Det Springende Punkt
Det Springende Punkt
presents
presents
Keys
Keys
to unlock the secrets
to unlock the secrets
of the harmonic series
of the harmonic series
and overtone singing
and overtone singing
From the perspective of the harmonic series music is the language of integers From the perspective of the harmonic series music is the language of integers
- its atoms and molecules are primes and compounds of primes - its atoms and molecules are primes and compounds of primes
1:2 First octave:
1:2 First octave: 1:2 octave.1:2 octave. 2:4 Second octave:
2:4 Second octave:2:3 perfect fifth; 3:4 perfect fourth.2:3 perfect fifth; 3:4 perfect fourth. 4:8 Third octave:
4:8 Third octave:
4:5 just major third; 5:6 just minor third; 6:7 septimal third; 7:8 septimal second. 4:5 just major third; 5:6 just minor third; 6:7 septimal third; 7:8 septimal second. 8:16 Fourth octave:
8:16 Fourth octave: 8:9 major whole-tone; 9:10 minor whole-tone;... 15:16 major semitone.8:9 major whole-tone; 9:10 minor whole-tone;... 15:16 major semitone. etc.
etc.
One winding of the octave spiral corresponds to one
One winding of the octave spiral corresponds to one octave – we return to octave – we return to the same quality on athe same quality on a new pitch level:
new pitch level:
1-2-4-8-16-1-2-4-8-16-... are octaves of the fundamental.... are octaves of the fundamental. 3-6-12-3-6-12-... are octaves of the perfect fifth.... are octaves of the perfect fifth.
The correspondences between tone, body resonance and phonetics should not be in
The correspondences between tone, body resonance and phonetics should not be interpreted tooterpreted too rigidly! In this example the harmonic series springs
rigidly! In this example the harmonic series springs forth from a deep G but forth from a deep G but naturally any tone in any naturally any tone in any pitch will carry the harmonic series with i
pitch will carry the harmonic series with it. What is invariable is t. What is invariable is the sequence of intervals between thethe sequence of intervals between the elements – the simple integer relations of
elements – the simple integer relations of time and space (frequency and wavelength).time and space (frequency and wavelength). The body is a very complex resonance system, so you may also f
The body is a very complex resonance system, so you may also find resonance for deep tones high ind resonance for deep tones high up inup in the body and conversely. But generally: Deep tones ~ 'down', high
the body and conversely. But generally: Deep tones ~ 'down', high tones ~ 'up', as indicated tones ~ 'up', as indicated intuitively inintuitively in the language.
the language.
The vowel sounds can be generated artificially by a
The vowel sounds can be generated artificially by a compound of two or three frequencies but by compound of two or three frequencies but by overtoneovertone singing you may accentuate elements from the harmonic series by
singing you may accentuate elements from the harmonic series by shaping the vocal tract to positionsshaping the vocal tract to positions similar to vowel pronunciation. Please notice again
similar to vowel pronunciation. Please notice again that the correlation is not absolute: You that the correlation is not absolute: You may be able tomay be able to accentuate the harmonics with different vowel qualities depending om voice
Generally the lower elements of the harmonic series are accentuated at the
Generally the lower elements of the harmonic series are accentuated at the same regions of the vocal tract assame regions of the vocal tract as the rounded back vowels, whereas the higher elements correspond with the front
the rounded back vowels, whereas the higher elements correspond with the front vowels.vowels. To accentuate distinct overtones demands mastery of the tongue
To accentuate distinct overtones demands mastery of the tongue as a precision instrument.as a precision instrument. The integers indicate multiples of the
The integers indicate multiples of the frequency of the vocal folds.frequency of the vocal folds. Please bear in mind that overtone singin
Please bear in mind that overtone singing technique is not limited g technique is not limited to the vocal tract. A to the vocal tract. A complex interactioncomplex interaction between abdomen, chest and throat musculature, breathing and body posture is essential.
It is a great
It is a great advantage to become aware of theadvantage to become aware of the three areas of the vocal tract where you may three areas of the vocal tract where you may fundamentally widen or narrow the passage fundamentally widen or narrow the passage of the sound waves emitted by the
of the sound waves emitted by the vocalvocal folds:
folds:
Between the lips: Between the lips: mm
Between the tip of the tongue and hard Between the tip of the tongue and hard palate:
palate:nn Between the
Between the back of thback of the tongue ae tongue andnd soft palate:
soft palate:ŋŋ
By consciously opening from these humming By consciously opening from these humming sounds into open vowel sounds you may sounds into open vowel sounds you may accentuate the elements from the harmonic accentuate the elements from the harmonic series very distinctly.
series very distinctly.
The overtones – like the flageolet tones The overtones – like the flageolet tones on aon a string instrument are created at the
string instrument are created at the shortershorter part of the divided sound wave (strin
part of the divided sound wave (string). Thatg). That is between the point where the passage has is between the point where the passage has been narrowed and the lips.
A vibrating string gives rise to a range of simultaneous frequency A vibrating string gives rise to a range of simultaneous frequency
conditions. conditions.
Imagining using a finger against a fretboard to divide the string in Imagining using a finger against a fretboard to divide the string in smaller fractions, the
smaller fractions, the 1/1, 1/2, 1/3, 1/4, 1/5 and 1/61/1, 1/2, 1/3, 1/4, 1/5 and 1/6 (( bold bold) markers) markers indicate the points of natural harmonics of the string.
indicate the points of natural harmonics of the string.
Furthermore you may find other fundamental musical functions. 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 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
The bowed lines of these illustrations do The bowed lines of these illustrations do notnot indicate a vibrating string but interval relations indicate a vibrating string but interval relations (
(italicitalic) between elements of the harmonic series) between elements of the harmonic series
(upright figures). (upright figures).
The length proportions refer to the size of the The length proportions refer to the size of the interval.
interval.
Here the harmonics #7 and #11 have been
Here the harmonics #7 and #11 have been omittedomitted because the interval names refer to tonal systems because the interval names refer to tonal systems
(Pythagorean, just tuning, equal tempered etc.) (Pythagorean, just tuning, equal tempered etc.) where these nature tones do not have a
where these nature tones do not have a place butplace but actually sound out of tune in the context.
actually sound out of tune in the context.
The just intervals: The just intervals: 1:2
1:2 octaveoctave 2:3
2:3 perfect fifthperfect fifth 3:4
3:4perfect fourthperfect fourth 4:5
4:5just major thirdjust major third 5:6
5:6just minor thirdjust minor third 8:9
8:9major whole-tonemajor whole-tone 9:10
9:10minor whole-toneminor whole-tone 3:5
3:5just major sixthjust major sixth 5:8
5:8just minor sixthjust minor sixth 5:9
The vowel mandala is a The vowel mandala is a map for singers giving an map for singers giving an organic structure to the organic structure to the various sounds which can various sounds which can be used in the rhythmic be used in the rhythmic language (primarily the language (primarily the plosives), for humming plosives), for humming (the nasals) and for (the nasals) and for producing sound colour producing sound colour (the vowels).
(the vowels).
The lastly mentioned are The lastly mentioned are here represented by here represented by initials of Danish girls initials of Danish girls names.
names.
The three fundamental The three fundamental organic sequences can be organic sequences can be practised in either
practised in either direction with long direction with long sustained tones. sustained tones.
Going from the open [ Going from the open [ɑ] inɑ] in
the center they all converge
the center they all converge
towards the nasals.
The vowel mandala was not introduced in an attempt to
The vowel mandala was not introduced in an attempt to
replace the standard IPA phonetic chart, which is here for
replace the standard IPA phonetic chart, which is here for
reference.
Another diagram elucidating the close
Another diagram elucidating the close
correlations between music and speech.
correlations between music and speech.
It shows the formation of the Swedish
It shows the formation of the Swedish
vowel sounds as a result of
vowel sounds as a result of
two
two
dominant frequencies.
dominant frequencies.
(from Johan Sundberg: Röstlära)
(from Johan Sundberg: Röstlära)
The formants are not only resonance
The formants are not only resonance
frequencies but are also linked to the
frequencies but are also linked to the
degree of opening or narrowing
degree of opening or narrowing
particular areas of the vocal tract
particular areas of the vocal tract
-incarnating music!
English is missing the
English is missing the term 'klang' which in German and Scandinavian languages indicates term 'klang' which in German and Scandinavian languages indicates the quality the quality aspect of any sound - which
aspect of any sound - which may be conceived as the sum of imay be conceived as the sum of its overtones.ts overtones.
Overtone singing forms a unity of three very fundamental fields of knowledge essential to Overtone singing forms a unity of three very fundamental fields of knowledge essential to consciousness as such.
Tone is making a braid
Tone is making a braid out of time (frequency) and space (wawelength) according to the out of time (frequency) and space (wawelength) according to the formula for theformula for the correlation between the two aspects:
correlation between the two aspects: f x λ = cf x λ = c Here
Heref f is the frequency of the tone,is the frequency of the tone, λ λ is its wawelength andis its wawelength and cc is the constant of velocity of sound wawesis the constant of velocity of sound wawes in air at about 20
Albrecht Dürer
Albrecht Dürer (1471-1528) who was active in(1471-1528) who was active in Nuremberg made this proportion study of the human Nuremberg made this proportion study of the human anatomy.
anatomy.
Do notice the measure at the far
Do notice the measure at the far left - the proportions of left - the proportions of the harmonic series:
the harmonic series:
1/1- 1/2- 1/3- 1/4- 1/5-... 1/1- 1/2- 1/3- 1/4- 1/5-...
Dürer's masterly hand is also behind the sketch pasted Dürer's masterly hand is also behind the sketch pasted into the note system at the fourth page of this
into the note system at the fourth page of this presentation.