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Only the octave stays perfectly in-tune in equal temperament

Only the octave stays perfectly in-tune in equal temperament

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Sep 20, 20262 min read

Only the octave stays perfectly in-tune in equal temperament

Related

  • Equal temperament makes combination tones slightly out of tune (similarity 0.89)
  • No keyboard tuning can make every key sound justly intonated (similarity 0.89)
  • Tenors need not tune their tracts because their pitch-to-formant ratio stays high (similarity 0.86)
  • Even steady-state musical notes vary in amplitude envelope over time. (similarity 0.85)
  • Vibrato produces tremolo when harmonics sweep across resonant peaks (similarity 0.84)
  • Flute playing frequencies are impedance minima; trumpet’s are maxima (similarity 0.84)
  • Equal temperament tuning relies on learned memory with no physical beating guide (similarity 0.83)
  • A capella groups can adopt just intonation, causing overall pitch to drift through keys (similarity 0.83)
  • A pianoforte with raised dampers can physically re-echo sung vowels via sympathetic resonance (similarity 0.82)
  • Musical scales universally favor intervals with small integer frequency ratios (similarity 0.82)
  • A strictly periodic tone can still be perceived as two distinct notes (similarity 0.82)
  • Hard reeds fix pitch, freeing resonators to shape only harmonics (similarity 0.82)
  • Raising a tone’s level lowers low-frequency pitch but raises high-frequency pitch (similarity 0.81)
  • A scale built from pure major-triad intervals yields the just diatonic scale. (similarity 0.81)
  • Halving a bar’s length raises transverse modes two octaves but longitudinal modes one octave. (similarity 0.81)

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  • Only the octave stays perfectly in-tune in equal temperament
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  • A baffling card against a tuning fork makes it dramatically louder
  • A capella groups can adopt just intonation, causing overall pitch to drift through keys
  • A pianoforte with raised dampers can physically re-echo sung vowels via sympathetic resonance
  • A scale built from pure major-triad intervals yields the just diatonic scale.
  • A strictly periodic tone can still be perceived as two distinct notes
  • Equal temperament creates tuning conflicts for mutation stops
  • Equal temperament tuning relies on learned memory with no physical beating guide
  • Flute playing frequencies are impedance minima; trumpet's are maxima
  • Halving a bar's length raises transverse modes two octaves but longitudinal modes one octave.
  • Hard reeds fix pitch, freeing resonators to shape only harmonics
  • Musical instrument acoustics reduce to a source-modifier model
  • No keyboard tuning can make every key sound justly intonated
  • No musical tuning system can be proven superior to another
  • No tuning system can make all diatonic scale intervals perfectly consonant
  • Piano hammers and drumsticks produce repeated impacts creating non-linearity
  • The mel scale conflicts with musical logarithmic scales but remains useful in technical applications
  • Trumpet valves combine with lip synchronization to expand pitch range
  • Vibrato produces tremolo when harmonics sweep across resonant peaks