Formant Analysis

         Most acoustic instruments produce prominent formant frequencies. Formants are resonances that are characteristic of a sound. Phonemes can be characterized by 3 prominent formants or frequency regions. A particular set of formant frequencies characterize each vowel and are relatively independent of a voices pitch. Female and male voices obviously have different formant frequency ranges, however the ratio between formant frequencies is consistent across males, females, adults, and children. The following analysis will show how acoustic instrumental sounds can be analyzed to determine their formant frequency or frequencies. This is used to place each instrument within a "formant space" mapping instrumental timbre to vowels.
The soundfile of the cardinal vowels was analyzed to create the following spectrogram.

The dark bands denote the formant frequencies. These results were used to plot each vowel on the vowel formant chart.

I performed a similar formant analysis of several acoustic instruments using the COLEA analysis toolkit for matlab. The results are shown in the following plots. Some instruments exhibit only one formant frequency, while others, like saxophone and violin, tended to exhibit three or four. These plots where generated with analysis of the following sound files: sax.wav, flute.wav, clarinet.wav, oboe.wav, bassoon.wav, violin.wav, cello.wav, bass.wav, allstrings.wav, flute_clar.wav. Muting, vibrato, and tounging will alter the timbre of an instrument and produce a change in these formants. It is important to understand that formant regions are independent of pitch.

 
results for the formants were derived from the mean values as in this graph

<top>

What is the purpose of all this analysis?

        I am not suggesting that every single acoustic instrument or combination of instruments need be analyzed in this way.  I hope that from a generalized framework as in the chart below, which I am calling the "vowel space", each instrument class can be identified and the timbral mixture of particular instruments can be accurately predicted and described within this system. 
The musical examples that follow take a different approach. Acoustic instrument sounds or their combinations are being selected to mimic vocal phonemes. So rather than describing acoustic timbre in terms of phonemes, the phonemes are being emulated by acoustic instruments. These experiments are offered as an attempt to verify the validity of a phoneme based system for timbre classiicfation. This system is under development and I encourage comments, questions, and feedback. 

This chart shows the formant frequencies for the various
instruments plotted in the "vowel space".These values were
calculated with COLEA.

The formant chart or "vowel space" shows that each instruments, irrespective of family (brass, woodwinds, strings), exhibit formant properties which allow them to be classified in terms of a particular phoneme or pair of phonemes.  Now I can say that the tuba's timbre has a 'U' sound or (oo) as in the word who, or the trumpet has an 'ae' timbre like the work actor.  For a more detailed exploration of phonemes look at this UCLA linguistics site which has sounds samples for most the International Phonetic Alphabet.

Mimicking cardinal vowels with acoustic instrument samples:

The sonogram at the top of this page shows the cardinal vowels spectrum.  The sonogram below is made up of different acoustic instrument samples which closely match the formant properties of each of cardinal vowels.  Compare the vocal and instrumental sound files to hear the relationship.
Spoken Cardinal Vowels
Instrumental Cardinal Vowels
Instrumental Cardinal Vowels pitch shifted for consistency