I am studying musical scales. It makes no sense to me. Words like fifths, diatonic, pentatonic go right over my head. I would like to understand major and minor scales and chord formations. I have science background and I get the feeling that if the pattern of the scales could be converted to frequencies then I would understand them better.
I wonder if I’m asking for a whole course to be condensed into a few paragraphs. If so, can you refer me to a web site?
Here’s a couple of previous threads you might find helpful while waiting for someone to show up who can answer your questions:
I’ll try…
Take a very simple scale - a C Major scale consists of the notes C D E F G A B C. If one were to go from C to C all in half steps you would have:
C, C#, D, D#, E, F, F#, G, G#, A, A#, B, C. This is a chromatic scale (Notice that the interval between E to F, and B to C is a natural half step)
The notes of the C Major scale within the chromatic scale is:
C, C#, D, D#, E, F, F#, G, G#, A, A#, B, C
Scales can be thought of as patterns of half steps or the distance, in half steps, from one note to the next. The pattern of half steps for the C Major scale is:
1 - 1 - 1/2 - 1 - 1 - 1 - 1/2
The distance between G to A is two half steps (or 1 step), between A to B is two half steps (or 1 step), between B to C is one half step, etc.
If you think of the major scale in terms of half steps and the pattern above, then you would be able to play a major scale starting from any note you wanted to - that is - if you wanted to play a G Major scale, the you would apply the Major scale pattern starting on the note G:
G A B C D E F# G
A simple natural minor scale would be:
A B C D E F G A. The pattern of half steps for the natural minor scale is:
1 - 1/2 - 1 - 1/2 - 1 - 1
A harmonic minor scale would be C D D# F G G# B C
1 - 1/2 - 1 - 1 - 1/2 - 1 1/2 - 1/2
Other scales can be played using patterns of the same type. There are also scales that have one pattern going up, but another pattern going down.
Please note (heh) that all of the above was shown using sharps or raised notes - sorry, I don’t know how to make a “flat” symbol on this board. Also, it’s been a VERY long time since I’ve had to think about this. Active musicians, please correct if I’m wrong.
I hope I didn’t confuse you.
Chords can also be described in patterns. A simple C Major chord would be C E G. In this case, the pattern is not half steps, but the position of the notes within the key of the root scale - in this case C Major:
C - D - E - F - G - A - B - C
or
1 - 3 - 5
Remember to think of the root note as the scale you want to base the chord on.
A simple minor chord could be C minor:
C Eflat G
Since C is the root, and could be considered the “key”, you would have:
C D E F G A B C. But the second note in the chord is Eflat, therefore the pattern would be 1 - flat3 - 5. In this case, think of “flat3” as a lowered 3 in relation to the root key.
You can add other notes to the basic “triad” (usually some form on 1, 3 and 5) to add richness, tension and color to the chord:
A basic dominant 7 chord would be C E G Bflat. The pattern for this, in relationship to the root is 1 - 3 - 5 - flat7. Again, the “flat7” is a lowered 7 in relationship to the root key.
Can anyone help me out with how to make a “flat” symbol?
Again, I hope I am not confusing…
[QUOTE=Fritz]
Can anyone help me out with how to make a “flat” symbol?
QUOTE]
It’s supposedly Unicode U+266D but my system won’t display that. I use a lower case, italicized “b” with size set at 1.
Ab
Flat symbol? Just use a lower case “B”. Eflat = Eb.
The equal-tempered chromatic scale can be described mathematically. For example, fret placement on a guitar (each fret representing a half step) is such that each successive fret is closer to the bridge by a factor of the 12th root of 2. Google on chromatic scale mathematical for all you want and then some in this area. Here’s one site that comes up: News, Politics, Sports, Mail & Latest Headlines - AOL.com .
If you’re interested in a math explanation, the chromatic scale is pretty easy:
There are 12 notes in an octave. (Why “oct” for 12? It’s due to historical nomenclature from before there were equal-tempered scales.)
One octave is a doubling of frequency. The international standard for the A above middle-C is 440Hz. So the A above that is 880Hz. How do you calculate the notes in between? You need some constant to multiply the first frequency by that, when done 12 times, will double the original frequency. So you use the 12th root of two, which is roughly 1.059.
So:
A# = 440 x 1.059 = 465.96Hz
B = 465.96 x 1.059 = 493.45Hz
C = 493.45 x 1.059 = 522.56Hz
C# = 522.56 x 1.059 = 553.39Hz
…and so on.
These frequencies approximate the frequency ratios originally described by Pythagoras, who found that whole-number ratios made the most pleasing harmonies. But whole-number ratios become misaligned if you try to construct them across many octaves (the difference is called a pythagorean comma) and so equal temperament was invented to solve this problem.
A great book about not just temperament but the history of common musical theory (including the origins of many strange words like octave and fifth and so forth) is Temperament: How Music Became a Battleground for the Great Minds of Western Civilization. It’s a quick read and very enlightening.
If you get a chance to watch it (It’s not on DVD, but it might turn up on some cable or satellite channel), How Music Works is an excellent and accessible primer on these topics.
For another general primer, scroll down to the ‘Melody’ programme here. Relating scales to the more general concept of melody is vital if you’re to get beyond the “oh, so it’s a sequence of notes, and…?” puzzle.
Adding to this, an “octave” consists of the eight notes of the do-re-mi scale - the jumps between which aren’t all of the same size (mi to fa, and te to do, are smaller steps called “semitones”, the intervals between other pairs of notes are “tones”). The “pleasing proportions” also correspond (and this is no coincidence) to the different notes you can get out of an open pipe such as a valveless trumpet, or a trombone if you don’t move the slide - which is related to how many air-vibrations go exactly into the length of the pipe! So a jump of one octave represents a doubling of the frequency (half the wavelength), a fifth after that represents another one-and-a-half times (three times the original frequency), and so on. Harmony sounds nice because the various wavelengths fall into step with each other; discord sounds nasty because they all “jostle” each other. ← major oversimplification, but you have to start somewhere.
First, I hope you’re using a keyboard, these are very visually friendly; everything goes in a straight line and it’s color coded, the sharps and flats are black and the naturals (non sharp or flat) are white.
An octave is a doubling of the frequency of the note, a scale is a way of dividing up the steps between an octave.
the chromatic scale uses every note from C (or whatever) to C, all the keys. Other scales use only some notes, they divide the octave up differently and have a different sound because of it.
A pentatonic scale has 5 notes, a diatonic scale has 7, this covers most western music, we’ll cover altered jazz scales and sitars later.
Chords are built by stacking every other note in the scale, thus
c major scale
C D E F G A B C
1 2 3 4 5 6 7 8
C+E+G This is a C major chord(triad)
1+3+5
A 3 note triad is the basic chord, you can extend, alter and complicate them later, but just start with this.
Major and minor refer to whether the interval between the root note, in this case C, and the 3rd note, in this case E, is a major 3rd consisting of four 1/2 steps, or a minor third consisting of three 1/2 steps. A half step is one fret on the guitar, or one key on the piano. This applies equally to chords or scales.
Next you harmonize each note in the scale using the same pattern of 3 notes, every other note
DFA is a Dminor chord, EGB is Eminor, FAC is Fmajor, GBD is Gmajor, ACE is A minor, the B is weird, worry about it later.
The 1©, 4(F), and 5(G) chords are the primary chords and the 2(Dm), 3(Em), and 6(Am) are the secondary chords.
There’s lots of shorthand to learn, for example a chord with just the note, ie C, is major by default, some kind of symbol has to be added to designate it minor, ie Cm.
I think that’s enough for now
This is almost making sense. A couple of questions.
- What is a step or half step? Does it have frequency or mathematical equivalent?
- Who made these rules? Is it simply a case of what sounds nice?
More questions
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So a third is the third note in the scale and a seventh is the seventh note in the scale. Right? So what is the significance of a chord like Am7?
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There must be different triads for each chord. How are they developed?
This was way over my head. Thanks for the effort.
This was helpful. So in other words, the 12 notes of the chromatic scale are evenly spaced in terms of their frequency.
It’s a chord played with both a minor 3rd (which is a half-step lower than a major 3rd) and a 7th.
Not sure what you mean by this. Not every chord is a triad. A triad is a chord formed by three notes. Usually a root, a 3rd and a 5th. Frequently others notes are added in addition to those (like a 7th or a 6th) sometimes a 2nd or a 4th may be substituted for a 3rd (giving you a suspended 2nd or 4th). The chords are basically named according to the root and whatever notes are added which are not part of a standard major/minor triad.
I would love to watch this. Any ideas on where is can get it?
This is all more easily intuited if you can look at a piano keyboard. A major scale goes from c to c on the white keys. A minor scale goes from A to A. Those scales tell you where the intervals are. Look where the half-steps are (where there aren’t any white keys between the black keys) and you can figure out any other scale just by making sure you keep the pattern of whole steps to half steps the same.
A pentaonic scale is what happens if you just play on the black keys. Keep those intervals the same and you can play it anywhere. It’s all about patterns of intervals.
Modes are the same. A Dorian mode starts on the 2 (D to D on the white keys). Phrygian on the three (E to E), Lydian on the four (F to F) and the Mixolydian on the 5 (G to G). A minor scale starts on the 6 (A to A). You really only have to remember one pattern when you get right down to it. It’s all the same circle. The only thing that changes is where you start on the circle.
A minor (A-C-E) plus a seventh (G) (which is a “minor” seventh) Interval (music) - Wikipedia. It’s a bit more complicated though, because “7” is generally shorthand for one kind of seventh. For example A7, in most notation systems means A dominant seventh (like the seventh chord built on the fifth note of the major scale). So A7 would be played A C# E G, built on the fifth note of the D major scale (D E F# G A B C# D) not the A major scale (A B C# D E F#** G#** A). The seventh chord that looks like the one built on the first note of the scale is called a major seventh chord.
Now your getting into a concept called diatonic harmony. http://urp.home.cyberverse.com/Diatonic.html Diatonic harmony builds chords based on a scale (usually the major). So in C
C E G B Major 7
D F A C Minor 7
E G B D Minor 7
F A C E Major 7
G B D F (dominant) 7
A C E G Minor 7
B D F A gets called a lot of different names, depending on the genre (half-diminished and minor 7 b5are the most common)