Hello!

If you would like to participate in discussions, please sign in or register.

Sign In with Facebook Sign In with Twitter

In this Discussion

Most Popular This Week

    Introducing: A new alternative standard for Chord identification

    I have just finished set up a web page to introduce one of my research on Chord.

    The idea is to collect all possible musical note combination that can be used as chord and scale. I'm using mathematical approach (permutation) to calculate the result and I also have created Javascript code to generate all combinations (chords). The whole result offer a new alternative standard for Chord identification.

    Please visit the page at my website for details: Harmony System

    I also invite whoever that might be interested to join the development of the system. 

    Any suggestion are welcome.

    Regards,

    Sign In or Register to comment.

    Comments

    • 15 Comments sorted by Votes Date Added
    • Ronald,

      Glancing at your webpage it looks like there is a lot of re-inventing the wheel going on here: the objects of your system are ordered pcsets (or Tn-type set classes). What is novel is just the system of nomenclature, but there were well-rehearsed reasons for adopting tonality-agnostic systems of nomenclature in pcset theory. This is something that was hashed out in the 60s and 70s in American music theory. I can see virtues to more tonality-based systems of nomenclature, but it seems to me the assumptions that could be brought to bear to substantiate such a system would mitigate against certain other assumptions you make: enharmonic equivalence and the simple combinatorial any-collection-of-notes-is-possible assumption.

      —Jason

      --Jason Yust

       

    • I use a somewhat simpler system and classification that allows me to process muscal information faster. I differentiate between intervals and chords. A chord must have at least three notes. Theres are only 5 prime chord types (from which all other chord types are built): major, minor, diminished, augmented, and suspension. This works well for the gamut of traditional chords including jazz language. 6ths, 7ths, 9ths, 11ths, 13ths, can be added to any of the 5 prime types. Suspension primes may contain one or more suspension within the triad (0, 2, 8) for example.

      On a more abstract level I still like to differentiate between interval and chord. A chord being any three pitch classes as a prime unit - any three pitch classes can form a chord at the simple "triad" level (0, 2, 4) for example. Thereafter harmonic "chords" increase in density and complexity similar to a comparison of Hydrogen atom and Uranium atom - the Hydrogen atom has a simple structure of a few electrons in comparison to the Uranium atom's many electrons. Harmonic chord structure has the same outcome - either simpler or more complex sound density.

      Don't Strauss and Rahn cover a comprehensive listing of pitch class sets in their books on Post Tonal Theory? Haven't those possibilities already been codified?
    • Hello Ronald,

      A few years ago I've written a somewhat similar program which uses all possible permutations but limiting them by length of the chain of fifths for any chord and limiting the succession of chords (also in chain of fifths) and limiting the highest and lowest note.

      Here is a link to a few results of this program. Completely computer generated music (nothing serious though, just a little experiment which took me a week or so to write, but perhaps you will still find it interesting)

      https://soundcloud.com/justintonation/computer-composer-first-test

      https://soundcloud.com/justintonation/computer-composer-third-test



      What I do think about using your particular system for chord classification is that you seem to allow no intervals more remote than a diminished sixth and augmented third. (G# - Eb and Eb - G#).

      There may be very good reason to believe that indeed any interval more remote than this should always be classified as a nonchord tone. I myself think this is most likely the case and has a foundation in how our brain handles chords.

      Yet I'm curious what lead you to this decision?

      As far as I know most theory books currently very much leave open the question on any limit.

      (I will take a better look at the specifics of your system later, but very interesting!)

      Kind regards,

      Marcel de Velde

    • Hello Ronald,

      Sorry, I should have read your page one more minute before answering. It's now apparent to me that you do not make any distinction between enharmonics?

      It's my personal opinion that making a chord naming system based on enharmonic equivalence is not a good thing in music. You may feel free to disagree of course :)

      But to have a naming system which does not distinguish between for instance a German sixth chord and a dominant seventh chord is to do away with a musically very important distinction.

      Kind regards,

      Marcel de Velde

    • Thank you everyone!

      I'm sorry, I forgot to mention the reason why I started this. I started to do the research because:


      1. Nowadays, composers/songwriters/musicians demand more resource for their music. They then begin to experiment to find unique music with progressions, rhythm or a new harmony. The harmony list is to give them more ideas.

      2. In high level discussion about harmony, there always strong debate on chord identification and its function.

      So I started to collect all possible note combinations. The chord name will still need a hard work, that's why I'm still looking for help. But the chords are already coded to make the process easier.

      In this case, the harmony system don't rely on particular genre or style, it listed harmonies mathematically and named them with just simple logic. This way we can get more general field such as popular music.

      There are 1485 possible combinations per root; theoretically, this number is 'absolute', no more combination outside the list. We will find any type of chord on the list. But not all of them can be good in music composition as many of them will make extreme dissonance sounds. 

      However, we can sort the combinations in the list to: 'usable chord', 'used chord' or 'impossible chord'. So we give a name to chord that music can use as chord or scale, and keep the rest remain unnamed, but all chord/scale are documented and has a code. Whenever needed, we can just use its code to identify a chord.

      ..

       

       

    • I use a somewhat simpler system and classification that allows me to process muscal information faster. I differentiate between intervals and chords. A chord must have at least three notes. Theres are only 5 prime chord types (from which all other chord types are built): major, minor, diminished, augmented, and suspension. This works well for the gamut of traditional chords including jazz language. 6ths, 7ths, 9ths, 11ths, 13ths, can be added to any of the 5 prime types. Suspension primes may contain one or more suspension within the triad (0, 2, 8) for example. On a more abstract level I still like to differentiate between interval and chord. A chord being any three pitch classes as a prime unit - any three pitch classes can form a chord at the simple "triad" level (0, 2, 4) for example. Thereafter harmonic "chords" increase in density and complexity similar to a comparison of Hydrogen atom and Uranium atom - the Hydrogen atom has a simple structure of a few electrons in comparison to the Uranium atom's many electrons. Harmonic chord structure has the same outcome - either simpler or more complex sound density. Don't Strauss and Rahn cover a comprehensive listing of pitch class sets in their books on Post Tonal Theory? Haven't those possibilities already been codified?

      I too use the basic to sort the listed chords with conventional chord naming rule. It's an interesting analogy with the Hydrogen =) Permutation is also a powerful combinatorics system.

    • What I do think about using your particular system for chord classification is that you seem to allow no intervals more remote than a diminished sixth and augmented third. (G# - Eb and Eb - G#).

      Yes, this is to prevent complexity and confusion on the chord naming process. All chords begin from the triad (1, 3, 5). The first modification on the triad is: minor, suspended, augmented and diminished chords. The 3rd change to: 2, 4, 2b and 4# (suspended chords) and b3 (minor). The 5th change to: 5b and 5# (augmented). But of course many of the chords will demonstrate wider interval sounds.

    • Hello Ronald,

      Sorry I'm a bit confused I think.. On the one hand you state you use the notes Eb to G# as a basis. And then after reading more I got the impression you use note names with enharmonic equivalence. And then I see in your list chords like C-Gb-G# which spans far beyond a chain of 12 notes connected by 11 perfect fifths.

      So is this a bug in your list or are you semi randomly using note names and is your system based on enharmonic equivalence as it's basis (so a Gb = F# = Ex = Abbb)? I get the impression it's the latter?

      And if this is indeed the case, do you not feel this is incompatible with current theory and notation where the enharmonic distinction is made? I think this would cause more confusion than it would possibly clear.

      Kind regards,

      Marcel

    • Hi,

      (I'm sorry for the delay, I had to reinstall the browser)

      I mean the basic is the triad of root, 3rd and the 5th. To think of a chord name, I always look for changes that affected the 3rd and 5th note.

      The system differ enharmonic equivalence for the naming process. 5b and 5# used when the neutral 5th affected like in Caug (C E G#) and Cb5 (C E Gb). When the altered 5th exist while the neutral 5th does too like Csus#4 (C F# G), then "F#" is used with understanding that the chord has altered third and the 4# not come from the 5th, so it's not a Gb.

      In case that the 5th doesn't exist while both altered 5th does like in combination {C, Gb, G#}, we need to choose its main form first, it's either Caug or Cb5.

      Combination {C, Gb, G#} is not a bug, it's the part of the permutation. The point is we may never use chord like this but the combination does exist, further step is to choose wether it can be considered as main chord or not. (but we can't restrict composer to use it either)

      And the chord names on the system are not final. It still need more hard work to get proper name that can be acceptable in theory.

       

    • That's true! This is more like a set theory. The main goal here is to collect all combinations and then sort them to have a list of 'reasonable' chord and scale. All note combinations has been generated and is possible indeed, this is the general statement. But there will be further classification to implement chords in vary style of music. 

      The combination list generated first with integer (1-12), once completed, the numbers were translated to note names. It does not need to differentiate between enharmonic equivalents on this step, but when the enharmonic name options required for particular need in music (such in the chord naming process), then the name will need adjustment.

    • Well if I may make a suggestion.. I would make the basis for the permutation the perfect fifth, not the triad. This is a much more logical, consistent and musical method in my opinion. It also matches normal music theory much better.

      I would also increase and limit the permutation"level" by perfect fifths / chain of fifths length.

      So for root D the first permutations would be D-A and D-G, the second "level" would be D-A-G, D-E-A. D-G-C, D-E, D-C, etc.

      This is what I did in my algorithm, I did not model in any other musical rules or rules for consonance etc. And the results are still somewhat musically logical even though I switch between random permutations of chords up till a certain complexity level / length of chain of fifth. Try doing this with any other permutation system and the result will be non musical random notes.

      Here two more examples of the output of this algorithm:

      https://soundcloud.com/justintonation/computer-composer-second-test

      https://soundcloud.com/justintonation/computer-composer-fourth-test

      Even somewhat musical melody arrises automatically in this system by succession of random permutations limited in complexity. Also this system does not require one to assume enharmonic equivalence, it is perfectly consistent with regular spelling practice and theory.

      The reason I find what you're doing interesting is that I've been thinking about adding a naming system to my permutation system. Will have to get to that eventually (though I'm working on other things currently). Would be very nice if something acceptable and usefull to all came from this discussion. Do you see any merrits in the system I describe above?

      Kind regards,

      Marcel

    • Well if I may make a suggestion.. I would make the basis for the permutation the perfect fifth, not the triad. This is a much more logical, consistent and musical method in my opinion. It also matches normal music theory much better.



      I would also increase and limit the permutation"level" by perfect fifths / chain of fifths length.



      So for root D the first permutations would be D-A and D-G, the second "level" would be D-A-G, D-E-A. D-G-C, D-E, D-C, etc.

      ..

      Even somewhat musical melody arrises automatically in this system by succession of random permutations limited in complexity. Also this system does not require one to assume enharmonic equivalence, it is perfectly consistent with regular spelling practice and theory.

      What does it mean by make the 5th as base and 'limit' the permutation 'level' by perfect fifths? would it make the whole list incomplete?

      Even the chords generated by permutation are considered as 'nonchord' combination, we can still documented them and composers can still use it. We take all and then sort chords for different needs in music.

    • Hello Ronald,

      The list would not be incomplete when based on the chain of fifths. It would get a different order. The chain of fifths (and octaves) is the principle behind our western notation system and with it most of our theory. I've done research in this area for the past 10 years and I can say that this corresponds to how our brain handles the musical pitch space.

      Here 2 images of this pitch space:

      It's the same space in both, just displayed differently.

      In the images the chain of fifths length is 17 (17 tones linked by 16 perfect fifths), going from Gb to A#. You can limit the length of the chain of fifths to your choosing. If we take 5 we get the pentatonic pitch space, if we take 7 we get the diatonic pitch space.

      The current chord naming system is based on the pentatonic pitch space (F-C-G-D-A-E-B) which is then handled in thirds, for instance in C major: C-E-G-B-D-F-A corresponding to root C, 3rd E, 9th D, etc. So our naming system is actually a particular form of permutation of the pentatonic system. Something which you tried to base on the major triad yourself to base your permutation system on.

      I suggest basing it purely on the chain of fifths by simply lengthening the chain of fifths instead of this augmenting / diminishing of the diatonic system. While this goes very easily in generating a more coherent ordered space to find/generate chords, it does go against the conventional naming system. So I was wondering what would be a preferred naming system for chords. Still go with the "diatonic + thirds" based system, or perhaps something more in line with extending the chain of fifths would work better. I don't know.

      Kind regards,

      Marcel

    • Btw, if you were to take 12 as the limit for the chain of fifths length, then you would not get a chord like C-Gb-G# like in your current system. Though you'd get C-Gb-Ab and C-F#-G# and C-F#-Ab.

      What's also good is that you would get the clear distinction between a dominant 7th and a German sixth if you do not artificially impose enharmonic equivalence afterwards.

      And furthermore. I personally use a definition of root where I see the root as not a single note but as a perfect fifth interval. And relative to that root I personally have the opinion that only intervals up to an augmented fourth and minor second can serve to form a true chord with that root. Any intervals more remote I designate as nonchord tones. This has come forth from personal research and is not solidly "proven" to be a limit of our brain, but I do have fairly strong "hints" in this direction. And it is also a form of definition, where to draw a line. In any case, this is not normal theory, but for me it works better.

      Here is an example of all intervals that can form a chord with root C-G: C-Db-D-Eb-F-F#-G-Ab-A-Bb-B-C. There is no difference in major or minor for this, they both exist within this. The chain of fifths is unbroken from Db to F# for root C-G. Any intervals more remote than this cannot be interpreted as such but have a closer enharmonic equivalent interval which is part of the Db to F# chain, this is why when the chord is heard in isolation we cannot hear more remote intervals relative to this root, minute tuning differences if we were to tune the intervals pure are not strong enough to convince the brain otherwise, the brain goes for the more simple interval interpretation regardless. We need context outside the chord to create the circumstances where we can hear more remote intervals relative to this root, but this is why I designate them nonchord tones. They do not come from the context of the root of the chord but from other chords instead, and if we were to hold the chord as for instance a final chord then also the more remote intervals will not survive but become interpreted as the simpler enharmonic equivalent interval.

      One of the results of the above way of defining root is that for instance a German sixth is no longer a chord as it is currently defined. We need to see it as either having a nonchord tone (the augmented sixth above root) or as being an inversion of a different chord. In this case seeing the third of the German sixth as the root is most likely (C-Ab-C-Eb-F#) and actually makes a lot more sense (as has already been written about by other theorists).

      Kind regards,

      Marcel

    • Hi,

      Thank you, I will go for further study on this. But I feel like working on the circle 5th is 'the next step' of the harmony system. The permutation I made collects all possible combination and named them with conventional chord naming rules, and go for the spesific circle fifth is kind of sort the list by seperating enharmonic equivalent elements.

      Spotting the changes of the 3rd and 5th from basic triad is important for identification of the whole combination list. How the chord naming process based on chain of fifths would be?

      Dom7th and German 6th chord has different name and functions but consist similar combination: in C (C E G and A#/Bb). The harmony system try to be more general.

      In the harmony system, level 2 chords are limited to additional 6th (in C: A) and b6, because when higher note than the 6th added, it will form a 7th chord. So German 6th doesn't exist as a name, augmented 6th has changed to a standard name which is: dominant 7th. This will lead to contradiction in analysis, is it an altered pre-dominant or it is a dominant.