Intervals: Diatonic Expression
Preface:
Recap:
By now we have some frameworks established that will start to be filled in throughout the following blogs. We know that notes and their relationships are derived from pitches which are derived from quantizing the frequency range of audible sound. We can also start to use these notes to create modes which can then be used to create motifs and melodies. Before we get that far we need to finish developing the idea of notes and intervals that will be organized into the modes (and later scales).
The Western Notation System:
While my goal may be to keep these blogs as culturally agnostic as possible it's still necessary to work within a given system to produce examples, and to clearly explain concepts. Rather than try to pretend to be knowledgeable about all systems in all places it'll be much more productive to work within the western system I'm already familiar with, and try to leave open the possibility that other systems can apply these concepts as well. For pitch and note names I will be using the alphanumeric system mentioned in a previous block (i.e. C4, A2, etc.). If you have access to a daw with a piano roll this will be easy to look at and follow. If you're going the staff paper and pencil route it's good to have some landmarks. C4 is 'middle C' sitting between the treble and bass clefs. The numbers roll over at each instance of C so going up from C4 would be D4, E4, F4, G4, A4, B4, C5. I'll generally keep examples between C2 to C6. Just keep in mind the distinction being maintained between pitch and notes. Pitches d
On to Intervals:
Intro:
Most music theory training centers around intervals to some degree. We use it to describe the pattern of sequences (scales, motifs, melodies), the distance between stacked notes between voices or in a chord, to describe the consonance/dissonance of a given set, and the relationships between different sections in different keys. The reason for this importance being that when we experience music it's not just notes in isolation, but within the context of other notes. The way we discuss this experience is via intervals. Even if not being done explicitly, a listener may describe a feeling from a particular part of a song that was the result of how notes interacted (the interval content).
What is an Interval:
The most basic definition of an interval is the distance between two pitches. To describe an interval you need two parts. The first being a root or starting pitch, and the second being the interval name. We'll use the term root here since it'll be useful in later blogs, but for now it doesn't necessarily mean the root of a chord. Instead it simply identifies the initial pitch that we're using for comparison.
Meeting the Intervals:
To get started we're only going to focus on the intervals relevant to the modes that we're currently working with. Most have a full name and abbreviation, and I would suggest getting comfortable with the abbreviations as quickly as possible as they will be used exclusively beyond this blog. The terms minor, major, and perfect describe the quality of the interval. Not in terms of good or bad, but distance. The minor quality of an interval is closer to the root than the major. The concept of perfect intervals is something of a hold over from previous practices, but it still has some utility in modern contexts. Specifically when it comes to cadences and key relationships. Tritone is a special case, and there's usually one instance in any standard scale/mode. Again, this is something of an outdated concept, but there's some utility in recognizing it as a distinct interval.
In modern contexts there's no particular reason for having perfect intervals, and we could just as well get by with minor and major 4ths and 5ths. We'll explore specific work-arounds and use cases for the non-perfect qualities of these intervals in future blogs, but for now knowing they exist is sufficient for our current goals. There's also the topic of consonance and dissonance which has gone through many changes from one era to the next. Originally it was a distinction between intervals that sound nice and those that don't, but in modern contexts the water gets muddied. For now I think it would be best to side step this topic until later discussions. In part because it quickly becomes rather subjective as you dig into what exactly it means for an interval to have one characteristic vs another. The intervals we'll focus on now are the following.
Unison
Minor 2nd (m2)
Major 2nd (M2)
Minor 3rd (m3)
Major 3rd (M3)
Perfect 4th (P4)
Tritone
Perfect 5th (P5)
Minor 6th (m6)
Major 6th (M6)
Minor 7th (m7)
Major 7th (M7)
Perfect Octave (P8)
Unison:
Starting with an odd duck of intervals, unison is only used to describe two voices meeting at the same note. It's not typical to describe a single voice as moving to a unison, but it wouldn't technically be wrong.
Minor and Major 2nd:
Taking unison as the root of a mode we move on to 2nds which are the step-wise interval, and you'll usually see them describing the space between adjacent notes in a sequence. In the case of modes you'll often hear the terms 'half step' for m2 and 'whole step' for M2, and any given mode will have a specific pattern of m2/M2.
Minor and Major 3rds:
Adding another half step we get to m3s, and a half step farther a M3. These are the main intervals used in describing the quality of a mode. If the first 3rd from the root in minor then the mode quality itself is minor, and same with major. 3rds are also a significant interval in voice leading as will be discussed in the future.
Perfect 4ths and 5ths:
P4s and P5s serve special purposes depending on the context, and generally mirror each other in terms of function. From the perspective of the root note in our mode, jumping up a P4 feels puts you on the same note (different pitch) as jumping down a P5 (and vice versa). This type of leap is usually significant in cadences and key changes. As an interval between different voices it almost has a kind of doubling quality, and as we'll see in the blog about voice leading there are certain pitfalls associated with its use.
Tritone:
The tritone has a complicated past going from a once forbidden interval to a common modulation feature. Part of it's complexity comes from it being an uncomfortable jump for past singers as it consisted of three whole steps as well as it being considered an "unstable" interval between P4 and P5. This "unstable" characteristic would later become it's main feature that would allow it to be used in more complex harmonic contexts.
Minor and Major 6ths:
6ths are the inverted counterpart to 3rds, and they'll be a huge part of harmonic analysis in later blogs. Within a single voice it can be a dramatic leap. If you're familiar with Chopin's Nocturne op. 9 no. 2 you're already familiar with the minor quality. For modal voice leading we'll generally treat 6ths the same as 3rds.
Minor and Major 7ths:
7ths are the inverted count part to 2nds, but with certain exceptions for major 7ths. Leaps of a 7th are not particularly common, and to the degree they do occur they're paired with some opposing movement even if only a 2nd.
Perfect Octaves:
Octaves and unisons are generally treated the same, but as we'll see in voice leading some care has to be taken with octaves (same as 5ths). As with other perfect intervals there can also be augmented and diminished variants, but those are highly specific and special cases that are typically uncommon in modern practice, but do occur in the more chromatic works of Common Practice composers.
As Relates to Modes:
As mentioned before, but I want to highlight again, the modes we'll be working with contain and are defined by these intervals. Each mode is effectively a unique pattern of intervals. For example, C Ionian when analyzed as a sequence of 2nds looks like M2, M2, m2, M2, M2, M2, m2 (C, D, E, F, G, A, B, C). Starting at the same root, but only looking at 3rds we would get M3, m3, M3 (C, E, G, B). Looking only at 4th we would get P4, Tritone (C, F, B). Fifths would give us just the P5 (C, G). 6ths would give us a m6 (C, A), and 7ths a M7 (C, B).
Conclusion:
At this point I encourage you to take the time analyze each mode the same as done above for C Ionian. Consider the pattern for each, and even go back to the previous blog exercise. Play each version of your melody and each mode, and analyze the intervals being used in each mode. Then consider how each of the intervals are contributing to the unique sound of the motif as it's played in each mode. You may even find some similarities. Some aspects of this process will involve some exploration on your own, and I encourage you to spend some time playing with these ideas on your own before moving on to the next reading.
