hello my name is dr. Jacob gran and this is the second video in the course on Sheng karien analysis this video lays a lot of the groundwork for the subsequent videos we're going to be going over some of the basic ideas that will help us to understand the linear approach to analyzing music as well as ideas that will prepare us to understand Schenker's use of analytic notation in the 18th century music theorists grappled with a sort of chicken and egg problem which came first harmony or melody do composers first compose a chord progression and then try to find a melody that fits it or do they first write a melody and then find chords that support it the two different responses to this question will greatly influence your viewpoint on how best to analyze music the most famous theorists of the Harmony first camp are John Philip bromo with his theory of fundamental base and Hugo Riemann who developed a theory of harmonic function to explain chord syntax when one analyzes from the harmony first perspective it is useful to think in terms of chord roots Roman numerals chord tones and non chord tones and in terms of function categories like tonic dominant and sub-dominant this is the tradition of analysis that is most often taught at American universities and conservatories but it isn't especially useful for preparing you to understand Shang karien analysis as I alluded to in the first video Schenker's approach is based on melodic analysis and although he makes use of several of these ideas he traced his lineage primarily through contrapuntal theorists like Fuchs or through theorists of the Thoreau based tradition like CPE Bach as I hope you'll understand by the time we reached the end of the last video in the series Schenker provides an explanation for chord syntax that doesn't rely so strongly on a notion of harmonic function and his theory of levels neatly addresses the chicken and egg problem of the relationship between harmony and melody the first step in understanding the melody first approach to analysis sometimes also referred to as linear analysis is to rewind the clock to the 18th century and reset our perspective to think in terms of figured base figured base refers to the numbers written above a given baseline as in this example the figures refer to intervals above the base that would be improvised by a continual player usually on a keyboard instrument we call the improvised upper parts a realization the same figured base can have multiple good realizations since the specific chord voicing register and doublings are left to the performers discretion all of these figures should look familiar to anyone who has studied harmony in the past since they happen to be the same figures that are used to indicate chord inversions chord inversion symbols originated as base figures that eventually became attached to Roman numerals for harmonic analysis here is one possible realization of this passage once a continual player has chosen a register and voicing for the first chord he is to an extent locked in for a while since realizations are expected to maintain smooth voice leading and to obey the rules of counterpoint that means not abruptly changing register for each chord and avoiding things like parallel fifths the most common figure is the 5/3 which indicates a root position triad five threes are so common and eighteenth-century musicians wanted to save ink and not clutter the score that they can be left out of the figures five threes are assumed as the default for any blank bass note notice here that I have removed the 5/3 figure from the first and last cord without affecting the realization but that I've left in the 5/3 in the second-to-last cord that is because it is customary to show five threes and any other kind of figure when the specific voicing between adjacent chords is relevant I've put dashes connecting the six and five of the first two cords of that measure as well as the four and the three that is meant to show the connections between specific upper voices whichever finger the continual player has chosen to use to realize the six above the bass in the first chord that voice needs to move down by step to a fifth above the bass in the next chord and the same can be said for the four three figures another shorthand is to simply write six whenever a 6-3 is indicated a third above the bass is assumed and you would need a figure to indicate the slightly less common six four or six five chords here is an example of a figured base over a tonic pedal point from CPE Bach's essay on the true art of playing keyboard instruments that goes well beyond the familiar chord inversion symbols if you want you can pause the video and try to come up with how you would realize these figures before I show you Bach's realization this example demonstrates why figure base is so useful in linear analysis figure base is very good at showing the upper voice structure of a passage Roman numerals for instance would not indicate specific voice leading connections between adjacent cords figured base also has a deep connection with counterpoint since these figures happen to be identical to the harmonic intervals we would have written if this were a three voice species counterpoint exercise figured base also does not distinguish between chord tones and non chord tones this is an advantage in situations like this where there is a sustained pedal point and we care more to analyze the linear motion of the upper voices rather than any notion of harmonic function figure bass also encompasses chromaticism quite easily we simply include accidentals in front or as in this case behind the figures to indicate how they are altered historically you might also see slashes to indicate chromatically altered figures but most shink Aryans nowadays don't do that and neither will i if you want you can pause the video again and try to figure out how you would realize this pedal point notice in this example that the first and last chords could have been figured as simply 5/3 or not given any figures at all and we would have realized the same pitch classes above the base but the 10-8 five-figure of the first chord and the eighth 5/3 figure of the last chord represent a different voicing and the figures in between show the specific voice leading connections between them just to reiterate the point figured base is quite useful in showing the voice leading structure of the upper voices and for streamlining your harmonic thought with the rules of counterpoint the succession of intervals eight seven six in this inner voice for instance is something that one might have seen many times while practicing dissonant passing tones in second species exercises one last convention before moving on an accidental that appears to be floating in the middle of nowhere is actually used to indicate an altered third above the base remember that thirds and five threes are assumed if there are no figures given and hanging accidentals are assumed to alter the third above the base this is very common at Cadence's in the minor mode for instance where we frequently raise the leading tone perhaps the most unique aspect of Schenker's methodology is his use of graphic analysis which is accomplished using analytic notation to understand two analytic notation we'll have to make a semantic distinction almost all musicians use the terms note and tone interchangeably as perfect synonyms but some Sheng Koreans have taken to using the two terms differently notes are the symbols in a score that indicate pitch they are written by the composer and are performed by the performer tones on the other hand are our mental representations of notes and other pitch structures Schenker's graphic analyses represent relationships between tones and they aren't in any way intended to be a replacement for the score itself this brings us to another shin carrion concept called the imaginary continuum which combines figured base with the note versus tone distinction and will provide a framework for understanding how analytic notation works here we have an unfitted bass note see the figured bass realization of this C would be a C major triad which would include the notes C E and G in some sort of configuration but before the court is realized by the continual player we don't know anything about the register or voicing of the chord you could say that in one sense although these pictures are not literally present as notes until they've been realized in performance they are still present as tones in our heads the tones are relevant because they illustrate our understanding of the possible upper voice structures one thing that would not make it into our imaginary continuo would be this here we have competing versions of E and E flat in different registers of our imaginary continuum if a performer realizes a C minor triad in the middle register of the keyboard our ears would not assume that the ease and the other registers would remain unchanged CPE Bach wrote that intervals express the same tones and retain their names in all octaves so in other words they're either all Naturals or all a flats but not a mixture and cross relations and other dissonant augmented intervals do not play a role in our imaginary continuum now let's use what we've learned so far in the video to analyze this short passage from the beginning of je s box B flat major partita here's a quick listen you instead of reducing this passage to a string of Roman numerals as most of you watching the video have probably been trained to do let's instead pretend that this composition is just one of many possible realizations of an imaginary continuum and reduce the passage to the figured base that could have produced this realization this is what these figures would sound like if we gave them a sort of paint-by-numbers realization [Music] this figured base reduction has basically one set of figures per base note and there happens to be only one base note per measure notice at the end of measure one though where we had to introduce a chromatic flat seven to account for the appearance of a flat a flatted tendency tone such as this is expected to resolve downward by step but Bach doesn't do that how best do we explain this missing resolution did the a-flat resolve upward by seventh to the top note G on the next downbeat or did it resolve to the G on the seventh sixteenth note of the next measure even though there was an a natural before that note neither of those explanations is completely satisfactory Schenker's explanation would be to say that the resolution down by step in the correct register is implied on the downbeat of measure two implied tones there's that word again are always shown in parentheses in order to distinguish them from the notes that Bach actually composed try thinking of it this way of all the possible realizations of this figured base reduction Bach happens to have chosen one that doesn't put the dissonance and it's realization in the same register but in the majority of realizations the a-flat would resolve downward by step and we want to include that tonal feature in our analytic notation despite the fact that it isn't realized in the first video I mentioned that part of Schenker's goal was to explain the discrepancy between strict composition and the free compositions of the common practice era the imaginary continuo helps us to partially explain that discrepancy thinking in terms of figured base for instance helps to highlight non-obvious voice leading connections first glance this piece seems very leafy a far cry from the predominantly stepwise motions of fuchs is species counterpoint but if we look at the upper voice structures that are implied by the figure based symbols we can pick out coherent stepwise patterns such as this ascent in the top voice from F to G to A to B flat as we listen to the passage a second time try to focus your attention on this long term stepwise connection [Music] we're going to end this video by introducing the two most basic elements of Sheng karien analytic notation stems and slurs stamens slur notation is a little like a training wheels version of full-blown graphic analysis and the rest of the videos in this series will build on these concepts and introduce new notational conventions we start here with the notes of Beethoven's Ode to Joy I'm going to do three things as I convert this melody into stem and slur notation first I'm going to eliminate all of the note repetitions since they don't contribute to the Melody's goal direction and shape I'm also going to eliminate the rhythmic differences between notes so the dotted quarter and the half note in the final measure for instance will be reduced to symbol filled in note heads and we're doing that because we want to sort of hijack the rhythmic hierarchies of standard notation to show instead the conceptual hierarchies in our analytic notation finally I'm also going to sort the tones into two groups those that will have stems and those that will not here we have a reduced form of the ode to joy' theme that still preserves its basic shape and goal-directed miss stems belong to structural tones while decorative tones or elaborative tones are unstamped at this point there are only two levels in our hierarchy the tones that have stems and the tones that don't but the full non training wheels version of Schenker's theory provides for an undefined number of levels next I'm going to introduce slurs which is the main tool for indicating the relationship between tones either of the same level or between levels because there are only two levels in this example all I needed to do to complete the stem and slur reduction was to simply add a slur between all of the structural tones the stemmed tones that won't always be the case though slurs are used to show either connection or dependency the structural tones f-sharp and a on the downbeats of measures 1 & 2 are connected by a slur the G between them in measure 1 is contained underneath the slur and this shows that it is conceptually dependent on that connection in other words the G is generated by the motion from F sharp to a all of the tones in a well-formed analytic reduction should be related to one another and to the whole melody either through connection or dependency there are many many different kinds of connections and dependencies but luckily they can all be grouped into only four categories and those were introduced in the first video in the next video we're going to cover the first category called horizontal ization