Well, not exactly notation in the traditional sense, but maybe useful for conducting and practice:
What may be the most remarkable about overtone singing is that it unites some very fundamental elements of speech (phonetics), music (intervals) and ... mathematics: each prime number incarnates a new tonal function through the harmonic series. The three fields share a common and very deep offspring which we may contact through our practice.
One of the oldest ways to indicate tonal functions is by hand and fingers (the guidonian hand etc.). And fingers have always been used to indicate numbers (a digit may be numerical or anatomical!).
Octaves are actually mirrored in the arithmetic series 1-2-4-8-16-... so it is obvious to find a finger counting system which may bridge the numbers and the tonal functions. The most interesting in my view would be to utilize the binary counting, where each digit position is exactly the 1-2-4-... (whereas the positions of our common 10-digit system are 1-10-100-1.000-...).
In practice it can be used by choir leaders to indicate which harmonic should be amplified, and for establishing awareness in personal practice... developing a harmonic finger language.
One hand can indicate numbers from 0 to 31 which should be sufficient for most overtone singers (and those who need wider frames don't need the fingers). This also gives the choir leader the opportunity to indicate two different harmonics for two different voice groups within one choir.
Hello everybody,
Thank you for this opportunity!
I should like to turn the issue upside-down:
Instead of focusing of a practical solution to bridging the gap between an inherent natural pattern (the harmonic series) and a product of culturally conditioned language (music notation system) I should like to return to the starting point with Filip's urge to make 'the octaves visible again'.
As a member of a choir called Spectrum (and thank you for your acquantaince by your choir's visit in Copenhagen) he is obviously aware that at least one octave - or really almost an octave has been visible since the days of Noah: the rainbow spectrum which covers just a little less than an octave. And by the fact that we consider violet and red neighbours on the painters palette, we are led to the conclusion that in human conception there is an analogy of the colour octave and the audio octave, both being defined by the frequency and wavelength ratios 1:2. The analogy being that in both worlds the octave means something like 'comming back to a quality already experienced but on a new level' - either higher or deeper.
From here it is necesarry to think calmly as most people fascinated by holistic approaches tend to spread their 'equals signs' to loosely and thereby harvesting a poor crop where planets, tones, colours, anatomy, etc. gets badly entangled!
First thing is that the visual octave, the rainbow spectrum is separated from the audible octave by more than 40 octaves which is a gigantic span. Already on the piano we tend to conceive the octave as something which is not absolute in the extreme ends, high and deep, and colur and sound as fields of conception are actually worlds apart!
Furthermore the light and and sound frequencies are basically two different waveforms (transversal and longitudinal respectively).
Lastly the very difference of range the human conception is tuned to between the two worlds (we see a little less than one octave but are open to about ten octaves of the audible spectrum) the structures which arise within these worlds obviously becomes very different. Basically you cannot detect the role of the perfect fifth (ratio 2:3) in the world of colours whereas it is most essential in music by the fact that 7 octaves is virtually the same as 12 perfect fifths.
Sorry for bothering you with all this but for me it is necesarry before we deal with the bridging between 'nature' and 'culture'.
It is not my intention to pull the discussion completely of its trail and I may contribute with ideas to the practical problem later.
Till then I should like to lead your attention to some of the videos I have uploaded dealing with this issue of visually enlightening some structural correlation between number, tones and colour:
Specially the octave spiral video (octave is the returning of an already known quality - structurally-visually: the spiral), the rhythm-tone transistion video (octave aspects) video and the video of pattern as music and number.
Best,
Skye
Filip Rydlo > Skye LøfvanderFebruary 8, 2010 17:31
Beautiful videos!
No need for so many words. :)
I really like Your comment! It is just a bit long.
But it was worth reading for me. Thank You.
I started thinking about using the spiral schematic as a symbol for every overtone.
for example: 5-th overtone could look like circle with dot in the center and 2 dots above it, for the 2 and 4 (octaves) and in addition, number 4 could be connected by a curve to the point where 5-th overtone is, on the spiral map ! Because it is in it's octave. :)
I see your system as having some advantages, i.e. visually having the fundamentals and overtones closer together so one does not have to also jump with their eyes (especially when reading complex polyphonic pieces). Also because we tend to perceive the intervals as being closer together than they actually are anyway. And the single line notation would save the need for so many extra pages in the case of longer works (and save trees!)
One possible drawback might be in the case where the overtone appears to drop below the fundamental (as in the 6th overtone in your example). Although the singer knows what is meant, it may be disconcerting.
I believe this drawback can be nearly completely avoided if this system is used properly.
( I mean: one 3rd or 6th overtone under the actual octave is no problem for reading the interval at all. Those who are reading notes are used to understand interval "perfect forth" under like "perfect fifth" from the tone which is an octave lower from our base-tone. )
In Czech we call the lower "G" under our "c" (when c is our actual fundamental of tonica) the
"Bottom fifth degree".
For example: Immediatelly, as the melody goes UNDER the 8-th overtone and it is gonna stay there for a while we just RE-DEFINE the "Sounds 22ma" to "* = 15ma" and we have 4-th on the same place as 8 before the change, and 5, 6, 7, 8, etc... above the fundamental again. :)
dear filip,
if i am right, your system tries to combine diatonic numbers and harmonics. for my practical work (both composing and performing) is it much easier to separate these systems clearly because they denote two very different contexts. counting in integer relations or harmonics (theoretically unlimited) belongs to one single fundamental pitch and refers to overtone music only. diatonic numbers are related to a system of harmonic progressions, means changing chord-fundamentals around a central pitch (cadence). it implies scales with limited steps. their array is necessarily different to the harmonic scale. a third system needs to count chromatically. so you have 12 intervalls resp. the number 13 for an ovctave without a central pitch. and if you are looking for microtonality (like indian or gamelan music) the amount of numbers and systems rises increasingly.
in my opinion we don't need to think in numbers while making music or try to express something. our imagination, ears and fingers/voice are directly connected and intuition is faster than a thougt. but to understand the rules of music and to use them as composing tools or to discover new functionally areas (means useful scales, chord structures and progressions) just needs that effort and patience to learn and to practise. finally, comparing the different systems we find a wonderous beauty. all these regularities are audible! mathematics and music, thinking and emotions are tightly connected.
best wishes, jan
Replies
What may be the most remarkable about overtone singing is that it unites some very fundamental elements of speech (phonetics), music (intervals) and ... mathematics: each prime number incarnates a new tonal function through the harmonic series. The three fields share a common and very deep offspring which we may contact through our practice.
One of the oldest ways to indicate tonal functions is by hand and fingers (the guidonian hand etc.). And fingers have always been used to indicate numbers (a digit may be numerical or anatomical!).
Octaves are actually mirrored in the arithmetic series 1-2-4-8-16-... so it is obvious to find a finger counting system which may bridge the numbers and the tonal functions. The most interesting in my view would be to utilize the binary counting, where each digit position is exactly the 1-2-4-... (whereas the positions of our common 10-digit system are 1-10-100-1.000-...).
In practice it can be used by choir leaders to indicate which harmonic should be amplified, and for establishing awareness in personal practice... developing a harmonic finger language.
One hand can indicate numbers from 0 to 31 which should be sufficient for most overtone singers (and those who need wider frames don't need the fingers). This also gives the choir leader the opportunity to indicate two different harmonics for two different voice groups within one choir.
Thank you for this opportunity!
I should like to turn the issue upside-down:
Instead of focusing of a practical solution to bridging the gap between an inherent natural pattern (the harmonic series) and a product of culturally conditioned language (music notation system) I should like to return to the starting point with Filip's urge to make 'the octaves visible again'.
As a member of a choir called Spectrum (and thank you for your acquantaince by your choir's visit in Copenhagen) he is obviously aware that at least one octave - or really almost an octave has been visible since the days of Noah: the rainbow spectrum which covers just a little less than an octave. And by the fact that we consider violet and red neighbours on the painters palette, we are led to the conclusion that in human conception there is an analogy of the colour octave and the audio octave, both being defined by the frequency and wavelength ratios 1:2. The analogy being that in both worlds the octave means something like 'comming back to a quality already experienced but on a new level' - either higher or deeper.
From here it is necesarry to think calmly as most people fascinated by holistic approaches tend to spread their 'equals signs' to loosely and thereby harvesting a poor crop where planets, tones, colours, anatomy, etc. gets badly entangled!
First thing is that the visual octave, the rainbow spectrum is separated from the audible octave by more than 40 octaves which is a gigantic span. Already on the piano we tend to conceive the octave as something which is not absolute in the extreme ends, high and deep, and colur and sound as fields of conception are actually worlds apart!
Furthermore the light and and sound frequencies are basically two different waveforms (transversal and longitudinal respectively).
Lastly the very difference of range the human conception is tuned to between the two worlds (we see a little less than one octave but are open to about ten octaves of the audible spectrum) the structures which arise within these worlds obviously becomes very different. Basically you cannot detect the role of the perfect fifth (ratio 2:3) in the world of colours whereas it is most essential in music by the fact that 7 octaves is virtually the same as 12 perfect fifths.
Sorry for bothering you with all this but for me it is necesarry before we deal with the bridging between 'nature' and 'culture'.
It is not my intention to pull the discussion completely of its trail and I may contribute with ideas to the practical problem later.
Till then I should like to lead your attention to some of the videos I have uploaded dealing with this issue of visually enlightening some structural correlation between number, tones and colour:
Specially the octave spiral video (octave is the returning of an already known quality - structurally-visually: the spiral), the rhythm-tone transistion video (octave aspects) video and the video of pattern as music and number.
Best,
Skye
No need for so many words. :)
I really like Your comment! It is just a bit long.
But it was worth reading for me. Thank You.
I started thinking about using the spiral schematic as a symbol for every overtone.
for example: 5-th overtone could look like circle with dot in the center and 2 dots above it, for the 2 and 4 (octaves) and in addition, number 4 could be connected by a curve to the point where 5-th overtone is, on the spiral map ! Because it is in it's octave. :)
very good ideas and videos!
One possible drawback might be in the case where the overtone appears to drop below the fundamental (as in the 6th overtone in your example). Although the singer knows what is meant, it may be disconcerting.
Yeah, sure! It can be drawback.
I believe this drawback can be nearly completely avoided if this system is used properly.
( I mean: one 3rd or 6th overtone under the actual octave is no problem for reading the interval at all. Those who are reading notes are used to understand interval "perfect forth" under like "perfect fifth" from the tone which is an octave lower from our base-tone. )
In Czech we call the lower "G" under our "c" (when c is our actual fundamental of tonica) the
"Bottom fifth degree".
For example: Immediatelly, as the melody goes UNDER the 8-th overtone and it is gonna stay there for a while we just RE-DEFINE the "Sounds 22ma" to "* = 15ma" and we have 4-th on the same place as 8 before the change, and 5, 6, 7, 8, etc... above the fundamental again. :)
( * symbolizes the small accental note.)
And this is Brother Jacob in "my Optimal notation" system:
if i am right, your system tries to combine diatonic numbers and harmonics. for my practical work (both composing and performing) is it much easier to separate these systems clearly because they denote two very different contexts. counting in integer relations or harmonics (theoretically unlimited) belongs to one single fundamental pitch and refers to overtone music only. diatonic numbers are related to a system of harmonic progressions, means changing chord-fundamentals around a central pitch (cadence). it implies scales with limited steps. their array is necessarily different to the harmonic scale. a third system needs to count chromatically. so you have 12 intervalls resp. the number 13 for an ovctave without a central pitch. and if you are looking for microtonality (like indian or gamelan music) the amount of numbers and systems rises increasingly.
in my opinion we don't need to think in numbers while making music or try to express something. our imagination, ears and fingers/voice are directly connected and intuition is faster than a thougt. but to understand the rules of music and to use them as composing tools or to discover new functionally areas (means useful scales, chord structures and progressions) just needs that effort and patience to learn and to practise. finally, comparing the different systems we find a wonderous beauty. all these regularities are audible! mathematics and music, thinking and emotions are tightly connected.
best wishes, jan
Music and mathematics, thoughts and emotions are tightly connected.
I agree that this is beautiful! (and helps connecting both hemispheres together) :)
Please, try to create some suggestions, so that we have something to discuss and choose from. :)