More Insights on The Harmonic Series and on Music Theorists.
The following blogs post shows my (email) response to an email I received from someone asking me about the harmonic series and about the research of a music theorist. It is slightly redacted to improve the flow and to clarify or improve the points I was trying to make in my email, and better fit this blog.
Your article on “The harmonic Series & its Implications on Composition” was interesting. However, I’m confused by its practical application.
When music theorist Ernő Lendvai performed such an analysis on Béla Bartók’s music, he referred to the composer’s scale as an acoustic scale after noticing how closely the notes acoustically mirrored the 8th-14th partials. How?
Did he divide the frequencies of each of those partials by the corresponding fundamental piano key (e.g., F(D4, based on C1)/D1? Or was he looking strictly at intervals?
If I wanted to ascertain the acoustical richness of a given scale, then I’d need to examine its harmonic content. I get that. But the steps aren’t straightforward.
For example, I assume I’m not plotting the scale itself but rather the harmonic series as plotted notes. So if I take the partials out far enough, I will find a subset sequence of notes containing the notes — and perhaps a couple of unwanted others — of my scale. After rearranging the notes, if necessary, to align with my scale, what do I do next?
The blog the writer of that email is referring to, can be read here: The Harmonic Series & Its Implications on Composition.
My response to the above email.
The practical application of the harmonic series, I feel, is prob more focused on chords, and not so much on scales.
Reason being that a scale is just really a series of notes/pitches climbing up from lowest to highest note organized by their frequency, from lowest to highest frequency of vibration that produces that note… which means by their cycles per seconds, which creates the highness or lowness of the pitch.
So that is what a scale is: x number notes played and organized from the lowest note to the highest note within an octave. i.e C D E F G A B C, which is a C major scale; the notes climbing up from the note that has the lowest frequency to the note that has the next faster frequency, to the note with the next faster frequency, and so on till we hit C again, which vibrates exactly 2x as fast as the lowest C.
As you know we work with a 12-note system.
While I’m aware that there are certain Arabic and Indian scales that have more than 12 notes in an octave, I always felt that they don’t really use all their extra notes with the same importance, or in other words, don’t attach the same level of importance to the extra notes. Case in point: when I play the notes C D# E F# G A# B C I get a scale that is used in Arabic music, but it lacks the true Arabic music sound because I don’t have the extra (in-between notes, microtones) they have.
However: If I apply light pressure on my Floyd Rose whammy bar so I produce all the in-between microtones, anybody from Pakistan, Saudi Arabia, or any Arabic country, immediately feels what I’m playing sounds EXACTLY like their music back home.
The point I am trying to make about this: it seems to me their music is really still mainly a 12-note system framework with extra microtones, which they merely only use as “embellishment” notes, more than actual melody notes that carry weight in the melody. Otherwise, I would never be able to reproduce their music/melodies on my 12-fret guitar.
All that being said: THAT is why I feel all music on the whole planet is really all written and based on a system dividing an octave into 12-notes. (The cultures that have more notes tend to really only use the extra notes as melodic embellishments, added to the 12 notes system the rest of the world uses)
A 12-note system provides a definite number of possible note combinations:
12 notes = 2 to the 11th power = 2048 possible note combinations.
Meaning: there are only 2048 scales (which you can also think of as “interval combinations”, or “note combinations”, or “scale formulas”) in music.
Taken the above point of view into account, that the cultures that use scales with more notes, still appear to work within a 12-note system with added embellishment microtones, one could argue that the 2048 scale formulas cover every possible music scale on the planet.
So as you see, the whole study of scales specifically, is based on and geared towards math/intervals, meaning mathematical note combinations (also called: “scale formulas”), not on physics really, which is what the harmonic series is.
The harmonic series is physics.
Well of course it is math too: the harmonic series shows the order of sine waves organized by frequency, each sine way having its own frequency, which means a number of vibrations per second (which implies math), that make up the composition of one single note, sung or played on an instrument.
More importantly: The harmonic series relates more to the study of chords than to the study of scales.
Because in essence: the harmonic series actually IS a chord, comprised of a series of sine waves that all sound simultaneously. The first 7 sine waves all together sound like a dominant chord. For example: the sine waves, which produce what we call harmonics, that ring when we hit a single C note on an instrument, are C C G C E G Bb. These 7 harmonics, are also the notes that make up a C7 chord.
Conclusion: there is a C7 chord embedded within ONE SINGLE C NOTE. This of course goes for every note: there is a D7 chord embedded within a D note, etc.
So when you hit one note, the harmonics that make up that note from a chord within the note.
We only HEAR 1 note, because the first 2 harmonics overpower the rest of the harmonic series in strength/amplitude/loudness.
Of course, there is also the valid point of view that every chord is also a scale and vice versa.
For example: C E G = a C chord and can also be thought of as some kind of 3-note C scale.
However: in THIS particular case, I think I should bring up the point that the harmonics that make up one note when we hit that note, all ring simultaneously, meaning: as a chord.
Hence: the harmonic series ties into a better understanding of harmony/chords and explains a lot about chords, but not really about scales, scales just being organizations of different notes within a 12-note system, which are played one after another.
In order for a chord to sound like a scale, we need to hit the notes one after another, or in other words like an arpeggio, which can be thought of as a scalar approach to playing chords.
In other words: a chord in which the notes are separated and hence played as a scale.
Conversely: if you hit all notes of a scale simultaneously, you are hitting a chord. i.e An E minor pentatonic scale, E G A B D is also an Em11 chord when you hit all the notes of that scale together.
So I think that might possibly be where some of the confusion arises that you expressed in your email.
The application of harmonic series is with chords more than with scales: mainly creating a deeper understanding of intervals, which makes up chords, and showing through mother nature’s organization of the harmonics, why certain notes behave or feel a certain way within a chord.
Moving on to the topic of “music theorists”.
I tend to stay away from music theorists myself haha, because of who I am as a person.
I tend to be more geared towards a very pragmatic, practical approach to life.
It’s a personality thing, meaning: it says more about me than it says about theorists.
My (boring/predictable haha) practical and pragmatic way of doing things, analyzing things, outlook, and side to my personality, makes that I have a hard time buying into the way theorists like to do things because that side to my personality makes me believe (and hence also look at things from the perspective) that things in their core are always actually much more simple than theorists like to make us believe.
That is also why I do badly with the longwinded, complex explanations many guitarists sometimes tend to come up with describing one of their techniques or compositional tools used in one of their songs.
Those oftentimes overly complex dissections of their music to me, pardon my language, oftentimes comes across (or feel) like “Bogus BS” lol haha.
I’m not saying btw that they are “wrong” or “seeking attention” or nothing like that.
Maybe they’re not aware they’re doing it, or hey maybe it’s just me, maybe I’m not practical or pragmatic but too “black and white” about things, maybe there is much more multi-dimensional complexity than my black and white outlook can notice or grasp… then again: maybe not. 🙂 (my apologies for the run-on sentences btw: stream of consciousness writing. I write as I am thinking right now this moment as things come up in me)
However, back to what I was talking bout.
A great example to illustrate my point, I think, would be Joe Satriani’s self-named “Pitch Axis Method”.
He claims this is “the compositional technique” he uses in the solo of Satch Boogie.
I frantically researched this when I first heard about Joe’s self-proclaimed “pitch axis method”.
How could I, after years of intense composition study, have missed this “groundbreaking, revolutionary, etc.” compositional technique?
How could my music schools have omitted this in their curricula?
I read Joe’s complex, thorough explanation of this “compositional tool” as explained by him in the “Surfing With The Aliens” transcriptions book.
LOL. It’s a FRIGGIN PEDAL POINT!!!
It’s been around for over 400 years!!!!
Bach and all Baroque composers used it in every composition they wrote.
The only difference, Joe uses it in a harmonically more modern way using more complex harmonies than in the 1600s and combining various different scales on top of the pedal…
BUT it IS STILL just a pedal point. 🙂
Many guitar players specifically do that exact thing, and so do, in my humble opinion, for whatever it is worth, ALL music theorists. 🙂
And so, by analogy, to me “acoustic scale” sounds a bit like “pitch axis method”. 🙂
Are there non-acoustic scales??
Maybe scales played on synth in an anechoic chamber?
You see how my practical mind works: I tend to get rid of the “extraneous explanations” so I can see the essence? 🙂
“Pedal point” is what the “pitch axis method” is.
The new, extra name given to “pedal point” and the “extra explanations” invented around that new name for “pedal point”, are all extra clutter and distractions one could do without in life (or in the study of music for that matter).
The fact of the matter: there are only 2048 scales!
Practical, clean, easy to understand, just math permutations within a 12-note system.
Are there connections between the harmonic series and certain scales?
I’m sure you could find them if you really wanted to.
But that approach almost seems a bit forced to me.
Of the 2048 scales, you would have to pick the ONE scale that comes close to resembling the notes that make up the harmonic series, AND you would have to limit yourself to only a part of the harmonic series, or otherwise explain certain harmonics in the series away as “added chromaticism” (for example the 7th harmonic that makes up a C note is Bb, and later in that series, there is a B natural).
So then, again my practical mind taking or seeing things as presented, without the need to make more of it than it is:
That scale could only possibly be the Lydian b7 scale.
Because the harmonic series in the first 10 or so harmonics, adds up to being all the notes of a Lydian b7 scale.
However: because the notes in the harmonic series, are largely organized in what appears a tertial arrangement, this leads back to the prior discussion about chords being scales in which you play all notes together, and scales being chords in which you separate the notes and play them one after another.
The harmonics of a C note are again: C C G C E G Bb D F# A
Because of how these harmonics are organized, looking like 3rds (which is how you build chords), any musician looking at this would mostly think this looks like a chord: C E G Bb D F# A, which is a C7 (9/#11/13) chord.
However: when you rearrange these notes in alphabetical order, you get a C Lydian b7 scale. (C D E F# G A Bb)
This is just a matter of looking at the facts as presented, without forcing things to fit an explanation or viewpoint.
Meaning: I don’ think one should try to infer or deduce any special or secret meaning behind this.
It just so happens that that is how nature organized the vibrations that make up one note, and it just so happens that the interval pattern that these vibrations are organized at, is locked in like 1 2 3 #4 5 b7, which is the 4th mode of the melodic minor scale, which is called Lydian b7. (which can also be thought of as a Mixolydian #4)
When you go further up the harmonic series, things get a bit more complicated as we have a B natural appearing, but:
1) theorists would prob find a way to explain this away too.
2) this doesn’t negate the fact that there is still the possibility that one might be engaging in the act of trying to find explanations, connections, and relationships where none are due.
Everything else, to me at least, just seems like superfluous theorizing.
THAT leads to another problem, the whole problem that for example all of “New Age” is founded on: trying to see or infer connections and explanations where there are none, or confusing correlation – causality, and that is an entire another new topic.
Anyway: all that is just to give my take on why I don’t get into theorists all that much. 🙂
However: if that theorist you mentioned, came to his conclusions after studying a Bela Bartok composition that happened to be written using the Lydian b7 scale, then yes, he would be at the same time correct and yet also mistaken:
1) Correct in assessing that many of the harmonics resemble the scale.
2) Incorrect with that above statement: cause all first 10 harmonics in the series totally ARE that scale, not just the 8th and 14th harmonic. (Important to note: I am here commenting on your email, not on the work of that theorists. I can only go by what I know, which is the info I got from your email. I am not familiar enough with the work of that theorist to comment on his research.)
Just some thoughts.
Hope the above helped. I got to get back to work haha.
That was my email response.
In closing: I feel it’s important to mention that my above email response was nothing more than a response to the email I had received from Joseph, and not a review or critique of the work of music theorist Ernő Lendvai or any music theorist.
My writing merely expressed how I feel (“a personal opinion”, in other words) about the work of music theorists, without really saying anything factual about their work or the importance of their research.
I know of Ernő Lendvai’s book on the topic the writer of the email touched upon, but have never had a chance to read it.
Tying into that, another reason, not mentioned in my email response, why I tend to not get into music theorists too much, is that their work and research oftentimes tends to lean over into other disciplines that interest me, but not as much as the act of playing and studying music.
As an example: one of the things that Lendvai is famed for is his research into how The Golden ratio and Fibonacci series can be found in Bartok’s music.
This I think, serves as a good example in trying to make my point: Lendvai’s research is really about math (applied to music).
So there is a certain personal line I draw, beyond which it is “not enough” about music anymore, and I just want to go play guitar and write songs at that point. 🙂
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