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To get right to the point, what I want to know is: what makes a claim acceptable in the world of music theory?

From my understanding, music theory has very little to do with any "natural law" or inherent property of the universe, save consonance from the harmonic series, 12-TET as an approximation for simple harmonic ratios, and major and minor as maximally even in a 12 note system. Still, there isn't any underlying reason for why the harmonic series, simple ratios, or maximal even-ness should affect us in the first place.

Why then can a claim like, "the leading tone wants to rise to the root," go unchallenged, but saying that certain intervals elicit certain emotions is taboo? (Just to give an example)

It seems to me that the only difference between the two previous statements is popularity. Am I wrong? Is there actually a science underlying music theory?

I would say that music theory spans a range of 'types' of statements, from almost totally objective to quite subjective...

You've got elements that are pretty much scientific facts, such as what the harmonic series is, or how the physics of instruments works, or how the mechanics of the ear work.

Then you've got a level of stuff that is technically 'subjective', yet that has been somewhat scientifically observed (through formal experiments) to be reasonably common human experience - things like how dissonance is perceived, and how pitch relates to frequency.

Then there are things that seem very common (perception of a 'tonic'), (perception of tension and resolution) the specifics of which still seem to vary a little with musical culture. Somewhere around this level are some of the more obvious explicitly 'emotional' rules too - at least the most common things like people perceiving the minor as (massive simplification coming up...) 'sad'.

There are then the more culturally-specific things - things like the oft-quoted "no parallel fifths". These could be seen as opinions, or alternatively, as somewhat objective advice on how to write in a particular style based on the characteristics of a corpus of past works. In any case, these stylistic choices seem to be down to preferences - we're well away from the purely objective by this point. For further illustrations of these kind of culturally-specific rules, take a look at Tchaikovsky’s Guide to the Practical study of harmony.

Of course at some level, reaction to music becomes so personal that it can't sensibly be codified as any kind of theory. Sometimes it might seem unintuitive to me that not all others feel the same powerful reactions to certain chord motions and timbres that I do; if they did, some of my favourite music would be a lot more popular!

After so many years of music history, including a few generations now where we've had a lot of cross-pollination of genres around the globe, perhaps it's impossible to place perception of some phenomena precisely on the subjective/objective axis. I'm sure some will disagree with my assessments here!

Some might say that the more scientific stuff belongs in acoustics, or psychology. I understand the point, but I think if you chip away too much at each end (moving the scientific stuff into 'science', and the subjective stuff into 'opinion') a lot of music theory disappears. I prefer the fatter view!

...the leading tone wants to rise to the root...

Basic theory says things like...

• the leading tone is a half step below the tonic


• in a proper cadence the leading tone moves to the tonic, or if in a inner voice it may move down to the dominant.

...of course that isn't a complete theoretical overview of the leading tone.

A claim that theory simply says 'the leading tone moves to the tonic' is incomplete, and as a description of actual musical art it complete nonsense.

I think a lot of misunderstanding of music theory come from taking incomplete theory ideas and then misstating them as laws.

...saying that certain intervals elicit certain emotions is taboo?

Again, the specifics of wording matter, and it's easy to misstate things. 'Certain emotions' is not the same meaning as 'emotions.' Obviously intervals and all other musical devices can elicit emotions. The problem is trying to make certain claims like minor thirds are sad or diminished fifths are scary. Statements like that are too broad and won't withstand any scrutiny.

Good theory texts will describe expressive possibilities - not one to one formulas - and provide real musical excerpts to illustrate the ideas.

I think you want to distinguish between what music IS - an art - and music theory which is a way to describe music with some objectivity.

Art does whatever it wants. The theoreticians try to make a theory to describe what the art did.

Keep in mind it's a theory about art not a scientific theory. Acoustics is science and not the same as music theory. Confusing the two is another common mistake.

Music Theory: Facts or Hierarchy of Opinions?

Neither. I would say it's more like qualified statements about common musical practices using established terminology.

EDIT

Just adding something about rules after reading @topo-morto's answer.

You often hear "there are not rules in music." Well... there are, and there aren't. We need to distinguish music theory from specific style practices and pedagogy.

No parallel fifths is a good example to use.

These is such a rule... in Fux's species counterpoint. That's pedagogy.

You will see parallel fifth scrupulously avoided in most "classical" music... except in musettes, fanfares, and other specific cases. It's called common practice. On the other hand, in heavy metal parallel fifths are practically a requirement! That style.

Two voices moving in parallel fifth differ only in one voice being an exact transposition of the other. There is no difference in melodic contour between the two voice. Pitch-wise the two voice exhibit very little independence. That's an objective description, non-specific about style, is neither prescription nor proscription, and makes no aesthetic evaluation. That's music theory.

And just as an aside, I think the only thing acoustics and math will tell us about parallel fifths is that if you use an instrument with fixed tuning, it is mathematically impossible to play two absolutely perfect, consecutive fifths.

I like to think of music as a language, and like any language, you are able to pick it up just by being in its environment and acquire it just with your ears.

But just like any languages, to be able to effectively communicate with it, you’ll need to pick up the grammar and vocabulary so that you can be understood. Hence just like in language, music theory provides an agreed upon (widely accepted) set of terminology and standards (or norms) that makes communicating about ideas, concepts and phenomenons in music effective.

(Take for eg the unit for one beat in 4/4 time, the Americans call it a quarter note but in U.K., it’s crotchet. The notion that both are equally right but one is much more accepted than the other depending on which culture is just like how you’d say “football” in England but “soccer” in the states. They most likely don’t hinder any communication if you choose one over the other, but you’ll perhaps find one more comfortable than the other in conversation depending on the context. But if you were to use any other arbitrary word, e.g. “tick” to mean a beat, you’re much less likely to be understood.)

Also, just like grammatical rules aren’t discovered or established first before humans have speech and hence form their own languages (grammar only describes and seeks to explain the workings of language), music theory ain’t there first before composers started composing music. Hence music theory only seek to look at why (most) music work in a certain way, and how some don’t. “Composers compose, and theorists analyze.”

Theorists are just like linguists - they don’t invent rules to prescribe how a language should work - they look for the regularities and patterns within works that have already been written. And sometimes that also includes how some rules have been broken. And yes, music theory is very much still “alive”, and like music, it is still and will always continue reinventing and evolving with time.

It is worth noting that (just like some have shared above about “no parallel 5ths” in Bach’s music) our perspective of why certain harmony could work better and how others sound dissonance might also change based on cultural reasons. Take the interval of #9 and b9 for example, while they are likely deemed as problematic and highly dissonant in common practice music, they are widely accepted in altered dominant chords in popjazz music we hear today. And who knows? Perhaps decades down the road, we might find ourselves living in a time where these intervals are widely accepted even in chords which are non-dominant in function.

Hence to answer your question: what makes a claim acceptable in music theory?

Here’s my take: as long as it’s a widely accepted and agreed upon standard/norm within a given community (culture) of practice in that given time.