Thursday, November 20, 2008

Formant Tracking Charts

As my teaching schedule becomes more active and the level of my studies become more advanced the posts take more time to produce. It is for that reason that I open the blog to any of you who have an issue relevant to the advancement of our art form to bring it up here in any language that I can review. So don't be shy.

I have been working on these formant tracking charts for about three years and feel that I have finally gotten enough information to complete them. I am sure that some of you will have commentary and suggestions for improvements. Feel free!

The charts take into account the obvious on the one hand (i.e. plotting harmonic frequencies vs vowel formant frequencies), and the less common (i.e. consideration of vocal tract reactance in chosing the vowel appropriate for a given harmonic). Remember that the formant values represent the formant centers and that there are many vowel qualities between the ones I have chosen to represent on the charts. Following the principles we exposed here in my exchanges with Martin Berggren, formant frequencies are plotted within 50Hz above the relevant harmonic. In the case of an exact match of the formant with the harmonic (or a few Hertz difference), the formant is considered inertial instead of neutral when we consider that the vowel can be subtly modified to bring the formant above the harmonic.

For those who are new to the concept of vowel modification, a couple of things will be obvious: 1) The lower the fundamental frequency the more choice of vowels there are. Therefore male voices have more vowels choices because of the octave differential from female voices. For that reason, all things equal a male singer (particularly a baritone or a bass) will be more intelligible than a female counterpart. 2) In the Excel charts, the cells of F2 (second formant) frequencies are filled with a dotted pattern while those of F1 frequencies are kept clear. The colors correspond to the the colors associated with the vowels on the chart to the right of the grid. 3) The words are from four common operatic languages: English, French, German and Italian and are as follows:

/u/ susurro (Italian)
/U/ Duft (German)
/o/ chose (French)
/O/ tortora (Italian)
/ʌ/ up (English)
/α / father (English
/a/ voila (French)

/i/ midi (French)
/y/ fühl (German)
/Y/ Stück (German)
/I/ fit (English)
/ø/ feu (French)
/e/ été (French)
/oe/ coeur (French)
/E/ met (English)
/ae/ cat (English)

In some cases there is a good bit of distance between one vowel formant and the adjacent one. In the case of /ae/ to /E/ an extra frequency is placed as an intermediary marker. Although they are close in quality the vowels /i/, /y/ and /I/ cover a wide frequency range in the second formant area. Therefore, I take some liberties with the intermediary frequency range in pink.

More will be written about these charts in the coming weeks. However, I could not wait to make them available since I've been promising them for the past several months.

Finally, it should be said that these charts were done to improve upon the seminal work done on formant tracking by Berton Coffin. Coffin's chart did not take F2 frequencies into account for one. Furthermore, vocal tract reactance was not common knowledge during Coffin's time. As always, the posts are meant to generate discussion so that we may arrive at useful information.

Files are found here in PDF format:

Tongue and mixed Vowels

Lip Vowels

© 11/20/2008


George said...

Wow! Thank you for doing this! I have a ton of questions over the chart which I will gather together and post soon, but before I do I just wanted to thank you for being generous and sharing freely what looks like it must have been a considerable amount of work!


Toreadorssong's Vocal Technique Blog said...

My pleasure. It has been long coming. It feels like I gave birth. A relief to have the first edition of this out. Hopefully the discussion will yield lots of suggestions for improvement.


George said...

Okay, first question.
I don't understand how you chose which vowel to match a specific partial of a specific note. I had assumed that you would pick the vowel whose formant is closest to said partial. However, that is often not the case, and I don't see a pattern emerge.

As an example, let's take some of the first couple of notes, even though they are notes I'd never sing.

1. pitch 70Hz (C#/Db2) has a fifth partial at 350HZ. Why do you choose vowel [I] whose first formant is 400HZ, and not [Y] whose first formant is 350HZ, a direct match with this partial?

2. pitch 75HZ (D2) has a fourth partial at 300HZ. Why do you choose vowel [Y] whose first formant is 350HZ, and not [i] whose first formant is 280HZ, which is much closer to the partial at hand.

These are just the first two examples on the chart. Do you see the source of my confusion? What is the criteria for deciding which vowel is tuned to which partial of a given pitch, if the criteria is not which vowel's formant is closest to that partial?

I'll start with this question, before I get to the others, because this is the one that is bothering and confusing me the most.

Baritonobasso said...

TS, I eagerly await your commentaries on the vowel charts. For now, I hope you don't mind hearing of some reservations that I have about your notation, especially the following items in your index of vowels:

/o/ chose (French)
/o/ tortora (Italian)

(1) I had to look 'tortora' up in the dictionary to make sure that it had an open O in the stressed syllable. I believe that many people who know a fair amount of Italian will not know that, or will not know that the stressed syllable is the first one. Would it not be more effective to use a better-known and disyllabic word like 'poco' or 'cosa'?

(2) You use the same symbol for closed and open O, namely 'o'. Don't you mean to use a capital letter for the open vowel, 'O'?

(3) I notice that you use strokes / / rather than square brackets [ ] to mark phonetic symbols. In linguistics, strokes indicate phonemic, not phonetic transcriptions; square brackets are the symbols used for indicating phones, which are what you are talking about. (Just to make that point clear: vowel phonemes may be realized in sounds of different qualities, and the same vowel quality may in different instances be a realization of two different phonemes.) If you are going to use a scientific notation, don't you want to follow the conventions of the pertinent science?

Toreadorssong's Vocal Technique Blog said...

Dear George,

The question you ask above is the one that most people would scratch their heads about. The concept of inertial reactance of the vocal tract, which renders the phonation process altogether easier and more efficient requires that the vowel formant in question be ABOVE the harmonic in question.

In the case of vowel formants that have an exact match, the effect would be neutral. The vocal tract would neither assist nor hinder the phonation process. I try to pick the closest vowel that is above the harmonic in question within a 50 Hertz margin (conservative. I am doing further reading on the bandwidth of vowel formants).

The theories on inertial reactance also specify that inertial reactance is not really possible in the low range where the folds are relatively thick. In the low range (the octave and a half where even a basso profundo would consider low range) I am less strict about the exact or near exact matches because inertial reactance is not at issue according to the theories. However, I believe personally that a lean tone can be produced in the low range whereby inertial reactance would be at issue. Nevertheless, this is less crucial in the low range where the choices of resonant vowels are many.

In effect I could have chosen the exact match of 350 (fifth partial of C#2) because reactance is not at issue according to the theories. But I kept with the principle anyway.

I hope this is clearer. I look forward to your next questions.

Toreadorssong's Vocal Technique Blog said...

Dear Baritonobasso,

You make a lot of astute observations and as a singer I agree with every assessment you made. The first one about the /O/ is an obvious typo. I corrected.

As opposed the // instead of [], I was following a system developed probably spontaneously by vocal scientists at a time when it was not possible to publish phonetic symbols over the web that were not part of standard browser fonts. Since the symbols used where basically phonemic, they used the //. However vocal acoustics had always dealt with printed phonetics as opposed to phonemes. The dilemma what that neither system could be universal in all the media platforms used. So a hybrid of sorts became common. I was originally going to use phonetics (and I will attempt to correct this as well) but I ran into some walls with the character sets available to the Blogger editor. I am certain I can find a way around this if I search through all the available fonts and not use the default one.

Thank you for your expertise on that front. Happy to see you here again! This is a work in progress. Details of this sort will be addressed as I refine the charts.

George said...

Oh. So if the partial is equal to or within 50HZ above a given vowel formant, you use the next higher vowel...unless the next higher vowel formant is more than 50HZ away, in which case you use the vowel with the lower formant?

For example, 110HZ A2 has a 4th partial at 550HZ, and you use the vowel [E]550 rather than the next higher vowel 620 (which I presume is a sound halfway between [E] and [ae]?) because the next vowel formant is more than 50HZ higher?

My other big questions have to do with how one chooses which vowel to sing on which note, whether to sing a vowel that is tuned to the fundamental, or a vowel whose first formant is in tune with a partial, or whose second formant is in tune with a partial, or one in tune with both partials, etc, etc. But I believe you plan to address this in future posts, so I will hold off.

One teeny-tiny criticism I have with the chart is that I have a very hard time distinguishing between a few of the colors, mostly the two greens (620 and 690). I have a very good printer, but these two greens are nearly indistinguishable to my eyes. But perhaps it is just my own colorblindness.

Thank you for your responses!


George said...

Okay, one more question for now. You use the first formant but not the second for the vowel [Y] as in stueck, and the second formant but not the first for the vowel [y] as in fuehl, and the same color for both. Why is that?

Toreadorssong's Vocal Technique Blog said...

Dear George,

Great questions:

1. We do not tune to the fundamental unless it happens to be the partial that is most conducive to efficient resonance strategies. The [i] vowel has a first formant of circa 280 Hz (C4#). So someone singing that note will most likely find resonance at the fundamental. But that is happenstance. Most notes are not resonant at the fundamental until we get into the soprano high range where we usually have a single choice for resonance.

2. Which formant we chose has a lot to do with resonance strategy. Low larynx or high larynx. I have addressed this subject here relative to Kraus as an F1 tenor. If the larynx remains in its best low position throughout the range, the formant selection is almost automatic. For instance, for a tenor to sing the [a] on F4# without modification, the larynx will probably rise to match F1. If the throat remains low, the vowel will want to modify to match F2. The latter is preferable because it maintains strength in both low and high partials giving the voice a balanced quality. Kraus and Florez among others sing with a high larynx that raises as pitch is raised because shortening the vocal tract has a raising influence of F1. By keeping the larynx low, F1 remains low and is discouraged as pitch rises. F2 becomes the dominant resonance. This is the Italian approach. The Spaniards and some current American teachers (musical theater influence) have a high larynx strategy that takes the depth away and gives the voice a thinner quality.

There is also the choice of singing a note that is not resonant (i.e. the shape of the vocal tract/vowel does not facilitate the propagation of sound).

Your criticism of colors is a good one. I noticed that later on. I was trying to create a continuum that ended up being visually a touch confusing. I will repair this with time.

Toreadorssong's Vocal Technique Blog said...

Dear George, relative to your question about [Y] and [y]. If you follow the formant values [Y] and [y] would fall in different places relative to the 1st and 2nd formant spectra. Using [y] in the first formant spectrum would put it below the [i]vowel and [Y] in the second formant spectrum would appear between [I] and [e] (lip rounding lowers the formants). This would add some confusion at first sight and besides the one mixed vowel in the [i]-[I] spectrum is enough.

Mikael Pennanen-Dahlbäck said...

Hi, and thanks for your excellent blog!

I've only started reading your posts, and so far every one of them is very interesting. You focus on the very things that puzzle us singers and write in a very understandable way.

The PDF-charts don't seem accessible anymore. As a vocal coach and singer myself - and interested in Berton Coffin's work - I would like to have a look at those charts. Could you upload them again?

Jean-Ronald LaFond said...

Dear Mikael,

The PDFs should still be available. which hosts them is experiencing changes. I hope they will resolve the problem in the next few days. I will host them in a different place from now on. Will keep you posted.

mparky87 said...

Hi Jean-Ronald,

I've just discovered your blog and have read a good deal of it in one sitting. I enjoyed all of your posts immensely. Thank-you!

I have long been interested in the work of Berton Coffin and I tried to download your formant tracking charts but the links don't seem to work. Is there an alternative location to download these?


Kashu-Do said...

Hello Matthew. Sorry for the late reply! Fileden, which hosted my files went bust and so I had to take all the files offline. It's going to take a little time to relink 300 posts. In the meantime, email me at and I will send you the pdfs.