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In the singing voice, the overtones are harmonics; that gives the game away, because it means their frequencies are integer (whole-number) multiples of the fundamental frequency (fo). Fo rises, harmonics rise; Fo falls, harmonics fall.

Extent of oscillation in singing is expressed as a percentage or in semitones (1ST~= 5.9%). Take the A below Middle C (A3 = 220Hz). Fo=220, 1st harmonic=440(ie 2x), 2nd harmonic=660(ie 3x) etc. If we take the example of modulation of 5% (ie 2.5% above and 2.5% below the Fo), then each vibrato cycle starts at Fo=220, then Fo rises to 225.5 (220+2.5%), then turns downward to 220, then continues downward to 214.5 (220-2.5%), then rises back to 220 - total range, 11Hz. Meanwhile, the 4th harmonic is also modulating at 5%: 1100Hz (5x220Hz), up to 1127.5Hz, back to 1100Hz, on down to 1072.5 (1100-2.5%), and back to 1100 - total range 55Hz. The 9th harmonic at 2200Hz (220x10) is going 2200Hz, 2255, 2200, 2145, 2200 - total range, 110Hz (but still 5%).

If the spectral analysis program is set to linear, as most tend to be, rather than logarithmic (remember that the musical scale is logarithmic), then the oscillation in the Fo is very hard to see: on a y-axis scale set to 1-4000Hz, to include the singer's formant region, you'd be looking for a movement of just 11Hz. If your harmonics were oscillating, so was your Fo - to get a rough idea of the vibrato extent, choose any harmonic, subtract the frequency at the bottom of the cycle from that at the top (your program should show this information to you when you point your mouse at the spots), divide it by the average of the two and multiply by 100 to give a percentage; eg 2255-2145=110; (2255+2145)/2=2200; 110/2200x100=5%. Average the result over a number of consecutive cycles to get a more reliable estimate.

Also, most published vowel formant frequencies are derived from speech and refer to speaking fundamental frequency ranges.

Linear predictive coding is a common technique to estimate formant frequencies. Monsen and Engebretson** found its accuracy was +/-60Hz for formants 1 to 3 over a fundamental frequency range of 100-300Hz. LPC's accuracy lessens greatly as fundamental frequency rises above 350Hz, which is only around E4-F4. So the weather forecast for estimating formant frequencies when singing above E4 is 'cloudy, becoming dangerous'.

There's research on vibrato vs wobble vs tremolo, but it's been hampered by the challenge of finding two 'expert listeners' who'll agree on what they're hearing.

Click Here for Spectograph Frequencies article by Martyn Clark.
Read Spectral Analysis also by Sally, explains the basics of how spectral analysis works.

Visit the Vocal Software section for freeware and shareware spectograph and vocal manipulation software.

Article published by permission from Sally Collyer.
Originally posted to Vocalist USA Discussion Group

** Monsen, Randall B., and A. Maynard Engebretson, 1983. The accuracy of formant frequency measurements: A comparison of spectrographic analysis and linear prediction, Journal of Speech and Hearing Research, 26: 89-97.

Sound & Spectograph Links

These are just a small example of the extensive links to online exercises and lessons we have available in the Singers Articles section, which contains complete listings of lessons, exercises or articles available on each site with direct links to the page (when not a framed site) plus answers to pretty much everything a beginner, intermediate, advanced singer or teacher needs to know! (All links open in a new window).

A Pictoral Introduction to Fourier Analysis/Synthesis
This tutorial contains diagrams and pictures to aid in understanding Fourier Analysis, Sinewaves, Square-wave's, frequencies and their uses.

A study of the formants of the pure vowels of British English
Written by J. C. Wells contains information, diagrams and tables.

Acoustics of Consonants
includes an overview of frictaves and oral stops with graphs of exaggerated formant transitions for some consonant-vowel pairs. Other articles in this collection of course study material includes broad phonetic transcriptions of English, vocal tract anatomy, properties of consonants and vowels, acoustic and general phonetics plus spectram diagrams.

Acoustics of Speech & Hearing
This course overview from Mark Huckvale University College London contains information on speech, hearing and sound with links to related internet resources including their associate site Speech & Hearing FAQ.

Analysis Using Spectogram and Timeline
Interesting thread with link to examples available at The International Electroacoustic Community Discussion Group.

Hearing Loss & Speech Intelligibility
Why we have trouble understanding speech provided by Hound Dog Hearing includes graphs showing the frequencies in Hz of vowels and consonants.

James L. Fitch, Ph.D.
Hidden away amongst the CMDS pages is a wealth of information on speech, hearing and spectographs.

Phonetics and Theory of Speech Production
This informative article is taken from a more comprehensive project on Speech Synthesis Technology from Helsinki University of Technology. It provides an overview with mathmatical workings, descriptions and pictures of the speech mechanism plus graphical representations of the time- and frequency-domain of vowels /a/, /i/, /u/ and other diagrams.

Resonant Voice & Formants
Message from Lloyd W. Hanson at International Discussion Group.

Singer's Formant
Documentation of the elite singing voice, a research data-gathering documentation project designed to quantify some of the measurable aspects of the singing voice. These spectograph images and sound samples from vocevista spectograph software looks at a descending chromatic scale over a perfect fifth (8 semitones) from ranges selected to show how the singer's formant might show characteristic and variable patterns among and within subjects.

Speaking of Speaking
by Peter Mapp takes a look at how speech is constructed with spectograph diagrams and a list of consonant phonemes.

Spectogram Reading
provides information on how to read a spectogram, explanations of waveforms, phonemes, formants plus exercises for improving your spectogram reading skills.

Spectral Analysis of Sound
in pdf format by Robert Mannell provides an overview of complex waves, line spectra, fourier transforms, linear prediction analysis, filtering, two dimensional spectra and spectrograms with diagrams.

Stirling University's on-line phonology course
Includes useful information, diagrams and exercises to enable readers to learn more about vowel, consonant and speech production.

Studying Phonetics on the Net
This site provided by the University of Washington contains information and links to IPA Phones and Phonemes of English, Speech Waveform Analysis, Text to Speech (TTS) Synthesizers and Speech Recognition, many of which contain audio examples and software.

The Style and Development of Lotte Lehmann
As preserved in recordings of Schubert's Lieder. The site includes aspects of the singer Lotte Lehmann's vocal performances.

Voice analysis and balancing tone generation software including spectographs, analysers, tone generator, chord / emotion and other related programs, most are freeware (donaware) or trustware.