Note that when I named the 12 notes of the scale (F–C–G–D–A–E–B–F# etc), their very name implies that there are seven of them (A through F), and that we build the other five by using alterations. The most common alterations are #, or "sharp", denoting that we increase the pitch by a semitone and ♭, or "flat", denoting that we decrease the pitch by a semitone. Seven notes (heptatonic) has become a standard, but there are ways to create scales with six (hexatonic) and eight (octatonic) notes. And we'll be looking at five-note (pentatonic) scales below. So let's find out why Western music gave names to seven notes, and let's understand how this happens when you are concerned with things like “balance” and “harmony”.
A note on "balance" and "harmony": I'm not claiming the scales described here are superior or inferior to any other way of arranging musical notes. By all means, musicians should explore and play with quarter tones and imbalanced intervals to create evermore creative scales. Romanian/Hungarian scales contain asymmetry, and what I refer to as "balanced" here will be called "boring" by someone else. I'm only going down this path because a culture (my culture) (and my subculture) created a musical system with a particular logic, and "balance" is the idea that you don't have all your semitones at the bottom of the scale and all your tones (or 1.5 tones) at the top, while "harmony" corresponds to the idea that you want your chords (and your chord progressions) filled with as many perfect fifths and perfect fourths as possible, i.e avoiding the tritone. Many composers and musicians have had fun playing with the rules of Western music and breaking them, but the psychoacoustics of musical intervals ultimately play a big part in how scales and chords are crafted.
Let's go back to the fourth and fifth being the first two harmonics of a musical instrument (besides octaves): because of this friendly relationship, it's common in Western music to transition from a tonic chord to a fourth note chord or a fifth note chord, so for this to work harmoniously (according to Western tastes) it's important for these notes to be in the scale!
Now let's try to build a scale with six, seven, and eight notes. When listing the notes in the scale, I'll use "S" to denote a semitone interval, "T" for a tone (two semitones) interval, and "+" for a tone-and-a-half (three semitones) interval. Remember that the 12-note scale is composed of semitones – the fact that the base unit is a half tone (not a tone) is completely arbitrary. Each scale must add up to 6 tones exactly.
With six notes, you can build either a tonal scale TTTTTT (which has no perfect fifth or perfect fourth), or a scale that has a gap of a tone and a half.
Not having a perfect fourth and fifth violates the "harmonious" rule (all the triads are dreaded tritones). Having a 1.5-tone gap violates the "balanced" rule, so we’ll need to add at least one more note to the scale.
Many, many catchy tunes were built on hexatonic scales, so I'm dismissing them rather summarily, but for the purpose of this exercise, we'll consider their combinations of 1.5 tones and semitones as being detrimental to building a versatile, balanced scale.
With eight notes, you must create a scale with 4 tones and 4 semitones (since we want to avoid 1.5-tone intervals – the reason we dismissed the hexatonic scales). You don’t want TSTSTSTS (the “ancohemitonic symmetric scale”) or TTSSTTSS because there is no perfect fifth available. You can create TSTSSTTS which is an interesting scale that I can't find evidence of anyone adopting or developing.
You can also split your tones or semitones into a group of 1 and a group of 3 (e.g TSSSTTST), which is imbalanced compared to seven notes, where tones are in groups of 2 and 3. And there is SSSSTTTT, which is just silly.
To build a scale with seven notes out of twelve semitones, using only tones and semitones, you must arrange 5 tones and 2 semitones. The only way to do this while keeping things in balance is TTSTTTS, which is the sequence of white keys on the piano!
Other options like TSTTTTS would have three tritones in its triads: TTT twice and TSTS! TTSTTTS only has one tritone (that's STTS), which will become meaningful when choosing modes.
Side note on triads – chords are built by stacking a root note and even-intervalled notes above. The most basic chord is the triad, or notes 1–3–5.
You can also create many interesting asymmetries with seven notes and three-semitone intervals. An example is S+STH+S which is a scale that goes by many names e.g phrygian dominant scale. Another is TS+SS+S or the Hungarian minor scale The seven modes discussed here are the only ones that you can construct with only T and S, and balancing them out.
So here we go! We have a scale of TTSTTTS, which has many perfect fifths, and is well balanced. What is a mode then? It’s the way one arranges these intervals from a tonic. The possibilities are:
Ionian TTSTTTS
Dorian TSTTTST
Phrygian STTTSTT
Lydian TTTSTTS
Mixolydian TTSTTST
Aeolian TSTTSTT
I criticized this approach for describing modes at the very beginning of this article, but you can see that, if what you have is a piano with only white keys, you would want to know what tonic to choose when writing music. So let’s look at the characteristics of these modes besides their sequential arrangement of tones and semitones.
How many modes can we play? Let's use the Irish flute as an illustration.
The notes available are D–E–F♯–G–A–B–C–C♯.
This gives us the following possibilities (I'm skipping the scenario where the first note is the C or the C♯):
Ionian D E F♯ G A B C♯
Mixolydian D E F♯ G A B C
Dorian E F♯ G A B C♯ D
Aeolian E F♯ G A B C D
Phrygian F♯ G A B C♯ D E
Locrian F♯ G A B C D E
Lydian G A B C♯ D E F♯
Ionian G A B C D E F♯
Mixolydian A B C♯ D E F♯ G
Dorian A B C D E F♯ G
Aeolian B C♯ D E F♯ G A
Phrygian B C D E F♯ G A
That's a lot! Surely all these are not used equally, and not all are as convenient to improvise on.
Let's now review the characteristics of these mode.
Before we pick winners and losers, let's dig deeper into the Ionian mode.
Next post: The modes