Frequency

Frequency is one of the most fundamental properties of sound and is central to musical analysis. It is measured in Hertz (Hz), the number of vibrations per second.

Basic Principles

When air molecules vibrate in a regular pattern, we perceive the frequency of the vibration as a musical pitch — the faster the vibration, the higher the perceived pitch. In the displays of VoceVista, faster vibrations appear as more closely spaced peaks in the Waveform, and as higher positions on the frequency axis of the Spectrum and Spectrogram.

Musical Context

Frequencies map to musical notes:

  • The musical note A4 (concert pitch) corresponds to 440 Hz by convention. VoceVista can be reconfigured for non-standard tunings.

  • Each octave represents a doubling of frequency.

  • Each semitone of equal temperament multiplies the frequency by the twelfth root of 2 (about 1.0595).

  • One cent is one hundredth of a semitone — a useful unit for measuring fine deviations in intonation.

Linear and Logarithmic Frequency Scales

The Spectrum and Spectrogram can show frequency on a linear or a logarithmic scale, and the choice has a strong effect on what stands out in the display.

A linear scale spaces frequencies equally: every Hz takes the same amount of space. The harmonics of a held tone are evenly spaced, which makes harmonic structure easy to see and to count, and the upper part of the spectrum gets a generous amount of room.

A logarithmic scale gives each octave the same amount of space. This matches the way we hear pitch: equal musical intervals appear as equal distances on the screen, and piano keys, drawn against the scale, are evenly spaced. A log scale is usually preferred for musical and pedagogical work.

Frequency Resolution

The frequency resolution of the analysis is the smallest difference in Hz that the analyzer can resolve as two separate frequencies. It depends on three interacting choices:

FFT size

The number of samples in each FFT calculation. Larger FFTs resolve finer differences in frequency.

Time window

A longer analysis window lets the FFT see more cycles of a slow vibration, and so resolves low frequencies more precisely. A shorter window, conversely, responds faster to changes over time.

Window function

The shape applied to the samples before the FFT (see FFT Window Function). It controls how cleanly two close frequencies are separated and how much each peak smears into its neighbors.

There is no single best setting: better frequency resolution always costs time resolution, and vice versa.

Limits

The lowest measurable frequency is set by the analysis window: if the window is shorter than one cycle of the signal, there is no full cycle for the FFT to measure. A 50 Hz tone has a 20 ms cycle, so a window shorter than that simply cannot represent it as a frequency.

The highest measurable frequency is set by the sampling rate of the recording. The Nyquist limit — half the sampling rate — is the highest frequency a digital recording can encode. A 44.1 kHz recording reaches up to 22.05 kHz; a 48 kHz recording reaches 24 kHz. The microphone and playback chain further restrict what can be captured and reproduced in practice.

For comparison, healthy young human hearing covers roughly 20 Hz to 20 kHz, so the analyzable range usually exceeds what you can hear.

Applications

Understanding frequency is at the core of many uses of VoceVista: precise pitch measurement for intonation work, harmonic analysis of complex tones, identification of formants in vocal pedagogy, assessment of tuning, characterization of vibrato, study of vocal registration, and comparison of timbre.

In VoceVista

The frequency scale of the Spectrum and Spectrogram is configured in Scale Settings; FFT size, window function, and resolution are in Analyzer Settings.