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Music Theory Tidbits

I originally posted this comment about time-signatures under "The Creative Process" thread, but decided to move it over here, and occasionally muse about some specific topic and try to boil some heady topic down in a concise way.

I was inspired by Patterning 2's use of a time-signatures, to type a quick blurb about how Time-Signatures actually work (and how they don't).

Over the years, I've griped about how time-signatures seem to promote a bias that cycles of 4 beats are inherently more valid than other beat groupings. For example, a Whole Note is four beats-- so if it is "whole" it must be more "complete" or more "perfect" than some other number of beats. And this is frequently how it is taught, and certainly what we see and hear in content and in apps.

A more comprehensive way to think about time-signatures is that they simply describe the relationship between a measure and a whole note. The bottom number shows how the whole note is sliced up, and the top number is how many slices are in a measure. In 3/4, the whole note is divided into 4 parts (bottom number), and each measure contains 3 of those parts.

If the fraction described by the time-signature equals one, (e.g. 1/1, 2/2, 4/4, 8/8) then one whole measure contains one whole note. If the fraction is smaller than one, a whole note won't fit into a measure, and if it is greater than one, than more than a whole note will fit into the measure.

Usually, the bottom number gives a hint about "a slice equals a beat" but with 3/8, 6/8, 9/8 and 12/8, we usually think of the dotted quarter as a beat. Because we don't have a way of cutting the whole note into slices of 3/8's, we must accept some quirks in a system that is biased toward binary rhythms.

There are more quirks. For example, it is never clear which note value equals one beat. And, when you transition from one time-signature to another, it might not be clear which note value might be carried over from the previous to the next. Additional notes are often used in notation to clear up the confusion.

The additional challenge with music software, is that unless time-signatures are used in a way that is standard and expected, it can make the app more difficult to use (rather than easier) and can limit options, rather than enhance them.
August 09, 2018  | favorite_border stub
In the most general terms, rhythm just refers to the placement of musical events in time.

Our brains and experience dwell eternally in the present moment. Contained in this present moment is a well-calibrated sense of what has happened in the "recent" past- and a sensation of "flow". That flow could be described as us moving through time from past to present to future. But in "reality", experiences are flowing from "anticipation" (future), to present experience, into memory.

We have learned to feel not only a pulse, but to hear more multiple pulses and structures at different rates-- then... the mojo (magic) happens. We some how experience this as a groove that gives is a different satisfaction that we would get hearing raindrops at random on a roof. (Don't get me wrong, I love that, too.)

The biggest organizational feature is that we have pulses or beats. We enjoy music at all different rates of beats (tempos). We generally enjoy when the beats have a regular and predictable rate, neither slowing down or speeding up. But we also have notated and customary ways to speed up and slow down to add excitement or drama.

Those beats are grouped into cycles of 2 or 3 or 4 or 5 or 6 or 7, etc. beats. We call them measures, as that's an almost customary way of approaching rhythm. Some cultures group beats in more elaborate, ornate or complex ways.

Next, we have a division of beats into smaller/faster units. It's almost a fractal kind of thing. Slow measures made up of beats; beats made up of faster sub-divisions.

We can have secondary ways of grouping the beats and subdivisions to create more intricate patterns. For example, we can be in 4 beat cycles, but make melodic patterns of 3 beats super-imposed over that bigger structure. Or we can take beats divided into 3 and group them into 4's to create a longer more interesting pattern. And we can have secondary ways of dividing beats, using tuplets of various kinds. You can divide beats into 2, 3, 4, 5, 6, 7, 8, etc. Or you can divide 2 beats into 3, 4, 5, 6, 7, 8, etc. And so on, any number of beats divided into any number of subdivisions, expressed as a ratio; e.g., 5 notes over 1.5 beats, etc., etc.

We can create these super-imposed "grids" of time, and place events of varying lengths on that grid. Using accents and ghost notes, we can add another dimension to a single line on a simple grid.

Those are most of the structural elements that make up rhythm in the real world.
August 09, 2018  | favorite_border stub
ULTIMATE RHYTHMIC FREEDOM:

1. Beats or no beats. You can decide if your music has a beat or is "free time". Music without a beat can still have structure, even a rhythmic structure, but it won't be based on regularly spaced beats or patterns. It might be more natural sounding or more "conversational" or perhaps more soulful and flowing. The listener will hear the flow of sound, melody and/or harmony; you may even hear "shapes" of longer and shorter notes, but you are not compelled to feel a pulse.

2. If there are beats, that forms your main grid. You can decide how the beats are grouped into measures, and whether that grouping changes or not.

3. You can divide the beats into a higher resolution of grid; and that division can change from moment to moment or from part to part.

4. You can choose a fixed tempo (rate of beats) or have the tempo change either abruptly or gradually.

5. With any of those structures in place, you can create a groove with percussion that is fun. Use the grids to quantize the events of your groove tracks to make them more precise, or leave them sloppy for a more human or looser feel.

6. When composing, you are either taking your existing ideas and working out the rhythmic structure that already is implied, or you can begin by building the structure first and develop ideas from there. Listening to the beat and the feel of the groove, you can pull in new ideas and let happy accidents happen.

7. Be adventurous. Don't get stuck in 4 beat measures and beat-divisions of 4. Try to write in 3-beat measures at different tempos. Get to know 5, it's like a 3 and a 2, and it's really cool. I've spent the last few years just getting comfortable with quintuplets (dividing beats into 5), and it has unlocked a cool little secret room. It's tricky because I know that if my audience doesn't feel quintuplets, they won't connect with the ideas. But some music I just do for me.

That's all for rhythm for right now. In my next post, I'm going to talk broadly about scales, melody & chords.
August 13, 2018  | favorite_border stub
Before we get to Melody and Harmony, we have to start with the pitch tuning system, which gives us a super-set of notes from which to choose. From those pitches, we choose a scale; and then we choose (mostly) scale notes for melodies and chords. I think sometimes the terms tuning system and scale are used interchangeably. It is possible to create a tuning system that IS the scale you will use.

If we wanted to create a tuning system from scratch, we'd need to choose a set of frequencies. Imagine finding a harp with unbreakable strings. You could just start tuning it as you like within the range of your hearing.

Perhaps starting from the lowest note, you can listen to the relationships that are made when you play one note and tune the next. If you were going slowly and carefully, at some point you would probably stumble upon what we call an "octave". Where some higher note is vibrating twice as fast as a lower note. This 2:1 ratio of frequencies has a distinct quality, every bit as pure sounding as a unison (1:1). You might also find ratios like 3:2 ("perfect 5th") or 4:3 ("perfect 4th") to be almost as pure sounding. But you could make some mischief and avoid anything pure sounding, if you want. It's your scale.

After you have finished tuning all your notes; you can decide if that is your tuning system. If so, you then choose a subset of those notes to be your scale. Or, you can just decide that what you have tuned IS your scale.

In your scale, you can now make melodies by plucking one note at a time, or make chords by plucking any combination of notes at once. You will notice that some combinations sound "comfortable" and some sound "intense". After that, the music you make, melodies and harmonies will create contours of comfort and intensity, which music theorists call "tension and release" (which sounds unnecessarily dirty, doesn't it?).

The limitation is that your tuning system will work with that original set of notes, but if you want to shift everything higher or lower, the relationships might change as you move up one or more notes in your tuning/scale. The relationships are "fixed" at the original key.

Now with digital synths, there are several ways to create custom tunings/scales. A sampler app may allow you to create custom key maps where each key can have it's own pitch. A standardized method for creating and exchanging tuning maps is called the "Scala" format. Some iOS synths (like Sunrizer and Z3+a) will allow you to load custom tunings using scala files.

In the next post, we'll talk about our familiar 12-tone equal temperament tuning system.
August 20, 2018  | favorite_border stub
QUICK NOTE ABOUT SCALES:

I've griped about how software developers tend to follow a half-assed version of "traditional theory" when it comes to rhythm. The result is often a confused half-assed mess, as expected, and almost no flexibility. Many ways to do one thing, rather than many ways to do many things.

The same is true when some devices include "scales". If you see a scale selector and it includes:
Major, Minor, Dorian, Mixolydian, Aeolian, Phrygian, Lydian, Locrian. It really only has one scale. Essentially, modes are just major scales with the root offset to a different note.

Today, I looked at the scale selection of an "intelligent" pitch shifter, and it had a Major scale, and modes (like minor, dorian, mixolydian, etc.) and Harmonic Minor. So it had two scales. In their minds they think they've provided 9 scales.

It is a can of worms, clearly. But if they included just 6 scales: Major, Harm Min, Mel Min (asc), Whole Tone, Dimished, Chromatic, for most applications, that would cover LOTS of ground.

For any modes, the end user would need to shift the root in their head. I.e., if I want Eb Lydian, I have to set the scale to Bb Major. That's not so difficult.

If you haven't ever tried this, play around with C harmonic minor, but with F or G as the root (i.e., a mode of the harmonic minor scale). Play C melodic minor ascending (C, D, Eb, F, G A B) but with F as the root. This is also known as Lydian b7. It's beautiful.
My $0.02:

Over the years, I've griped about how time-signatures seem to promote a bias that cycles of 4 beats are inherently more valid than other beat groupings. For example, a Whole Note is four beats-- so if it is "whole" it must be more "complete" or more "perfect" than some other number of beats. And this is frequently how it is taught, and certainly what we see and hear in content and in apps.
I, like just about everyone was taught this way too, probably because it’s simple. Start with the basics. The problem is that even though most of us advance from the basics, some don’t, or simply try to keep it simple. There is definitely a bias as “Common Time” (and to a lesser extent “Cut Time” or alla breve) has had their very own symbols in music notation since when? Probably since the beginning of common notation itself. What could be more biased than that? I suggest getting out of your comfort zone to anybody who struggles with less common time signatures. Practice is literally the only way to learn.

If the fraction described by the time-signature equals one, (e.g. 1/1, 2/2, 4/4, 8/8) then one whole measure contains one whole note. If the fraction is smaller than one, a whole note won't fit into a measure, and if it is greater than one, than more than a whole note will fit into the measure.
Sad, but true. I guess we could say to at least some degree that sustaining a whole note could make it longer than one bar under 4/4 time, but what if we had a way to lengthen a note, rather than to shorten it, like a “reverse dot”, or something? Wouldn’t that be great? I would think that music notation will not change, even for the better, but isn’t it nice to wonder!

Usually, the bottom number gives a hint about "a slice equals a beat" but with 3/8, 6/8, 9/8 and 12/8, we usually think of the dotted quarter as a beat. Because we don't have a way of cutting the whole note into slices of 3/8's, we must accept some quirks in a system that is biased toward binary rhythms.
I personally support non-binary rhythms!

There are more quirks. For example, it is never clear which note value equals one beat. And, when you transition from one time-signature to another, it might not be clear which note value might be carried over from the previous to the next. Additional notes are often used in notation to clear up the confusion.
That's just sloppy! A composer needs to figure a way to make it work, perhaps a tempo change? Why not a time change for a bar and then switch to a different time, if only to make it work. Like I said above, music is about learning, and lifelong practice, and what’s better practice than to challenge your own skills?

The additional challenge with music software, is that unless time-signatures are used in a way that is standard and expected, it can make the app more difficult to use (rather than easier) and can limit options, rather than enhance them.
I can’t agree enough! I just did a cover of a fairly complex piece that uses multiple times & tempos, and as a challenge, I made it my first project in NS2 (after doing the same project in Cubasis a day earlier), and I discovered that NS2 handles time changes much better than any DAW that I’ve used in the past. My only gripe was when changing both time & tempo simultaneously, I would hear an audible stutter with a high pitched squeal if only for a few (hundred) milliseconds. I eventually had to change only the time signature, leaving the tempo alone, and it sounded fine, but perhaps because it was only for a bar or two. I am thinking if it was any longer it may have been noticeable that the tempo should have been halved for only a second or two. Like I said, first project using NS2, so maybe it was on me.

So, that’s my $0.02 on the subject. Great post, and certainly some good points, both revenant, and got me thinking!

~ Jay
October 30, 2019  | person SuperFlyEDSguy
Thanks, Jay @SuperFlyEDSguy

I really appreciate your thoughtful comments and observations.

At one point, I was going to suggest (to the world) that a time signature should include:

Units per measure, units per beat (as reflected by the tempo). One issue is that the units per beat might shift between triplets and 8ths, or 8ths and 16ths. It's a problematic commitment.

For most music software, this is a necessary commitment, as the software won't allow you to have more than one step-rate either in a track, or in the entire sequence.

This is my strongest argument for abandoning time-signatures-- if there's no flexibility-- as I've just described, or problematic glitches, like you described in NS2, then simple lay down whatever the simple rules.

For example:

Can you change tempo steadily throughout the track? In any case, a starting tempo, and, if possible, a track with tempo change events.

Can you change the step rate- either on a track song basis, or a track basis, or a beat basis-- then allow those settings to be exploited.

Can you set a non-standard beat grouping (beats per measure)? Can this change throughout the track? Add a track to define the time signature either globally or per track.

Thanks again for reading, Jay.
October 31, 2019  | favorite_border stub
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