A New Theory of Harmony? – Isocords & Palindromes

So my gentle bit of advice would be: In the moment of thinking about some aspect of the theory, try to find an example by yourself, improvise about a little idea, compose a bit of a piece – only to see how your thinking develops into a making of new music.

My (rather not) gentle bit of advice is actually do what you've been told time and time again and write music.

I repeat.

Write music.

Since at this point in the narrative nobody cares for your idea and quite possibly nobody understands it as well and honestly nobody is about to bother with it unless you put some effort into actually generating music out of it. You're not doing it and nobody will do it for you, end of story.

Fail to acknowledge this and, well, you're welcome to continue bumping your own thread pretending anyone gives a scraggy, like you did until I interrupted (again.)

Am I being harsh? Sure thing, but you sort of forget that just like your theory there are millions of others, and here's the thing, there's actual music to back them up. Yours? Just a bunch of (confusing) words so far.

But oh well, I have the feeling that you'll just repeat the same thing as a reply as you've been doing ("No guys you should do all the work, that's how it works!") and fail to provide any music.

Hopefully I'm wrong and you finally got the point.

My (rather not) gentle bit of advice is actually do what you've been told time and time again

This thread is about theory and not about composing. And if you haven't recognized it so far, I've said that the isocord theory is not a method for composing, but a prescriptive means of providing (new) material for composition. And I've shown, at least in one example, how this material can be used

Yeah, alright dude, sure thing. It's not a composition method because it has nothing to do with writing music!

Oh wait...

In fact, considering the other stuff you've posted, this is VERY MUCH a composition method regardless of what you may call it.

Are you schizophrenic? Just twist and turn the words as you like it? No wonder that your behavior is so erratic.

Yes, you "tore the whole method apart", and you did it in a downright unqualified manner when, for instance, speaking about clusters where there are none (etc. etc.).

Stack 5ths together within an octave and you get major second formations (clusters.)

That's the best for all when you quit the field. (SSC "Gone?" Hopefully soon, forever!)

Did I hurt your feelings? :<

I'm almost the only one, in case you didn't notice, that actually gave your ideas any actual consideration! In fact, most of the thread has been me commenting on it and TRYING TO HELP YOU explain them better.

But, hey, let's see you present this in real life to actual musicologists. You'll get laughed right out of the room in a couple of minutes, no doubt. I'm just trying to prevent that embarrassment from happening but you just seem to want it so badly.

So, why am I laughing?

1) You made a big deal out of pointing out "isochords" != "isocords", right? See:

Your lengthy reply indicates that you still not yet have understood the concept of isocord (note: not isochord!). I repeat its original definition from my post #1 of this thread: Superimposing equal intervals, one above another, yield vertically symmetric sounds which are more or less dissonant, depending on the particular interval used. Let's call those equal-interval, or iso-interval, sounds isocords.

Note, that I talk about sounds and not about chords – in order to prevent misunderstandings regarding the traditional concept of chords. In this sense even unisons of primes or octaves are sounds, but, as correctly seen in traditional understanding, not chords.

Then in the wiki you wrote:

Superimposing tones by an equal interval yields a symmetric sound, an iso-interval chord (or isocord for short). All intervals within an octave, including the prime and the octave, may be used for building isocords.

Huh? "Isocord" is short for "iso-interval CHORD?" I was right all along then?

Or probably you haven't made up your mind as to what your terminology actually means.

2) I already pointed out that the different sounds you'll get out of stacking up equal intervals are not anything new, nor is anything you may do with them (as well as some of those results being rather prominent in classical and modern literature already.) So much for "new" on that front.

3) You're playing "let's rename things" most of the time. A cluster is a cluster, even if you want to call it cheeseburger or airplane. Stacking up major 2nds, 9ths, 5ths (within the octave), etc is GOING TO NET YOU A CLUSTER. All you've said so far points that it's a chord building method, therefore this is the actual result of it. I already went into detail as to why this isn't going to fly, nothing's changed so far.

See:

Superimposing tones by an equal interval yields a symmetric sound, an iso-interval chord (or isocord for short). All intervals within an octave, including the prime and the octave, may be used for building isocords.

Sorry dude, but even spreading minor/major 2nds across octaves is ...the exact same thing as within the octave. You even go out of your way to say:

Isocords built on primes and octaves are consonant, isocords built on minor seconds through major sevenths are dissonant.

(emphasis added)

Oh really? Don't even try to explain how any stacking of minor seconds is NOT a cluster, you already failed at a much more fundamental level.

4) Your understanding of "Atonality", "harmony" and such other terminology is practically made up or nonexistent, IE:

Isocords are basically non-tonal ("atonal") in that they don't convey a tonal center (escept for sounds of primes and octaves, which are consonant by definition and therefore "tonal").

This statement is absolute nonsense: a C major chord can be "atonal" just fine if the point is "tonal center" which can only be argued to exist through the actual horizontal dimension of the piece (form, repetitions, etc.) A single chord standing alone is nothing but a single chord standing alone. Context and context alone defines what it may be (specially since "tonal" and "atonal", etc are words used to describe the overall situation and relationships of an entire musical passage, NOT A SINGLE CHORD.)

As for the distinction that primes and octaves are somehow "tonal", that's also an assertion with as much academic merit as claiming triads are modal or pianos are flutes.

5) Your definition of "composition" seems to be rather strange. Take:

Isocord theory is not descriptive (there are only sparse examples, Sch

Good job, it's hard to see someone fail so spectacularly.

SSC, be honest. It's not hard for YOU to see someone fail so spectacularly. Maybe your tone and the OP poster's general reaction to it are responsible for the downfall of the thread so far. But what I really had a ball laughing at was...

Honestly, the reality is that you are just a kid trying to play theorist who has no clue as to either what he's doing, the terminology he is using or the consequences of what he's proposing.

Congratulations, you just won the internet's academy award for melodrama in a forum post. Take a bow.

By the way, what exactly are the "consequences" of this proposal anyway? I have a difficult time coming up with how the theory (in spite of the flaws) has any counter-productive tendency in reality. Even if the theory was more fleshed out, there were more works out there using his methods, and the overall terminology was clearly defined and more accepted by the general community, THE THEORY IS NOT GOING TO FORCE YOU OR ANYONE ELSE TO USE IT!

Lol...

Moving on...

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Look Hansen, this is SSC's method (generally) of pointing out what he doesn't agree with, and I don't agree with it in the least. It doesn't foster discussion. All it does is makes tempers flare and takes all the 'intellect' out of discussing music. But there's substance to his comments that you really should consider.

First, I disagree with SSC that there is no distinction between 'Isocords' (and really, what's the point of misspelling this? there is no point, IsoCHords, please) and tone clusters. It has a lot to do with the overtone series and the difference in how tones relate to each other within that series which is a BIG part of your underlying structure in explaining the 'sound' of Isochords. I listened to your work and really appreciate what I hear, honestly. Isochords don't 'sound' like tone clusters. YOU have to tell me why in your theory (I already know why, but that's not something you can assume with your theory - be more descriptive and thorough is all).

Second, what I hear in Isochords is too similar to other harmonic theoretical products. If you want this to matter, you must, MUST establish a more unique sound with Isochords. You have to take me somewhere harmonically that I've NEVER BEEN before. Throw out EVERYTHING you've ever learned about music and create, for me, a universe where all harmonic theory is based on Isochords. Additionally, this should SOUND completely different from what I hear in tonal and atonal music.

You're not doing yourself or your theory any favors by pandering to the tonal and atonal worlds of music. You'll get these responses like SSC's again and again, because these are established traditions in music that people like SSC, in spite of their statements to the contrary, have no willingness to entertain another perspective on music. They don't have a reason to care, they're happy with what they have in tonal/atonal tradition, and they have no interest in ANOTHER theorist coming along and telling them "the next great idea" they could use to make their music within these traditions better. Before you say, "But that's not what I'm saying..." I'm telling you, right here, right now, that's what they're reading into all of this, and that's partly why you're seeing these attitudes in SSC's posts.

Do something else with Isochords, something that has nothing to do with tonality or atonality. Make music that sounds like Isochord music. Find other places to draw out the uniqueness of sound in using these chords. Again, this is about being thorough with your theory, leaving nothing to question or doubt. You shouldn't be trying to re-invent the wheel here either by trying to provide an "all-inclusive" theory that, again, panders to the interests of all realms of music (i.e. tonal and atonal) unsuccessfully. Don't argue why it's different from tonal or atonal music at this point, either. If it were me, I'd just ignore both and build the theory from the ground up as though neither exist at all (at least at the initial stages of development - explain the differences later when the theory is more complete).

I think you should keep at it, don't ignore the substance of SSC's post, but definitely write off his attitude at this point and move on. There are bigger, better minds than his in the world of music. You should be pandering to them.

Congratulations, you just won the internet's academy award for melodrama in a forum post. Take a bow.

Don't be a drama queen, AA. I was just talking about the music product that is the result of what he's suggesting which you yourself have noted:

Second, what I hear in Isochords is too similar to other harmonic theoretical products.

You are in fact agreeing with my position on many fronts, insults aside.

I just don't agree with the standards you're setting for him. I find them to be rather unreasonable considering what he's proposing:

You have to take me somewhere harmonically that I've NEVER BEEN before. Throw out EVERYTHING you've ever learned about music and create, for me, a universe where all harmonic theory is based on Isochords. Additionally, this should SOUND completely different from what I hear in tonal and atonal music.

Is this even possible? I mean, look at the material he's working with, do you seriously propose that the listener is just going to throw out the window all the literature that already exists when they're hearing this as to make no relations to it what so ever?

As long as his theory is still using traditional concepts such as chords, intervals, etc, it will still invite comparisons to other music. In that sense, it may as well be impossible to distance it from what already exists unless he went the music concrete way or using entirely different sound sets or parameters.

But, he's more than welcome to try anyway. That's the main reason I want music, not words. Maybe he can do it, maybe he can't, but so long as there's nothing solid to look at it's impossible to tell just by looking at his vague propositions.

Oh, and as for this and other insults:

There are bigger, better minds than his in the world of music. You should be pandering to them.

Like yourself? ;>

Sure, we disagree on a lot of things, SSC, but you just don't have the justification going for you to make such dramatic statements and pass final judgment on anyone. You and your "time" argument (among other attitude-based, overgeneralized arguments) are demonstrable proof of how much you still have to learn about music and art, not to mention argumentation. But to stay on topic...

Of the harmonic products Isochords actually sound like, TONE CLUSTERS is at the very BOTTOM of my list. I'm inclined to view Isochords as generically similar to jazz harmonies that have no real defined flight plan in hierarchy. The symmetric quality of the sound is different to a trained ear, but the treatment of the harmony itself is too similar to other styles.

It's not up to me to define the usage of Isochord harmony or how it interacts with other elements of music to produce a final product. That's why I recommend throwing everything out (at the onset of discovery) to really try to define what Isochordal music is supposed to sound like to Hansen. Once he does that, THEN and ONLY THEN should he start comparing it to other styles of music, when he's established a theoretical framework and can then draw comparisons against established traditions.

You and I both agree he needs to write more music, but your method and my own are quite different in terms of what is and is not helpful. You can talk at the guy all day long, but he doesn't have to listen to you if all you'll end up doing is flame him when he tries to explain his disagreement with you. Patience is a virtue you appear to have little interest in, so for what it's worth, I'm simply trying to assist where needed. If you don't have the patience to help the guy, then bow out of the discussion and move on.

You and your "time" argument (among other attitude-based, overgeneralized arguments) are demonstrable proof of how much you still have to learn about music and art, not to mention argumentation. But to stay on topic...

After all this time you're still spitting venom over that? I guess it happens when you're owned so hard. Please, let's not bring it up again, ever.

Did

I think you should keep at it, don't ignore the substance of SSC's post, but definitely write off his attitude at this point and move on. There are bigger, better minds than his in the world of music. You should be pandering to them.

Yes, I'll do! You have touched so many fundamental points in your recent posts that I'd like to think more about them than replying on the fly. So, please, give me some more time.

Oh, I'm sorry then. I sensed sarcasm/junk and you meant none.

Did you realize that I didn't speak to you but to AA?

Nice list of dots. But what if CSS were right? I would have to eat humble pie. Happily, I have no cravings for such a one. So let's bury him in dots.

Are you high?

I just want to point out the blatant irony of the fact that somebody with the alias of "Antiatonality" is contributing, let alone leading with high confidence, the discussion of a thread about music theory.

Are you sure you're interpreting my alias correctly? I'll refer you to Schoenberg's quote in my signature.

I think the world of music needs more genii like you to put pompous names to arbitrary and inevitable patterns in music.

Right, because everything that ever happened in the entire history of music occurred arbitrarily without purpose or design...

Look, if the guy thinks he's onto something, then let him discuss it without being bludgeoned by stupid commentary from the peanut gallery.

I stand corrected. Still funny seeing it, though.

I went for the humor/oddness a bit in the alias, actually. It usually gets people's attention though, so it serves its purpose.

It's a funny experience for me, as a non-native English speaker, how the spelling of a technical term like 'isocord' may cause an upset. As far as the spelling is concerned, 'isocord' as well as 'isochord' is used in different areas, from mathematics, physics to music as well (but in a different sense). However, I liked more the association of 'isocord' with 'discord' and 'concord' as exemplified by Dolmetsch Online. And the German use of "Iso-Intervall-Akkord" immediately leads to an English shortcut translation as 'isocord'. Anyway, whoever wishes to write 'isochord' may do so. For the time being I prefer to use 'isocord' as a well-defined technical term.

Well, at least there's a reason behind it... although I'm prone to see this as more of a semantic game than a musical justification.

That's an interesting point to establish something completely new with isocords. In a way the theory does it with the idea of "thinking in sounds" instead of single tones out of which chords are built. Of course, isocords are also built of individual tones, but with two unique features: the number of defining tones for a full isocord sound varies, from 2 through 12 (see the figure and table of isocord building in the article) and the resulting sound is always dissonant in a perceivably new way of varying degree (except for primes and octaves – but even there's a difference in sound between tow and, say, seven octaves). Nevertheless, "throwing out everything you've ever learned about music" is not sensibly working since you need some fundamental concepts like tones, scales, intervals, chords, etc.

A couple of things...

1) The theory doesn't really promote "thinking in sounds"... that's aleatoric and non-tone music (Elliot Carter and Edgar Varese come to mind). What your theory actually promotes is "thinking in polarities of pitch intervals", at least the way I see it.

2) This isn't a discussion of consonance and dissonance (or really shouldn't be, lest you continue clinging to tonality). What you're really defining with your theory is the space in between pitches, not the pitches themselves. What fascinates me about Isochords has very little to do with what's on the page. I'm more interested in the unwritten pitches that result from the equidistant intervals. There is a deeper sound occurring in the interval space that you really should investigate in more detail. Your theory could carry much greater significance if you consider what's NOT being written, what 'remains' in these interval spaces because of the chordal structure.

That's what interests me about this whole Isochord theory anyway. Consider the presence of a melody... but it's not a "written" melody. The impression of overtones within the interval space is where the melody is produced... perhaps a solo instrument could merely 'trace' that melody within the Isochordal structure. That, I believe, is a very unique place to start... maybe not "melody" per se, but definitely examining the interval space. Also, there's nothing preventing you from examining Isochords like G# 11-11-11, F 19-19-19, and so on, as each of these interval combinations yield individual overtones opening more space to explore.

Although my (theoretical) thinking about music has always been dominated by the antitheses, so to speak, of tonality and atonality, it's possibly a better idea to go without them, at least for a while, as long as the theory is in its developing stage. On the other hand, with the rule of minimal tone-step resolution of isocords you're really on the edge to (functional) tonality so that there's a way to integrate both approaches to write music in a new, 'integral style' of non-functional sounds and functional harmonies.

Ugh... basing your theory of Isochords on two polar opposites, both of which operating as a pre-established harmonic syntax, is not helping you right now. This was the whole problem with Schenker's analytic method... it was extremely applicable to the classical models while ignoring, almost entirely, the 20th Century dynamic developing in Europe and America. You may fail to realize it, but your theory panders generally to a very limited number of musical styles. It "seems" larger in scope to you because you're thinking, "Wow, this bridges the divide between tonal and atonal music." The reality is how you're approaching this theory now is a very limited, tunneled vision of the world of music.

Think bigger. :)

Those are some really interesting observations AA, why don't you write something using them? Specially with the "spaces between intervals" and so on. It seems you're thinking of something really distinct here and I'd love to hear it in action.

If anything, you're actually proposing things that I can see potential in rather than just theory garbage.

Those are some really interesting observations AA, why don't you write something using them? Specially with the "spaces between intervals" and so on. It seems you're thinking of something really distinct here and I'd love to hear it in action.

If anything, you're actually proposing things that I can see potential in rather than just theory garbage.

I think I will. I'm all inspired and stuff...

But I have to work tomorrow, so I might have to sleep on it and get to it later.

2) This isn't a discussion of consonance and dissonance (or really shouldn't be, lest you continue clinging to tonality). What you're really defining with your theory is the space in between pitches, not the pitches themselves. What fascinates me about Isochords has very little to do with what's on the page. I'm more interested in the unwritten pitches that result from the equidistant intervals. There is a deeper sound occurring in the interval space that you really should investigate in more detail. Your theory could carry much greater significance if you consider what's NOT being written, what 'remains' in these interval spaces because of the chordal structure.

That's what interests me about this whole Isochord theory anyway. Consider the presence of a melody... but it's not a "written" melody. The impression of overtones within the interval space is where the melody is produced... perhaps a solo instrument could merely 'trace' that melody within the Isochordal structure. That, I believe, is a very unique place to start... maybe not "melody" per se, but definitely examining the interval space. Also, there's nothing preventing you from examining Isochords like G# 11-11-11, F 19-19-19, and so on, as each of these interval combinations yield individual overtones opening more space to explore.

That said, Hansen, I find your new theory of harmony, especially the part about isochords, excuse me, isocords*, completely brilliant :). I think the world of music needs more genii like you to put pompous names to arbitrary and inevitable patterns in music.

Nico, I'm not sure whether your quote is in earnest. Nevertheless, if you, as a prolific young composer at YC, would seriously get involved in using isocords

I immediately generalized the approach to any chords which could be built by superimposing equal intervals – so I came to my "isocord theory". Meanwhile I've gone even a step further, identifying the 'interval space' of an isocord as spanning a 'spatiotemporal range' of ('particles' of) sound which basically might be understood with the concept of 'spectrum' as defined by W. A. Sethares in his book "Tuning, Timbre, Spectrum, Scale" (you may find excerpts in Google Books: Tuning, Timbre, Spectrum, Scale). Sethares shows the – beforehand incredible – mutual interrelations of tunings, timbres, spectra and scales in harmonic AND inharmonic music (hence the title of Sethares' book – by the way, his website is a fascinating source of inspiration: Bill Sethares).

As in, 1) you came across this after I pointed out my interest or 2) you initially began your isochord theory based on this information?

See, I'm a little perplexed because none of that seems to be incorporated into your initial thesis, let alone your Original Post. I'm getting the impression you're trying to backdate your findings instead of just openly, honestly adding them in after the fact.

I hope that's not the case. I'm hoping you'll simply include this information in establishing the theoretical framework of your theory. See, if you had this information to begin with, you've done a lot to skew that information with your attempt to bridge tonal and atonal music. This was the point I was trying to get across earlier. Tonality/Atonality is secondary to what your theory is really about... so I'd focus in more on what is material to Isochordal music and explore that first.

As in, 1) you came across this after I pointed out my interest or 2) you initially began your isochord theory based on this information?

I'm not sure what exactly you're asking. So let me recapitulate the short history of my isocord theory.

Early in March I read the German translation of the Cook/Hayashi article in the German Journal "Spektrum der Wissenschaft". In the context of this reading I had my first idea of building symmetric chords on all intervals of the 12-tone system (instead of thirds only) and resolving them into concords by a rule of minimal tone-steps. Working with these ideas I continued, in April and May, to formulate the theory with paper and pencil (including musical tables of chords and their possible resolutions).

On 19 May I posted in the YC thread Atonal Competion [sic!] an idea for participation (more as a joke than a serious enterprise). In the end of May I finally decided to check out whether I couldn't do a kind of atonal/aleatoric piece with my "isocords" (at this time I fixed the term after some study of related literature). Thus my "Isocordal Piece" came into existence, delivered on 9 June at Atonal Competition(BLM22) Subs. After some discussion in this thread, Gardener proposed to start a new thread for the "isocord" idea, which I then realised with A new theory of harmony? – Isocords. So, that's the story so far.

Only later in May I encountered the availability of the original Cook/Hayashi article in the internet. There I found also a list of references which was lacking in the German translation. From this list, the Tuning, Timbre, Spectrum, Scale book by Sethares aroused my curiosity most, and after a short Google search I ordered the book. Thus I came to the idea that the distance feature of tones within an isocord – your "interval spaces" – (which was prominent in my considerations of the peculiar sonority of isocords from the beginnings) is best described with Sethares' Spectrum concept.

Tell me whether this answers your questions and whether I have cleared your worries.

I hope that's not the case. I'm hoping you'll simply include this information in establishing the theoretical framework of your theory. See, if you had this information to begin with, you've done a lot to skew that information with your attempt to bridge tonal and atonal music. This was the point I was trying to get across earlier. Tonality/Atonality is secondary to what your theory is really about... so I'd focus in more on what is material to Isochordal music and explore that first.

You're probably giving him way too much credit as he honestly never thought as far as you during the entire discussion. If anything, you might as well take the thing and develop it as Hansen clearly can't. Plus I think that what you're talking about is something completely different than what he had in mind (so take your own ideas as your own, I guess?)

As far as I saw he was trying to work WITH tradition (hence why everyone was confused since all he was doing is renaming things.) What you're talking about seems much more inclined to be a bigger sound-theory altogether detached from any given number of traditional parameters.

Hell, starting with different tuning systems/frequency arrays and playing with different interval spaces, overtones, etc, that sounds all very interesting if maybe not 100% new (but who cares?)

Don't make the error of applying your interpretation to it (as interesting as it may be) and thinking that's what he meant all along since it apparently isn't and he hasn't been clear about it (despite it being obvious.)

In fact, why don't you actually explain more what you mean with the overtones/etc? I'm still sort of curious, but wouldn't it be cooler to simply ditch the traditional temperament/12 tone system altogether and work with pure intervals/frequencies? It'd certainly help bring out a totally different sound, as simply organizing the same'ol 12 tones in the same'ol tuning is something that will inevitably go against what you've been saying about being completely different/new.

Another thing that occurred to me is that by changing the tuning system of the 12 tones the interval stacks are going to have wildly different sounds. Ditching the 12 tone system altogether I think allows for a cleaner (pure?) mathematical interval progression since you only have the starting frequency and then the intervals are handled based on a math model rather than simply "which notes are in X interval from it."

Just sayin'.

Another thing that occurred to me is that by changing the tuning system of the 12 tones the interval stacks are going to have wildly different sounds. Ditching the 12 tone system altogether I think allows for a cleaner (pure?) mathematical interval progression since you only have the starting frequency and then the intervals are handled based on a math model rather than simply "which notes are in X interval from it."

Just sayin'.

Yeah, I wouldn't even know where to begin "ditching" the 12-tone system since most all music is understood as operating within the frequency parameters of a thoroughly established system of pitches. But, I do like the idea of doing away with Octaves and attempting to broaden the intervals out to larger spaces just to make room for using more overtones.

I had in mind formulating a chart of the overtones of a symmetric chordal structure (i.e. "Isochord") and using those tones as a basis for some kind of pitch material. For example, distinguish what happens linearly from what happens harmonically and perhaps shift within the dimensions of the space.

Thinking out loud of course, my thought was to create some kind of melodic idea based on the overtone series of a given symmetric chord. From that, I'd use more of a stasis harmony while the linear material sounded (I had some pointillism in mind, actually) to trace and highlight the space. Then, I'd completely flip the whole thing around, using big gigantic chords to accent the overtones with piercing soli trumpets sounding the symmetric chord.

I'm going to play around with that idea a bit and post it when I get time, but that's generally my initial thought about how to implement it. Simple? Yeah, but we've gotta start somewhere.

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@ Hansen: All I'm saying is you need to be more thorough in explaining the framework of your theory, not just stating a bunch of analysis and telling people how it can unify tonal and atonal music. Your theory has to stand APART from everything else before you can start comparing/applying it TO everything else.