Toward a Better Music Theory (2013) | Hacker News Reader

Toward a Better Music Theory (2013)

ethanhein.com

110 pointsbrudgers77 comments

I strongly agree with the article's premise! I also agree with this guidepost for how we should be moving music theory past its highly entrenched and institutional attitudes:

> We should be asking: what is it that musicians are doing that sounds good? What patterns can we detect in the broad mass of music being made and enjoyed out there in the world?

I would personally add one more leading question: Can we explain music in other ways than by its harmony and chords?

A harmonic approach to analysis works fantastic for old European music, and pretty damn well for jazz too. For rock, it starts to oddly leave out important aspects of the music like rhythm, timbre, the way effects like distortion inform the harmony, vocal delivery, etc. And in the modern era, with all the advances and innovations made in the last 30 years in the now dominant genres of hip hop, pop, and electronic music, harmonic analysis is very poorly equipped to make sense of things in any meaningful way.

One music theorist who is attempting more competent analysis of contemporary music is https://www.youtube.com/c/12tonevideos. I'd love to see more of this.

> I would personally add one more leading question: Can we explain music in other ways than by its harmony and chords?

Yes. We can get a lot of mileage by talking about the form and texture.

E.g., at the end of Haydn's so-called "Lark" quartet (Op. 64 No. 5) he's got a fast-paced Rondo in D major that features a virtuosic 1st violin part with continuous fast figuration. The other voices do a light accompaniment of that fast-moving line.

It moves along about as you'd expect-- you get the main rondo theme. It gets repeated. Then a contrasting theme appears in the dominant, with a little bridge back to the original theme in D. Now that section gets repeated.

You can just hear a theory teacher outlining the form and writing the boring letters of a typical rondo form on a whiteboard while the class yawns. It's nearly the same as any other boring rondo, save for the virtuosic 1st violin.

Then, for reasons known only to Haydn, the music switches to the parallel minor key and commences a full-on four-voice fugal exposition at the same fast tempo. After about thirty seconds of some highly unexpected harmonically active imitative development, the pieces changes on a dime back to the original theme in D major, as if the fugue had never happened.

Why did he do that? Was there an arrogant 1st violinist who he wanted to challenge? Was he just fucking around? I don't know the answer. But that Finale is fucking hilarious and you only need the most basic harmonic understanding to hear it.

Mozart and Haydn were constantly playing with form in similar ways to the example above. Mozart in particular played around with dynamic contrasts-- a sudden loud chord followed immediately by a soft one. That was an influence on Beethoven, for example.

I have a more conservative critique of traditional music theory, along the same lines. Forget pop, jazz, and rock - standard music theory courses don't even equip students to properly analyze Western art from music the late romantic period, including things like impressionism. Most voice leading textbooks have very little material on post 1850-ish classical music, and some have essentially nothing. They seem to focus on Mozart, Beehoven, Haydn, etc., or aspects of later music amendable to the analytical tools they develop for those classical period composers.

Here's an exercise you can try. Choose a more harmonically adventurous French or Russian composer from around the turn of the 20th century (perhaps Debussy, Ravel, Scriabian, maybe even Shostakovitch), and get some sheet music for a solo piano piece off the internet. Grab any of the standard college harmony textbooks and attempt to write down a harmonic analysis of that piece. You're going to have trouble.

Maybe -- but the context to understand what Debussy and Ravel were doing (maybe not Scriabin) is to get the Bach / Haydn / Mozart / Beethoven / Schubert under your belt.

Source: I've taught this at university.

I agree! But it seems that the books all stop at 1850. Or they toss in a few cursory chapters at the end. (If there's some text that doesn't do this, I'd love to read it.)

I'm going to keep plugging https://www.amazon.com/gp/product/B08BT17M4S/

Answers all the questions, TBH.

I've looked at that book before, and while I agree that it's probably worth reading it sure doesn't answer all the questions. It just talks about voice leading and gives scientific explanations for why the 18th century rules of part writing reliably turn out pleasing music. It doesn't account for all the music that satisfies listeners somehow even while violating some of those conventions. Nor does it cover anything aside from tonality, from what I remember.

Why does the blues scale (pentatonic minor + tritone) work on top of major scale chord progressions with the same tonic?

But yeah, the development of tonality kinda stopped in the 1850 range, with maybe Stravinsky, Tatum, and the 1940s Bebopers extending it as an exception. But at that point, tonality had passed out of the "art world" -- everything post-Duchamp's "Fountain" has been a bit more deconstructive and nihilistic.

Maybe of note, pun intended, Schoenberg was pursuing the "emancipation of the dissonances" while the Bolsheviks were destroying Russia. And of course, that's part of why nobody listens to Schoenberg or performs his stuff -- it's grating and kinda horrible, at least after he abandoned high Romanticism after Opus 5.

Even then, though, Schoenberg was still following voice-leading principles usually. He'd just abandoned tonality and harmony.

> (maybe not Scriabin)

There is a fairly clear line of influence from Bach -> Chopin -> Scriabin's Preludes -> Sonata no. 2 -> Sonata no. 5.

I'm not sure where the cross-cutting idea of Sonata no. 5 came from. But a lot of the harmony/voicing he's cutting across is courtesy of Chopin. :)

To be clear, I agree with you on the mindless labeling of stuff that's in current music pedagogy at universities -- that's mainly out of Yale. With my students, we wrote Lieder.

The Common Practice Period [1] still forms the basis for standard music education, just as equal temperament tuning [2] forms the basis for standard teaching scales and chords and as the piano (forte) acts as the reference instrument in music education.

Basically the Period of Common Practice still provides a useful way of communicating musical ideas without performing…e.g. through sheet music and textbooks.

Hein seems to be advocating letting the way music is performed influence the way music is communicated without performance a bit more than it has traditionally.

But there is a lot of economic incentive to maintain the focus on the Common Practice Period. A lot of jobs and institutions depend on continued interest and it is what conservative wealth tends to want…suburban parents aren’t sending their kids to scratch and sample lessons.

[1]: https://en.m.wikipedia.org/wiki/Common_practice_period

[2]: https://en.m.wikipedia.org/wiki/Equal_temperament

"Standard college harmony textbooks" don't even properly account for Mozart, Haydn or Beethoven, let alone these later composers. The shared structural framework that helps explain them all is thoroughbass, combined with a repertory of common patterns and moves (known as "schemata" in the recent music-theory literature) and styles of melodic elaboration that ultimately come from the improvisation-heavy performance practice of vocal music. (Conversely, melodic reduction would've been needed to understand complex melodies as elaborations of simpler ones. We now know that this was standard practice in the 18th-c. equivalent of solfège!) None of these things are explored, however cursorily, in the standard textbooks. Even counterpoint is not really developed properly - the way it would've been understood by successful 18th-c. musicians - and is often presented in a needlessly obscure and unfamiliar manner as a result.

I don't really understand your comment. Figured base and and common harmonic sequences are well covered in most standard theory texts (as is melodic/harmonic reduction).

I'm also amused by your remark that counterpoint is not taught in "the way it would've been understood by successful 18th-c. musicians." Most contemporary counterpoint instruction still follows the method of Fux's 1725 textbook (species counterpoint). Indeed, the fact that the pedagogy hasn't really changed for hundreds of years is often advanced as a criticism of current-day instructional practice!

In fact, Fux was basically a reference text on 16th-c. counterpoint in its most complex and developed form, as it was understood after-the-fact in a 18th-c. context. It doesn't do much to pedagogically explain even the simpler foundations of 16th-c. style (as they show up in earlier texts), let alone tonal counterpoint in the common practice period.

> common harmonic sequences

Common harmonic sequences are not voice-leading schemata. If anything, the former are a side-effect of the latter. Even teaching cadences as a "harmonic" motion rather than a pattern involving the melodic motions of tenorizans (2^--1^) cantizans (8^--7^--8^) and bassizans (5^--1^) is a very flawed understanding that would've been quite foreign to 18th-c. musicians.

As for the thoroughbass, the older textbooks may give a cursory explanation of the notation involved, but what about the practice of it? Where is the règle de l'octave - the "harmonic" bread-and-butter of so much music of the common practice, known even to amateur accompanists back in the 18th c.? A lot of the time, it isn't there. And that's literally the simplest and most basic part, there's plenty of more involved patterns that musicians back then would've known in some way.

Again, I am confused by your claims. The species system taught by Fux is, as far as I recall, the exact same way that counterpoint is introduced in, e.g., Gauldin's "A Practical Approach to 18th Century Counterpoint." (Gauldin goes into much more detail on other things, but the approaches are consistent.)

The fact that the upper voice goes 2-1 or 7-1 and the bass 5-1 at cadences is one of the first things taught in a counterpoint class. The rule of the octave is in most theory textbooks. The first example that comes to mind is Laitz, "The Complete Musician."

You're right that these textbooks don't teach how to improvise an accompaniment from a figured bass, but I'm not sure that's a good use of time for a theory class.

> They seem to focus on Mozart, Beehoven, Haydn, etc., or aspects of later music amendable to the analytical tools they develop for those classical period composers.

At least wrt voice-leading, I'm not sure what your after. Even the custom cadential formulae Wagner came up with tend to follow the voice-leading rules that Bach would have been familiar with. Hell, his "crash landing" cadence from Götterdämmerung[1] even avoids parallel fifths!

1: start with a half-diminished seventh chord in root/close position, reinterpret the outer voices as an augmented-sixth and have them resolve outward to the octave to form the root of a minor triad. (Oooh, evil is afoot!)

I'm thinking mainly harmony and the much more liberal use of chromaticism, unusual chord progressions, and so on.

I don't agree that anything beyond common practice harmony is necessary, although it can certainly be helpful.

Moreover, even common practice harmony doesn't include all the tools needed to analyze the harmony of the common practice period, but we get by. For example, in the first movement of the Symphony in G minor, K. 550, Mozart inverts the motive toward the end of the development section over a dominant pedal and harmonizes the initial lower chromatic neighbor of that three-note motive. So you get a fully-diminished 7th chord built on d that is immediately followed by a dominant seventh build on d. What do you call that fully-diminished 7th chord in Roman numeral analysis? Perhaps there's a standardized name or symbol for this now, but even if that's the case there wasn't always. But it didn't matter because you could trivially come up with something like calling it a "neighbor seventh" or some other such name and everyone would know what you are talking about because 18th- and 19th-century music was full of that chord progression.

Now look at, say, the opening to Prelude to the Afternoon of a Faun. Debussy's solo flute solo holds a note over the ensemble playing the first chord of the piece-- a half-diminished 7th chord. This sounds similar to the beginning of the Tristan Prelude cellos when they hold a note over a half-diminished 7th chord. But unlike Wagner, Debussy has it resolve to a dominant seventh on the same root as the half-diminished seventh. (In fact, I'm not sure Wagner ever used that progression to resolve the Tristan chord throughout the entire opera.)

Just as we could talk about the function of that same chord progression in Mozart without a name for the "neighbor seventh," so too can we do it in Debussy. It just so happens there are a lot more harmonic shifts in the Debussy to talk about, so its more work, added to a discussion of the various allusions to Wagner and how they come off.

I guess having some common language for discussing the historical development of octatonicism would help in this case. Still, this was an experimental time in harmony with a lot of bespoke forms. I'm not sure how much a common extended toolset would add to any given piece. (Not to mention you had your Rachmaninoffs and others who are almost fully analyzable using Roman numeral analysis and tonal chromatic voice leading.)

Edit: clarification

Thanks, I think I basically agree. I guess my complaint is that these later composers generally involve more "bespoke" analysis because of the additional complexity, which is not treated adequately in the textbooks. (Whereas, for example, for a lot of Mozart piano sonatas you can just write down all the roman numerals and call it day -- I'm joking but only slightly.)

Also, I think you'd call your Mozart example a common tone diminished chord, notated CT7. I think this is pretty standard nomenclature now; see this book excerpt for example: https://viva.pressbooks.pub/openmusictheory/chapter/common-t.... Especially the example under the section "recognizing CT7 while analyzing."

I’m sorry what? Did you actually study harmony at college level? I can assure you the textbooks are more than adequate to analyse late romantic and all 20C music. My functional harmony teacher used to use “Structural functions of harmony” by Schonberg. Can easily handle everything up to the second viennese school and then we used to use “A New Music” by Reginald Smith-Brindle after that

Thanks for the book recommendations.

I used Aldwell-Schachter, Voice Leading and Harmony. Part VI is relevant to the composers I mentioned but didn't really explain many of the things I was wondering about. Sure, I can name the chords (most of the time), but on a compositional level there's much more going on.

Structural functions may be better for what you want because the thing that it does well (better than other books I have read certainly) is explain the sorts of harmonic substitutions that start happening as you get into the late romantic period. He believed (“Theory of Harmony” is also like this) in explaining harmonic theory entirely from the perspective of composition so it explains from first principles what you see composers actually doing rather than trying to find rules and then examples of those rules. So in “Theory of Harmony” he builds up an entire theory of harmony starting from simple 4 part voicings and voice leading, in “Structural Functions” he sort of condenses that into a couple of very quick chapters and then moves on to talk about key relationships in more depth.

It also breaks sharply with the old orthodoxy where authors used to talk about everything as key modulations and then struggle to explain things which were really related to the original key area but seem very remote in the new “modulated” key. What Schoenberg points out is that music actually very seldom actually changes key. In fact almost the only time this happens is in the classic “Whitney Houston” where a pop tune just goes up a tone for the last chorus and never goes back. Music in the classical tradition almost always ends up in the same key that it starts in even if it visits some remote areas along the way and therefore as Schoenberg argues it makes sense to understand key areas that are temporary in relation to the original tonality. It also means you end up with a harmonic theory that works perfectly to explain jazz standards and pop music.

Thanks for the explanation! That sounds exactly what I'm looking for, and I will definitely read those Schoenberg books. Really appreciate the pointer.

I think these basic arguments are valuable and musicians should be focussed on whether a better understanding of music theory actually produces music with desirable qualities such as surprisal (e.g. that moment when Dj Screw slowed the record or groups of monks decided to chant together etc).

IMO the answer is a big nope. One reason is that music theory is always explicated in retrospect and contributes little to the invention of new music or enjoyment. It's useful (not devaluing it wholesale) if you want to do x in the style of y (e.g. I want this to sound like Miles Davis!). H/w an accurate picture of musical performance and general cultural activity surrounding would never reduce it all to just that.

Trad theory will enhance existing talent but do nothing for people who have no instinct for music, no matter how much learning they do.

It's very directly and obviously useful for certain kinds of music, especially Hollywood pastiche and some genres of game soundtracks.

It's also very handy in some areas of pop. Pop's dirty secret is that a lot of it is written/arranged by professionals with some kind of classical background. The lead band/artist are typically front people for an entire team which includes a producer, various engineers, and possibly session players and arrangers. These people don't get a lot of attention, and only industry insiders have heard of them. But they have a huge impact on pop of all kinds.

Vocal harmonies, string parts, and sometimes brass parts have to be written and arranged, and that's a challenge for anyone without dot-writing skills.

But there's also a kind of fluency and ease that comes with solid training, and that spills over into vocal and instrumental contributions of all kinds.

Trad theory on its own doesn't guarantee interesting or successful music. There are plenty of composition graduates who have no feel for the art of music at all.

It also doesn't help with transformative developments and new techniques.

But it's far from useless. People with solid theory skills and some creative flair are in a sweet spot that's hard to beat.

I find it best to think of music theory as a language musicians can use to describe what they just did, not what they are about to do.

That's likely to be true even if/when we improve "music theory" to cover much more than 18th century European harmonic forms.

Pretty much. It helps with giving language and notation to particular sounds. It condenses sounds to something you can write down and communicate, without having to think of each note individually.

It’s like design patterns for music. Not necessarily prescriptive (it’s your music, do whatever you want), but helpful for reducing music into something more concrete.

It has helped me a lot in learning (classical) music. It’s also kind of like watching a sport where you understand the rules vs. one you don’t - knowing the “rules” helps you engage more, and peek into the composer’s mind, or give you ideas for your own compositions.

That makes a lot of sense!

For me theory is most important as a debugging tool - I write without considering it and if something sounds “off” in a bad way theory will often help me pinpoint why. It’s also useful for analysis when I’m trying to capture a certain sound. Either way it is not a composition tool and shouldn’t taught that way except for exercises to understand theory.

This article reveals conflicting goals: "...we should take an ethnomusicological approach" vs. "It would be better to have some hard data on what we all collectively think makes for valid music" Embracing musical balkanization akin to Los Angeles in contrast to distilling musical practice akin to the melting pot of New York City. I am much more supportive of the former approach yet it is impractical when representing musical form in a rightly finite curriculum. It requires a more decentralized effort, and students receive a scatterplot of perspectives. Perhaps sharing the extraordinary depth of theory and musicology focussed on canonical artists such as Beethoven isn't so bad after all. Though I have personally challenged professors who dished it to me repeatedly. I think there are serious feasibility issues with effectively addressing timbre as a musical dimension; this is problematic for adequate theories of music given the centrality of timbre in many forms of modern music. However, it remains embarrassing for the academy not to be able to coherently address what is so obviously saturating their students ears.

Do not forget that Bach's music needed to feed 20 of his children over the course of his life. (10 survived)

I have a hard time believing that he was intentionally carving out the rules of eg _Gradus ad Parnassum_ rather than consistently trying to make music that sounded good with good timbre given the constraints of his living situation and employer.

What seems prescriptive to the children is often originally descriptive to the elders.

He was definitely aiming for a certain style, which involved following certain rules. There are surviving draft manuscripts where he makes edits to follow voice-writing rules like avoiding parallel fifths, etc. It seems pretty clear based on this (and his training, and even a cursory study of what he wrote) that his compositional practice was intensely theoretical. The dude was not out there freestyling.

In fact, the places where he broke certain fundamental rules are so rare that they form a rather short list, despite his voluminous output: https://www.bach-chorales.com/ConsecutivesInChorales.htm.

Coming from this field personally, this feels like typical Temperley and de Clerq sorts of things. Davie Temperley was in David Huron's lab once upon a time, I believe.

The systematic musicology world, especially the portion doing corpus studies, often is just doing descriptive research. The article linked is a bit more prescriptive.

The best book on music theory ever written, IMO, is David Huron's "Voice Leading -- The Science Behind a Musical Art." Definitely recommend.

https://www.amazon.com/gp/product/B08BT17M4S/ref=dbs_a_def_r...

This article is about "we should change things because we know more!" Huron has always been more about "we should know more!"

For me, I'm with the latter.

This is my corpus study. https://online.ucpress.edu/mp/article-abstract/31/1/32/62590...

It’s interesting that the article refers to “classical music’s obsession with the major scale”. I was raised on rock guitar, where the minor pentatonic scale was king. For that reason I often thought of keys in terms of their relative minor.

Whole heartedly agreed that our current model of theory is excessively academic relative to the music most people are making and consuming (at least in America).

All that said, a grounding in theory is still a wonderful thing to have as a musician. Even if you choose to ignore what you’ve learned (and you should sometimes!), it allows you to understand a lot of music more deeply, allowing you to learn it more quickly.

I don't think current music theory is excessively academic, I think it's not academic or rigorous enough. Many institutions languish in studying harmonic theory to the exclusion of many other modes of musical analysis. This leaves them equipped only to study archaic styles of European music and jazz where harmony was one of the defining factors. The expressive power and applicability of music theory would be served best by focusing study on areas that have been underexplored. Those areas are too numerous to even list, but standouts that apply to music more recent than mid-century are rhythm, timbre, movement (as driven by elements other than harmony), instrumentation, electronic techniques, and cultural aspects of music like references and interpolation.

Based on the standard tuning of a guitar E, A, D, G, B, E and assuming you use E as your tonic, the scale I, 2, 3-flat, 4, 5, 6, 7-flat which translates to E, F#, G, A, B, C#, D should be a base scale. If you strum a guitar open, all the strings fall within this scale. It does have a flat seventh and a corresponding flat third.

If you take out the 2 and the 6, this becomes the Minor Pentatonic Scale.

My music theory is very weak, but I have some difficulty understanding the point of supermode; if it includes 10 out of the 12 notes, then does it really function as a scale anymore or would it be just simpler to think in terms of the chromatic scale and abandon modes altogether?

Not to mention that it excludes the b5, and saying that's not a substantial part of the RS top 500 is laughable. So really what they're saying is b2 can go to hell.

> It would be better to have some hard data on what we all collectively think makes for valid music.

"Valid"? As opposed to "invalid music"?

> As you’d expect, the tonic I is the most commonly-used chord in the Rolling Stone corpus.

If it wouldn't be the most used, would it be used as point of reference and called the tonic?

> Rock uses plenty of V-I, but it uses even more IV-I. And the third most common pre-tonic chord in rock is not ii, like you’d expect if you went to music school; it’s bVII, reflecting rock musicians’ love of Mixolydian mode.

I-V and IV-V seems to be the same with the point of reference moved to IV. And IV-bVII-V is I-IV-V.

Is a fixed point of reference really needed? Doesn't it just add unnecessary complexity?

> "Valid"? As opposed to "invalid music"?

I think it's fair to say that sometimes people attempt to make music and aren't successful. That doesn't mean music that gets played on the radio that some person doesn't like isn't "real" music. I'm thinking more like a musician tries out a chord progression and decides it's not working musically so they never record it in the first place. Or if a cat walks across a piano the result probably isn't music. There will always be grey areas, but I think there are things that are almost universally regarded as music, and other things that are almost universally regarded as not-music. Some part of musical appreciation is subjective and culturally influenced, but some parts are innate and based on mathematical relationships and psychoacoustics that are the same for almost every human.

> I-V and IV-V seems to be the same with the point of reference moved to IV

I-V moves up by a 5th, whereas IV-V moves up by a major second. I would buy that I-V is the same as IV-I, but with a different point of reference.

> "Valid"? As opposed to "invalid music"?

Yes, I think it's clear the author means things we collectively agree fall under the category of music. And the question of what is or is not music is surprisingly complex and disputed, analagous to the question of what is or is not art.

E.g. is John Cage's 4'33" [1] music? What about a Spotify track of silence for meditation? Is a purely percussive piece music, or merely rhythm? Is atonal music, well, even music at all? Classical musicians would pretty much all say yes, but a lot of non-musicians might disagree.

[1] https://en.wikipedia.org/wiki/4%E2%80%B233%E2%80%B3

> If it wouldn't be the most used, would it be used as point of reference and called the tonic?

Yes. The tonic is determined by what the key is, not what chord is most used. (It's hard to establish the key without slipping the tonic in somewhere, but that doesn't mean it needs to appear frequently.)

> I-V and IV-V seems to be the same with the point of reference moved to IV. And IV-bVII-V is I-IV-V.

I don't think this is right. V-I has the root moving by a 5th, while IV-V moves by a second. And the second example can't be right because the relative distances of the roots of the first and last chords are different (again, a second versus a fifth).

> Is a fixed point of reference really needed? Doesn't it just add unnecessary complexity?

Yes, it's a useful analytical tool.

Totally agreeing with the article, this "supermode" ie in C: all white keys plus Eb, Ab, Bb, is exactly what my rock band's noodles have intuitively followed.

In the context of existing music theory that supermode could be considered Eb/Cm.

I’ve been learning a couple pop songs lately that essentially seem to use this supermode by switching between the major and minor on verse/chorus. Seems pretty versatile.

I don't see how the supermode can be useful to anyone starting to learn music theory. The hard part is figuring out the rhythm, vocabulary, and phrasing that make those notes sound "good".

I still think one of the best ways of learning theory (for guitar at least) is to start with the pentatonic and diatonic scales, then add triads and "colour" notes.

I'm curious to know other people's opinions though.

Yeah, I don't quite see what the notion of the "supermode" does for anyone, either.

Maybe he's going to elaborate it somewhere else? Or just hoping that someone else does.

it's a useful device like the circle of fifths but i don't see it displacing existing models.

The main problem I see with (occidental) "music theory" is its historical baggage. Most of it is useful, beautiful by its own merits but, specially if you have a scientific/logic way of looking things, much of its structure and nomenclature really gets in the way. After many years of doing false starts I sat one day, started from scratch, looked at just the facts (= math), and then everything fell together:

- The Pythagoreans dealt for centuries with the known conundrum of figuring out irrational numbers. I had a computer so I just run a script for measuring the total error with different bisecting rational quantizations (up to 256 IIRC) of note frequencies in the equal-tempered scale within one octave (2^(1/N) splits). Oh, peaks at 12, 19 at 24 on the low side of the counter. That is why they settled on 12 notes, middle eastern has 24 (just double the resolution) and why 19 also sounds good [1]. 12 seems like the minimum acceptable then. Ok, 10 minutes, move on.

- Since we know we can only approximate to irrationals and our brain tries to makes things even, moving through scales with increasing intervals (2^(n/12)) will normally accumulate "tension". Half notes sound spooky. Whole notes are a bit better. Too bad sound perception is logarithmic (= tempered scale) and has non-linear compression on both amplitude and frequency (Fletcher-Munson, etc). Double the frequency is an octave. Perfect fit, brain happy (2^(12/12)). Try to split an octave in half? Again, fitting a peg in the only wrong hole available when using half-note resolution. Welcome to accidentals and the Circle of Fifths. "Try", because of course you can't: 2^(7/12) = 1.498307.... Close to 150%, but no cigar. Close enough for a crippled monkey brain that can only hear up to 20kHz or so. They even named it "Perfect". Moving up: F to C, G to D, A to E...

- Music would be very dull and inadequate if we cannot shift notes up or down. However our brain still recognizes the patterns. We can even play those patterns at the same time, even on different instruments. So that pattern with the same scale on a G sounds good with the other guy playing C (harmonies). What if the guy playing the C wants to play like the guy on the G? Enter modes... Oh yeah, cool Myxolydian tunes. And minor scale too - don't forget that looks THE SAME as an Aeolian.

- Your new singer cannot hit that low notes. What about now moving everything up then? Transpose. We have "physical instruments" like a guitar. Easy, just play the same pattern some frets up. Done. Poor piano player who has a "logical instrument" with notes separated nicely in two different kinds based on half notes and that ugly 1.498307 fraction. Good that he is also good at math. So that C scale becomes a D. He just replaces on the fly some white keys with black keys... F# and C#. But wait a sec. Didn't the Circle of Fifths also moved F to C too? Does it continue like that for all notes? Yes it does! Transposing has the same structure as modes the other way around! So what if instead of moving up we move down, or play the same pattern in the original C scale? For every raised (sharp) accidental we get it's complement lowered (flat) one. Of course, since 7 + 5 = 12! The Circle of Fifth is complete. B to E, A to D, G to C... That G pattern moved down to C? G major scale (aka Ionian) has one accidental: F#. The first flat is Bb. C scale with B lowered to Bb... Yep, Myxolydian indeed!

- We can also use those interval numbers to name chords when we play notes together. We can also name the scales when adding and removing notes, maybe borrowing from other scales. Sounds pentatonic or exotic. The sky is the limit.

- Piano player now teases the guitar player. Now it's her turn to do the math. Looks like "physical" and "logical" instruments are also complementary. What is easy on one needs thinking on the other, and vice-versa. Win-win.

Honestly, that covers like 95% of practical music note theory. Of course there is much more to it (note, rhythm, history, etc). If they have just started explaining it like that without all the mumbo-jumbo it would have made sense since day #1 and I would have saved many years of my life hitting my head in the wall and trying to learn things I forgot within a week. Perhaps the main issue is that not many music teachers are good at math or they would think their students would get scared if they told them it's all math underneath?

[1] - https://en.wikipedia.org/wiki/19_equal_temperament

Equal temperament makes it easier to design simple musical instruments. Older music and current music in other genres (e.g. Indian Classical) is based on a harmonic scale, taking its roots in vocal music.

Read this.

https://www.amazon.com/gp/product/B08BT17M4S/

The author mentions the data is available, but the link appears to be dead. Anyone know where it might live?

wayback machine to the rescue:

https://web.archive.org/web/20150513214912/http://theory.esm...

https://web.archive.org/web/20120218081940/http://theory.esm...

The title is a bit misleading. I was expecting some polemic about Western music ignoring indigenous peoples, etc. etc.

Instead, I kinda liked it. I took some classical piano and my teacher got very impatient with me approaching some pieces like a jazz musician would: assigning chords to measures that were quite obviously melodies over those chords. She was all about plagal cadences and all that stuff she learned at Oberlin.

The Bach Prelude in C is especially entertaining to treat that way. There's one bar near the end that it's almost impossible to give a chord symbol to.

Plagality is a pretty deep musical concept within tonality, though -- you have to deeply grok counterpoint and tonal harmony first, and then you can start to hear and perceive different aspects of tonal gravity.

For plagality, it's the "dark side" of the tritone, specifically with iiø or iv6.

Start putting together that tritone with the major standards of vii° or V7, and you're really rolling with the joy of traditional harmony.

For further reading, this was https://en.wikipedia.org/wiki/Hugo_Riemann and harmonic dualism.

Yeah, Rameau is the "Louie, Louie" French fellow who was the "Newton of Music" who gave us the Roman numeral notation, while the Germans were still doing counterpoint and harmonics.

I very seriously believe there's a link between that, the revolutionary attitudes and kinship of the French and Americans, with the Rock and Roll movement of the 1950s / 1960s.

> Rameau is the "Louie, Louie" French fellow

Another win. I know Rameau and of course I know Louie, Louie, but the connection eludes me. I'm sure you'll tell us.

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