responded to a comment about the division of the octave, by rambling about the fibonacci sequences supposed (not actual) relationship to scales.

The musical notes used in western music are based on the division of the octave according to the harmonic series. Of course, this is imperfect, as the harmonic series is actually uneven, and would stretch the octave beyond an exact doubling of frequency if followed exactly, so rather than do that, the harmonic series is "tempered" by moving the exact frequencies of the tuned notes very slightly in order to both rectify that issue and maintain the consonance between as many notes as possible in as many contexts.

As these are compromises, there are varying temperaments which have been used over time - Pythagorean temperament is a sequence of 3:2 ratios of pitch, equal temperament is the system used in most modern western music, and well temperament is primarily used for historically correct recordings of older pieces. There are others but they're rare to hear.

Of course other cultures will use their own temperaments in their traditional musics too, and may even choose to divide the octave into greater or lesser numbers of discrete tones. Typically this will have precisely no relation to the fibonacci sequence unless by complete accident.

Oh, and you mean "Unwieldy", not unruly.