Intro to tonal harmonic theory Part 2: Stuff you have to learn.

Stuff you have to learn

Disclaimer:

This post contains dubious amounts of hand-waving and opinion, and you might get more from it by ignoring the text and just playing with the table below, and the harp from the previous post. For audio to work you need a Web-Audio-API compliant browser like desktop Chrome or Safari.

Introduction

Western music notation is not the de-facto standard in music notation... there are many standards. But western musical terms are the most prevalent, and more often than not, when attempting to collaborate with anyone, you will find yourself needing to communicate using western conventions. So you might as well learn it. It looks hard at first, but you'll get the hang of it!

Next up, a table with the basics of western tonal harmonic theory. In this table you will find the common chords and scales. The discussion part will gloss over why these are the "common" chords and scales. I will sometimes refer back to part 1..

The Table

Choose a dominant note, and then press the buttons to hear the intervals, chords and scales (if you have a Web-Audio-API-compliant browser). The darker rows represent the black notes on a piano, and a "X" in a row means that note will be played. Intervals and chords are played simultaneously, whereas scales will ascend. You will have to use the scroll-bar at the bottom of the table to get to the scales. The source code for the table is here if you are interested.

Discussion

Unlike many tables like this you might have come across, I followed the piano-roll convention used in popular sound production software... where "one row up" translates to "one semitone up".

The "note numbers" column is consistent with the interactive harp in part 1. Choosing a "Dominant note" is analogous to setting the "Base String" in part 1.

This file contains the meat of the table above. It is in essence the first principle starting point for deriving much of western tonal harmonic theory. Hopefully it is enough to get you going.

Western pitch encoding.

This is the naming scheme still in use today to describe the 12 semitones : A, A#, B, C, C#, D, D#, E, F, F#, G, G#.
After G# it "loops" back to A, but an octave higher.

The reason western music theory is filled with oddities in naming conventions is because of historical conservatism. We could have ended up with a pitch encoding which used Arabic numerals instead... in fact, music teachers are forced to do this to get many concepts across (eg. counting out 7 semitones from "B" to show its "5th" is a "sharp"( more on sharps just now). ). The seemingly strange lack of mathematical consistency becomes consistent once you ignore the western conventions and just count out the semitones.

Intervals are just relative spacings between two notes played together. A "5th" will always be some base note and a note 7 semitones above it.

The choice of terms for intervals demonstrate a lack of mathematical proficiency in its originators since the 6th semitone interval is assigned, not a number but, a mystical sounding name instead... "The Tritone". Imagine counting like this in maths class: "One, kinda two, really two, kinda three, really three, four, MAGIC THREE!, five, kinda six, really six, kinda seven, really seven, eight!" (when what you really meant was to count from zero to twelve). People will think you're mad, or worse, an idiot. That is kinda the point to western music theory though... a lot of it is convention rather than sense... which is why, if you wanted to communicate your compositions or play in a band, unfortunately, you just have to learn this... which, once you learn it, you realise that even though it is a bit clumsy (like doing calculations using Roman numerals), it still remains systematically consistent... so at least useful.

Why are only some pitches a "#"

In western music theory they have two operators called "sharp" (♯) and "flat" (♭). Basically a "sharp" is a shift "up" by one semitone. A "flat" is one semitone shift "down".

Back in the day they still thought there were 7 tones (not counting the octave) in an octave (hence the name "octave" from Latin for 8). The tones were not logarithmically equally spaced and looked a lot like the octatonic scale set-up in part 1.

Once it emerged that 12 tones would be a better idea, instead of adopting a 12-toned scheme, they instead adopted the concept of a "semitone" (which you should be familiar with by now). In other words: a semitone is what a tone would have been had western music theory adopted a 12-tone scheme. Instead they kept the 7 tone system and kludged in the missing tones with "semitones". From part 1 it should be clear that the missing notes will make up another pentatonic scale.

That is why only some notes are sharp: the "sharps" make up the "semitones" that were missing from the original octatonic scale. They make up the black notes on a piano.

Scales

The family of Major scales was similar to earlier octatonic scales and they remain prevalent in modern music. The harmonic minor scale is the odd-one-out... it is common for reasons outside the scope of this post... basically, it is around because it has a pleasant sounding system of chords associated with it.

Resonance

I mentioned previously that I would go into this, but I will really only be touching on it. Resonance is the ability of something to sympathetically vibrate with something else which is also vibrating. A String will most strongly resonate with vibrations that are the same as its harmonics. Most strongly with the 1st harmonic, and then progressively less with each harmonic after that. So, looking back to part 1, intuitively, early iterations should produce a set of strings with strong resonances (up to 4 iterations), but then quickly become less resonant (from 5th to 7th iteration), and then progressively more resonant again just before the iterations loop back (the last 4 iterations).

So, using this grossly-over-simplified-hand-waving explanation it seems that chords based on the pentatonic scale will resonate the strongest. Significantly, the Major and minor chords exist in the pentatonic scale and they happen to make up the bulk of popular compositions. Diminished and Augmented chords are basically extensions of the Major and minor into the 12-semitone scheme, and are examples of "dissonant" chords... important in Jazz compositions.

More?

This post has become large enough... If there is enough interest, I might do another post expanding on sets of chords within a scale... but I think you've been sufficiently "introduced" to tonal harmonic theory that I can leave that as an exercise for you, the reader.