Analyses of A cappella Tuning Practice

Anonymous 4 "O gloriosa domina"

Spectrograph and technical details

This graph was generated using Spectrogram freeware. The settings were as follows:

  • 8 kHz mono .WAV file, providing an upper band limit of 4 kHz (somewhere in the top octave of the piano)
  • Lower band limit 180 Hz (around F# below middle-C)
  • 1 Hz resolution logarithmic scale (8192 FFT points)
  • 30 ms Time Scale (horizontal resolution), somewhat compromised here by conversion to a small enough .GIF file to fit on a 640X480 screen. The actual frequency analysis was done on a 12 ms Time Scale for better resolution, but it didn't shrink down to browser size very well.

As always with group vocals, many notes have frequency bands several cents wide. However, there is always a recognizable center, and usually a particularly strong band only 2 or 3 cents wide. The yellow and orange are about 9 dB stronger than the light blue-green, which is a significant difference. When in doubt, the overtones were of use in narrowing down the strongest frequency.

This is only the first verse, so you can see some detail without having to scroll sidewise.

Interpreting this graph:
The light-tan-on-black area at the top is a simple time-vs.-amplitude waveform graph for reference.
The x-axis is time
The y-axis is frequency with 180 Hz at the bottom and 4 kHz at the top (not 8 kHz as previously listed).
Amplitude is indicated by color:

  • Black indicates little or no amplitude.
  • Dark blue is a little,
  • lighter blue into green somewhat stronger,
  • yellow very strong, and
  • orange strongest.
  • Purple lines indicate the 5-limit Just ideal that the analysis assumes. From the bottom up they represent C, D, E, F, G, A. 1/1 was fixed on the mean pitch of the 4 sets of Ds in the first verse.

It can be readily seen that the overtones don't line up very well horizontally, indicating that the overall tuning is not Just, not even Pythagorean. It might almost be described as chaotic*, on a small but significant scale (no pun intended). By comparison, when you look at a spectrograph of a 4-part, 7-limit JI synthesized piece, the upper partials look like a lattice, or like grid paper.
*"Chaotic" is not a bad thing. Chaos theory, which describes intricate patterns of a fractal nature, is at the root of the most interesting phenomena in the universe.

If you lose track of the accompanying Chart1 page, this button

should re-open it for you while leaving this page open, too.

Written by David J. Finnamore June 11-12, 1999
I look forward to reading your comments and suggestions!
You may email me at
or the whole Tuning List, on which this discussion is being held, at