A New Theory of Harmony? – Isocords & Palindromes

Well, stick with your "chords". So you'll never understand the concept and scope of isocords.

You'll never understand fnarf either, so I guess we're even.

And can you or can't you actually answer my questions? Remember: You're the person trying to convince people you got something here. If you don't bother to clear it up (cuz I'm not the only one confused by all this mess,) fine, but forget about your idea meaning anything to anyone else but you.

Now to end this off topic rambling nonsense:

anecdotically speaking, basketball is not explained in terms of football.

I'll just go with this and note that you're entirely missing the point. Entirely. What he's doing is trying to, again, is like explaining a word without using other words and/or making up NEW words which require further explanation and then not giving it.

If I tell you "Fnarf," without telling you WHAT IT IS, then what use is it to you?

If I explain "fnarf" as "Fnarf is Xlompo!" and then fail to define Xlompo, then what use is it to you?

But however, if I said that "fnarf" is LIKE a teacup and went on to say how it isn't much like a teapot, you have at least something to work with. A teacup is "old terminology," here. It may be even unrelated, so long as it communicates the right idea, it's fine.

If someone comes around and says that "Xlompo" is a relabeling of music "chords," and then explains why/how, then at least you have something to work with.

Basic communication requires context, which is sorely lacking in his idea and in his explanations. If your theory exists ENTIRELY in a vacuum, it's pointless and, indeed, science never works this way.

Back to the quote tho, it'll be like trying to explain basketball WITHOUT referring to the fact it's a "game," nor that it uses a "ball" nor that people "play it," etc. Instead making up new words for all of these things without explaining their analogue terms in other, similar, games. You obviously use shared terminology to explain games like soccer, basketball, football, even if the games may be different. In fact they are QUITE similar, enough so that someone who understands one is probably going to grasp how the others work without much effort.

If he wants to introduce a new theory of music, then he should make it so people who already are familiar with existing music theory can understand it. Basic communication, nothing more, nothing less.

State your questions in a clear, unambiguous way and I'll be happy to answer them in a clear and unambigous way!

the thing is that you introduced this offtopic material in applying metarule of allegedly necessary need for explaining new terminology in the definitions of old terminology. i stated that this is wrong, and there is no such need. theories do not come into world like that.

as for context, hansen firstly must proceed slowly expandinf the content of his theory and providing it with context by creating it using metaphors, other language games and most importantly works of art in his case. he does not need any outside explanation in regards to old theory. he may have to do that in a late process of unfolding his theory to render it more understandable to conservatives and 'methodologists' like you.

but, in first place, he invites you to the journey and asks to be faithful and not try to jump out and use some metalinguistc tricks in forbidding his theory beforehand. which your 'rule' is only good for.

he is insider. your rule is based on outside relation betwen two possible traditions. you rule violently wants to assimilate the other tradition by supposing that its terms are superior and provide a method and model for evaluation. but it is not.

on your last paragraph regarding sports. knowing how to compare basketball and soccer doesn't make you any good at these games. you may know all the rules and such, but without practice you're done. 'to grasp how they work' means little if it you cannot do anything with your nikes on. this is why coaches and strateges must have been at least decent players in first place. and that is seen a basketball theory from inside. the relation to other sports matters little.

you seem to put an emphasis on the outside meta logic of certain consistency in creating new theories, which, as i state, is pretty much useless and a dead fish to start with.

you came several steps to soon to put a requirement of certain translation.

Ah, I'm done with this. You guys have fun, I'll go write some pieces in the much better Pi theory of harmony!

Ah, I'm done with this. You guys have fun, I'll go write some pieces in the much better Pi theory of harmony!

Gorrick can be the Schoenberg of Pi... I want to be the Webern of Pi! You can be the Berg of Pi... let's dominate the next 100 years of music!

If I explain "fnarf" as "Fnarf is Xlompo!" and then fail to define Xlompo, then what use is it to you?

Crap, Fnarf is Xlompo?...I guess I misunderstood it the first time.

There's an interesting empirical fact of general music theory: 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 (comparing well to the usage of discords for dissonant chords and concords for consonant chords

Then why bother calling them isocords for isochords? Isocord apparently means dissonant, symmetrical chords. Whoopdeedoo.

Let's look at some examples.

Minor thirds chords:

B-D-F (= diminished triad, a 3-tone chord)

B-D-F-Ab (= diminished seventh chord, a 4-tone chord)

There are no more higher-toned minor thirds chords from B since the next minor third above Ab would be Cb which is enharmonically equivalent to B.

Minor sevenths chords:

B-A-G (a 3-tone m-7ths isocord)

B-A-G-F (a 4-tone m-7ths isocord)

B-A-G-F-Eb (a 5-tone m-7ths isocord)

B-A-G-F-Eb-Db (a 6-tone m-7ths isocord) – which is the highest-toned minor sevenths chord from B.

Major seconds chords:

B-C#-D# (the 3-tone M-2nds isocord from B)

or

Bb-C-D-E-F#-G# (the highest-toned M-2nds isocord from Bb)

If you can create a tone cluster and have it resolve anyway you want simply because there are so many possibilities, why bother calling it an isocord simply because it CAN be derived from a verticle pile up of perfect fifths or minor 7ths? Like other people are saying, it just seems to be that you are trying to apply a new word to an old rule. So what, symmetrically built chords are an interesting phenomenon - why confuse people by calling it something else? You're not really pioneering something here. And if you are, you sure aren't explaining it well again because nobody seems to understand you.

An interesting feature of isocords is that they're all (apart from primes/octaves isocords) "atonal", so to speak: They have no tonal center to them nor do they imply one when played in progressions. Insofar they are a new kind of harmony which might be useful for contemporary composing. In particular, for 12-tone composition as well: Instead of solely building a 12-tone row you can have, for each tone of the row, a distinct isocord built on it, thus yielding a 12-isocord row. Just experiment with this idea. And if you're ingenious enough you may even build an all-interval 12-tone row of isocords!

They're only atonal if you use them in an 'atonal' context. So I guess if you use them in tonal music they aren't isocords anymore - they're tone clusters. And diminished chords. And augmented chords. Why relabel? So I make a tone row. Now I build a chord around each note in the tone row - it's like I'm harmonizing a Bach chorale. I use chords that have evenly spaced intervals. What makes this so special?

Your quotes and others' comments show that I should become more enfolding with my theory since the concept and the scope of isocords is indeed more universal than the present discussion might suggest. Otherwise I would not need to introduce new terms, that's for sure.

Therefore I'll go to prepare a comprehensive overview of the isocord theory, complemented with a sample of isocords, put together for further elaboration – and, by the way, for improvisation on a piano (or two)!

Seems to me if you're going to propose a theory on this subject matter, it needs a driving philosophical idea behind it. Like Enigmus is pointing out, so what if you can stack pitches at equal intervals on top of each other to create harmony? That's nothing new. What's really missing here (if this helps) is a syntax, a context for what isolates this harmonic theory from all the rest. A blanket application of harmony across all spectrums really defeats the purpose of what I'll call "iso-tonal" music (to coin the term in the way I might understand it better). It's not that the harmony behaves in a common-practice tonal manner. The tones themselves are unique to the syntax because... well, you'll have to elaborate on this.

Does this make sense? The theory is merely a guide to understanding why something works, not how it's applicable across the board. I think that's the misnomer I operated under for many years... but I see the error of my ways on it. Hope that helps.

Seemingly basic and fascinating... yawn...

Seems to me if you're going to propose a theory on this subject matter, it needs a driving philosophical idea behind it. Like Enigmus is pointing out, so what if you can stack pitches at equal intervals on top of each other to create harmony? That's nothing new.

Well, not necessarily a philosophical idea, but a musicological intent: To unify the different, but sporadic approaches to non-tertian harmony (e.g. quartal harmony, tone clusters, polychords) under the general concept of symmetric chord building

Well, not necessarily a philosophical idea, but a musicological intent: To unify the different, but sporadic approaches to non-tertian harmony (e.g. quartal harmony, tone clusters, polychords) under the general concept of symmetric chord building – or isocords, as I named it. The musicologically most interesting fact is, that traditional harmony, including 20th century harmony, builds upon non-symmetric structures of sound. Even the fundamental features of consonance and dissonance of chords are based on the symmetry property, as shown in an influential article by Norman D. Cool & Takefumi Hayashi, "The Psychoacoustics of Harmony Perception" (in American Scientist, Vol. 96, Nr. 4, p. 311 ff., July-August 2008).

As far as I have developed the theory, there's a definite syntax to operate with. Therefore I'm interested in the question, how far the isocord theory is applicable in the wider range of functional and modern harmony and in which way it should be improved or augmented to do this better. As promised before, I'll post a survey of the theory, together with some examples, in one of my next posts.

Did you know... that by unifying those different... uh... non-tertian harmony ideas and tertian harmony ideas.. (which... um... some aren't non-tertian at all)... you would just be, theoretically, utilizing different techniques at different times... or by whatever is the functional harmony... utilizing one technique with coloration... since most things are... uh... clustered anyway. Geeze... this is just really stupid.

It doesn't make sense. If you don't have any examples before you show yourself... as in MULTIPLE, TESTED examples... well.. then you obviously didn't think that much about it.

This thread can be knocked out with one word

POLYTONALITY

Alright, game's over, do not pass go, do not collect $200, STICK A FORK IN IT, IT'S DONE BYE!

:(

This thread can be knocked out with one word

POLYTONALITY

Alright, game's over, do not pass go, do not collect $200, STICK A FORK IN IT, IT'S DONE BYE!

:(

Wait

Wait

Should've followed your own advice, eh? Next time, write stuff, THEN make a thread about it!

With regard to the axiomatic side of the isocord theory, there's "stuff" written enough. On the other hand, the deductive side of the theory can be explored almost endlessly

Meanwhile I've prepared a comprehensive survey of the isocord theory, combined with some musical examples for exploration and improvisation. However, in its essay form it would be more appropriate for publishing it in [[Category:YC Music Articles]] (not yet done, however). Therefore I'll only pick particular topics from it for further discussion.

So let's go with an illustrative example.

Here you find some isocords which show interesting similarities. Take the first chord, Gb-Eb-C-A, built on the major sixth interval, the major 6ths isocord (M-6ths for short). Measured in semitone steps, the four notes are 9 semitones equidistant to each other, noted 9–9–9 (three major 6ths, yielding 4 different tones). There exist three transpositions of Gb:9–9–9, in which the intervals remain the same (besides enharmonic re-spelling, e.g. in the first transposition of Gb:9–9–9). As can be seen in the second bar, inversion of this M-6ths results in the minor 3rds isocord F#:3–3–3, which happens to be the well-known diminshed seventh chord of traditional harmony theory. It has also three transpositions which are likewise the inversions of the respective M-6ths tranpositions (again with some enharmonic re-spelling).

With respect to the constituent tones, there are only three different M-6ths isocords in the 12-tone system of western music. Similarly there are also three different m-3rds isocords, which are versatilely used for common practice modulation: By suitable enharmonic re-spelling you can modulate into four different keys with a single m-3rds chord, and with all three m-3rds you can achieve all possible 12 keys of our tone system (suitable enharmonic respelling provided). Nevertheless, you may start with any other tone than the three examples, but the resulting M-6ths will be some transposition of these examples.

A special case of transposition arises when an isocord has less than its maximum number of tones, e.g. in the 3-tone M-6ths in the following example.

Strictly speaking, a regular transposition of an incomplete isocord isn't possible, since the symmetric structure gets lost: Eb:9–9–9 transposed upward would result in A:6–9–9. The solution to this problem is to do a pseudo-transposition: Add the missing tone(s) of an isocord (without raising the number of voices/tones) and then do a regular transposition. See how it is done for the three M-6ths above.

Another question concerns isocords which are necessarily incomplete because of unplayability of some of its tones (basically, this affects the M-7ths with ultimately 12 tones – its range would extend to nearly 11 octaves). There's only a pragmatic solution possible: Repeat the isocord on the basis of a pseudo-transposition including the missing tones.

These examples show, that on the basis of transposition and inversion there's a rich variety of interrelations of chords: Structural relations by the build-up and sound relations by the tone composites of isocords.

As an exercise, do similar transpositions and inversions with some other, less-tones isocords, e.g. M-2nds, M-3rds, and the tritone variants (which are of particular interest in 12-tone music). And then start some improvisation with these isocords – there's no limit to your creative imagination!

For your information I've uploaded an outline of the isocord theory

I think I speak for mostly everyone who may have an interest in this potentially when I say:

Until you have at the VERY LEAST a couple of actual finished pieces using this system, nobody will care.

So, go write some music instead of posting all this theoretical scraggy.

For your information I've uploaded an outline of the isocord theory

I do agree with SSC on this.

I think if you'd like to propose any new theory, or even a personal method, that you should, as SSC has said, be a CREATOR with that theory first and foremost. Right now, you explain the theory in an ex post facto way. Theory arises from explaining things in hindsight. Even if this is just a theoretical way of composition, the only way to tell if it is a valid way, or in more acceptable terms, a way that works is to utilize it.

Well Schoenberg was notorious for coming up with the 12 tone theory before actually using it. However, he DID use it quite a bunch, as did others. Nobody at any point forgot that they were actually talking about writing music instead of just playing theorist.

Well Schoenberg was notorious for coming up with the 12 tone theory before actually using it. However, he DID use it quite a bunch, as did others. Nobody at any point forgot that they were actually talking about writing music instead of just playing theorist.

That's exactly who I had in midn when typing what I did! :)

And yes, they were trying to write music instead of playing theorist. That's why I emphasized the word creator in my reply to Hansen. I hope he can move forward with his thoughts.

I hope Hansen can make something unique from his theoretical 'meanderings'. Sorry, I mean no disrespect with that, but this sort of panders between the very general tonal and atonal realms of music. There's a LOT of specificity within these realms to be cherished or appreciated. Let's be honest. This is the break down of the theory: build chords by rigidly following some equal proportion rule, invert them if you choose, and go make music. That's about it. It's so general, there's no uniqueness to the theory, nothing that makes music produced this way sound unique from, say, well anything.

Tonality is very distinct. 12-tone Serialism is, too. They're unique, generally, because the underlying approach is very different. Tonality is a functional process of creating a harmonic center we hear as "home" and manipulating the surrounding harmonies to delay or postpone our arrival to "home." Serialism is ENTIRELY different. The theory behind this is exploring pitch and interval relationships, not necessarily harmonic unity or a preparation for arrival to a certain harmony. This yields a completely different sound.

What is the APPROACH to using isochords in making music that sounds like ISOCHORDAL MUSIC? Again, the theory "may" apply to both tonal and atonal compositions. You may be able to derive a new sound from mixing elements of ISOCHORDAL MUSIC with other brands like Serialism, Spectral Music, Post-Romantic, etc. But ISOCHORDAL theory isn't going to stand alone if it relies on these forms to justify its use... just because it COULD be applied to other forms of music doesn't mean it SHOULD be applied. Instead, what you have to do is level your approach against the objective of making original sound.

When you do that, come back and report your findings. THAT'S THEORY.

What is the APPROACH to using isochords in making music that sounds like ISOCHORDAL MUSIC? Again, the theory "may" apply to both tonal and atonal compositions. You may be able to derive a new sound from mixing elements of ISOCHORDAL MUSIC with other brands like Serialism, Spectral Music, Post-Romantic, etc. But ISOCHORDAL theory isn't going to stand alone if it relies on these forms to justify its use... just because it COULD be applied to other forms of music doesn't mean it SHOULD be applied. Instead, what you have to do is level your approach against the objective of making original sound.

When you do that, come back and report your findings. THAT'S THEORY.

Agreed.

So far this discussion is about the status of the isocord theory. Let me clarify as I do see it.

Generally, a theory can be either descriptive to explain existing facts or prescriptive to explain producing (new) facts

IsocordalPiece(mm1-9).pdf