COMPARATIVE LAW LAWSO 160
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Music 160A class notes Dr Rothfarb November 2 2007 More on Beethoven op 182ii 0 page 26 in the anthology 0 Review of Wednesday s lecture 0 Overall form ternary I mm 1 26 A section I mm 27 52 B section I mm 53 59 re transition back to C major I mm 60 end A section The A section of op 182ii 0 mm 1 6 0 The first six measures make up a parallel period with a C major HC in m 3 and a C major PAC in m 6 It is odd that there should be a PAC so early in the piece but in this case the cadence is imperfected by the suspensions 0 mm 6 10 0 Following the opening period there are two half cadences in C major one in m 8 and another in m 10 This puts the G major harmony in the listener s ear and hints at the modulation that follows shortly 0 mm 10 14 0 These measures make up what might be thought of as a miniature b section within the larger A section F s first appear on the downbeat of m 11 indicating that Beethoven is modulating to G major the dominant key 0 After several secondary dominant chords there is a big G major PAC in m 14 0 mm 14 26 0 Although it is not entirely explicit m 14 marks the return of the opening theme in the tonic key The G major arpeggio in the cello in m 14 leads to an F on the downbeat of m 15 making the chord into a dominant seventh sonority This V7 chord leads us back to C major o A provocative chord is heard at the end of m 21 a German augmented sixth chord This sonority resolves to a dominant chord with a 2 suspension leading to a PAC on the downbeat of m 23 o The cadence in m 23 however is not the final conclusive cadence Looking at the opening measures we see that the cello begins on the C two octaves below middle C The four measure extension following the cadence in m 23 brings the bass back down to this register I The following diagram maps the harmonic motion of the A section risectlon e h j e 1113 IIHC 1116 IIPAC 1118 IIHC 110 IIHC 11V iigt VII 114 VIPAC VII iigt 11V 125 CIPAC It s fine that the A section doesn t modulate In fact in ternary form it shouldn t modulate The A section should be harmonically closed This is an important characteristic of ternary form The B section of op 182ii 0 mm 27 36 0 It is immediately apparent that mm 29 36 are sectioned off from the rest of the piece by repeat signs These measures are also immediately recognizable as having some of the qualities of a period They make up a double period with two bar phrasing You could think of it as a single Music 160A class notes Dr Rothfarb October 17 2007 More on Baroque binary forms and their remnants in the Classical era 0 Baroque pieces were typically limited to a single theme and its spin offs o A fugue is a good example of this even though a fugue is a procedure not a form 0 The purpose of having only one theme was to present a single affect lamentation for example from different perspectives These perspectives of course are the different keys to which the piece modulates This differs from the Classical ideal which was to present two contrasting themes The first half of a binary form presents the theme in the home key The second half often presents the same theme in a new key 0 Because there is only one theme key structure becomes the primary organizing factor 0 Oftentimes there is a third key Even though it may constitute a real modulation as opposed to a tonicization this third key area functions only as a stepping stone to return back to the home key 0 It often sounds like a very distantly related key It is only with the return of the home key that one is able to grasp its function o The key of the submediant vi is often used for this purpose 0 Key structure with a third key section 1 I tion I M Key 1 1 Key 2 V Key 2 V Key 3 Vi Key 1 1 0 Just as it is quite common for the vi chord to be used as a pivot in modulating from the tonic to the dominant in the opening section it is also commonly used as a stepping stone on a larger scale for returning to the home key in section 2 lncipit and cadential parallelism 0 Often the two sections of a binary form will begin with similar if not identical material differing only in key This is known as incipit parallelism 0 Similarly the two sections of a binary form often end with similar cadences again differing only in key This phenomenon is known as cadential parallelism 0 For examples of these types of parallelisms look at Bach s French Suite no 5 IS Bach French Suite no 5 BWV 816 1722 Allemande 0 page 12 in the anthology 0 lncipit and cadential parallelism o Returning to the Allemande of Bach s French Suite no 5 we notice the cadential parallelism between m 12 and 24 These measures are identical except for the fact that m 24 is transposed down a fifth to end the piece with a PAC in the home key 0 Compare m 1 with m 13 Although in different keys m 13 also has inner voices added the two measures are identical This is a case of incipit parallelism Music 160A class notes Dr Rothfarb November 15 2007 JC Bach 53i 0 page 38 in the anthology 0 The structure of this sonata movement is as follows 0 Exposition I First theme mm 1 8 I The first theme constitutes a parallel non modulating period with an G major imperfect authentic cadence in m 4 and a G major perfect authentic cadence in m 8 I Transition mm 9 16 I A brief transition follows the opening theme It modulates to D major by repeating the opening material Instead of the V6 chord in m 3 Each uses a V 2V chord in m 11 leading to the dominant harmony in m 12 This continues to a HC in m 16 I Second theme mm 17 27 I This is not really a theme it s just scalar passage work However if we had to call something Theme 2 or Group 2 the book uses the term group instead of theme for just such a situation this would be it This section builds to a big perfect authentic cadence in D major in m 27 I Terminative mm 27 32 I A short terminative section continues on to a section closing imperfect authentic cadence in D major in m 32 0 Development mm 33 65 I Starts out just like the exposition transposed to D major with a parallel non modulating period imperfect authentic cadence in D major in m 36 and perfect authentic cadence in D major in m 40 I Bach then modulates to the predictable key of E minor the submediant with an imperfect authentic cadence in m 44 I The piece then modulates to E minor v of E minor iii of G major with an imperfect authentic cadence in m 53 I Bach retransitions back to G major via a sequentialscalar passage consisting of a descending fifths sequence 0 Recapitulation mm 66 81 I In the recapitulation we only get the second theme This time as it should be in the recapitulation it is in the tonic key of G major It is for this reason that we will refer to this form as binary sonata form Binary Sonata Form 0 This piece is said to be in binary sonata form because of its heightened similarity to binary form Binary form you ll remember progresses according to the following layout Thematic material A Key I I Notice the reversal of relationships In the first section A is in the tonic and Al is in the dominant In the second section this is reversed A is in the dominant and Al is in the tonic This is what happens with the movement we just looked at The second section starts off with the opening material in the dominant key Then when the tonic key returns it s the secondary thematic material Hence binary sonata form for more information and a clarification of binary binary sonata and ternary sonata forms refer to the handout distributed in class Two types of sonata form I Binary sonata form vs ternary sonata form I Ternary sonata form is by far the more common of the two Pieces like the two Haydn movements we looked at on Wednesday are in ternary sonata form We refer to it here as ternary sonata form because even though sonata form is more directly derived from binary form there are three distinct sections the third of which is similar to the first exposition development and recapitulation Keep in mind that these two modifiers binary and ternary indicate resemblances more than anything else CPE Bach W554 I Despite the date this piece is early in regard to the historical development of sonata form There are a lot of Baroque holdovers and it is fast and frantic This is to be expected because even though CPE Bach was contemporaneous with Mozart he was still very much a part of the Baroque tradition This piece does however have a normal recapitulation it is in ternary sonata form The structure of the piece is as follows 0 Exposition mm 1 42 I Theme 1 mm 1 12 I The first four measures prolong the tonic harmony Following this we find a repeated progression in mm 5 8 and again in mm 9 12 Each of these ends in a half cadence I Transition mm 13 26 I The transition starts off sounding like a second theme in the dominant key but it is not for two reasons 0 1 It doesn t last very long before devolving into passage work which can t seem to shake the pedal A until m 21 o 2 It doesn t recapitulate properly There s a similar passage in m 94 but the harmonies are all wrong I Once Bach gets rid of the pedal A he moves along to a prolonged and emphasized dominant harmony in m 26 setting himself up for I Theme 2 mm 27 38 I Even though this mostly passage work it still constitutes a recognizable theme leading up to a big perfect authentic cadence in the dominant key E major in m 38 I Terminative mm 39 42 I A short terminative section follows ending with another perfect authentic cadence 0 Development mm 43 81 I The development begins with the Theme 1 material in the dominant key E major but quickly dissolves into a sequential passage In In 64 we get Theme 2 material in the mediant key C minor followed by a big caesura and another sequence As if to suggest that the passage in C minor was a false start Bach gives us Theme 2 material in m 73 in the dominant key E major followed by yet another caesura I For the retransition back to the tonic key scalar passage work returns us to E major Music 160A class notes Dr Rothfarb October 1 2007 Form 0 Our experience of music is much like our eXperience of daily life It is helpful to think of musical form as a goal oriented journey 0 Many of the words used to describe a journey may also be applied to our eXperience of music 0 Detour 0 Path 0 Landmark o Revisiting 0 Form is hierarchical Large units are subdivided into smaller units 0 We often use vocabulary derived from rhetoric phrases periods etc to describe formal units Phrases 0 A phrase is the smallest formal unit that still ends with a cadence 0 Phrases may be conclusive creating a sense of repose or inconclusiverequiring further motion 0 The degree of repose achieved by a phrase is determined largely by the cadence see below for more on cadences 0 There is also a sense of musical verticality involved here Musical tension is heightened as the melody ascends above the tonic Repose is attained as the melody descends back towards the tonic A melody that descends down to l will lend a greater sense of resolution than one that terminates on some pitch above l Periods A period consists of a pair of complementary phrases the first of which is inconclusive and the second conclusive The first phrase is often referred to as the antecedent and the second the conseguent The first two phrases of Oh Susannah make a period The first phrase ends with an inconclusive half cadence on 2 The second phrase begins exactly as the first but is altered slightly to end on 1 Oh Susannah Not all phrase pairs form periods The first two phrases of Deck the Halls are identical They do not form the necessary antecedent consequent relationship required for a period Deck the Halls Cadences A cadence is a point at which a relative sense of resolution is achieved A perfect authentic cadence PAC is referred to as such because it gives the greatest sense of repose The outer voices also resolve to a perfect octave the interval that gives the greatest sense of resolution Criteria for a PAC 0 Bass V to Iin root positions 5 l o Soprano 2 l orl An imperfect authentic cadence IAC is less conclusive than a PAC Certain factors can imperfect the degree of repose given by a cadence Examples of cadences EX 1 Is example 1 a PAC even though we have 2 3 l in the soprano 0 Yes example 1 is still a PAC The B is an echappee a melodic decoration Which does not affect the true motion from 2 to 1 Ex 2 Is example 2 a PAC despite the 2 3 21 5 in the soprano A 0 Yes example 2 is still a PAC The 3 4 5 figure forms a melodic embellishment to 2 Ex 3 Is example 3 a PAC A A 0 Yes The resolution from 2 to l is simply delayed Music 160A class notes Dr Rothfarb October 22 2007 A quick word on analysis 0 One of the purposes of analysis is to give a basis for performance decisions Analyzing a piece will help you become aware of what makes the piece unique This awareness can help immensely in your decisions as a performer guiding you in what elements to bring out or play down Hallmarks of binary form 0 see handout 0 Typically a binary form is a three key structure Here are the typical key plans for piece in major or minor Majorkeys 11 V1V1 v11 11 Mmorkeys 11 1111 or V1 ll 1111 or V1 V1 11 0 Binary form is usually constructed using two phase periods These periods can be expanded of course and often are 0 Usually a binary form is monothematic 0 Incipit and cadential parallelisms are common If the cadential parallelism goes so far back as to repeat the entire first section it is called a rounded binary 0 As mentioned before for a binary to be rounded the return of the opening material must be in the original key Sometimes composers will toy with the listener s expectations by bringing back the original material but in a different key or returning to the original key but not the opening material Elements to address in a written analysis 0 see handout 0 Structural functions 0 In this assignment you may find that the piece is too short for real structural functions to be brought out very prominently You should still consider them in your initial analysis 0 Tonal profile 0 This should be a big part of your paper 0 Cadential profile 0 Consider the relative weightiness of the various structural cadences you encounter 0 Phrase profile 0 For this assignment the phrase lengths will probably be pretty regular because these pieces are Baroque dance forms You may want to address the phrase profiles anyway particularly if they are irregular 0 ThematicMotivic profile 0 Parallelisms should be discussed if present Motivic operations should also be discussed but make sure that the motives you mention are actually motives that is they must be developmental 0 Harmonic profile 0 Are there surprising or unexpected harmonies or progressions How fast are the chords changing I Rhythmic profile 0 Like phrase profile this tends to be pretty regular in pieces from this period particularly in dance pieces 0 Are there irregularities If so mention them Hemiola is an example of this These sorts of things happen at strategic locations and for good reasons I All of these things are issues that could happen in a piece They may or may not Regardless these are all topics worthy of consideration particularly in the planning stages of your written analysis The paper I Topics choose ONE of the following six pieces to write about 0 IS Bach English Suite in A minor Sarabande JS Bach English Suite in A minor Bourree II JS Bach English Suite in F major Minuet I or II JS Bach Partita in Bb major Minuet I Haydn Hob XVI 2d in Bb major Minuetto I o Haydn Hob XVI 27 in G major Minuetto Administrative details 0 The paper will be due in class on October 31 2007 CE late submissions will be penalized 0 Papers should be no longer than five pages and no shorter than two or three pages Planning 0 You should definitely make a copy of the score for your piece All of these pieces are available in the music library You will find it very helpful to number the measures so that you can refer to the exact locations of various events and developments in your paper I Your thesis 0 This is the easy part Since you are being assigned a piece in binary form your thesis will be that just that the piece is in binary form I Paper structure 0 For the bulk of the paper you should concentrate on the details of the piece Which of the U 0000 features are standard Which make the piece unique Bring out these details in your paper Do NOT just go down the list on the handout writing a paragraph for each topic Your paragraphs should bring out the details that you feel are significant to your analysis of the piece Bach French Suite no 6 Polonaise I from the handout for the practice writing assignment I Here are the structural cadences for this piece 0 M 4 IAC inE I I The cadence is imperfect because the soprano lands on scale degree 3 It is also on beat two 0 M 8 PAC inB V I Ali is introduced on beat one in m 6 to usher in the dominant key I The cadence may seem to be imperfect at first since the soprano has Eli on the downbeat of m 8 However there is no voice leading to the Eli Instead the Cli of m 7 leads to the B on beat 2 12 HC in Cli minor vi The submediant is a very typical modulatory goal for a binary form PAC in Cli minor vi At this point Bach s goal is to get back to E major 39 HC in E I PAC in E I i 0 O 33 3 3 NNI LM160ILM360 High Speed Differential Comparator General Description The LM160LM360 is a very high speed differential input complementary TTL output voltage comparator with im proved characteristics over the pA760pA760C for which it is a pinforpin replacement The device has been optimized for greater speed input impedance and fanout and lower input offset voltage Typically delay varies only 3 ns for over drive variations of 5 mV to 400 mV Complementary outputs having minimum skew are provided Applications involve high speed analog to digital convertors and zerocrossing detectors in disk file systems National Semiconductor Features August 2000 Guaranteed high speed 20 ns max Tight delay matching on both outputs Complementary TTL outputs High input impedance Low speed variation with overdrive variation Fanout of 4 Low input offset voltage Series 74 TTL compatible Connection Diagrams Metal Can Package TOP VIEW DSOO57074 Order Number LM160HI883 Note 1 See NS Package Number H08C Note 1 Also available in SMD 59628767401 DuallnLine Package v oun our cm a 71615 J 12 1 l1 TOP VIEW DSOO57075 Order Number LM360M LM360MX or LM360N See NS Package Number M08A or N08E 2000 National Semiconductor Corporation DSOO5707 wwwnationalcom JOIBJBdNOO lenueJeiiia needs u iH 09 II39ll09lllll39l LM160ILM360 Absolute Maximum Ratings Notes 6 a If MilitaryAerospace specified devices are please contact the National Semiconductor Sales Office Distributors for availability and specifications Positive Supply Voltage Negative Supply Voltage Peak Output Current Differential Input Voltage Input Voltage ESD Tolerance Note 9 Operating Temperature Range Electrical Characteristics TMIN 3 TA 3 TMAX Storage Temperature Range Lead Temperature Soldering 10 sec Soldering Information required 8V DualInLine Package 8V Soldering 10 seconds 20 mA Small Outline Package i5v Vapor Phase 60 seconds V 2 VIN 2 Va Infrared 15 seconds 1600 See AN450 Surfa 65 C to 150 C 260 C 260 C 215 C 220 C ce Mounting Methods and Their Effect on Product Reliability for other methods of soldering ace mount deVIces 55 C to 125 C 0 C to 70 C Parameter Conditions Min Typ Max Units Operating Conditions Supply Voltage veg 45 5 65 V Supply Voltage VCC 45 5 65 V Input Offset Voltage RS g 2009 2 5 mV Input Offset Current 05 3 pA Input Bias Current 5 20 pA Output Resistance Either Output VOUT VOH 100 9 Response Time TA 25 C VS i5V Notes 2 7 13 25 ns TA 25 C vS 15v Notes 3 7 12 20 ns TA 25 C vS 15v Notes 4 7 14 ns Response Time Difference between Outputs th of vm th of vN2 TA 25 C Notes 2 7 2 ns th of vN2 th of vm TA 25 C Notes 2 7 2 ns th of VIN1 th of VN2 TA 25 C Notes 2 7 2 ns th of vm th of vN2 TA 25 C Notes 2 7 2 ns Input Resistance f 1 MHz 17 k9 Input Capacitance f 1 MHz 3 pF Average Temperature Coef cient of RS 509 8 pV C Input Offset Voltage Average Temperature Coef cient of 7 nA C Input Offset Current Common Mode Input Voltage Range VS 165V i4 45 V Differential Input Voltage Range 5 V Output High Voltage Either Output IOUT 320 pA VS 145V 24 3 V Output Low Voltage Either Output SINK 64 mA 025 04 V Positive Supply Current VS 165V 18 32 mA Negative Supply Current VS 165V 9 16 mA Note 2 Response time measured from the 50 point of a 30 mVpp 10 MHz sinusoidal input to he 50 point of the output Note 3 Response time measured from the 50 point of a 2 Vpp 10 MHz sinusoidal input to the 50 point of the output MAMAnationalcom Electrical Characteristics Continued Note 4 Response time measured from the start of a 100 mV input step with 5 mV overdrive to the time when the output crosses he logic hreshold Note 5 Typical thermal impedances are as follows Cavity DIP J GJA 135 CAN Header H GJA Molded DIP N GJA 130 CAN ej C Note 6 The device may be damaged if used beyond the maximum ratings Note 7 Measurements are made in AC Test Circuit Fanout 1 Note 8 Refer to RETS 160X for LM16OH LM16OJ14 and LM16OJ military specifications Note 9 Human body model 15 kg in series wi h 100 pF Typical Performance Characteristics Offset Voltage Input Current vs Ambient 4 Temperature v 5v 35 v 5v 7 0 5 32 28 4 3 24 2 25 quot6 225 INPUT OFFSET VOLTAGE mV INPUT CURRENT MA 12 08 2 OFFSET 175 V 5V v 5v 15 55 35 15 5 25 45 65 85105125 AMBIENT TEMPERATURE Ci DSOO57078 55 35 15 5 25 45 65 85105125 AMBIENT TEMPERATURE 0C DSOO57079 Supply Current vs Ambient Temperature Propagation Delay vs Ambient Temperature 20 70 v 5v 9 v 5v 60 SEE AC TEST CIRCUIT 50 40 tP011 30 FANOUT4 20 10 tPIJ0 FANOUT 1 SUPPLY CURRENT mA PROPAGATION DELAY ns 0 55 35 15 5 25 45 55 85 105125 AMBIENT TEMPERATURE Ci DSOO570711 55 3515 5 25 45 55 85105125 AMBIENT TEMPERATURE OC DSOO570712 CommonMode Pulse Response E L 3 3 l S 2 39 E E 1 g 0 E g 150 lt 140 S 130 D F 8 0 40 so 120 150 TIME ns DSOO570714 165 CAN Still Air 67 CAN 400 LFmin Air Flow 25 CW Input Characteristics INPUT BIAS CURRENT 11A Delay of Output 1 With Respect to Output 2 vs Ambient Temperature DELAY ns 9 v 5v 8 Vquot 5v 7 5 4 3 2 1 0 1 2 345 DIFFERENTIAL INPUT VOLTAGE V DSOO570710 50 E l I I I OUTPUTI 15V 40 V DELAY 30 OUTPUT 2 15V ov l I l l 20 SEE Ac TEST CIRCUIT I m BOTHOUTPUTSLOADED l 0 FANOUT4 IV 1VFAN0UT1 40 l l I 55 35 15 5 25 45 55 85105125 AMBIENT TEMPERATURE C DSOO570713 wwwnationalcom 09910109 LIN39I LM160ILM360 AC Test Circuit vNJr5o mV 5V V395V OUTPUT T0 v OUTPUTZ INPUTZ VIN 0v W INPUT1 O 0UTPUT1 1N914 1N914 1N914 DSOO57073 FANOUT1 FANOUT4 R24k R630 2 C15 pF C30 pF Nmmvna onaLcon1 Schematic Diagram R7 1k NON INVERTING OUTPUT1 0 GND V39I39 O INVERTING HNPUH OUTPUTZ 39INPUTZ C Q3 1 R21 A 3 387 R4 400 011 Q12 Q13 D7 DSOO57071 5 wwwnationacom 099W39I09 LIN I LM160ILM360 Physical Dimensions inches millimeters unless otherwise noted 0254 508 00100020x45 0008 0010 0203 0254 TYP ALL LEADS 03500370 88909398 DIA 0315 0335 M 8001 8509 MAX 0025 0165 0185 0535 nggngSOLLED 41914599 I V REFERENCE PLANE a a L SEATING PLANE 039035 T f 0 0150 040 0500 0889 0381 1015 ll u ll 1 Lt 0015 0019 DIA WP 0405 0483 0195 0205 DIA 4953 5207 PC 00290045 07371143 0028 0034 0711 0864 lt 45 EDUALLY 0115 0145 2921 3683 DIA SPACED gt H080 REV E Metal Can Package H Order Number LM160H883 NS Package Number H08C U1BQ D197 4800 5004 8 7 5 02280244 5791 6198 0010 MAX 0254 LEAD 1101 1 2 3 4 an If IDENT WP 01500157 quot 38103988 39 0053 0069 1345 1353 3 MAX TYP M ALL LEADS 01020254 f l l 139 391 iED L 39Qn 39 SEATING 3939 39 1quot 0004 f f T T PLANE 1102 L014 0050 0014 0020 ALL LEAD TIPS I 1355 4 TYP r e 3 1270 0008 quot39 03550508 TYP ALL LEADS WP 39 TYP quotquot39 0203 Molded DuallnLine Package M Order Number LM360M or LM360MX NS Package Number M08A MUBA REV H wwwnationalcom Music 160A class notes Dr Rothfarb October 15 2007 A word on the upcoming writing assignment 0 The purpose of the writing assignment is to give you an opportunity to improve or refine your ability to write coherently about music This is a specialized skill that you may not have had much opportunity to develop very thoroughly 0 The piece that you will be asked to write about a short binary form similar to the examples we ve discussed in class will most likely be too short for formal functions expository transitional developmental etc to appear very prominently 0 Your introduction should discuss the readily apparent aspects of the music the form the key structure etc while the body of your paper should explore the specifics of this particular piece register density how cadences are created etc 0 Papers should be no shorter than two pages and no more than four Quiz example 1 Menuet 7 0 In the first example from the quiz shown above is the cadence in m 4 a half cadence or an imperfect authentic cadence 0 Many people wrote HC for this measure 0 This is an imperfect authentic cadence o The actual moment of resolution does not occur on the downbeat of m 4 but rather with the I chord on the third beat This placement on the third beat weakens the cadence providing a less conclusive sense of resolution to be answered by the PAC in m 8 This would be described as a feminine cadence to use the antiquated 19thcentury terminology Joseph Riepel 17091782 0 In an excerpt from his treatise on harmony Joseph Riepel points out through an imagined dialogue between student and teacher the similarity between a minuet and a concerto an aria or a symphony In other words the minuet is built on the same musical basis from which larger forms grow 18 Bach French Suite no 5 BWV 816 1722 Allemande 0 page 12 in the anthology 0 Before beginning an analysis it is prudent to have some idea of what to expect in terms of form and key structure In this case we are looking at a movement from a Baroque suite Since Baroque dance pieces are often in binary form a reasonable suspicion would be that this Allemande is also in binary form 0 Be aware when listening to this piece analytically that Baroque music is very uid It tends to go on and on without an abundance of articulation points Typically rests occur only at the cadences This can make it difficult though far from impossible to track formal patterns
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