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    Intervallic vs. Scale-degree (Functional) Hearing

    I was recently asked by a colleague to provide evidence of research indicating that functional (scale-degree oriented) thinking was more effective than intervallic thinking for dictation and aural skills. I have found plenty of statements asserting the benefits of scale-degree thinking in more recent aural skills texts, as well as in Karpinski's Aural Skills Acquisition and Rogers's Teaching Approaches in Music Theory. But what I'm looking for now are some studies in music cognition and perception as it relates to aural skills. Karpinski states that "a good deal of persuasive research has demonstrated the importance of tonally functional thinking, specifically in terms of scale degrees and their characteristic functions" (Manual for Ear Training and Sight Singing, xiii), but he does not cite that research specifically. Can someone help me out with some quick citations? Thanks!

    Note: our current curriculum (which I am now revamping) contains growing interval chains that culminate in twelve-tone rows by semester four. My gut feeling is that the time spent acquiring these skills could more effectively be spent doing other things (gaining more applicable skills).

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    • I can tell you that my instinct when driving and singing "The Itsy-Bitsy Spider" is to sing it in scale degrees, and singing in twelve-tone intervals is not as quick a process (especially because of the danger of repeating the approaching interval instead of 0 on a repeated note).

      Are you be refering to twelve-tone (numbers) or major/minor/etc. intervallic thinking?  I imagine there is a difference  just between these two types.

    • Brent raises an interesting topic, one that has been investigated by a variety of music theorists, cognition researchers, and music educators over the years. Although I merely mention the existence of this research in my textbook Manual for Ear Training and Sight Singing (as Brent noted), I survey the sources (as of 16 years ago) in my monograph Aural Skills Acquisition and discuss their implications at length on pp. 52-56. I recommend that anyone interested in this topic start with that discussion and the many sources I cite there.

      Based in part on this research, in my own work in designing and implementing theory curricula focused on tonal music I've arrived at an approach that eliminates most intervallic strategies and emphasizes tonal function as a means of understanding pitches in listening, sight reading, analysis, part writing, and other areas. Nevertheless, there are certain skills and topics in such curricula for which specific kinds of intervallic training (and thinking) can be helpful or even necessary, such as establishing diatonic collections from a single given pitch, navigating certain kinds of modulations, and dealing with atonal music, which is -- after all -- mostly a separate curriculum of its own.

      As an aside, I'd suggest that anyone pondering this issue try a little pseudoexperiment I've been foisting on unsuspectig victims for decades: Waylay musicians who possess at least a decent ear and play or sing for them a phrase from tonal music (I often use the first 4 measures of Haydn's Symphony 104, mvt. 2), then ask them, "Tell me about the pitches you just heard." You'll get many responses about scale degrees (as either numbers or movable-do syllables) and some about absolute pitches (from those with AP or who know the score), but almost no one will respond with "minor second up, minor 3rd down, perfect 4th up, perfect 5th down, major 6th up..." It seems that nearly all musicians attend to pitches in tonal music through their function in relation to a key, not their distances from their immediate neighbors. I think this could make an interesting, publishable ethnographic study.

    • Thanks, Gary. I've prepared my report from the references on these pages, and we'll see what happens!

    • Related to this, are there any resources that assist in teaching a functional approach to musical thought to non-trained adult singers on a once-weekly basis (such as for a church choir, e.g.)?  Simply trying to explain consonance and dissonance, suspensions, etc. can be a difficult endeavor.  Has much research been done on training the musical minds of such groups?

    • Conor, What about basic Kodaly? It was designed for children, of course, but many of the concepts can work well for adult singers with little to no training. 

    • I am somewhat surprized to see that Bret Yorganson's initial question and the subsequent answers are formulated in terms of "functional vs intervallic" thinking.

      Western musical notation, which conditions most of our approach and thinking about music, is a notation of pitches, and certainly not of intervals. I cannot imagine any case, since the invention of diastematic notation in the 9th or 10th century, and the subsequent abandonment of neumatic notation, of a musical thinking in terms of intervals – which is not to say that such a thinking may not be "more effective".

      On the other hand, I wonder what is meant by "fuctional thinking", especially with the additional specification "scale degree oriented". In a rigorous usage of the terms, functions should not be equated with scale degrees: several degrees share a dominant function, others a subdominant one, and other still a tonic one (not forgetting a predominant function about which not eveyone agrees).

      The question seems to me, rather, to arise between a thinking in terms of pitches and one in terms of degrees – which has to do with what has been termed "fixed" vs "mobile" solfege, or letters (C D E F etc) vs syllables (do re mi fa etc). The pros and contras of these systems has been a recurrent matter of discussion on the late SMT-Talk. It also was in 18th-century France (and Germany, and probably other countries as well), between those advocating fixed (transpositional) solfege and the advocates of le chant au naturel (i.e. singing everything major in ut, anything minor in la or in re, etc.) – as today in Kodaly, or tonic sol-fa, or other similar systems .

      I have no particular opinion on any of these. But as Bret Yorgason's initial question was "to provide evidence of research" about these, I'd like to say that there are numerous 18th century treatises and other more or less indirect sources about these matters (including Bach's title page for WTK vol. 1, when he wrote about 12 preludes and fugues in major "or ut re mi" and in minor or "re mi fa", or Rameau's statement in his Traité that it is difficult to ascertain the key from the notation).



    • There is plenty of published materials on this subject in Russian. In general, I have a recipy for success and a recipy for disaster in theory pedagogy. The recipy for success: Absolute Do solfege, obligatory keyboard harmony for all students (strictly in SATB texture, with SA in the right hand and TB in the left), the only type of exercises--melody and unfigured basses harmonizations, harmonic analysis in tonal-functional style. Start at the early age (a course in harmony--for the ages 14-16, solfege--from 5 to 16). The recipy for disaster: teach abstract concepts (Schenkerian et al.), use predominantly paper exercises (written tests), "figured bass realizations," relative Do (in memory of Ms Grover) and no keyboard harmonizations ("they are not pianists'). Spice this up with great deal of "innovations"--and here you are.

    • In the later 17th and the 18th centuries, both in Germany and in France, fixed solfege was practiced by instrument players, movable solfege by singers. That is to say that, as children musicians were first taught to sing, everybody began in movable solfege. Those who turned to instrument playing later learned fixed solfege, in which their scores were written.

      The vocal scores of course were written in the same key as their instrumental accompaniment, but the singers had tricks to determine the mobile solmisation from the key signature: if the piece had sharps in the signature, the last sharp always was to be sung si, irrespective of whether the piece was in major or in minor; if it had flats, the last flat always was to be sung fa, even if, as often was the case in minor, one flat was "missing" with respect to our modern conventions.

      The singers did not need to know whether the pieces were in major or in minor, i.e. whether the tonic would fall on ut (do), la or re; on the other hand the intervals mi-fa and si-do always were semitones, and the movable system was considered much better for a good intonation, i.e. correct singing. Whether one system was considered better than the other therefore depended mainly on whether their advocates were singers or instrumentalists – both being convinced that their system was the best. It seems also that mobile solfege may have been used more by amateurs, fixed solfege by professional musicians.

      One drawback of the mobile system was that any accidental sharp or flat in the course of the piece necessarily resulted in a change of solmisation, which was considered a change of key. France turned to the fixed system at some point in the second half of the 18th century, but retaining the note names as in the former mobile system, that is the (solmisation) syllables still in use today in French (and Italian) speaking countries.



    • This is the best explanation I have seen so far! Thank you, Nicolas! I have been trying to formulate this same difference for many years. It is true that movable Do is for less technically-oriented music majors that fixed Do. And the fixed Do was introduced into professional training at the Paris conservatoire at the end of the 18th century. (Apparently, it existed in Italy earlier, but I have not information on this topic). It was used for training musicians that deal with large-scale compositions, either as instrumental performers, or composers and theorists. Moveable Do is proto-modal (I use this term for the embryonic stages of musical training). There is a common misconception that fixed Do is for "perfect pitch people." Unfortunately, the essence of fixed Do is not very well-known outside French tradition. 

      The fixed Do develops the sense of tonality. Moveable Do precludes that. Tonality is not just a given seven-note pitch collection. It is a system of relationships of 24 such collections, in one context. In order to control all the octave species of this collection (and especially, in order to develop functional differentiation of its elements) one has to operate within a single system of notation. If the scale is schifted--then the tie between two collection breaks.

      What is interesting, the fixed Do should be combined with a selection of other pedagogic tools. It does not work by itself. The age group is also of ultimate importance. As for the right combination, fixed Do works the best with Schenkerian theory. In both modulation is perceived not as complete change of a key, but as an offspring, unfolding off the main trunk--which is, in this case, a white-key diatonic, or the main key. I asked Dr. Carl Schachter, and he supported my adherence to fixed Do solfege! Exactly for this reason.

      French system of ear training--is the most advanced and the most solid. One day it will be brought to our places--just as a Statue of Liberty was.

    • Ildar, I think that fixed do became the norm in France some time before the creation of the Academie royale de musique that was later to become the Conservatoire. I think that Rousseau's writings (and others) express a preference for fixed do, not long after the mid 18th century – and of course the duality existed before.

      There is at least one early-18th-century (or late-17th?) German theorist – his name escapes me just now, perhaps Niedt – who wrote that written "transpositions" (i.e. written keys other than C in major and A or D in minor) were there only to trouble the singers. The matter also has to do with temperament, as keys sounded different from each other. And several treatises on "transposition", especially in France (e.g. Alexandre Frere, 1706) actually dealt with the technicalities of "reducing to natural" (réduire au naturel), i.e. to a key without accidentals.

      18th-century texts state that movable do makes intonation (singing in tune) easier, and I can imagine that this is true. It may mean that movable do also could be a help for playing in tune, on instruments of movable pitches such as the violin. It would be interesting to know whether any recent research has been done in this field.

      As to fixed solfege favoring the perception of monotonality (of which I'd credit Schoenberg as much, if not more, as Schenker), I can assure you that this definitely is not the case in French Conservatoires (including the Paris one), where students have kept the early-18th-tradition (François Campion) to see and hear a modulation at each accidental note. This certainly comes from movable solfege, but fixed solfege does not prevent it.

      I am less convinced than you are by the qualities of French ear training... I don't know enough about the situation in Russia. My own experience is that it is quite difficult, once you have been trained in one system, to fully grasp the other. I am probably more aware than many of how medieval solmisation functioned, but I'd remain unable to perform it in real time. At any rate, I would not be as absolute as you are in prefering fixed solfege: I think both systems have their qualities.

      But this all may not answer Brent's initial question: I'd very much like to know more about what is meant by "functional" and "intervallic" thinking – which may or may not have to do with movable and fixed solfege.



    • Dear Nicolas,

      thank you for further clarification! This is fascinating story, it should be published in English one day. I know that our colleagues at the Conservatoire are not fond of speaking English but that is the exigency of our days. I see what you are saying: the system of solgefe by itself is not sufficient to encourage monotonal perception of tonality or other important aspects. The system can be compromised by its users--that is true. Yet, I respect the contribution of several generations of French teachers into the difficult affair of a student with the aural perception of musical structures.

      Brent's question is more narrow, I think. It is locally oriented. In the United States tonal-functional theory has been banned for several decades. Now it is coming back (to my great surprise). This includes ear training that develops hearing the direction in which a note is pointing. That cannot be done in a simplified PCset approach, IC vector does not tell us about the telos of melody.

    • Nicolas, my question was answered pretty well by Gary's reply (above). I wasn't really asking anything about solfege (fixed or movable), interesting as this may be. My "more narrow" question was regarding different approaches to understanding / processing melody in an aural skills course. In previous generations, students were sometimes encouraged to think intervallically in melodic dictation (i.e. what interval was that leap? ... a minor sixth). Now this has mostly shifted to a model that relates pitches to a tonal center using scale degree functions (i.e. how did the melody leap? ... from LA to FA; or from ^6 to ^4, etc.)

      Oops - I replied as SMT Discuss (this is Brent)
      SMT Discuss Manager
      Somewhere in the Universe
    • Yes, Brent, in the meanwhile I had seen Gary's Aural Skills Acquisition and I got a better idea of what was at stake. Even so, it seems to me that what you (and Gary) call "functional" thinking is linked with mobile solfege, and your mention of "a model that relates pitches to a tonal center" only confirms it.

      First of all, it should be obvious (it is, at least, to me) that neither la-fa nor ^6-^4 are functional designations. Ildar will easily agree with me that functions are something else, that "dominant" or "subdominant" are functions, while "V' or "IV" (or "^5" or "^4") are not. This is because in some cases a "dominant" may not be V, or even more that V might not be a dominant. I am aware that in [American] English the term "function" is employed more loosely, but I think it shouldn't. Anyway, the choice seems to be to designate the intervals either in terms of fixed pitches (say, A-F), or of pitches in a diatonic scale (say, la-fa) or of pitches in the local tonal scale (say, ^6-^4).

      All these denote pitches, or notes, not functions, even if Gary speaks of "a functional solmization system". A system of syllables such as la-fa connotes the diatonic scale and implies that the interval is a minor 6th of the type TSTTS (T=tone, S=semitone), but it could also denote ^1-^6 in minor. A system of careted numerals says that the interval is a sixth, but does not say its size (in major, ^6-^4 is a minor 6th while ^1-^6 is major, but both may be either major or minor ones in minor).

      Intervallic thinking, especially in a melodic context, appears to me rather problematic:

      First, because the perception of the size of intervals remains all the more uncertain that they are less consonant, unless they are perceived in superposition – memory might allow a kind of superposition, but this seems tricky. It might be difficult to ascertain whether a 7th was major or minor, especially if the two sounds are separated by a silence.

      Second, because such a way of thinking hardly relates with notation, while I think that the visualisation of music is deeply embedded in our thinking. Since now more than a thousand years, our music notation has been a notation of notes. As Charles Seeger stressed (in Prescriptive and descriptive music-writing), our traditional notation (and, I think, most notations in the world) corresponds to a conception of melody as a succession of separate sounds, as a chain. An intervallic thinking may correspond to the conception of melody as "a stream, function and movement itself", as Seeger described it, but I don't think that such a conception is very common, in our music at least.

      In short, I don't think that the question of a "functional" vs an intervallic thinking is a matter of tonality (which is another way of saying that I don't think that it has much to do with tonal function). Rather, it has to do with the conception (and the mental representation) of music as a chain of notes, vs its conception as a stream. One additional reason to think so is that the exact size of the intervals is nowhere considered in this discussion: the intervals we are speaking of are mere intervallic categories (semitone, tone, minor third, etc.), considered as abstract entities, without any attempt to exactly quantify their size. And even if the dictations do not end in actual notation of the melodies heard, the mental image produced will usually be one of a chain of notes.



    • Dear Bren and Nicolas,

      This is a discussion of the part of music theory that exists mainly in oral tradition (there is not enough published material, at least, in English). So, each of us can contribute something that has been instilled at a very early age. Not that there is anything wrong with that (c. Jerry Seinfeld). I remember from by solfege lessons (from age 4 until second year at the Conservatory) that we were trained in many different ways. Anything goes when one needs to overcome an ultimate difficulty, which is ear training. So, I have nothing against, for example, a set of exercises on phenomenal interval hearing. Simply, play a fast series of intervals in random order, such as P4, M2, m7, A4, m6 from randomly chosen notes. Students this way will get used to identify the interval itself by itself, by its timbral and spectral specificity. Recently, in Russia, in St. Petersburg, professor Litvinova is working on so-called timbral solfege (if necessary, I can provide the link to her texts). On the other hand, intervals should be studied in the key, so that the tritone will be linked to the interval of its resolution which is at the same time part of tonic harmony. This should be done very very slowly, and in fixed Do, for each key separately! Then, as Nicolas mentioned, an entirely different plane of events is entered---tonal-harmonic functions, such as T, S, and D. There should be trained as well, but at the last stage of study. In fact, students start hearing functionality by themselves, just as many of them obtain the perfect pitch ablitiy (which by itself is of no used in theory, as we all agree). But functional hearing in a monotonal space (a la Schoenerg and Schenkerh) is very useful. Again, you cannot start by teaching functional relationships since those are the most complex cognitive mechanisms acquired in the process of training.

    • Once you know interval content any scale is much easier to grasp.  I use this approach for jazz and improvising in general as well as my teaching method.  If you know a scale has a b2 for instance, it's much easier to process that information instantaneously.  This is why I incorporate world scales into my regular practice routine - if you know the interval content you can understand most scales and it moves the emphasis away from the name of notes and more on the interval patterns which can be transposed to all keys.  I think that focusing on intervals is also excellent for ear training because one really learns to hear each interval as a characteristic sound.  I never really cared for the scale approach to playing jazz and prefer to process interval content in changes, harmonic structure, soloing, etc.  I like Persichetti's chapter on using unusual scales in composition in "Twentieth-Century Harmony" which talks about using exotic scales and their harmonization independently (as a possibility from stricter scalar harmonizations inherent with chord tones).  

    • One small correction: Rousseau is actually an advocate of moveable do. This is the system that's consistent with his notation system, as laid out in the Dissertation sur la musique moderne. The clearest expression of his preference, though, comes in the comments on music pedagogy in Émile. On this latter passage, see Roger Grant's article in the most recent issue of Theoria, as well as Michel Termolle's article in Claude Dauphin's collection Musique et langage chez Rousseau (SVEC 2004).

    • @nmarti11 You may be right, Nathan. I didn't read Roger Grant's article (I will, as soon as possible), but Rousseau's opinion on this point is all but clear.

      He reproduces in the Dictionnaire (1768, art. SOLFIER) what he had written in Émile (Book II, p. 237): Il n’y a rien de plus bizarre que ce que les François appellent solfier au naturel ; c’est éloigner les idées de la chose pour en substituer d’étrangères qui ne font qu’égarer. Rien n’est plus naturel que de solfier par transposition, lorsque le mode est transposé. ["There is nothing stranger than what the French call "singing solfa in natural"; it is removing the ideas from the thing, and substituting foreign ones that only mislead. Nothing is more natural that singing solfa by transposition, when the mode is transposed."] And as early as 1742, he had already written En général, ce qu'on appelle chanter et exécuter au naturel est peut être, ce qu'il y a de plus mal imaginé dans la Musique. ["In general, what one calls to sing or to play in natural may be what is the worst conceived in music."]

      Chanter au naturel certainly means to sing transposed keys (i.e. keys with accidentals in the signature) in ut (in major) or in la (in minor) (I neglect here the case of re in minor with flats). Solfier au naturel, Rousseau writes in the article NATUREL in the Dictionnaire, c'est solfier par les noms naturels des sons de la Gamme ordinaire, sans égard au Ton où l'on est. ["To sing solfa in natural is to sing by the natural names of the sounds of the ordinary scale, without considering the key in which one is."] Singing in natural, in other words, is singing with moveable ut: the above quotations are the reason why I thought that Rousseau was against it.

      But he writes, in Émile again: qu’il sache établir son mode sur chacun des douze tons qui peuvent lui servir de base, & que, soit qu’on module en D, en C, en G, etc., la finale soit toujours ut ou la, selon le mode. ["He [the student] should be able to establish his mode on any of the twelve tones that can form its basis and, whether one is in [or: modulates to] the key of D, C, G, etc., the final always be ut or la, according to the mode."] This, which is not taken over in the Dictionnaire, appears advocating mobile solfege, but it is exactly what was called solfier au naturel, to sing any key as "natural", i.e. without accidentals. And Rousseau's own system of notation, presented to the Academie des sciences in 1742, is a mobile solfege!

      There is a full contradiction in all this. On the one hand Rousseau rejects what he calls "singing in natural"; on the other hand he advocates moveable ut. I had thought that he changed his mind between Émile and the Dictionnaire; but now I don't know anymore...



    • Again and again I keep seeing this strange tendency to revise everything that has been done on the continent. If musicians on the continent were working with tonal-harmonic functions--we have to revise that, overturn, and try to prove that a) they were wrong, b) they actually did not do it, c) the concept is wrong to begin with. This healthy competition with Europe very often goes so far that we start doing things that are absolutely counterproductive, harmful, and baneful to our own teaching and research. Oswald Jonas claims in the Preface to Harmonielehre that theories of Rameau were baneful. Mr, Jonas was an accountant. He liked music. He wanted to express his opinion. This opinion was, for sure, the opposite of the mainstream European 19th-century views. For that we love him and accept him. The bitter truth is that exactly his manipulation of the idea of counterpoint was baneful, not the theory of Rameau. The same applies to solfege. And yes, we can read any books in any language from any remote period and interpret (read in) anything in our way. After all, Derrida was right--reading and translating are doomed by default. Unrewarding business. What a pity--an article in Theoria is already published, we almost agreed that Rousseau was against fixed Do solfege (and against everything that we are against), and here comes a native speaker, one of the most revered and authoritive scholars who says that no, not at all, that a) Rousseau was not exactly against fixed Do, b) he did not have a clear answer, and c) perhaps, he is not the most authoritative source on musical composition in the French tradition of the 18th century. Gratias!

    • Dear Brent,

      I have found an interesting text, written by professor of St. Petersburg Conservatory Yuri Nikolayevich Bychkov on French system of solfege. Here is the link: http://yuri317.narod.ru/ped/parissol.htm

      It is in Russian, but the text is technical and can be translated using GoogleTranslate. In particular, professor Bychkov suggests that at Paris conservatory the emphasis is given to melodic exercises and that, in his view, develops intervallic hearing (he uses the term in approximately the same way as you do); however, the harmonic hearing is not emphasized there: Quote: Ни пение гармонических последовательностей, ни гармони­ческий анализ на слух не входят в программу занятий по сольфеджио. (Neither singing harmonic progressions, nor analysis of harmonic progressions by ear are included into the courses in solfege). This is the deficiency of the system at Paris conservatoire, according to Byhkov. I am not sure if he is right (I guess Nicolas could object). However, this component is significantly stronger in Russian system. It is intended to develop so-called lad hearing, or harmonic and functional hearing (that is, I assume, what you describe as the opposite of intervallic). So, I would narrow the question to relationship of French and Russian (Soviet) systems. The moveable Do is not the part of this comparison. It is simply too amateur and reduced. Other interesting differences include the technique of writing the dictations. In Paris it is two-part tonal dictation, played 2 measures at a time. In Moscow it is 3-part tonal, played strictly from left to right 8 times during 45 minutes, with no time signature or key signature announced. In general, Russian system is 7 plus 4 years before the conservatory, French--1 to 3 for the first stage and 1 to 3 for the second stage (first is given at regional conservatories, the second--at the national). Russians start earlier and spend more time in the formal classroom environment. There are deficiencies as well in Russian system. Elementary theory (rudiments) is taught as a separate course, while in Paris it is included into solfege. Singing in clefs and transposition is not as strong in Moscow. And the system in Moscow is less flexible (all students take the study of the same length and there are no concourses. 

    • Wow, this is super interesting and a ton of information. Thank you.

      I came across this when I was looking for information about this so-called "functional vs intervallic" manner if approaching ear training. From what I had read of people's experiences, I couldn't discern the two. Here's my experience with the example that was given. If I'm listening to a basic cadence and then I'm asked to identify a note, I'm automatically comparing that note to some aspect of the cadence, whether the tonic or dominant, or other function. Doing that comparison makes it an intervallic identification, regardless of whether I'm actually naming the interval.
      Gary's first response, particularly at the tail end, helped somewhat to explain this difference that is being raised.

      It's interesting the question of solfege systems has come up along with this. Clearly there are many relationships, and I think that the history of these systems, as detailed by one respondent, is crucial in understanding their use and application. Moveable do makes much more sense than fixed for many purposes. I will always teach and advocate that first. It's more innate, it overtly contains these concepts of notes within a key's construct that's being discussed. But it can be a bit complicated for a comprehensive music theory analysis. I know this topic has been exhausted and continues to be so, and that is what I think is so invigorating - a constant discussion of the pros and cons of a great many approaches. This kind of conversation is crucial for the development and growth of any field.

      It would be most helpful to have terms such as these that leaders in the field could agree to use in at least approximately a similar way. It's difficult to discuss otherwise.

      Thank you all for many contributions which I will continue to peruse, and thank you for allowing me add even just a very little.