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  1. The spectrum analyzer samples the sound wave forms, and displays a graph of magnitude as a function of frequency. When the spectrum of a periodic wave form is viewed on such an instrument, there will appear a peak at the fundamental, and a series of peaks at each harmonic present in the wave form:

  2. Converts the incoming signal to an Intermediate Frequency (IF) signal and performs: Carrier frequency tuning – selects desired signal. Filtering – separates signal from other modulated signals picked up. Amplification – compensates for transmission losses in the signal path.

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  3. Scales are anchored pitch systems. The anchor is the tonic, first note in the scale. The pitch intervals of the notes re: the tonic give the scale its characteristic tonality. Scales include both consonant and dissonant intervals that provide tonal contrast.

  4. To go from A 4 up three semitones to C 5 (a minor third), multiply 440 Hz three times by the twelfth root of two (or once by the fourth root of two, approximately 1.189207). For other tuning schemes, refer to musical tuning. This list of frequencies is for a theoretically ideal piano.

    Piano Key Number
    Midi Note Number
    Helmholtz Name [5]
    Scientific Pitch Name [5]
    108
    119
    b′′′′′
    B 8
    107
    118
    a ♯ ′′′′′/b ♭ ...
    A ♯8 /B ♭8
    106
    117
    a′′′′′
    A 8
    105
    116
    g ♯ ′′′′′/a ♭ ...
    G ♯8 /A ♭8
  5. Tuning: to hear minute changes in relative frequency (tuning of guitars, violins, pianos) • Amplitude measurement with an adjustable reference

  6. To satisfy equal temperament and inharmonicity in piano tuning, complex and subtle adjustments are made. This paper explores the theoretical and practical details and challenges involved in piano tuning.

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  8. However, piano strings have some degree of sti ness, which implies that their spectrum is slightly inharmonic, and this explains why the tuning of the piano is actually \stretched", with octaves slightly larger than should [6, p.389].

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