Musical Improvisation depends on Grammar for expression

I've noticed some threads on language here lately and since it seems like the appropriate "season," I wanted to open a discussion for any musicians out there who practice improvisation.

Improvisation has been a huge facet of music through our whole history. Even during the classical periods when orchestras began following written music note-for-note, composers like Bach, Beethoven, and Mozart were still well-known for being impeccable improvisers, which no doubt contributed to their ability to compose.



So what does this have to do with language.

Well, first of all, all Western scales you hear (from classical music to rock to dance to hip-hop) depend almost mechanically on 5 notes known as the "pentatonic scale," "pentatonic" literally meaning "five tones."

You can have more notes than this in a scale and be even more expressive, but the realization I had when I really got into improvising, is that it really is like you are "talking" with your instrument, in that you are basically mimicking inflections from our languages, and this is where we derive perceived emotions and etc. in the music based on the sequence of notes.


I'm curious how many other musicians here have made this connection between grammatical syntax in our language, and musical syntax, especially in improvisation.


Of course there is always music that completely defies a predictable order, and in the right hands it's usually (though not always) that much more expressive and beautiful because of it!

Here's a new way of illustrating musical form that connects repeating sections in the music with circles:

Seeing Sequences

From melodies to text to DNA, many interesting types of information come in the form of a sequence of symbols. Although it's natural to try to analyze these sequences graphically, they present a unique challenge for data visualization. A good visualization method should provide a broad overview of the "shape" of the data--yet with sequences, the only structure ab initio is the completely uniform micro-level connection of each symbol to its immediate neighbors.

This page describes a technique, the matching diagram, designed to deduce and display macro-level structure in long sequences. (If you want to skip this description, go directly to these pictures of music.)

Matching diagrams are based on the fact that sequences often represent a hierarchy of ideas. Melodies, for instance, are usually based on combinations of smaller repeated musical passages; text has repeated words and phrases. A natural way to find macro-level structure, therefore, is to use these repeated units as signposts.

Unfortunately the human eye is bad at spotting repetition. (Try to find the longest repeated subsequence in 28746391479735648274639137. It's irritating.) Matching diagrams avoid this difficulty by having the computer find the repetitions and highlighting them explicitly.

www.bewitched.com...

That page goes on to show how they illustrate that ugly number:





So they apply it to some musical pieces to get a sense of all the structure of the piece, from the "micro" level of individual notes repeating, to larger passages of music repeating in their entirety. Repetition is what gives music a reference point, so that a "structure" based on some kind of pattern can emerge. That doesn't stop people from writing music that never repeats at all, it's just that most musicians seem to use repetition anyway.

Mary Had a Little Lamb:



Beethoven's Fur Elise:

The next diagram visualizes Beethoven's Fur Elise. Again, matches are based on equality of pitch; where chords occur we consider only the top note. Despite this extremely limited definition of musical similarity, the resulting matching diagram reveals an intricate and beautiful structure.

The picture shows how the piece begins and ends with the same passage, while a longer version of that passage repeats throughout at increasing intervals. You can also see a long stretch in the second half where that passage is not repeated at all and whose structure looks distinctly different, which corresponds well to what you hear when you listen to the music.

Bizet's Toreador from Carmen:

Not all pieces show as much exact repetition as Fur Elise. For instance, the "Toreador" song from Carmen, diagrammed above, looks completely different. Instead of a few long passages repeated exactly over and over again, it contains many repeated smaller phrases.

Bach's Minuet in G Major:

As a final example, consider Bach's Minuet in G Major. The diagram shows that the piece divides into two main parts, each made of a long passage played twice--or what a musician would call an "AABB" structure. It's not surprising to see this in a minuet, which shows that the matching diagram is picking out structures that correspond to conventional notions of musical form.

The diagram, however, provides much more detailed information than the simple "AABB" notation. For instance, you can see that the A and B passages are loosely related, as shown by the bundle of thin arcs connecting the two halves of the piece. And the fact that the two main arcs overlap shows that the end of the A passage is the same as B's beginning.

This is an old-school "AABB" aka "binary" form that consists of 2 parts that are loosely related, if at all, to each other in musical character/content. You can see the two distinct sections as two big circles in their illustration. And to connect them, since they didn't share much in common at the transition directly between them, you see how Bach worked in what looks like the structural equivalent of a band-aid to make them seem more related anyway (not meant to diminish Bach in any way).


I just thought that was interesting and worth sharing, related to forms and structure within music which is basically what I mean when I say "grammar" in music.

The best thing about music theory is how open to interpretation it has to be by necessity. You can take any "rule" about what something in a piece of music "is" and turn it on its head a hundred different ways.





I was strapped for time when I posted the OP because I had to run out, but I meant to elaborate on the pentatonic scale.

5 notes.



This scale or very close approximations of it have been found on flutes of indigenous people all over the world, even in ancient artifacts dating back to the birth of known civilization.

The reasons for these particular notes becomes clear in the mathematics, where you can see that these notes are actually the first overtones produced by a single note, because they resonate at very harmoniously ratios with the fundamental frequency.




When you pluck a guitar string, for example, if you watch it, it's hard to even comprehend how exactly it's moving because it just looks like a vague blur. But based on the harmonics the string produces (the actual sound wave it produces, which you can break down into various frequencies on a computer), it's actually vibrating at all the frequencies such as what you see above simultaneously. The whole string is vibrating up and down, but while it does so, there are other vibrations of various frequencies vibrating along it as well. And only the frequencies that resonate best with the vibration of the entire string survive, because all the others die off quickly from attenuation.

(Btw that last sentence exposes one of those truths about reality that make me consider music theory to be possibly the best spiritual study of all..)

The major pentatonic has an equivalent minor pentatonic scale that makes up basically all blues and classic rock music and a lot of metal, etc., not to diminish that,either.


But anyway these notes all have a definite relationship with each down to their very vibrating cores (resonate ratios with one another). And we even speak with inflections and suggestions of these intervals, especially when our speech is laden with emotion. For dramatic effect we'll drop from one tone to one about a 5th lower, and in music theory the 5th is what typically comes right before the typical last note, the 1st or root note again.

Their relationship with each other is one of those things you can turn on its head an infinite number of ways, but very generally and conventionally speaking:

The root note (1) of the pentatonic scale is the most resolved and commanding tone in the music. All other notes are basically in reference to that note, and that carries over into how you actually psychologically interpret the sequence of notes believe it or not. It all goes back to the physics of the overtone series.

The 5th or dominant is considered the next most resolving and commanding note of the scale because the other notes of the scale revolve around it most similarly to the way they revolve around the root note. Another reason for that is because it's also the first natural harmonic to appear besides the octave. In classical music composers would typically modulate to a key a 5th higher, because the difference was enough to create tension but not dramatically, since they are naturally so similar anyway.

The 4th degree is somewhat similar to the 5th in relation to the root note but is considered to have a slightly weaker connection to it, and obviously of a different character, and the 3rd isn't traditionally considered to have much of a connection to the root note at all except to define whether the scale sounds major or minor. But especially in blues scales the minor 3rd is used all the time to release to the root note, even more than the 5th is.

The interplay of these basic notes with each other, how they are arranged, how they repeat, the patterns they form, is the basic core of what I mean by musical grammar in a series of notes or melodies. There is a definite pattern in most music that is comparable to what you see in literature and even the grammatical structure of sentences.

[edit on 31-1-2010 by bsbray11]

adododoadadadaisalliwant2say2u...................its really so simple..............
a caveman could do it dont u suppose?

Great thread , i was looking for something like this last night funnily enough.

Thankyou - when i get back home, i'll have a proper look and comment with some thought.

Music, and especially an individual's connection to a specific piece of music, is all about grammar. As your second post demonstrates, it's not important that we're playing C E G, because we could move that up or down without discrimination and it would feel the same; and one could even say it's not about 1 3 5, but it's really about the interval between 1 and 3 and between 3 and 5... Our built-in pattern recognition is hearing "major third followed by minor third" even if it doesn't know what those mean. The relationship between the notes is more important than the actual notes.

Taking that further, in medieval music, you don't find many thirds... It was all about the perfect forth and perfect fifth. In some cultures the augmented fourth/diminished fifth or "tri-tone" is more readily accepted than others. (And we're not even going to get into cultures with micro-tonal scales.)

Even within Western tradition, as a guy who grew up on Texas Blues, there are things happening in Delta Blues that I don't get. Or aspects of Jazz from Chicago, with long held notes that convey an emotion in simple phrasing, that I can totally empathize with, while New York's Bebop-based improv with five-million notes in the space of a few bars, with no tonal center, leaves me flat & confused.

Originally posted by mr-lizard
Thankyou - when i get back home, i'll have a proper look and comment with some thought.

You ever get home? o.o


I was kind of looking forward to possibly having some insightful discussions about this because I have a lot of trouble trying to properly express these ideas myself.


For example when you say,

"I hate you"

it would take on different tones through your vocal cords, colored by your emotions, than if you said,

"I love you."


And if these were translated into affective music (not lyrics but only tones) it would be easy to tell them apart from one another, but the specific content of the message becomes lost and the music simply becomes an emotional metaphor for such an idea, not the exact expression "I love/hate you," which you could only get explicitly with lyrics.


I guess what I'm getting at is that there is some inherent order to our emotions and how they come across in rhythms and tones, and this is really what I'd like to explore: the ways different emotions can be expressed in the grammar of so many tones and rhythms.

I think a lot of it has to do with pre-learned culture and language, but not all of it... There is something universal about this "language" that is music that transcends cultures and languages, too.

The basic music intervals common to all human cultures are the 1-4-5 intervals. The 4th overtone has the inversion as it's root -- 3:4 since the 4 is the home tone as the octave.

Western music uses amplitude as the inverse square of frequency -- based on wavelength -- so that undertones are used -- not harmonic overtones.

In other words the Western harmonics uses "harmonic mean" and "geometric mean" and "arithmetic mean" originally from Archytas.

So the harmonic overtones actually do not line up with the Western scale used to create the pentatonic measurement. So in the nonwestern 1-4-5 intervals you get C to G as 2:3 and G to C as 3:4 -- as the overtones.

But in your pentatonic scale you're excluding the 4th interval. So the basic meaning of real improv music is the 1-4-5 interval not the pentatonic.

The secret of the 1-4-5 interval is exactly the "complementary opposite" relation of the 1-4-5 overtones which violates the Western commutative property of A x B = B x A. The commutative property is the basis for the "arithmetic mean" and the "geometric mean" and the "harmonic mean" -- which has to convert the harmonic overtones to the "undertone" ratios -- 4:3 and 3:2.

I have a blog on this top naturalresonancerevolution.blogspot.com... which lists my free online articles, interviews, etc.

reply to post by bsbray11

Hello there.

Sorry i've been busy.

I would be fascinated to see these images combined with a pitch visualistion or frequency range image.

I'm also fascinated by the 'syntax' the 'nothing' between the notes, which without the pause and silence as a counterpoint , we could not have melodies...

I'm a little tired, but i'll keep checking on this thread.


-- edit: Has anybody ever carried out any research to compare pitch and vocalisation of notes in various emotive states and compared them culturally?

I.e what note do we hit when suprised? or scared?





[edit on 8-2-2010 by mr-lizard]

Originally posted by drew hempel
But in your pentatonic scale you're excluding the 4th interval. So the basic meaning of real improv music is the 1-4-5 interval not the pentatonic.

The minor pentatonic includes the 4th, and that is the most common pentatonic scale in most popular music that stems from "blues" and in turn "rock." But I agree that the 1-4-5 is the basic crux of all these scales. Or 1-5-4 in order of musical dominance. And that the "4" comes in as a relation to the root note in the same way the root note relates to the 5th, not as the next note after the 5th in the overtone series, you're right.

Originally posted by mr-lizard
Has anybody ever carried out any research to compare pitch and vocalisation of notes in various emotive states and compared them culturally?

I.e what note do we hit when suprised? or scared?

Possibly, but not that I'm personally aware of. But one of the things I'll do personally is listen to music, find a place where the emotion is almost concrete and tangible, and then look up the melodies/harmonies/rhythms/etc. they use to actually pull that off, and learn from it. And I know most musicians do the same thing, consciously or unconsciously, because there tend to be only a handful of methods in any given genre to evoke a certain emotion and different artists will use the same technique over and over in different ways.

Any note is different based on the different levels of different overtones in the note -- so you have frequency as the note and then you have different amplitudes of the overtones and undertones -- and then you have phase shift of the frequency. So if you shift the phase -- that is stepping outside the realm of the inverse square measurements of amplitude -- and you can get an inversion of the frequency -- the 1-4-5 relation -- based on the phase shift of the frequency.

Overtones and undertones are dealing with the pure frequency relations whereas a sound of a word or phoneme -- a letter or syllable or an instrument -- all are based on the different amounts of amplitude of the overtone and undertones which creates the "timbre."

Human perception of sound is tied to vision as well so if you see someone make a sound and at the same time you hear a sound your brain perceives a third sound which is the combination of the vision sound and heard sound.

In fact humans can hear ultrasound -- but only internally -- and also nonwestern music is based on the idea of frequency resonating into light -- so that sound, the real purpose of sound, is to create light energy for healing and spacetime travel, etc. That's what the Bushmen trance music is about.

reply to post by mr-lizard

Great thread.
I think you are trying to give grammar way too much credit than it deserves.
When it comes to grammar, one must adhere to certain rules to appear and sound remote intelligent or people won't even listen to what you have to say. Grammatical rules were probably developed and created by some arrogant elitist, once upon a time, in order to allow for the opportunity to distance himself from the his fellow grunters and groaners.

Of course music has it's own set of rules too. These are rules that are much more complex, yet are more forgiving in its use.
Ever heard the saying "you've got to know the rules before you can break them"?
Unfortunately, this doesn't be apply to grammar because even if you know the rules of grammar you'll never be daring enough to break them.
With music you can break the rules and still get the point across quite effectively.

Music also has the ability to come to life and tell its own story.
It speaks dynamically through emotion, something that would be extremely difficult, if not impossible, to do with words.
People who try to explain and describe emotion turn out to be poets or end up working for Hallmark.

A picture tells a thousand words, and so does music, because it is also an art form.
Music styles may change but the very foundation of music does not. Grammar, on the other hand, is constantly changing.

When crooners from the 1950's found themselves trying to make the transition to this newfangled music called rock and roll, one popular artist was presented with a song called "Ain't that a shame" but he immediately wanted to change it to "Isn't that a shame". Proper grammar perhaps, but obviously not very effective musically.

Music is also cultural and different cultures rely on their own set of scales.
One scale I've always found extremely interesting is the harmonic minor scale.

Btw, the images you present resemble very much the designs of a mandelbrot.