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多么刺耳的是被增添的三人組合？
Hoe tegenstrijdig is het vergrote drietal?
Combien dissonante est la triade augmentée ?
Ist der vergrößerte Dreier wie unstimmig?
Πόσο ασύμφωνη είναι η αυξημένη τριάδα;
Quanto discordante è la triade aumentata?
増加されたトライアドはいかに調和しないか。
증강한 3 인조는 얼마나 부조화 인가?
Como divergente é a tríade aumentada?
Как несозвучна увеличенная тройчатка?
¿Cómo disonante es la tríada aumentada?
KEY WORDS:
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statistical abnormal psychologically normal population sample biases study participants representative excluded listeners music theory music theorists authority scientific research abnormal listening analysis composition thesis dissonance harmonic instability literature augmented triad
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interchangeable conclusion partial clarification definitions clarity problem roughness lack of resolution correlate musically correlation thesis augmented triad {C,E,G#} 3-12 {0,4,8} pitch-class structures treatment.execute semantic sleights of hand emphasize context spelling inversion intonation standard classification system for pc sets equal temperament traditional tonality analysisequal-tempered music string music vocal music augmented triad 3-12 verticalities octave-transposed major thirds augmented fifth diminished fourth interval simple mathematical ratios defined consonant divisions string monochord partials overblown wind instruments
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claims tonal theorists effect harshness augmented triad softened first inversion deduce treatment diminished triad derive grammars earlier music equal temperament verticalities free organum monophonist pitch collections {B,D,F} {C,F,G} sound consonant lowest voice consonant upper voices perfect fourth Renaissance pitch structures {0,4,8} hear pitch class 8 [0,4,8] G Ab representing nonsimple mathematical rati 0 C 4E determining tonal context preferred inversion hear equally tempered thirds just pythagorean thirds augmented diminished interval {0,3,7} register transposition
vertical sonority audible intended size obvious earlier systems intonation ironic monophonist equal-tempered perfect fifth unstable
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justly intoned augmented fifth derive rational division string dissonance {0,4,8} G# Ab intrinsic dissonance augmented triad defining tonal context research complexity ratios fundamental frequencies perceived pitch dissonance proximity audible overtones audible secondary frequencies instruments sine waves pure-octave timbres Shepard's tones conforming natural overtone series metallophone timbres harmonically stable major triad fundamental tones maximally distant musical timbres mathematically simple intervals acoustically dissonant tonal theory nonstandard internal harmonic structures harmonic timbres monophonic theory natural overtones simple intervals complex equal temperament
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augmented triad dissonant augmented fifth monophonist criterion) assumption normal overtone structures monochord idealized systems intonation equal temperament applied tonal theory consonance equal-tempered tonal music contradictory assumptions triadic dissonance major triad mistuning chords monophonist model misalignment overtones minor sixth diminished fourth infer {0,4,8} harmonically stable {0,3,7} timbres pitch collections horizontal diagonal pitch collections vertical presentations {0,3,7}
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perceived instability {0,4,8} compared {0,3,7} function conditioning innate psychoacoustic preferences inference observations limited scientific inquiry augmented fifth arguments consonance augmented triad conditional plausible counterargument perceived instability point of contention survey of available literature theorists of record limit opinions visceral consensus test hypothesisconditions short-term conditioning cause significant changes perception {0,4,8} {0,3,7} harmonically stable
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conditions conditioning sufficient induce hear 3-12 stable 3-11 musically abnormal timbres nonstandard intonation complex pitch structures experimental stimuli tonal atonal music
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manuals of theory augmented triad interval content consonance dissonance dissonant defined implied criteria
Music theorists unstable rough lacking a clear root acoustic numerological psychoacoustic perceptual cognitive tonal-syntactic phenomenological psychoacoustics limitations human senses acoustic events cues cognition notation acoustic signal
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music theorist's augmented triad significant theorist inclusion perspectives numerological perspectives acoustical perspectives physics physiology physiological responses complex cognitive responses learning construction conception dissonance.
music theorists Johann Mattheson (1681-1764) mathematically-minded music theorists Early Western music theorists Pythagoras minor sixth Franco of Cologne contemporaries major and minor thirds major and minor sixths criterion of dissonance
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musician dissonant sonorities describable augmented triads
Zarlino harmony two intervals
species perfect imperfect inharmonious
dissonant combinations numerological objections consecutive harmonic intervals Sixteenth-Century style appeal to practical utility objections parallel fifths octaves direct fifths perceived ugliness observation vocalists sing parallel gesture Duplication intervals smooth sounding intonation arithmetic derivation major third interval deliberate superimposition debatable intervals

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