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I understand this to be true: chords are basically just intervals. Our modern way of thinking about harmony is based on thinking about chords rather than intervals. This seems wrong. It seems like we're complicating things. The fundamentals of harmony are really only intervals. Chords are intervals put together. In the old days they actually never talked about chords. They just wrote a bass note and added e.g. 6 4. Simple organum or basso continuo talked about intervals. It seems only modern musicians talk about chords.

Is harmony based on intervals rather than chords?

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    I really like this question, but the way it's been asked makes it seem like your mind is already made up and you are looking for affirmation of the position you've articulated. Instead of "seems like we complicate stuff," would you consider an edit: "Does harmonic theory based only on intervals and not on chords offer a simpler way to conceptualize harmony (harmonic progressions, etc.)?" These types of edits throughout will make the question seem less like a "rant in disguise" (to quote the help center). Or, you could simplify the question, & then post your own answer to your question. – jdjazz Dec 7 '19 at 17:10
  • You have an interesting perspective to share, and valuable insights, but I think your arguments deserve to be in an answer instead of in the question. I'd be really interested in hearing how the perspective you advocate has an impact on our approach to Roman Numeral analysis, etc. Those are things I'd really enjoy reading about in an answer that you could no doubt articulate really well. I'll remove my downvote if you make these changes. – jdjazz Dec 7 '19 at 17:13
  • Can you explain what the implications of this would be in your opinion? If the interval thing is right and the chord thing is wrong, then in your opinion, something somewhere should be taught or written or practiced differently than it is now? By this I mean ... what is it that inspired and motivated you to ask this question. You feel that something is wrong in the world and needs to be corrected? And with this question and its anticipated answers you would have leverage to be able to say, "look, I'm right, you have to change ... this behavior/teaching/practice has to change?" – piiperi Reinstate Monica Dec 7 '19 at 19:53
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    You have got some great answers and I would like to answer with Ernst Kurths Grundlagen des linearen Kontrapunkts but I haven’t finished reading it since I’m stuck on this SE-site with so interesting questions like yours and the book is very complicated for reading but it has been translated in English and there are some good thesis and resumes about it. And I can’t resume it in some sentences. But the main points are the tensions of intervals and melody lines and their relationships with chords. – Albrecht Hügli Dec 7 '19 at 20:07
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    Btw: here’s a link to one of the books discussing the writings of E. Kurth epdf.pub/… – Albrecht Hügli Dec 7 '19 at 21:09
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History certainly suggests that thinking about "chords" instead of "intervals" affects the end product.

Baroque harmony, based on interval-thinking, is a lot "wilder" than early classical harmony based on chord-thinking.

That is hardly surprising. If your idea of a "seventh interval" includes every possible type of 7th chord, you don't have any hangups about treating every type of 7th chord the same way harmonically. As soon as you say that "dominant 7ths" are OK but only if resolve them in certain ways, and "secondary 7ths" are something exotic that you don't really want to meddle with at all as a beginner, you have music theory which says "don't do stuff, because it might sound bad".

An example that I've quoted here before (from the 16th century) is a set of variations on a theme with the basic chord sequence G Em D G (which isn't going to give anybody a theoretical problem) - until the composer got a bit bored with that, and just threw in G Bb Eb G for one variation instead. You can try to make sense of that as common-practice chord-based harmony if you like, but it's 100% certain that wasn't what the original composer was thinking about.

Actually the real inhibitor might not be "chords" in isolation, but that "chords" always seem to bring "keys" and/or "modes" into music theory - together with the idea that using notes "not in the scale (or key, or mode)" is somehow "wrong". (Not to mention all the convoluted terminology, and the angst about whether improvising a Mixolydian or Hyperchondrian scale over a partical chord is "right" or "wrong"...)

(Note for pedants: the "Hyperchondrian mode" is a joke. But there really ought to be one, for worried theorists to use!)

  • Why would you think that early classical harmony is based on chord thinking? What musical theoretical revolution occurred between Bach and Haydn? – phoog Dec 9 '19 at 18:10
  • This answer gives a misleading impression about Baroque vs. Classical harmony. Both were based on figured bass and used the same harmonic palette. Where classical harmony seems simpler than Baroque I would say it was for the needs of sonata form and the bold contrast of tonic/dominant and recapitulation effect. Beyond that difference in formal treatment, chord to chord progressions and the contrapuntal orgin of harmony was mostly the same. – Michael Curtis Dec 9 '19 at 21:29
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All chords certainly contain intervals, and could be talked about using those terms. However, it's much simpler, and more easily inderstood now we use chord names that most players are aware of. Take a humble dominant seventh chord. Straight away, people know what it is. Try using intervals to describe it, and it just gets muddy very quickly.

There's also the confusion caused by the sound of an interval having to have, due to various technical reasons, at least two names. It already befuddles a lot of folk, as witnessed in questions on this site. So, keep it simple, thus clearer, by using chord names. The only time it might be advantageous is where particular voicings are necessary, but even a lot of that is conveyed in naming chords correctly.

And of course harmony is based on intervals, but not 'rather than chords'. When harmonising a simple tune, for example, sometimes the harmony will need to be a M3 abov e the melody, sometimes a m3. But that usually goes with the flow of the spread of the diatonic notes. Most times, we don't even think too hard about it - especially when singing.

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I don't necessarily think that all of the historical assumptions in the question are accurate.

In the old days they actually never spoke about chords. They just wrote a bass not and added eg 64. Simple organum or basso continuo talked about intervals.

Well, they didn't always think of "chords" in the way we think of them (i.e., as collections of pitch classes that can be inverted and are all the "same thing"). To Bach, a C-E-G "chord" was definitely not the same as a G-C-E chord with the G in the bass ("6/4"). In that, you are certainly correct. Those entities had completely different functions -- the former was a consonant triad, while the latter was a dissonant collection of notes that required resolution according to specific rules.

However, it's one thing to recognize that earlier composers put a greater emphasis on intervallic relationships between parts and on the counterpoint that results. It's much more extreme, though, to claim that they never thought about the vertical sonorities as a whole. Whether they called them "chords" or some other term, Bach knew what a 6/4 figured bass represented and how to resolve it, and he knew it was different from a 6/5 and also different from a 6/3. He also likely recognized a significantly greater kinship between a 5/3 with the same notes as a 6/3, but these were definitely different from a 6/4 with the same notes.

It wasn't just the intervals by themselves, but the vertical collections that assumed functions. And composers from their very first keyboard lessons would have spent learning patterns of vertical structures for harmonization. (See, for example, the well-known "Rule of the Octave" which taught chordal patterns for harmonizing ascending and descending scales.) When they learned counterpoint patterns, they would have known that it wasn't just two voices combined to create certain intervals, but often interactions between three or sometimes four voices that made certain kinds of textures and patterns possible. Again, whether you call these vertical sonorities "chords" with the modern meaning, historical composers definitely understood vertical collections as having particular functions and patterns before Roman numerals existed.

On the other hand, you have a good point that modern theory that tends to focus on vertical classification can miss a lot about how historical composers understood their own music. A lot of harmony did ultimately develop out of intervals and melodic interactions. Even the basic authentic cadence, which we may think of as the quintessential "harmonic" vertical gesture, was gradually built out of individual motions of melodic lines over centuries.

That is, the standard chant tenor line often descended through scale degrees 2-1. In the earliest organum, this began to be harmonized with 7-8 melodic patterns introducing a leading tone. By the 14th century, a standard other voice could be added that resolved 4-5 (or #4-5 in a "double-leading tone cadence"). In the 15th century, a fourth voice gradually was added, and eventually it migrated to the bass and became the 5-1 bass leap. In the 16th century, the 4-5 motion often became a 4-3 motion to create a complete triad at cadences, as the triad was accepted as a reasonable consonance to end on (rather than the "open fifth" sonority that was generally viewed as the best cadence in earlier times).

Thus, all of the voices of the standard V-I cadence developed out of intervallic relationships and melodic interactions. However, once that motion became a standard pattern, composers began to use those vertical collections of notes to create something akin to modern "functional harmony." One begins to see "circle of fifths" motion in sequences as in a iii-vi-ii-V-I progression as early as the time of Palestrina. Composers took those vertical patterns of voice motions and used them to build up the counterpoint patterns I mentioned above. Thus, by the time of Bach, there was a whole repertory of these sorts of patterns that composers would have learned, and a large part of some of those patterns were the vertical sonorities as well as the contrapuntal motion.

In sum, historical composers likely understood harmony a lot differently than we do today. However, back to the earliest forms of polyphony, composers also understood that certain kinds of vertical patterns of "chords" could be reused in different circumstances. It would be more accurate to say that historical composers based their "harmony" both on vertical structures and on horizontal motion, and the horizontal element was likely of much greater importance to them than it is often taught today. That only really began to change significantly in the 19th century.

For a final example, I recall a fascinating article a few years ago on cadences in Mozart that showed that Mozart clearly still was thinking of cadences as collections of individual voices resolving in particular ways, rather than as purely vertical structures. This is apparent because of the way Mozart treats cadences with the old characteristic suspension dissonance differently from cadences without the suspension. The suspension is the 8-7-8 motion found in a strong-weak-strong pattern that is a common to such diverse cadences as I64-V-I, ii65-V-I, V65/V-V-I, and a V with a 4-3 suspension resolving to I. All of these have the characteristic dissonant suspended tonic note resolving down to leading tone that dates back to the 14th century. Mozart treated those cadences differently -- and as stronger -- than, say, a IV-V-I cadence that lacks the traditional suspension. Such a distinction appears to fall away gradually for many composers in the 19th century.

So, by ignoring this historical emphasis on intervallic and contrapuntal relationships, we're likely missing out on a lot of details about how 18th century composers (and earlier) understood their music. On the other hand, it's inaccurate to say that Mozart simply "wrote a bass note and added a few intervals on top." Mozart understood that vertical sonorities ("chords") created patterns that could be reused. And it was those patterns that theorists like Rameau and his followers built theories of functional harmony on, which ultimately led to things like our modern Roman numeral method of analysis and understanding.

4

You're working with two different definitions of "harmony." When you're just talking about two notes and whether they are harmonic, it's a simple matter of looking at the interval; i.e., the ratio between the notes' pitches. If this ratio is one of two simple integers, the notes are harmonic. Otherwise, the notes are disharmonic.

When you're talking about the harmony of a piece, you're talking about how the non-melody notes support and lend voice to the melody. This generally means you have chords, and every note interacts with every other note in the chord. Often, you'll have eight notes at once, leading to twenty-eight different intervals involved. Not every combination of eight notes is tolerable, though, so it's much easier to speak in terms of known chordings and what kind of texture they lend. (E.g., an open sixth vs a closed sixth, or doubling a four-note chord in treble and base vs. taking a 5-note basic chord and adding two octave notes and a fifth in the base.)

In lead-sheet music, you're just given a melody and the fundamental chord that should be played in each a measure, e.g., E or E minor. It's up to you to know what notes fit in an E minor chord, and how their positioning will affect the emotional content of the piece, but you'll never be playing the exact same thing in different performances. That's the point of a lead-sheet. So understanding how chords are constructed from notes is more important than memorizing one set of intervals.

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It's good that you are questioning the validity of the concepts you learn about.

While it is true that chords are ultimately made of intervals, both intervals and chords have turned out to be an effective way of analyzing and composing music, even if there was a time period and style that treated intervals as more important, or at least treated harmony differently than we do nowadays.

I think an analogy might be quantum mechanics versus chemistry. While you could technically describe all of chemistry as quantum mechanics, it is useful to consider the larger concept of chemistry when doing mixing chemicals, etc. because it's simpler without losing much detail. There are definitely times when one does want to consider physics when doing chemistry, but usually chemistry can be considered separate.

Similarly, there are things that are easier to do or more intelligible in the context of chords rather than intervals, such as writing chord progressions and analyzing functional harmony, among other things. This is true even though chords are technically ultimately made of intervals. When you say that chords complicate things, I would argue that it simply offers a different way of thinking about harmony, and like any new subject / concept, there is going to be new stuff that you have to learn.

In fact, I would argue that it doesn't really make sense to say that "harmony" is made of any singular thing. Many other musical cultures have completely different harmonic systems, and it makes sense to look at the harmony of a song through both chords and intervals. On an even more abstract level, one could analyze a song's harmony based on what mode or scale it uses or only look at the movement of the root note or the movement of the bass note.

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Intervals and chords are different elements of structures in harmony on different levels, (comparing with atoms, molecule, chemical compound, matter, life).

As letters are elements of words and words are structure elements of a sentence:

tones are elements of intervals, intervals are elements of chords, chords are elements of harmony and harmony is an element of music.

I would say: Harmony is based on chords, intervals, tones as well on “according” of two or more different polyphonic voices, their independence and their “Klang”.

Is harmony based on intervals rather than chords?

In different historical eras and in different life periods of a composer and in different works of the same writer the one or the other aspect has been dominating.

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To complement the other great answers, I'll try to be as simple as possible:

Intervals are the building blocks of both chords and scales. You build chords using intervals played at the same time (harmonic intervals). You build scales using intervals played sequentially (melodic intervals).

Intervals build chords, and chords build harmony. So harmony is based on both intervals and chords. You can't have chords without intervals, so saying that harmony is based on chords implies that it is also based on intervals.

But you could argue that pitched music in general is based on intervals (melodic, harmonic, or both), so saying that harmony is based on intervals might come as redundant to some.

  • Lots of pitched music has no harmony. In those cases, intervals are only melodic (and as far as I can tell, from very casual observation only, the intervals in such types of music are more likely to bear little or no relation to the overtone series). – phoog Dec 9 '19 at 18:16
  • @phoog Absolutely! Not all pitched music has harmony. Edited the answer to better reflect what I was trying to say. – Von Huffman Dec 9 '19 at 18:39
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Your question seems to hinge on a notion that counterpoint/figured bass and chords are mutually exclusive. But they are not.

In the old days they actually never talked about chords.

I don't know what time period you are thinking about, but during most if not the entire Common Practice period, when the harmony system was figured bass, musicians had a clear idea of chords. Rameau talked about chords. Daube's General-Bass in drey Accorden is form 1756 and uses the word chord (translated, modernized) right in the title.

Surely a figure like this...

enter image description here

...wasn't thought of only in terms of interval and counterpoint (dissonant tritone needs to resolve by contrary motion to a third), but would also be understood as a chord of the sixth resolving to the tonic chord.

Of course the modern thinking about that progression is root progression by descending fifth which is considered a strong progression. The old contrapuntal view considers the strength of the progression coming from an unstable chord of the sixth moving to a stable (un-inverted) triad and the half step motions of TI to DO and FA to MI. The important thing to understand is within the old view people still recognized root position chords even if they didn't use the terms root or inversion.

I feel like part of this question has been left unspoken. I get the impression that harmony based on chords may be assumed to mean something like this...

enter image description here

...a flow chart of root progressions (mostly descending fifth combined with the three functional categories) which certainly presents harmony devoid of any of the contrapuntal origins.

Personally, I think a deeper understanding of "classical" harmony comes from learning counterpoint and figured bass. But, I wouldn't overstate that as no one had a concept of chord during that time period. It just means people should include counterpoint and figured bass in their harmony studies.

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