Sonic Visualiser

h1. About the Measure tool and its limitations

The Sonic Visualiser Help reference "describes the Measure tool":http://www.sonicvisualiser.org/doc/reference/2.0/en/#measurements like this:

> The measure tool enables you to obtain measurements in scale units (such as time in the X coordinate, or whatever the Y coordinate of the current layer represents) corresponding to certain pixel positions. To measure a region, just click and drag a rectangle covering it, using the left mouse button with the measure tool selected ...

> It's important to note that the measurements shown in this way are based entirely on the pixel coordinates of the measurement rectangle, not on properties of the data being displayed.

The measure tool also has the ability to produce an automatic bounding box for a graphical feature, when double-clicked:

> The area enclosed by the rectangle is based on the extent of similarly-coloured pixels surrounding the click position: it is entirely graphical, involving no audio analysis, and so depends on the gain and colour scheme in use in the spectrogram.

Here's an example of what that means in terms of the practical limitations of the tool.

!>measure.png!

This is a recording of a singer, with vibrato. For this illustration I have switched off all of the spectrogram interpolation options in the preferences. The image shown here is a composite of three separately-highlighted measure boxes, because it isn't actually possible to highlight all three at once in SV. Let's imagine we want to measure the variation in pitch of the singer's vibrato about a nominal note pitch.

The *bottom* measurement box shows a box with a frequency-scale range from 268.3 to 296.2Hz. These are the values that you would find if you took the green-line pixel positions and read them off against the scale on the left, interpolating appropriately (and taking into account that it's a log frequency scale). The frequency difference from top to bottom is 27.9Hz, but we want it in semitones, which corresponds to a frequency ratio rather than a frequency difference. Our ratio here is 296.2/268.3 = 1.104, for a semitone range of 12 * log2(1.104) = 1.712 semitones.

How accurate is that as an estimate of the singer's vibrato range? This is an 8192-bin spectrogram; the bin resolution of 44100/8192 = 5.38Hz corresponds to 0.34 semitones at this pitch -- that is, 12 * log2((268.3 + 5.38) / 268.3). Not very accurate.

Moving up, the *middle* measurement box shows the same rectangle around a higher harmonic of the same note. This time the range from 537.9 to 581.8Hz gives a 1.36 semitone range. This harmonic has double the frequency of the first; if we just doubled the frequency limits from the first box, we'd have 536.6 to 592.4Hz so this is tighter at both top and bottom, but particularly at the top where our placement of the green line was a bit optimistic in the first box.

However, this still overestimates the vibrato range. That's partly because the spectrogram still has limited bin resolution here: at twice the lower frequency, it now has a 0.17 semitone per bin resolution. It's partly because of the width of the central spectral lobe: even a pure sine tone gets smudged a bit across three visible bins at this colour scale, when the transform is windowed with any window that produces less leakage elsewhere than a rectangular one does. And it's partly because the signal is moving across bins, so it looks "thicker".

The *top* measurement box appears around a far higher harmonic (the 23rd) of this note, in a 2048-bin spectrogram. Up here the air is nice and clear and there is much higher resolution available in semitone terms. Also, I've made more effort to place the green lines through the "middle" of the trace rather than simply drawing around it. Here the frequency range from 6229.8 to 6580.2Hz gives us a semitone range of 0.95, a lot more conservative than the other estimates.