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

    Functional Interpretation of the Tristan Chord

    edited March 25 in Theory

    Dear colleagues,

    Some musicians have written long articles or even books about the Tristan chord, they plunge into a jungle of linear connections and interpret it in a very abstract way, making a big deal of this sonority. However, apart from the multidirectional potential of the half-dim. 7 per se –something that Wagner explores to a certain extent throughout the prelude, the opening chord may have a simple interpretation. I am offering you two interpretations of it, beginning with the simpler one.

    1. If we consider the tone G# an appoggiatura, then the chord is not half-dim.7, even enharmonically. Its structure only crystallizes in the next moment, when the appoggiatura resolves into the tone A. Then we can hear the chord B7-5 in second inversion as a double dominant with a lowered fifth (V7-5 of V) in the key A minor. This interpretation is confirmed by the resolution into the E7 chord (elliptical resolution). Thus the progression B7-5 – E7 will be heard as DD 4/3 alt.- D7 in the key A minor. Yes, the altered dominant contains an augmented sixth, but the geographic nickname "French" is irrelevant to harmonic function anyway.

    Jazz people will hear the chord as F7-5 instead of B7-5 and will call it "a tritone substitute for V of V" but this is just another way of labeling an inverted and altered dominant of the dominant. Whenever they write bII7-5 of....they shall be aware that the true meaning of this chord is V4/3 (b5) of...because these chords are enharmonic.

    2. If we do not consider the gone G# as an appoggiatura, then the sonority F-B-D#-G# coincides enharmonically with F half-dim7, and may be interpreted as an altered and inverted DVII7 in the key of A minor: VII2 (with a raised fifth). Here the half-diminished seventh chord is reinterpreted as a chord of the augmented sixth. When this chord is placed in root position, it reveals G#-B-D#-F, stemming from the VII dim7 chord, whose fifth then is raised. This interpretation is not so natural, because it ignores the appoggiatura, but the sequence DVII2 alt – DD 4/3 alt – D7 makes sense (two dominants of Am surrounding a double dominant).

    Not a big deal. As for other resolutions of the half-dim. sonority that reveal other interpretations as a true altered chord, yes, one could write a whole chapter about them.

    Thank you,

     

    Dimitar Ninov

    Texas State University

     

     

    Sign In or Register to comment.

    Comments

    • 17 Comments sorted by Votes Date Added
    • Thanks Dimitar,

       

      I agree more with  the 1st interpretation, I hardly see the 2nd one.  

      In any case the so called french sixth can not  be seen also as a DD4/3 with 5b (or alt) ?  Nothing new. What I knew if that composers of  '800 started to interchange between  the two interpretation of V7 as italian/german sixth (and viceversa) and the french sixth as V75b (and viceversa). That is the real origin of the triton substitution. I can  remember now an example from Schubert Sonata op 42, I.

      The G# is the origin of the 'fog' , such a timbral character,  with tonal ambiguity, starting any debates. 

      Wagner himself indicates the solution, with the semitonal movements he demonstrates that the 3d of a sounding half-diminished 7th,  can be interpreted as the appoggiatura of a french sixth, at least in the specific context of a minor. 

      Thanks and best regards

      Diego Dall'Osto

      Conservatory of Music - Vicenza (Italy)

       

    • Thank you, Diego,

       

      If you get rid of the geographic nicknames which bear no reference to harmonic function, all that remains in this context is D4/3 (b5) of D...

      I doubt it if in the near past the French knew what a French chord was, The Italians - what an Italian chord was, and The Germans - what a German chord was. Perhaps they have been introduced in this geographic realm by the Americans. It is like the so-called English muffin that is sold in the coffee shops the US, but no one in England knows what an English muffin is...or like the French Fries and the French horn, etc....:)

      The mentioned geographic nicknames reveal either altered subdominant chords (dominants of the dominant) or altered dominant chords. Thus, when you lower the fifth of V4/3 it does not cease to be a dominant, neither does it loose its root...This is why I am amused when someone analyzes V4/3 - I correctly as D - T and then suddenly loses his/her memory when, in the next moment, this V4/3 appears with a lowered fifth. Such musicians are usually confused in the midst of various altered chords that do have a diminished third/augmented sixth, but do not match the conventional geographic description. The only things that they can do is describe them as "linear" and leave things like that. But "linear" is not always an equivalent of "non functional", and great pages of music are left unattended because of the inability of the analyst to identify chromatic chords. For example, the Chopin prelude in E minor.

      Having said that, I do use geographic names when I teach altered chords to my students (right now) because of the tradition in the US, but we also use Roman numerals and explain the function of the chord in context. Otherwise, it does not make sense. The "rootless" claim is very funny when it comes to chords which are so sharp and characteristic modifications of diatonic S and D, that you cannot get it better, especially in four parts.

    • Thanks Dimitar,

      I agree that the nominal question about  geographical nicknames is not very interesting. In fact  is quite natural that the same phenomena can be called differently in different periods. Similarly for much musical vocabulary.  Did Neapolitans  knew about their own 6th chord?  who called this way at the time ?  This is not the relevant question obviously. Names are labels to identify things, just so. And 'functions' are names too, indicating some kind of relations, helping a lot, but not explaining any possible questions.

       

       

    • Dimitar,

      I am one of those who spent six months of my life trying to understand the game plan of the Tristan Prelude and ended up writing a 10,000 word paper that no one wants to read because reading about theory is narcoleptic. At any rate, I am amused that so much time and effort has been devoted to the Tristan chord without appreciating what precedes it. The opening A-F-E cello line predicts D minor so, when the chord enters, we are shocked by the juxtaposition of a ii7 in E flat minor (a tritone away from the supposed key of A minor). What we expect next is a B flat 7 and a cadence in E flat minor but that is not the game Wagner is playing with us here. He saves that ii-V for the climax. What he does here is morph the Fø with a upward semitone motion and the harmonic function shifts dramatically to a B7b5 in the second inversion that resolves correctly to the dominant of A minor. Once we understand that harmonic material on the downbeat is rarely the real chord, and we have to wait until the end of the measure to know what's what, the syntax becomes clearer.

      Wagner must have had a good sense of humor because the theory joke comes at the end of the prelude when the Tristan chord reappears above a timpani roll on G so the chord now become Gb9#5, the dominant of C.

      He may have been the first composer to pose the musical question, "When is a chord not a chord?" which sounds a lot like his contemporary Lewis Carroll.

      Best regards,

      Steve Jablonsky

      The City College of New York

       

       

       

    • Hello Dimitar,



      I had started a thread about the Tristan chord 2 days ago only to delete it again after realizing it's a more tricky chord to analyze than appears at first and there was a good chance my interpretation was incorrect. I have therefore spent a good 2 days looking at this very chord and will share my views.

      I did consider the G# an appoggiatura at first. But I have actually changed my mind on this. I think it must be a chord tone. To me this actually excludes F as the bass. F as the bass would give an aug9th aug11th chord. In my opinion the augmented ninth is always a nonchord tone (even if not described as such in tonal theory, I have my own opinion on this which I won't elaborate on now). If a chord tone it would be an Ab in my opinion (this could work in jazz btw) and I think can hear clearly I'm hearing a G#, a true leading tone to A. Btw, if G# were to be heard as an appoggiature then still I no longer think that F is a likely bass. It would also mean that the D# is actually an Eb. Like this: F B Eb G# -> F C Eb A -> E B D G#. The Eb goes down to D in this interpretation it would not be a D#. But, in Tristan und Isolde prelude the B does not resolve to C first. And I think related the case for G# being a extremely long held appoggiatura is weak.

      As for enharmonic equivalent interpretations. I don't think this is a good way of interpreting chord without writing out the new interpretation. F half diminished gives a Cb for instance. Cb in the key of A, can this even exist? I don't think this interpetation makes sense. It can indeed be seen as a tritone substitution. Similar to how a tritone substitution of a dominant seventh chord preserves the tritone, G B D F (dom7) becomes Ab B Db F (German sixth chord), preserving B F, the Tristan chord can be seen as a tritone substiution of the subdominant sixth chord of A minor (the mirror chord of a dom7): D F A B becomes D# F G#  B which if you put F in the bass is the Tristan chord F B D# G# (the mirror chord of a German sixth chord).

      Another interpretation that works both when seeing the G# as a chord tone and as an appoggiatura is to see the chord as a subdominant chord. (D) F B Eb G#. However this doesn't seem like a perfect fit to me either, If a subdominant chord with b9 and aug11 then the b9 should be able to resolve in a natural sounding way together with the aug11 going to the fifth. Doesn't sound fitting to me though.

      Another interpretation would be to see the chord as a first inversion dom 9th chord on C# giving: (C#) E# B D# G#. This one actually sounds very natural and good to me (play it on the piano with that extra C# in the bass). The progression to the E dom7 chord is then a mediant relation. However, this doesn't make much sense anymore in the key of A minor, it would be fitting to for instance the key of A major. It doesn't strike the same feeling of tension anymore and that somewhat minor colour it has. I think to play that extra C# in the bass changes my interpretation of the chord.

      Another possibility is to see it as a long streched out dominant chord all on E. But I don't like this interpretation either. One little trick we can always use is to play assumed root of the chord below the chord. If we play E below it looses a lot. That G# may or may not be a chord tone, it does sound resolving when moving to A, if E were the root it doesn't resolve at all as A is a fourth above E. I greatly would prefer to see it as a modified subdominant as described earlier than to see it as a modified dominant chord.

      And now one of the final ones that make sense to me. To see it as a tonic chord! Root A, giving: A F B D# G#. Here the G# can be a chord tone, the major seventh, yet it resolves to the tonic A, the F is a minor sixth which wishes to resolve to E fitting to how I hear this tone, the B is a major second wishing to resolve to the minor third C, and D# is the aug11 wishing to resolve to E. All the tension the chord has to me fits this interpretation. The progression to the E dominant 7th chord is then natural as well, a simple perfect fifth progression from tonic to dominant.

      To me, these two make the most sense (at the moment), a tonic chord or a subdominant chord.

      -Marcel de Velde

    • I think one of the things that make the Tristan chord so hard to analyze is that we're so used to chord tones being in consonant stable positions relative to their root. The third and fifth, with the seventh already having some tension. The Tristan chord however is all tension, possibly every single tone is longing to resolve! This is the magic of Tristan und Isolde. I've analyzed about the first 30 measures or so and this is featured throughout, tension longing to resolve. The Tristan chord isn't even the most crazy chord, for instance in measure 11 we find this chord: C F G# D resolving like this -> C F G# D# -> C E G# E -> B D# A E# -> B D# A F#. I think the spelling is probably actually correct.

      Yet somehow Tristan und Isolde does not sound at all like wild chromatic music but instead sounds like standard even almost simple very tonal music to me, with the exception that it has tension all over longing to resolve. I think this is the result of mostly simple perfect fifth based root progression and as mentioned before the tension is created through extended chord tones (and suspensions of course).

      -Marcel de Velde

    • Dear Diego,

      Thank you. The difference between Neapolitan and the French-German-Italian packet lies in the difference between historic tradition and local speculation. The name N comes from the city of Naples where the Phrygian Subdominant on the second degree was introduced systematically in the opera music of the opera composers. The nickname was formulated later, of course, this is normal. However, no one can say precisely on what historic tradition American theorists leaned when they decided to give the world the labels French, German and Italian. I suspect Europeans are not aware of such tradition, and this made me refer to the English muffin, French fries and French horn.

      Secondly, the names of T, S, and D have developed as an attempt of 18-19th century scholars to describe the levels of stability and instability through which harmony breathes. These are universally accepted names which may comprise chords with different structure that could be either diatonic or altered. When you say the word "Subdominant", you know that this is a chord that brings concrete level of instability towards the tonal center, has a clear acoustic connection with it ( a 4th or a 5th apart), and lacks intensity. Therefore, this is not a concrete nickname but a general category which describes how numerous similar chords behave towards the tonal center.

      When you say "German", on the other hand, you do not know what the role of the chord is in tonality: it can be a dominant chord if it contains the leading tone, or it can be a subdominant chord if it contains the root of the chord of resolution. Let us take the chord F7, for instance, which appears in the key of C major and resolves like an augmented sixth chord into four different directions: A/a, C/a, E/e, and C#m. The label "German of scale degree three" is totally irrelevant to the different roles (functions) the altered chord performs in these different occasions. If you were a professor of harmony, how would you explain those functional nuances to your students - just by saying the word "German"?

      This why it is wise and practical to have three main harmonic functions in the tonal world, but it is impossible and nonsensical to give nicknames to all the chords in tonal music.

      Best regards,

       

      Dimitar

       

    • Dear Steve,

       

      Thanks. We know that occasionally a melodic line may imply one key but could be harmonized in another. However, in the opening melodic line I hear an implied A minor, not D minor, even if it were a naked melodic motif.

      The ascending leap A-F at a minor sixth followed by a half step repose downward to E naturally implies the key A minor which is supported by the harmony as well. You could possibly hear the sole melody in D minor, but the basic melodic line is A-F-E-D# (not Eb). This D# points back to the tone E, but later moves elliptically downward to D for harmonic reasons: B7-5 resolves elliptically into E7 and the leading tone moves down to the seventh of the next chord, which is very common in a chain of dominant sevenths. I think that is the philosophy of the opening.

      I agree with you that the complex F-B-D#-G# may be very easily interpreted enharmonically as an incomplete V7+5-9 in C which is the most exploited altered dominant in jazz. If C is not present, the chord may also be explained as VIIdim7+3 which is the little altered dominant.

      This is why in my initial announcement I made the disclaimer that one could write long pages on the functional metamorphoses of the half-diminished 7th sonority in general, and on its applications in Wagner's prelude in particular. But my posting only concerned the initial progression.

       

      Thanks,

       

      Dimitar

       

    • Dear Marcel.

       

      I will reply to you later in the week, when I have read carefully what you worte. For now I can say that there is no problem in the tones F and G# being in the same chord; F is a bass tone, it is not the root of the chord.

      The chord coud have different roots as long as the acoustic half-diminished sonority may be interpreted in a variety of ways: as a diatonic chord or as a true altered chord, complte or incomplete. For example, if you do not like the idea of appoggiatura (which I still prefer), you may take a look at my second interpetation: G#dim7 with a raised fifth is an altered dominant on the seventh degree in A minor. In C major this same complex will be B dim7 with a raised third (spelled with Ab) which is an incomplete V7+5-9.

       

      Best regards,

       

      Dimitar

    • Dear Marcel.

       

      I will reply to you later in the week, when I have read carefully what you worte. For now I can say that there is no problem in the tones F and G# being in the same chord; F is a bass tone, it is not the root of the chord.

      The chord coud have different roots as long as the acoustic half-diminished sonority may be interpreted in a variety of ways: as a diatonic chord or as a true altered chord, complte or incomplete. For example, if you do not like the idea of appoggiatura (which I still prefer), you may take a look at my second interpetation: G#dim7 with a raised fifth is an altered dominant on the seventh degree in A minor. In C major this same complex will be B dim7 with a raised third (spelled with Ab) which is an incomplete V7+5-9.

       

      Best regards,

       

      Dimitar

      Hello Dimitar,



      I'm looking forward to your other reply.

       I agree there's no problem with F and G# being in the same chord. What I meant earlier is that I personally have a problem with it if we were to see F as the true root of the chord and G# as a true chord tone. There would be no problem with G# relative to the root of F either if G# were an appoggiatura which is a form a nonchord tone.

      I know that many would allow a G# as a chord tone relative to a root of F as an augmented ninth. The reason I don't personally see it that way is a personal unconventional theory which I don't expect anybody here to agree with. I personally think that the true root always implies a perfect fifth above it and that only the minor and major intervals can be true chord tones relative to that root with the addition of the augmented fourth but not the diminished fifth. In this way I can see an augmented ninth chord as having the augmented ninth as an accented or unaccented nonchord tone or as having a different root altogether. The most controversial thing to come from this way of seeing things is perhaps that I do not see the diminished chords as having the same root as regular theory analyzes them as I do not see the diminished fifth as a possible chord tone relative to my concept of root. Instead I usually analyse them as a dominant 7th or 9th chord with omitted root or minor subdominant chord with added sixth and omitted fifth. (This will actually work and even makes some sense as to why the "root position" diminished triad sounds so bad in root position and is usually avoided, but it does sometimes make communicating about analyses such as these a bit harder. Sorry for that.)

      -Marcel de Velde

    • Yes, perfect fifth root progressions are at the bottom of some of those harmonic relationships. If you think B7 resolving into  E7, that is the diatonic basis of the beginning. Just lower the fifth of the first domiant and suspend a major sixth over it, then resolve that sixth first, and then the whole dominant. As we already mentioned, the bass note F is not the root of the chord; it is its lowered fifth.

    • Yes, perfect fifth root progressions are at the bottom of some of those harmonic relationships. If you think B7 resolving into  E7, that is the diatonic basis of the beginning. Just lower the fifth of the first domiant and suspend a major sixth over it, then resolve that sixth first, and then the whole dominant. As we already mentioned, the bass note F is not the root of the chord; it is its lowered fifth.

      I understand this analysis. But as I explained before, I have a different concept of what constitutes the root of a chord. I do not think one can simply stack thirds, the augment or diminish some of them, and this gives the root. I think that the root always implies a perfect fifth above it which cannot be diminished. Often this will not give problems in communicating about analysis, but in this instance it does of course. Sorry about that. But I personally can't see it as a chord on B with a diminished fifth.

      After spending yet more time with it my preference goes out to seeing it as an iv6 chord , with an Eb (b9) instead of a D#, an added sixth B and an augmented fourth (A#) that one can see as an appoggiatura or as an aug 11th belonging to the chord. That Eb/D# really resolves to the D, making it an Eb. And the way that G# of the Tristan chord moves to A sounds exactly the same as that aug 11th A# of the V7 moving to B. So an iv6-V progression. I have a nice extra way to do a sort of check for these kinds of things, This is to play the root and its perfect fifth below the analyzed chord and see if this fits the interpretation. So if I play D A F B Eb G# -> D A F B Eb A -> E B E G# D A# -> E B E G# D B does this progression still have the same expression to me? It does. This also shows the logic of an Eb instead of a D# I think. D and "D#" don't mix in this case.

      So even though in this particular case we may have a communication problem about analysis (entire my fault of course due to my unconventional personal theory of root). Can you agree that by playing the extra D A in the bass does not modify the chord for you? (unlike for instance playing an extra C# in the bass which for me does modify how I hear the chord) And can you therefore also agree that we are hearing an Eb in the Tristan chord and not a D#?

      -Marcel de Velde

    • Marcel,

      You say: "I do not think one can simply stack thirds, the augment or diminish some of them, and this gives the root. I think that the root always implies a perfect fifth above it which cannot be diminished."

      Let us see...what is the root of the II diatonic chord in natural minor and what is its fifth? What is the root of the so-called "common tone diminished seventh chord" in major (#IIdim7) when it resolves into the tonic? If you add a major third below this diminished chord, you will destroy it, because it is not a part of a secondary dominant function to the III chord in this context.

      Also, what do you call an altered chord if you deny the dominant's fifth to be lowered or raised? Can you refer to any musician in the world who would claim there is no V7-5 or V7+5 chord? How do you explain a G7+5 resolving into the tonic? Do you know that jazz people often play these chords directly, with no preparation with diatonic notes first?

      I am interested to know what is your concept of a chromatic chord - which member of the chord can be altered? Until then, I can tell you mine: the fifth of the dominant chord may be lowered or raised. The fifth of V is the third of VII, so a V7-9 may have a VIIdim-3 as a substitute chord. Besides, subdominant chords may have their root raised or lowered (because it is an auxiliary tone) and they may still function as subdominant chords in the main key. Examples are many, but let us take #IV half-dim7 (which is diatonic in Lydian mode) when it resolves into the tonic or cadentials 6/4. In this context it is not a secondary dominant of V. We also have an augmented S chord in minor (IV lowered root) which resolves into I6). I already mentioned the CTdim7. Altered S chords are much more, of course.

      In general: Any auxiliary scale degree: 2,4,6,7, may be altered into the direction of a tonic member if there is a space of whole tone in between, and it may be a part of an altered chord which works into the main key. That is the concept for me and for many others.

      Thank you,

      Dimitar

      Dr. Dimitar Ninov

      School of Music

      Texas State University

      601 University Drive

      San Marcos, Texas 78666

    • Dear Dimitar,

      Often (but not always) I analyze the root of the dim II chord in minor as an added 6th /13th IV minor chord, btw if you extend the II chord in natural minor to the 7th chord you will have all the pitches of the IV minor chord with added 6th / 13th. And often in major I analyze the dim VII chord as a V chord with omitted root. Especially in the latter case I'm not the first to see greater musical logic in this.

      As for the #IIdim7, lets say D# F# A C, if it is spelled correctly then the root in my system can be B, E or A. I would have to see the chord in context of actual music to see if it comes from some form of nonchord tone(s), if it is spelled correctly (quite possibly not, making it an alltogether different chord) and what is its root in that specific case. Similar for the V7+5 chord. Often in classical music it will be a form of nonchord tone (it is in Tristan und Isolde prelude measure 25) and any nonchord tone does not have to fit my concept of root for the sounding chord of course, it can be a diminished or augmented fifth amongst other things. As for jazz / blues, there are often harder to interpret nonchord tones implied there, there are also more often more remote root progressions and on top of that there are also often resolutions by augmented prime steps instead of minor second leading tones. In addition jazz/blues spelling and analysis is very often completely wrong. Not only by the many unschooled jazz/blues composers/musicians but also by schooled jazz/blues composers. While its rare to find a spelling error in works by great classical composers (though we may have one here in the case of the Tristan chord if it indeed has an Eb instead of a D#), it is almost the opposite in jazz/blues compositions. In part due to lack of good theory to analyze some of the progressions in jazz/blues music and in part because it doesn't seem to matter how you spell things amongst especially American jazz/blues composers/musicians. Just last week I was analyzing part of Gershwin Rhapsody in Blue and these are the very first chords: Bb F D F Bb -> Eb A C# Ab -> Eb A C# Gb -> D Ab C F which is absolutely horrible, that is actually a double diminished fifth between C# and Gb amongst other horrors. And this is still part classical and by a well schooled composer. (it should be spelled Bb F D F Bb -> Eb Bbb Db Ab -> Eb Bbb Db Gb -> D Ab C F). I also think that some things in jazz/blues are indicating some things we're not used to in classical, especially with regard to resolution by sometimes augmented prime instead of minor second. Sometimes something similar can happen with the +5 of V7, when an actual chord tone and an actual V7 it can be heard as a b6 / b13th in jazz/blues I think while still going up a half tone which is easily mistaken to be a minor second leading tone (though most often it will be a nonchord tone or sometimes not a V7 to start with).

      I've invented my system of root many years ago and worked with it since and can tell you that in actual music it actually does work out and to me makes much more sense than the current system, but although I'd like to write about it it is a very long story to fully explain it and the reasons I came to this system. Much too long for a forum like this. I'll be writing a book and articles about it (and other things, like polyphonic makam music and "functional just intonation") sometime in the future. And I actually didn't mean to start a discussion about it. I only brought it up to explain why I could not personally go along with the leading analysis of the Tristan chord as a modified II chord.

      But I do hope you can answer my question. When you play the Tristan chord like this: D A F B Eb (G# -> A) -> E B E G# D (A# -> B), do you hear the added tones in the bass as modifying the chord or do you hear them as fitting the chord as I do? If you hear them as fitting the chord, do you agree that this indicates an Eb instead of a D#? And by seeing it as an Eb do you agree that this does not fit the analysis of the Tristan chord as a modified II chord? Edit: btw this will sound clearer if you only play the D (instead of D A) a tenth lower than the F, too many voices at once have a tendency to make things sound more crowded of course. You can play the first few chords of Tristand und Isolde like this: A->F->E->D F B Eb (G#->A) -> E E G# D (A#->B) ->B->G#->G->F Ab D Gb (B->C) -> G G B F (C#->D) ->D->B->Bb->A->A C F G# (D->D#)->A C E G# E -> B B D# A (E#->F#). So the root progresses like D->E->F->G->A->B.

      -Marcel de Velde

       

    • Marcel,

      I understand, but all this sounds quite formalistic to me. It looks as if you try to implant a root below each bass note that does not fit "your system", thus seeking mandatory perfect fifths ovet each root. Of course, the #IIdim7 resolving into the tonic is not a B chord, because this would change its function and destroy the linear subdominant effect.

      Schoenberg made the mistake of explaining the #IIdim7 as II7-9 chord, thus completely destroying the altered S effect, colliding diatonic 2 with raised 2 (thinking of the latter as minor 3)...this only shows how formal theory sometimes destroys music by imposing non-existing factors. Even the dim7 chord as dominant has its own flavor and the automatic addition of a major third below occasionally destroys the original nuance sought by the composer.  

      Of course, the true root of II dim or II half-dim7 is the second scale degree. If this chord is played in second inversion you could claim a subdominant with a suspended minor sixth or added minor sixth, as J.P. Rameau does, but when performed in position and followed by the dominant, it does not sound like a triad with an added tone. It has a quartal/quintal drive to V namely because of its acoustic root, which is different than the functional root of S.

      If you do not care of harmonic function (T, S, D) and altered chords, but you try to simplify everything at the level of pure major/minor triads and non-chord tones, this is your choice. But I can tell by such thinking that you do not play jazz or popular music...if you get involved into improvisation, scales, harmonization and jazz analysis, you will discover that practice suggests great diversity in harmonic treatment that goes beyond sticking thirds and constantly seeking a missing root and a perfect fifth. Yes, altered chords may have been derived via linear motion and non-chord tones, but I think all chords have been derived that way once...However, with the development of the homophonic style the door opens to the description of characteristic sonorities as seventh chords, ninth chords, altered chords, etc. If you do not recognize all that, it is OK with me. I do recognize it, however, and it helps me to do simpler analysis of homophonic music which is very compatible with the analysis many practicing musicians do on a daily basis.

       

    • Dear Dimitar,

      No, I do not think what I wrote is comming across as I intended. If you give me a specific musical example of tonal music of what you think is a good example of the #IIdim7 progressing to the tonic I will try to give a specific analysis of it in that context. Without further context I can interpret that #IIdim7 in many ways, including different spellings.

      Also, I play a root note below a chord merely to indicate how it fits the chord naturally. But of course I do not think that all chords should be played or made complete with the root note as the bass note or anything like that. It is merely a technique for helping analysis.

      As far as simplifying everything to major minor triads (or not caring about harmonic function). I think you must have misread what I wrote. I don't say anywhere that I do such a thing. In fact, my system seems to give a lot more extended and modified chords than regular theory (and since when is iv6->V in the Tristan chord progression, the only analysis I gave here, not caring about harmonic function?). Only the modifications are more limited. But in the case of for instance the Tristan chord I see a b9 (which is a lowered natural tone) and aug11 (raised natural tone)a 13th, and an omitted root. All as chord tones, not nonchord tones. Where did you get the idea I'm simplifying everything to major and minor triads? I only say that diminished triads and augmented triads are not in root position.

      But again, my intention was not to start a discussion about my system. I only mentioned it to explain why I can't go along with some of the regular analyses of the Tristan chord. And also to exaplin how I can come to this specific example: A->F->E->D F B Eb (G#->A) -> E E G# D (A#->B) ->B->G#->G->F Ab D Gb (B->C) -> G G B F (C#->D) ->D->B->Bb->A->A C F G# (D->D#)->A C E G# E -> B B D# A (E#->F#). So the root progresses like D->E->F->G->A->B. If the way of writing this makes it too unreadable I can put it in note writing and post the modified score. Or I can even render an audio file of it. Do you agree the extra bass (for analysis purpose) does not modify how we hear the chords? And if you agree with this do you agree that it is an Eb we hear instead of a D#. And do you agree that a modified II chord has a D# not an Eb therefore when recognizing it is an Eb this indicates that the analysis of the Tristan chord as a modified II chord does not fit? I'm not asking you to go along with my theory of root or anything here (which for the most part I haven't even explained), I'm only asking you to play the progression with the extra tones in the bass and tell me if you hear the Tristan chord etc and changed by this (as is the case when you add for instance a C# in the bass of the Tristan chord) or not.

    • Dear Dimitar,

      I'll be extra clear to avoid further miscommunication. I have not explained my theory of root, only wrote 2 things about it. To explain it fully and what it entails is a very long story which I'm not interested in discussing here in comments of a thread about the Tristan chord. Perhaps we can talk about it in a diferent thread somewhere in the future and perhaps you'll like my idea and perhaps not. But speculating about what it is probably isn't productive as to the thing we are discussing now, the Tristan chord.

      My point I'm trying to make is the following. If we play an extra D below the Tristan chord I hear that tone as fitting the chord. What theory lead me to playing a D below the chord and if that theory makes sense or not is not relevant to my question. If the extra D played below the chord sounds so natural to the chord, could it be that this is because it merely turns an iv6 chord into an iv chord? This is what I think. And how can one explain the D sounding natural to the chord if the chord were a modified II chord? That D# and D would clash very strongly. Would you agree that this indicates an Eb instead of a D#?

      -Marcel de Velde