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title: BTW 261 MP 1 part 1

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# BTW 261 MP 1 part 1

## Summary

In this technical description, I will be going through the basics of harmonic reduction in music. Harmony is basically the auditory perception of how different pitches sound together at the same time, and reduction is abstracting something into a more high-level structure, which makes such structure more suitable for further analysis.

Harmonic reduction is widely used in Western common practice music theory since a good share of Western music are of homophonic texture: one part as melody and one or multiple parts hinting the underlying harmony. Before we jump in to the actual reduction steps, let's see what a reduction actually contains.

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## Key Concepts

### Roman Numerals

Roman numerals will be a staple in most music theory and musicianship classes that follow Western common practice. Those numbers has much to do with tonality, which in a less theory-heaving setting is what we usually call the "key" of a piece of music. Therefore, Roman numerals basically means what's a chord's function within a certain key. For example, a C major chord in a C major piece would have the same function of a D major chord in a D major piece.

### Inversions

Even though chords in the wild can come in so many different shapes and forms, for the sake of simplicity and practical convenience, chords in harmonic reduction always has a third up and (most of the time) a fifth up from some "root note." That is what makes identifying chords sometimes not so easy; you have to find different combinations to finally get a root note that satisfy the requirement! Even though often times the root note is the very bottom note (the "bass note"), when they are not the same, an inversion happens.

### Intervals & Spelling

What is a "third" or a "fifth," you mean? It is actually not hard at all; just look at this example:
![](https://i.imgur.com/ggK0FME.png)
The note and other notes occupying the same vertical space is a "first" away from each other, and it increments when they move further away. Note that it's only the space or line the note it's on that matters, so you can just ignore all the sharps (♯) and flats (♭) when you're doing the counting. Therefore, notes that sound the same but are written differently (D♯ and E♭, for example) will be treated differently during reduction.

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## Steps

### Identify chords & write out their Roman numerals

Identifying chords can be very easy at times - just find all the notes vertically, use the appropriate names, and then we can call it a day! However, chords can often be missing notes, have extra non-chord notes, or sometimes even both! Reconstructing those chords is the most low level reduction process going on, and after that the proper Roman numerals are given based on the tonality of the piece (or section of a piece because a piece can change keys in the middle). This part is rather mechanical.

### Identify intermediate harmonic structures

Now that you have all the chords down, it is now time to figure out some higher level structure. For example, some chords are just a brief interim between more important chords (passing chords); some chords are holding a note that will later move down to relief the tensioned sound (sustained chords); some chords form a pattern that makes transition more interesting (chord sequences). Even though from this part on, there often isn't one definitive answer, there are still ways to help you determine what chords are to be reduced, such as the duration of the chords and whether they start on the strong beat.

### Identify phrases

Unlike the previously mentioned intermediate structures, phrases are slightly more well-defined. Phrases they are constituted of some of the three types of chords: tonic (most stable), predominant (less stable, tends to move to unstability), and dominant (least stable, tends to resolve to stability). The right combination of these chords form cadences, which is the part of a phrase that signifies a strong ending; this is how most phrases are being identified. After identifying the phrases, the harmonic reduction process is done! There are still even higher-level analysis on music, but that is another topic for another day.