* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download class9#
Survey
Document related concepts
Sonata form wikipedia , lookup
Microtonal music wikipedia , lookup
Pitch-accent language wikipedia , lookup
Figured bass wikipedia , lookup
Chord names and symbols (popular music) wikipedia , lookup
Consonance and dissonance wikipedia , lookup
Circle of fifths wikipedia , lookup
Chord (music) wikipedia , lookup
Mode (music) wikipedia , lookup
Traditional sub-Saharan African harmony wikipedia , lookup
Quarter-comma meantone wikipedia , lookup
Schenkerian analysis wikipedia , lookup
Transcript
01-11-14 13:46 class9.scm Page 1 1 2 3 STRUCTURE AND INTERPRETATION OF MUSIC CONCEPTS 4 ______________________________________________ 5 ============================================== 6 7 CLASS 9: The Tonal System 8 _________________________ 9 ========================= 10 11 WHAT IS TONALITY? 12 The tonal system organizes notes into a "context" in which they have 13 ROLES and EXPECTED BEHAVIOR. For that purpose, music in the tonal 14 system is always related to a SCALE, which is the context object. 15 The role and behavior of notes in a tonal piece is determined by their 16 position (relative status) in the scale. 17 18 The central, most important role is "played" by the TONIC note of a 19 scale -- its first note: 20 "Tonic is the tone of ultimate rest, the other notes tend 21 to move toward the tonic" (L. B. Meyer 1956). 22 23 The definition emphasizes the expected behavior role, that the tonal 24 system attributes to its different notes. The behavior role is 25 classified as STABLE or DYNAMIC. The tonic is the most stable tone 26 in the SCALE. Usually it is the last note in a melody or music 27 piece. The tonic or the notes of the tonic triad are usually the 28 beginning notes. 29 30 A small experiment about the sense of tonality: 31 =============================================== 32 1. Listen to a "typical" tonal music piece and try to perceive the 33 feeling of tonality -- identify the tonic note. 34 Suggestion: The first movement of Mozart's "Eine Kleine Nachtmusik" 35 (~5 min), 36 or, 37 the Minuet (only 2 melodic lines; 38 ~1 min. without the trio). 39 The end should feel like the (a?) ultimate rest of the piece. 40 41 2. The following example includes a small segment, with various ending 42 43 stable). 44 45 46 47 48 49 3. Kleine 50 51 52 53 54 4. 55 56 suggestions. Rate the ending notes from 1 (most unstable) to 5 (most Do it fast and intuitively - only 2 seconds for rating between the examples. Repeat the process (for a refined rating). Tonal-ending-1: Different endings. Listen only to the first 4 bars of the first movement of "Eine Nachtmusik" . Try to answer the same questions as above. Does it feels like we get to the (an?) ultimate rest? Listen to the first 4 bars, as in (3), and to various ending suggestions. Rate the ending notes as in (2). 01-11-14 13:46 57 58 59 60 61 62 63 64 scale, 65 66 67 68 69 70 their 71 72 73 74 catch: 75 76 77 78 79 class9.scm Page 2 Tonal-ending-2: (3) with different endings. TONALITY -- A CIRCULAR VIEW: ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * A tonal piece can be conceived as a scene whose meaning, interpretation, content, and almost anything one would like to attribute to it, derives from its CONTEXT (its scale, primary embedded scales, scale-inter-relations). --> THE SCALE DETERMINES THE PITCH BEHAVIOR. BUT: * The context of a piece (scale) is defined by its pitch content and its interaction with the rhythm dimension. Pitch content -- simultaneous and sequential combinations, and interaction. --> THE PITCH BEHAVIOR DETERMINES THE SCALE. So -- indeed, any definition of tonality gets into that circular The tonality of a piece is defined by its pitch content which is dictated by its tonality. Examples of pitch behavior, as determined by context (scale): ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 80 1. class) 81 82 83 84 Therefore, 85 86 87 88 89 notes are 90 movement 91 92 93 94 2. (attached 95 96 same 97 98 dictate 99 100 101 into 102 into 103 104 105 degree. 106 107 108 109 context 110 dominance 111 112 Consider the behavior of G# and Ab (same music-level pitch in C major. G# will be usually part of a transposition to A major (A) or A minor (Am), so it will function as a leading tone to A. Ab will probably be part of a modulation to Fm or Eb. it will go down to G. Ab and G# are not part of C, so they will point to some other scale and behave according to there function in that context. Another possibility: In a CHROMATHIC PASSAGE, the chromatic not assigned any harmonic function. In that case, an upward is indicated by an uplifting alteration -- #, and a downward movement is indicated by a downgrading alteration -- b. Consider the two chord progressions in the note example to these class notes). The first chord in both progressions consists of exactly the music-level pitch-classes (and music pitches as well). However, they consist of different tonal-pitch-classes, which the difference in their behavior. In the first progression (A), the first chord functions as a seventh chord on the dominant (V) of F major, and is resolved the tonic triad, with the Bb note (IV degree) being resolved the III degree. The IV degree here plays a central role, since it implies that this is a dominant chord in F major, and being a DYNAMIC degree, it "requires" a resolution into the III In the second progression (B), the first chord functions as a German chord (part of broader harmony repertoire of chords). It is interpreted as a subdominant chord (IV) within the of the E or Em scales. Therefore, it is resolved to the of E (a B major chord). 01-11-14 13:46 class9.scm Page 3 113 114 A large part of the research in Music Cognition indeed concentrates 115 on issues of the emergence of tonal sensation. Studies in music 116 analysis, traditionally, deal with the understanding of the music 117 content of a piece, with respect to its scale context. 118 119 Given that circular characterization, all that is left is to dive 120 into the components of the tonal system, and leave the philosophy 121 of tonal sensation for later discussion. 122 123 124 125 The TONAL DOMAIN OF NOTES 126 ========================= 127 128 The DOMAIN OF NOTES in the western tonal system is generated by the 129 selection of seven Pitch Classes from within the twelve Pitch 130 classes that generate the well-tempered domain of notes. These are 131 called the DIATONIC pitch classes. 132 The selected diatonic pitch-classes: 0, 2, 4, 5, 7, 9, 11 133 134 ** PITCH-CLASS ORDERING: a cyclic, modulo 12, ordering of the 135 pitch-classes 0, 1, ..., 11. 136 ** DIATONIC PITCH-CLASS ORDERING: a cyclic, modulo 7, ordering of 137 the diatonic pitch-classes: 0, 2, 4, 5, 7, 9, 11. 138 Names of the diatonic pitch-classes: C, D, E, F, G, A, B, 139 respectively. 140 Names of the diatonic interval-classes created by the diatonic 141 pitch-classes: 142 FIRST, SECOND, THIRD, FOURTH, 143 FIFTH, SIX, SEVENTH, 144 (OCTAVE), 145 respectively. 146 147 This "double-pitch-class" characterization gives rise to a rich 148 ***TONAL PITCH-CLASS*** terminology, that reflects both the diatonic 149 pitch-class and the 12-tone pitch-class orderings. For example: 150 C, C#, Db, D,...., with further possibilities for C##, Dbb, etc. 151 152 The tonal pitch-class domain is no longer totally ordered by a proper 153 < relation based on the music pitch-class, since it includes values 154 that map into the same music pitch-class. 155 Clearly, it can be totally ordered by a weak < relation, but it seems 156 the 157 158 159 160 161 162 163 class 164 165 166 spans 167 168 that a lexicographic like relation, defined by considering both diatonic and the pitch-class ordering is more meaningful. This is part of the tonal-music arithmetics, introduced later on. THE SCALES: =========== The scales of the tonal system derive from the diatonic pitchordering. * A SCALE-TYPE is defined by a sequence of intervals, that a whole cycle within the diatonic pitch-class ordering. The sum of the intervals within a scale type is the OCTAVE 01-11-14 13:46 169 170 171 172 when it 173 the 174 175 176 177 with the 178 179 semitones: 180 181 harmonic. 182 183 184 185 186 187 * 188 189 diatonic class9.scm Page 4 interval. The two main scale types are the MAJOR and the MINOR scales. - The MAJOR SCALE-TYPE (henceforth, we omit the word "type" can be understood from the context) is defined by starting sequence with the 0 pitch class. The major scale is defined by the sequence of semitones: 2, 2, 1, 2, 2, 2, 1. - The MINOR SCALE-TYPE is defined by starting the sequence 9 pitch class. The minor scale-type is defined by the sequence of 2, 1, 2, 2, 1, 2, 2. The minor scale-type has several variants: melodic, MELODIC SCALE-TYPE: 2, 1, 2, 2, 2, 2, 1. HARMONIC SCALE-TYPE: 2, 1, 2, 2, 1, 3, 1. - During the history of western tonal music, further "modes" have been used. A SCALE is an "instance" of a scale type: A sequence of tonal pitch-classes, obtained by projecting the scale-type on the tonal-pitch-class domain (using the 190 pitch-class ordering). Therefore, a scale is an ORDERED SEQUENCE 191 of tonal pitch-classes, that spans a whole cycle in the diatonic 192 pitch-class ordering -- an octave. 193 The pitch-classes in a scale are called: DEGREES. 194 A scale is named "after" its first pitch-class: 195 C-Major (CM for short), C-minor (Cm), .... 196 197 198 * Naming the scale degrees: 199 I -- Tonic. 200 II -- Super tonic. 201 III -- Mediant. 202 IV -- Subdominant. 203 V -- Dominant. 204 VI -- Submediant. 205 VII -206 207 208 Dominance ordering of the scale elements: 209 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 210 The degrees of a scale are ordered by their DOMINANCE status: 211 TONIC (I) 212 MEDIANT (III) 213 DOMINNAT (V) 214 SUBMDIANT (VI) 215 SUBDOMINANT (IV) 216 SUPER TONIC (II) 217 VII 218 219 That is, the scale is totally ordered by a dominance ordering (which is 220 different from its pitch-class ordering). 221 Note that the names of the scale degrees refer to their relative interval 222 with either the tonic or the dominant-- probably, reflecting the dominant 223 status of the latter. 224 01-11-14 13:46 225 226 227 class9.scm Page Stable/dynamic classification of scale elements and intervals: ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 1. Scale elements: 5 228 The dominance position implies a stable/dynamic characterization. 229 The tonic element is the most stable. 230 The leading element (VII-th degree) is the most dynamic. Its 231 occurrence requires a RESOLUTION -- move towards a more stable 232 element. 233 234 The stable/dynamic characterization follows the dominance ordering 235 position. Tonic -- most stable, VII -- least stable. 236 237 2. Scale intervals: 238 The scale intervals are classified as CONSONANT/DISSONANT. 239 The intervals of the tonic triad and their inversions 240 (complimentary intervals) are CONSONANT. The other intervals 241 are DISSONANT. 242 * Consonant intervals are stable -- can stand for themselves. 243 * Dissonant intervals are dynamic -- require resolution to a stable 244 interval. 245 246 The tonal domain of notes 247 ~~~~~~~~~~~~~~~~~~~~~~~~~ 248 The need for this, supposedly "redundant" domain of pitch-classes arise 249 from the diatonic role that pitch-class play with respect to a scale context. 250 For example, an F# might function as a VII in G Major, or as an uplifted 251 IV in C major, while Gb can function as a downgraded II in F major. 252 253 The number of pitch-classes in the western tonal music is larger than the 254 number of pitch-classes to which they are mapped on the physical dimension. 255 This rich domain is used to reflect the diatonic role of the pitch-classes. 256 257 * Tonal pitch-class domain (TPC): 258 TPC = Diatonic-value x alteration value = 259 = {C, D, E, F, G, A, B} x {bb, b, &, #, ##} 260 * Tonal pitch domain (TP): 261 TP = Octave x TPC = Int x TPC. 262 The Octave domain is taken as the set of integers. The exact meaning 263 of the tonal pitch-class values and the tonal pitch values is 264 determined by the mapping of the values on the tonal pitch dimension 265 to the physical pitch dimension. 266 267 HARMONY 268 ======= 269 270 Tonal harmony deals with inter-relationships among notes, that arise 271 from the interval-structures created among them. 272 The interval-structures are characterized by chord-types and their 273 properties. 274 275 This is a broad view of harmony, that concentrates on the interval 276 structures, and is not restricted to simultaneity of note occurrences. 277 278 The Triad: 279 ~~~~~~~~~~ 280 The interval structures of tonal harmony are generated by 01-11-14 13:46 class9.scm Page 6 281 TRIAD chords. 282 A triad consists of a sequence of two THIRD intervals. The various 283 kinds of triads arise from constructing them along a scale type. 284 The triads are also commonly referenced with respect to the 285 corresponding scale degrees. 286 287 - A TRIAD-TYPE is a sequence of two third intervals. 288 289 - A TRIAD is an instance of a triad-type, obtained by projecting 290 a triad-type in the pitch-class ordering. 291 292 - Main triad-types: 293 * MAJOR triad-type: 4, 3 semitone intervals. 294 * MINOR triad-type: 3, 4 semitone intervals. 295 * DIMINISHED triad-type: 3, 3 semitone intervals. 296 * AUGMENTED triad-type: 4, 4 semitone intervals. 297 298 THE TRIADS BUILT ON SCALE DEGREES: 299 - MAJOR SCALE: 300 Tonic (I), Dominant (V), and subdominant (IV) triads -301 Instances of the major triad-type: 302 I - C, E, G. 303 IV - F, A, C. 304 V - G, B, D. 305 II, III, VI triads -- Instances of the minor triad-type: 306 II - D, F, A. 307 III - E, G, B. 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 VI - A, C, E. VII triad -- instance of the diminished triad-type: B, D, F. - MINOR SCALE: Tonic (I), Dominant (V), and subdominant (IV) triads -Instances of the minor triad-type: I - A, C, E. IV - D, F, A. V - E, G, B. III, VI, VII triads -- Instances of the major triad-type: III - C, E, G. VI - F, A, C. VII - G, B, D. II triad -- instance of the diminished triad-type: B, D, F. - HARMONIC MINOR SCALE: Tonic (I), subdominant (IV) triads -- Instances of the minor triad-type: I - A, C, E. IV - D, F, A. V, VII triads -- Instances of the major triad-type: V - E, G#, B. VI - F, A, C. III triad -- instance of the augmented triad-type: C, E, G#. II, VII triads -- instances of the diminished triad-type: II - B, D, F. VII - G#, B, D. - MELODIC MINOR SCALE: 01-11-14 13:46 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 class9.scm Page 7 Tonic (I), II triads -- Instances of the minor triad-type: I - A, C, E. II - B, D, F#. IV, V triads -- Instances of the major triad-type: IV - D, F#, A. V - E, G#, B. III triad -- instance of the augmented triad-type: C, E, G#. VI, VII triads -- instances of the diminished triad-type: VI - F#, A, C. VII - G#, B, D. Harmony plays a major role in melody structuring, and in the construction of its accompaniment. Music analysis distinguishes between SMALL RANGE to LARGE RANGE harmony. 352 * Small range harmony -353 study of the chord structure, with respect to the scale 354 context (key). 355 * Large range harmony -356 study of key (scale context) relationships. 357 358 The scale context assigns ROLES/FUNCTIONS to the chords, based on their 359 consonance/dissonance or stable/dynamic characterization. 360 These roles determine various chord successions. 361 For example: 362 The CADENCE part in a major scale is based on the progression 363 of 364 I -> IV -> V -> I. 365 Finer chord progression rules refine the progressions, using 366 characterization of chord functions. In the cadence that 367 might imply the progression 368 I -> II -> V -> I 369 that arises from similar harmonic scale function of the II 370 and the IV degrees. Both degrees function as subdominant degrees 371 in the cadence. 372 373 The chord progressions provide the basis for the chord structure of 374 the piece. Each part in a progression can include a whole 375 segment/piece that carries the same chord function. For example, 376 the above cadence progressions, can be extended into: 377 I -> VI -> IV -> II -> V -> I. 378 379 This way, a basic cadence can be extended into a complex chord 380 progression, triads can be elaborated into richer chords (e.g., 381 in Jazz, chords are extended with additional notes -382 like 7, 9, 11, 13 chords). 383 384 In general, the way chords are combined into chord progressions 385 is dictated by the chord functions and by the pitch-class dominance 386 in the context scale. These properties yield "rules" (characterizations) 387 of typical voice leading for creating chord progressions. 388 389 390 STUDIES IN THE TONAL SYSTEM: 391 ============================ 392 01-11-14 13:46 class9.scm Page 8 393 Analytical research in the tonal system study, not only the content of 394 music pieces, but also the fundamental assumptions that underlie 395 the tonal system. 396 For example, there are studies into the essential SELECTIONS done by 397 the tonal system, and even the 12 note selection within an octave. 398 Such studies try to understand the advantages/limitations of different 399 selections of pitch-classes, on which music systems can be built (Dahlia 400 Cohen). 401 402 An intensive direction in the study of tonal music basics is in the 403 direction of MUSIC PERCEPTION. Such studies try to understand 404 when/why/how does the sensation of a tonal context arise. They also 405 try to find characteristics of various tonal contexts. 406 For example: 407 Experiments done by Krumhansl suggest that the perception of key 408 (scale) depends on the frequency of occurrences and duration of 409 the pitch classes. One product of these experiments is a table of 410 pitch class rating in a given scale. These experiments might imply 411 methods for creating tonal melodies (Krumhansl, Cognitive Foundation 412 of Musical Pitch, Oxford University Press, 1990). 413 414 415 416