432 tuning fork

On a facebook group we are debating about thia question (search IL diapason... "LA" a 432hz):
there is a theory (Ananda Bosman and others) that suggest to reduce the 440 frequency of the tuning fork to 432 Hz.
In my opinion it would be right to reduce the tuning fork frequency but it is a nonsense the number 432; you know what is the Hertz unit, it is in relation with the "second" time unit. If this time unit was more or less than the actual, the theory (and others) would be a poor bluff.
What do you think?

Tags: audio, fork, frequency, hertz, tuning

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Permalink Reply by Jens Mügge on September 25, 2010 at 6:20pm

Thank you Marco, for posting this topic here. I have heard that some instruments should be tuned in 432 hz - but you can tell me everything about music theory. Maybe Roberto Laneri or other composer and musicians would like to share their opinion. Interesting to read what they think about it.

What I think: I think it is nonsense to use a frequency of 440hz - but I can't explain it. I feel only that 440hz is not the frequency of our time anymore. Is that right that this frequency changed from time to time and that Bach composed on another basic frequency?

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Permalink Reply by Christopher on September 25, 2010 at 9:54pm

From my experience, music that is played in 440Hz system (yet 12-TET, logarithmic scale) - when you rescale it to 432Hz (it's about 1.8% resample ratio) - it sounds different. Sounds more emotional. Sounds better if listened longer than a few seconds. Sounds deeper and more resonant, harmonious (I mean 12-TET rescaled, not the native pythagorean!). Sounds with greater clarity of instrumental components and layers (reminds a focusing of multiple lens, to achieve best sharpness of depth/shape).

For "well trained" or just accustomed ear - first impression is - that the 432Hz music sounds a little out of tune. But in direct comparison with 440Hz sample of the same piece - the 440Hz version sounds out of tune. When you get used to 432 system - you don't perceive it out of tune at all, but you perceive the music better in many ways. 432Hz system sounds better if you deal with multi-instrumental music (more data to process by your brain, used to 440Hz tunings); the music may evoke a lot of feelings and emotions and can be good for therapy uses.

From my experiments, it appears that these effects can be related not necessarily to 432Hz re-tunig, but to tune the music with lower-than-standard frequency. Modern "440Hz music" is still acceptable at about 420Hz re-tuning, but not below; 432 tuning is in the middle of the lower limit and current system. Probably if you go higher, beyond 440Hz, to let say to 448Hz - you achieve not only birhgter sound, but also in some emotional ways - different and better. If you change tuning from typical standard - you learn the new world, brain gets rewired.

From the history, the "A" was tuned in multiple ways, from less than 400Hz to more than 500Hz. There was no general standard in Europe, and using higher tunings was always related to achieve "brighter sound". Higher sound reaches farther areas of... place where the music was made (no speakers at that times!). They had to create a "standard", because opera singers began to have problems with their vocal tracts, and perhaps because of "musical market" (when you get used to one system, it is difficult to change it in your trained voice). Why they created 440Hz standard and not 432? Perhaps the reason was laical - to avoid a connection to philosophy and religion. 432Hz tuning is deeply inovolved with ancient philosophy (and was perhaps to some underground movements). The standard was created by Germans in the beginning of XX century (around war period) and in strange circumstances according to internet. Another reason could be, that the 432Hz tuning had in fact something to do with more opened heart, and putting the music into head-oriented area - created less opened (less free) people.

Pythagorean tuning is based on whole numbers and easy-ratios. It was probably easier to tune string instruments and other ones using such system. 12-TET scale is more sophisticated, based on root proportions (base x2^n/12). 12-TET is transparent to octave multiplication, so it is better for multiple octaves sound creation (pythagorean transparency is limited to only a few octaves, and musicians will explain you why). Note, that from historical perspective, 12-TET scale was created long before the 440Hz tuning standard.

Is the 432Hz (12-TET or pythagorean) tuning really "better" - it depends on use. Tuning fork as a single tone generator, like on the computer - is not enough to know it (but the placebo effect is around 15-40%, so whatevery ou buy - you will be happy with it...). C-E-G harmonic resonance of 3 forks, in real pythagorean tuning (at C=256Hz, A=432Hz) will sound better than the resonance of 12-TET scale. All depends on what you are going to do, how many forks are you going to use, and how they are all tuned with each other.

p.s.: I can upload some sound examples if you wish.

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Permalink Reply by Skye Løfvander on September 26, 2010 at 8:00am

To be on common ground it may be good idea to call for Wikipedia on Concert Pitch.
The amount of deviance in between the two tones 440 and 432 Hz is about one third of a semitone. Christopher informs us that it is about 1,8% which is correct as semitone step is a little less than 6%, but in music theoretic terms it would be more correct to express it in the cent system where the semitone value is 100 cent (the octave = 1200 cent). So we are talking about a microtonal difference of 31.8 cent (log(440/432)x1200/log2). Since this is a forum for overtone entusiasts it should cast some light also to mention that 54:55 is the proportion in question. The Pythgorean comma is close to 74:73.
Pythagorean tuning may be used for dronal and modal music but as soon as you move in to the field of polyphony and chord based music (roughly speaking the last 500 years of west european music) it cannot be used because of the bad dissonances in between some of the chords - which is due to the mechanism behind the above mentioned Pythagorean comma - 12 perfect fifths in succession (Pythagorean tuning) deviates from 7 octaves from the same basis with this value.
2^7 ~ (3/2)^12.
This disturbance of course occurs due to beating notes, so even though the Pythagorean comma is smaller than the concert pitch deviation, you have to consider that there is a difference in circumstance because there are other tones activated for reference. So 55:54 is not a very drastic deviance when dealing with a fixed point for concert pitch but would be a terrible dissonance to deal with inside a tonal system- as you can read in the Wiki-article history has seen much bigger differences in concert pitch definition.
Personally I prefer to use c'=256 Hz, but that is more from a philosophical point of view as this is eight octaves above the time unit 1 second. But like Marco points out you may question whether a time unit which is defined as 1/24x60x60 of a day has a very strong foundation.

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Permalink Reply by Marco Tonini on September 26, 2010 at 12:37pm

Thanks to all,
we know our body/mind is more affected by some frequencies rather than others, but in my opinion the problem is to establish the mathematical meaning of a pitch and the relation between number and time unit.
We can assign a lot of meanings on number 432, but we know 432 Hz and 432 MegaHertz are not the same thing, 432 meters and 432 kilometers are different sizes, likewise 432 byte and 432 Gb, or 432 celsius/fahrenheit/kelvin degrees, and so on...
So I think the question is: why does world use the second as unit of measurement? Is it a conventional unit?

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Permalink Reply by Skye Løfvander on September 26, 2010 at 1:28pm

Well, actually the answer to that last question has got to do with music.

When the Mesoptanians divided the circle in 360 degrees it was because their mathematics had a sexigesimal (60 digit) basis. Many of us still carry a remembrance of that advanced culture on our left wrist where the hands of the watch takes turns of 60 seconds, 60 minutes and 12 hours.
I call it great fortune that the circular display of time survived the more linear digital (13:09:43). Not only is it important to emphasize the cyclical aspects of time. The clock also gives us an intuitive knowledge of how to divide a circle into primary geometrical shapes:

Trigon: 0-20-40 minutes; Square: 0-15-30-45; Pentagon: 0-12-24-36-48,... etc.

60 has more factors (divisors) than any other number of that size... and if we go into it we realize that the old boys constructed a frame of understanding which also included music. The names of the individual lyre strings were related to the gods:

60: Creator/ Sky God Anu
50: Mountain God Enki
40: God of the fresh waters Ea/Enlil
30: Moon God Sin
20: Sun God Shamash
15: Venus/Ishtar
12: Mars/ Underworld God, Nergal
10: Jupiter, Bel/Marduk

If you take the length proportions on the basis of a fundamental tone 60 units, you will find the harmonic series 2-3-4-5-6 as lengths 30-20-15-12-10. And 60-50-40 is a minor trichord
Furthermore the octave 30:60 contains a heptatonic scale expressed in natural whole numbers composed by the three fundamental musical functions octave (2), perfect fifth (3) and just major third (5).

30-32-36-40-45-48- (50)-54-60 (2x3x5- 2^5- 2^2x3^2- 2^3x5- 3^2x5- 2^4x3- (2x5^2)- 2x3^3- 2^2x3x5)

Interpreted as lengths with 60 units as the fundamental that is the major scale, which we use today although in a different tuning system.

do-ti-la-so-fa-mi-(mib)-re-do

Conventional?
Convenient!

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Permalink Reply by Skye Løfvander on September 26, 2010 at 2:05pm

If you want a C-E-G harmonic trichord you should obviously not go for Pythagorean but for Just tuning where the major third is ... just!
The Pythagorean major third is defined as 81:64 whereas the just major third is 80:64 - or more simply and convenient (this is an overtone forum): 5:4.
So the just harmonic trichord is defined as 4:5:6 - do-mi-so. (the Pythagorean: 2: 162/64: 3)
The Pythagorean major third is 'way out of tune', 16.7 cent, one third of a semitone, and if the other tuning forks are played within the same session the deviation will be grave.
The deviation between Pythaghorean tuning and 12 TET is much smaller as long as we stay by the fundamental major tricord (tonic). The deviation of the fifth is only 2cent.
The problem of those two tuning systems is that the just (pure/ harmonic) third has been sacrificed - like to some degree also the sixths.

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Permalink Reply by Christopher on September 26, 2010 at 2:28pm

Great explanation Skye, and thanks for the wiki article. I see that wiki really evolves in the background.

What I can add, from the "dronal space" experimentation - when I tried to figure out, how the pythagorean versus 12-TET works in more complex applications, I found that the pythagorean soundscapes sound more sharp and 12-TET - are much softer, when listened. Also it is natural (because of the ratios), that the pythagorean drones will be more regular than 12-TET.

Going back to simple tonal settings, when you create a C-E-G pattern (using pure tones, simple sinusoid sounds, for example in cool edit vel adobe audition) - the pythagorean version has deepest harmonic resonance within, 12-TET is less resonant and more soft, but what interesting - if the C-E-G is made of harmonic components (tested on 32 tone division from the "harmonic series" model) - the sound is simply without harmonic resonance (sounds neither soft nor sharp, but "hard"), and the C-E-G tones appear to be separated from each other. And yet - the harmonics are the foundations of overtone singing.

Regarding the time and the time units - I recently started a discussion here:

http://www.overtone.cc/forum/topics/time-and-frequency

It would be great to continue this time/frequency related aspect there.

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Permalink Reply by Skye Løfvander on September 26, 2010 at 2:39pm

I forgot to give some references:
Ernest McClain:
http://www.ernestmcclain.net/
Richard Dumbrill:
http://mustradme.weblog.leidenuniv.nl/#Dumbrill

And then to go back to the original question about concert pitch which has becomed linked to the frequency of a':
Maybe overtone singers should not advocate the Pythagorean major sixth, 27/16, but the interval which is pure and comes beautifully to expression in the harmonic series as singable with overtones (which 27/16 is not):
So, let's make a new fraction for a'= 426,667 (the just/pure major sixth, 5:3, from fundamental c'=256 Hz
;-)

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Permalink Reply by Skye Løfvander on September 26, 2010 at 3:22pm

More Richard Dumbrill

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Permalink Reply by Christopher on September 26, 2010 at 4:13pm

I understand these sexagesimal calculations, yet my unanswered question is: why 1 second = 1 second? Sexagesimal system is scalable, and yet - it has been connected to such and not different periodicity of time. I ask this question, because perhaps - there is some other "temporal period", that would be more natural or efficient to use (and perhaps it is comatible with sexagesimal division).

Another question that is related to tuning systems and time-unit foundations - I asked here:

http://www.overtone.cc/forum/topics/sound-octaves-and-levels-of

It might be interesting to investigate, because one way of selecting forks and some instruments (like singing bowls) - is according to chakral aspects of expression (which is note-based system), and another one - is naturally related to the general pitch of sound through several octaves.

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Permalink Reply by Skye Løfvander on September 26, 2010 at 4:25pm

I am not sure that I understand what piece of the puzzle you think is missing.
Maybe some Wiki pages about Mesopotamian sexigesial systems and measurements (?):
http://en.wikipedia.org/wiki/Ancient_Mesopotamian_units_of_measurement
http://en.wikipedia.org/wiki/Sexagesimal

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Permalink Reply by Skye Løfvander on September 26, 2010 at 4:26pm

I am a singer who occasionally perform for others, I am not into tuning forks but I suppose most of the following thoughts may apply to fork situations as well:
So when I tune my instrument, for instance my monochord (whose strings all have the same pitch so that is easy), what would I think of? Planetary frequencies?

It is a music instrument so of course what matters is the tension, material and diameter of the strings and how their resonance with the sound body with its proportions and material characteristics is facilitated. To put it shortly: I tune my instrument so that it sounds good!
Other considerations comes into question if I intend to sing a mode or scale where it does matter what function the drone has – so I also need to adjust the pitch of the instrument to that.

But the resonance of my instrument is only one level of a complex picture. I also need to consider at least two more levels of resonance involved:

1) That of human body resonances – being aware that body is obviously also a music instrument, a very complex one.
This perspective may again be divided in two:
- As I am a singer it is not enough that the instrument sounds good in itself it should also match the resonances of my voice optimally. This is not stagnant – my voice changes from day to day and depending on environment and situation.
- Furthermore I should somehow be aware of what you may call the resonance of the audience.
Both these aspects may be interpreted as having a physical perspective and a feeling 'soul' perspective.

2) Finally I should really consider that the room which lends its frames to my performance – however small it may be – is also an instrument with resonance characteristics. So actually I would say it is much more important to tune according to the acoustic space than any speculation about planetary resonances.

Planetary perspectives are great, specially when we acknowledge our own fundament: Planet earth!