Keys to Overtone Singing

Det Springende Punkt presents

Keys to unlock the secrets of the harmonic series and overtone singing

From the perspective of the harmonic series music is the language of integers - its atoms and molecules are primes and compounds of primes One winding of the octave spiral corresponds to one octave – we return to the same quality on a new pitch level: 1-2-4-8-16-... 1-2-4-8-16... are octaves of the fundamental. 3-6-123-6-12-... ... are octaves of the perfect fifth. 5-10-... 5-10... are octaves of the just major third. Etc.

1:2 First octave: 1:2 octave. 2:4 Second octave: 2:3 perfect fifth; 3:4 perfect fourth. 4:8 Third octave: 4:5 just major third; 5:6 just minor third; 6:7 septimal third; 7:8 septimal second. 8:16 Fourth octave: 8:9 major whole-tone; 9:10 minor whole-tone;... 15:16 major semitone. etc.

The correspondences between tone, body resonance and phonetics should not be in terpreted too rigidly! In this example the harmonic series springs forth from a deep G but naturally any tone in any  pitch will carry the harmonic series with it. i t. What is invariable is the sequence of intervals between the elements – the simple integer relations of time and space (frequency and wavelength). The body is a very complex resonance system, so you may also find f ind resonance for deep tones high up in the body and conversely. But generally: Deep tones ~ 'down', high tones ~ 'up', as indicated intuitively in the language. The vowel sounds can be generated artificially by a compound of two or three frequencies but by overtone singing you may accentuate elements from the harmonic series by shaping the vocal tract to positions similar to vowel pronunciation. Please notice again that the correlation is not absolute: You may be able to accentuate the harmonics with different vowel qualities depending om voice type, pitch etc.

Generally the lower elements of the harmonic series are accentuated at the same regions of the vocal tract as the rounded back vowels, whereas the higher elements correspond with the front vowels. To accentuate distinct overtones demands mastery of the tongue as a precision instrument. The integers indicate multiples of the frequency of the vocal folds. Please bear in mind that overtone singing singin g technique is not limited to the vocal tract. A complex interaction  between abdomen, chest and throat musculature, breathing and body posture is essential.

It is a great advantage to become aware of the three areas of the vocal tract where you may  fundamentally widen or narrow the passage of the sound waves emitted by the vocal folds: Between the lips: m Between the tip of the tongue and hard palate: n Between the back of the the tongue and and soft palate: ŋ By consciously opening from these humming sounds into open vowel sounds you may  accentuate the elements from the harmonic series very distinctly. The overtones – like the flageolet tones on a string instrument are created at the shorter part of the divided sound wave (string). (strin g). That is between the point where the passage has  been narrowed and the lips.

 A vibrating string gives rise to a range of simultaneous frequency  conditions. Imagining using a finger against a fretboard to divide the string in smaller fractions, the 1/1, 1/2, 1/3, 1/4, 1/5 and 1/6 ( bold  bold)) markers indicate the points of natural harmonics of the string. Furthermore you may find other fundamental musical functions. Here is only shown a part of the full picture as we have set the limit to 6 out of a potentially endless number of elements .

The bowed lines of these illustrations do not indicate a vibrating string but interval relations (italic) between elements of the harmonic series (upright figures). The length proportions refer to the size of the interval. Here the harmonics #7 and #11 have been omitted  because the interval names refer to tonal systems (Pythagorean, just tuning, equal tempered etc.)  where these nature tones do not have a place but actually sound out of tune in the context.

The just intervals: 1:2 octave 2:3 perfect fifth 3:4 perfect fourth 4:5 just major third 5:6 just minor third 8:9 major whole-tone 9:10 minor whole-tone 3:5 just major sixth 5:8 just minor sixth 5:9 just minor seventh

The vowel mandala is a map for singers giving an organic structure to the  various sounds which can  be used in the rhythmic language (primarily the plosives), for humming (the nasals) and for producing sound colour (the vowels). The lastly mentioned are here represented by  initials of Danish girls names. The three fundamental organic sequences can be practised in either direction with long sustained tones. Going from the open [ ɑ] in the center they all converge towards the nasals.

The vowel mandala was not introduced in an attempt to replace the standard IPA phonetic chart, which is here for reference.

 Another diagram elucidating the close correlations between music and speech. It shows the formation of the Swedish  vowel sounds as a result of two dominant frequencies. (from Johan Sundberg: Röstlära) The formants are not only resonance frequencies but are also linked to the degree of opening or narrowing particular areas of the vocal tract incarnating music!

English is missing the term 'klang' which in German and Scandinavian languages indicates the quality  aspect of any sound - which may be conceived as the sum of its i ts overtones. Overtone singing forms a unity of three very fundamental fields of knowledge essential to consciousness as such.

Tone is making a braid out of time (frequency) and space (wawelength) according to the formula for the correlation between the two aspects: f x λ = c Here f  f is is the frequency of the tone, λ  tone,  λ is is its wawelength and c is the constant of velocity of sound wawes o in air at about 20 C ~ 340 m/s

 Albrecht Dürer (1471-1528) who was active in Nuremberg made this proportion study of the human anatomy. Do notice the measure at the far left - the proportions of  the harmonic series: 1/1- 1/2- 1/3- 1/4- 1/5-... Dürer's masterly hand is also behind the sketch pasted into the note system at the fourth page of this presentation.

Links to more information and listening experiences:  www.overtone.cc  www.overtonesang.dk