* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Slides - UMD Physics
Survey
Document related concepts
Tone cluster wikipedia , lookup
Chichewa tenses wikipedia , lookup
Schenkerian analysis wikipedia , lookup
Mode (music) wikipedia , lookup
Pitch-accent language wikipedia , lookup
Traditional sub-Saharan African harmony wikipedia , lookup
Chichewa tones wikipedia , lookup
Tone (linguistics) wikipedia , lookup
Luganda tones wikipedia , lookup
Strähle construction wikipedia , lookup
Microtonal music wikipedia , lookup
Circle of fifths wikipedia , lookup
Consonance and dissonance wikipedia , lookup
Equal temperament wikipedia , lookup
Transcript
A little music theory (mostly notation, names, …and temperament) Nature or nurture Physical: It has nothing to do with human beings. Ex: beating Psychophysical, psychological: human anatomy. Ex: fundamental tracking Cultural: society dependent. Ex: appreciation of Beattles songs Doubling the frequency feels like the same pitch (pitch periodicity) f and its harmonics: f, 2f, 3f, 4f, … 2f and its harmonics: 2f, 4f, 6f, … This is not a cultural phenomena, it seems to be present in any musical culture. In Western music the pitch range from f to 2f is split in 12 steps (entirely cultural) f f0 2 f0 C, C#/Db, D, D#/Eb, E, E#, Fb, F, F#/Gb, G, G#/Ab, A, A#/Bb, B or do, do#/re b, re, re#/mi b, mi, mi#/fa b, fa, fa#, sol, sol#/la b, la, la#/sib, si C# D# ... F# G# A# C D EF C2 C3 G A B C C4 ... This has changed historically but now it’s standard to take: A4 = 440 Hz So A5 = 880 Hz, A3 = 220 Hz, … For the intermediate notes the whole thing is more contentious (we’ll discuss temperament later) higher What about the #’s and b’s ? C# Ab What about the duration of notes ? half half Measure time in beats four beats in a measure this will count as one beat slightly more complex several instruments Consonance and dissonance [Let us play some intervals and find what makes them consonant or dissonant] C C# D D# E F F# minor major minor major 4th tritone 2nd 2nd 3rd 3rd G G# A A# B C 5th minor major minor major 6th 6th 7th 7th ratio of frequencies = ratio of small integers consonance Examples: 1/1 unison 2/1 octave = 7 tones 3/2 fifth = 3 ½ tones (actually 1.4983) 4/3 fourth = 2 ½ tones (actually 1.22482) 5/4 major third = 2 tones (actually 1.25991) Consonance/dissonance and the overtone series unison = 0 tones octave = 7 tones fifth = 3 ½ tones fourth = 2 ½ tones major third = 2 tones consonance beating roughness consonance roughness … Temperament Problem: choose the frequencies of the notes (C, C#, D, …) in order to make the consonances very good consonances Remember: the best consonances are Octaves: 2/1 6 tones = 12 semitones Fifths: 3/2 3 ½ tones = 7 semitones Fourths: 4/3 2 ½ tones = 5 semitones Major thirds: 5/4 2 tones = 4 semitones … It is impossible to assign frequencies to the notes C C# D D# E F F# G G# A A# In such a way as to keep all fifths = 3/2, fourths = 4/3, … exact B C 7 octaves 27 C G 3 2 D A E 3 2 3 2 3 2 B 3 2 F# 3 2 C# 3 2 G# 3 2 D# A# F C 3 2 3 2 3 2 12 3 129.746 2 27 128 not the same 3 2 Pythagorean solution Make the octaves and fifths perfect C D E F 1 9/8 81/64 4/3 33 22 2 27 3 16 2 2 G A B C 3/2 27/16 243/128 2 one tone = 9/8 C D 1 9/8 ½ tone = 256/243 E F 81/64 4/3 G B C 3/2 27/16 243/128 2 1 tone = (256/243)2 = 1.1098… 1 tone = 9/8 = 1.125 A Pythagorean comma 1.58 1.60 close, but not the same ! Can you hear the bad Pythagorean thirds ? Perfect third : f2/f1 = 5/4=1.25 Perfect third : f2/f1 = 81/64 = 1.265… In the Pythagorean temperament some keys are better than others Samuel Barber's Adagio for Strings courtesy of G. Moore C Ab Other temperaments Pythagorean: good fifth (except one), bad thirds Just: some thirds and fifths are good (tonic, dominant and subdominant of some keys) Meantone: better thirds than fifths ... Equal temperament: split the difference equally among notes. Nothing is perfect, nothing is too bad Recap of Music Theory half tone tone C3 C4 same interval = same ratio of frequencies Consonances: sensation of calm and repose Frequency ratios 2/1 3/2 4/3 5/4 name octave fifth forth major third Dissonances: sensation of tension Frequency ratios name 729/512 tritone 243/128 minor second Temperament: an assignment of frequencies to all twelve notes from C to B It is impossible to find a temperament where all the octaves and fifths are perfect Pythagorean: all octaves and all but one fifth are perfect. One fifth is very off (pythagorean comma). Well or equal : split the differences equally. Every semitone = 1.059… Equal temperament C C# D D# E F F# G G# A A# r r2 r12=2 r12 2 r 12 2 1.05946... B C Nothing too good, nothing too bad … Fifths: r7 = 1.498 instead of 3/2=1.5 Fourths: r5 = 1.3348 instead of 4/3=1.3333 Thirds: r3=1.25992 instead of 5/4=1.25 …