Okie dokie.
Lace said:
I don't know much about chords that contain less than or more than three notes. However, I just assume that notes a further third above the highest note keep being added (a seventh?).
98% of the time, it is correct to assume that. Chords with 4 notes are usually called 7 chords, 5 notes = 9 chords, 6 notes = 11 chords, and 7 notes = 13 chords. The latter 3 are rarely seen outside of jazz. Extending that pattern in the opposite direction would have us believe that chords with 3 notes are called 5 chords, but this is not the case. Actually, the term "5 chord" refers to a chord with 2 notes - the root and the note a perfect 5th above the root. This is the same as a major or minor triad with the 3rd omitted.
Lace said:
Using those four chords, triads can be made using every note in a key and only the notes in a key. However, one cannot just use one type of triad, to remain in key except in very special cases. For example, in G Minor, the allowed notes are G, A, Bb, C, D, Eb, F. If these are used as roots, than the chords must be, respectively: Gm, Ad, BbM, Cm, Dm, EbM, FM.
Those 7 chords are called the diatonic triads of G minor. And now we get to the fun part of explaining why Ionian and Aeolian (major and minor) modes are the most widely used, Locrian is the least widely used, and the other 4 (Dorian, Phrygian, Lydian, and Mixolydian) are somewhere in between.
As you pointed out, the diatonic triads of G Aeolian are G min, A dim, Bb maj, C min, D min, Eb maj, and F maj. As it turns out, all Aeolian keys have diatonic triads that form the pattern: min, dim, maj, min, min, maj, maj.
You also mentioned seeing little numbers used to denote the chords. My guess is you're referring to the figured bass symbols. Roman numerals are used to indicate diatonic triads, (so the first is 1, the second is 2, etc.). Uppercase indicated major, lowercase indicates minor, uppercase with a plus sign indicates augmented, and lowercase with a degree sign indicates diminished. So the figured bass symbols used to indicate the diatonic triads of an Aeolian (minor) scale are: i, iiº, III, iv, v, VI, VII.
By taking this pattern and "rotating" it, we get the other 6 modes:
Ionian: I, ii, iii, IV, V, vi, viiº
Dorian, i, ii, III, IV, v, viº, VII
Phrygian: i, II, III, iv, vº, VI, vii
Lydian: I, II, iii, ivº, V, vi, vii
Mixolydian: I, ii, iiiº, IV, v, vi, VII
Aeolian: i, iiº, III, iv, v VI, VII
Locrian: iº, II, iii, iv, V, VI, vii
Also, each of the 7 diatonic triads is given a name based on its position:
1 - tonic
2 - supertonic
3 - mediant
4 - subdominant
5 - dominant
6 - submediant
7 - leading tone
The tonic is the most important, since it is the "home" triad, where everything should resolve to. Therefore, the quality of a mode is determined by the quality of its tonic triad. Ionian, Lydian, and Mixolydian are major modes, Dorian, Phrygian, and Aeolian are minor modes, and Locrian is a diminished mode.
The reason for the relative amount of use each mode gets stems from the placement of the tri-tone. You may recall me saying...
me said:
Remember how on that chart in the previous lesson, we covered all possible numbers of half steps except 6? Well, now we know how to name an interval with six half steps. You could either name it an augmented fourth (because a P4 is 5 half steps so an A4 would be 6) or a diminished fifth (because a P5 is 7 half steps so a d5 would be 6). This interval is also known as a "tri-tone" or "the Devil's interval" because of its very harsh and piercing sound.
From a physics perspective, the reason this interval sounds so harsh and piercing is because of its frequency ratio. Our ears "like" to hear simultaneous frequencies that are in "nice" ratios (i.e. 1:2, 1:3, 2:3, 1:4, 3:4, etc.). A very simplistic way to say this is that nice ratios sound good and not-so-nice ratios (17:23, 8:19, 21:64, etc.) sound bad. I don't like to use the words "good" and "bad" in this scenario, however, because they are overly simplistic. A better way to describe it would be "consonant" and "dissonant", or, in more familiar terms, "stable" and "unstable".
Because this phenomenon is based on the physical way our ears perceive sound, it is universal across all cultures and musical styles. What's not so universal is the way consonance and dissonance are used to create musical ideas. One of the most common paradigms (which we will be focusing on) is to have a sense of "tension and release" where more dissonant chords resolve to more consonant ones. Even within this paradigm, different styles differ significantly in what range of the consonance/dissonance spectrum they tend to use. To give a few examples:
Medieval/Renaissance: extreme consonance - moderate consonance
Baroque/Classical: moderate consonance - moderate dissonance
Romantic: moderate consonance - extreme dissonance
Jazz/Modern: moderate dissonance - extreme dissonance
As you can see, the general trend in Western music over the past several centuries has been one of ever increasing dissonance.
Some common intervals and their frequency ratios:
P8 - 1:2
P5 - 2:3
P4 - 3:4
M3 - 4:5
m3 - 5:6
M6 - 3:5
m6 - 5:8
M2 - 8:9
tri-tone - 1:sqrt(2)
This explains why the tri-tone is so dissonant - not only is it not a nice ratio, it's not even rational! It is worth noting, however, that, on a modern piano (or other keyboard instrument, as well as almost all electronic music systems like organya, pxtone, FLStudio, a digital piano, etc.), none of the intervals are rational (except the octave). The modern piano uses an "equal-temperament" tuning system, meaning every half-step is equal. In order to make the octave a 1:2 ratio, each half step must have a 1:2^(1/12) ratio. For all intervals except the tri-tone, the minor 2nd, and the major 7th, the irrational frequency ratio is so close to one of the nice ratios listed above, that most people's minds will subconsciously "round" the irrational interval to the nearest nice rational one, and the slight dissonance is not perceived. These three intervals therefore sound the most dissonant.
In Common Practice era music (recall from page 5 of this convo that this refers to Baroque, Classical, and Romantic period music), the tri-tone is used to create dissonance much more often than the minor 2nd and major 7th. The main reason for this is voice leading. We'll cover voice leading in greater detail later later, but for now I'll just say that voice leading is concerned with melody (the "horizontal" view of notes) while consonance/dissonance is concerned with harmony (the "vertical" view of notes). Common Practice era music tends to put a higher importance on voice leading than other styles do. The "proper" way to resolve a tri-tone (which usually gives the most satisfying voice leading) is to move one note down a half-step (sometimes two half-steps, but we won't worry about that for now) and the other up a half-step, so the tri-tone either expands to a minor 6th or contracts to a major 3rd.
One way I like to think of it is in terms of the chromatic circle from page 6 of this convo:
Suppose I have two instruments playing a piece of music. I imagine the two instruments as being two small objects moving around the edge of the circle, connected by a spring. When the interval between them is a minor 2nd or major 7th, they're too close together, and the spring is compressed, which pushes them apart. When the interval between them is a tri-tone, they're on opposite sides of the circle, and the spring is stretched, which pulls them together.
All this crap was allegedly leading up to a description of why some modes are more commonly used than others, so here we go (finally).
Consider the C major scale (all white keys, starting on C). There are 7 notes in this scale, so there are 7*6/2=21 pairs of notes. As it turns out, only one of these 21 pairs forms a tri-tone, namely B & F. To resolve this tri-tone, and stay within the key of C major, we must move the B up to a C and the F down to an E (going the opposite direction wouldn't work, because we'd end up with Bb/A# and Gb/F#, neither of which are in the C major scale). Notice that both of these notes are in the tonic triad of C major (C, E, G). This is very convenient, because it means that the only tri-tone inherent in the C major scale naturally "wants" to resolve to the home triad of C major. And since all major scales have the same series of intervals and only differ by their starting note, this applies to all major scales, and not just C.
That explain why Ionian mode (major) works well, but what about the other 6 modes? Recall that all 7 modes have the same series of intervals, just in different "rotations". This means that all 7 modes have exactly one tri-tone which has a specific way it wants to resolve. For simplicity, let's just look at the scales that consist of all white keys (D Dorian, E Phrygian, F Lydian, G Mixolydian, A Aeolian, and B Locrian). These scales all have the same notes as C major, so the tri-tone will be B & F resolving to C & E. In A Aeolian (minor), like in C major, C & E are part of the tonic triad, so the tri-tone resolves to the home key. In B Locrian, B & F are part of the tonic triad, so the tri-tone actually resolves away from the home key. In the other four modes, neither B & F nor C & E are subsets of the tonic triad.
So, to summarize:
Ionian and Aeolian are convenient to compose in because the tri-tone resolves to the home key.
Locrian is inconvenient to compose in becase the tri-tone resolves away from the home key.
Dorian, Phrygian, Lydian, and Mixolydian are somewhere in between because the tri-tone resolution is unrelated to the home key.