Overtone Music Network

a common space for harmonic overtones

# 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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### Replies to This Discussion

Sorry Christopher,
I didn't know you posted this: http://www.overtone.cc/forum/topics/time-and-frequency, it seems to me the same question...
Well, now I think I got what you are pointing at!
You are on a quest for some measure reference which may be easier to relate to for shorter time intervals than a day.
The metric system is somewhat comical as every time I need to weigh flour for a dough - a very common thing - I need to relate to the size of the earth (because one meter was defined as 1/40.000.000 of the circumference of the globe, and one kilogram was originally defined as the weight of one cubic decimeter of water... and they didn't even get the earth diameter right!).
But obviously all measures - time and space - in nature are subject to variances. The ancient measure systems got very confusing... so many versions of an inch because peoples thumbs are different.
I have also been on the quest and found some measures in the human body which hardly vary at all from individual to individual and during evolution. They are lengths, so you may convert it to wawelength and further to frequency.
If you find some time unit which would be suitable for a common fix point - preferably rooted in nature I am very curious to hear about it!
I guess with my search, I will result in a sound/frequency map, in which there will be some local and relative maximum/peak points, fuzzy spectral bands of acceptable deviations, and directional directives...

I always begin with asking a question. A system that I'm within "now" - how it affects me, how it affects my body/consciousness unit, what potential it has, and what limitations. Then I begin to look for an other system, that I can step into. The same questions I ask there. If you begin to step into variety of systems, you begin to separate the placebo effect (of philosophy that is behind a system) from real influence (from real properties, real beauty), that is however strictly related to your own configuration, habits and to your environmental circumstances. Yet you begin to perceive the systems like a "lens of focus". You also begin to look for some cues to develop an "effective standard" in your context, even if this will be a dynamic one, and not static. It's like with the differences between the pythagorean, 12-TET and harmonic tuning, and attaching it to lower or higher frequencies in relation to current ones.

But curious thing. As an artist - I work in general with non-linear systems and only with such ones - I achieve the most pleasurable results. ;-) The discovery of possible "structure" is always after a piece is created, not before.
I ask again: why one second time unit is exactly one second and not a second plus or minus some istants? I don't find a cosmic/universal/heavenly reason. So in my opinion it is a nonsense to try to call a pitch with a number. Obviously it is necessary to compare a pitch with another, for example 100 Hz is higher than 101 Hz and so on, but how can I say 432 Hz is better than 440 Hz only thanks to mathematical arguments?
I can say 432 is a magic number because .... or it is a perfect number because .... or it is a divine number because ... but in this case we talk about Hz, that is in relation with an other unit of measure, the second.
All of these considerations are useless in comparison for example with the sectio aurea and others, ratio between numbers.
I think we came to following conclusions here.

1. the pythagorean system as it is - is a system of "easy ratios", based on "regular proportions", which produce sharper harmony, but in limited range of octaves coupled together. a different system is 12 TET, where the ratio between following semitones is constant. this system is less sharp, but transparent to multi-octave structures. both - pythagorean and 12-TET, (as other systems, like the harminic one) - are "scalable" in terms of the point of attachement (to basic unit of time). their "meaning" is in regularity of inner and outer proportions.

2. modern "time measurement" that we use - is based on sexagesimal system, which is also an easy one for several mathematical applications. both - the sexagesimal formula of time and 12-note formula of music - are compatible with each other in terms of mathematics. the sexagesimal system is also scalable (like note systems), with no particular reason to be attached to "1 second".

3. both - "60-unit sexagesimality" and "12-tone musicality" - are used since hundersts if not thousands of years. thus - they are very compatible with our inner complexity development (like the way of how the brain is rewired, how we perceive the world of meanings, feelings, and so on; neuroscience).

I would guess, that from cultural point of view or from the point of view of one generation - important is, that in general - we... stuck. being stuck means - that we on and on - are influenced by mostly the same "patterns". there is a lot of music beyond the 440 tuning and 12-TET scale, but the modern western world - is saturated in many ways with these two. that why strange things like jazz or singing bowls and gongs or overtone singing - sound so mysterious and fresh, so different and creative.

I would guess, that in terms of cycles per second, explanation of "1 second reference" is explainable by the tuning systems from previous centuries. If the "A" was tuned between less than 400 Hz and more than 500 Hz (in different times and various locations), and if we a "relative unit of time" (let say, that our "base" is 440Hz; we shift 400Hz to 440Hz and 500Hz to 440Hz to achieve equality; sorry - I don't know how to express it in english) then: we result in "1 quasi-second" between ~0.85 to ~1.15 modern-seconds.

So I think, that it is not necessarily important where from "1 second" came from (even if we have it from some aliens...) as a reference time/cycle unit, if it was used in such diversity over the time. The limitation of this diversity may suggest one fact. For humans, more than for other animals (because of structural language we have) - the most important in sound - is our voice. So probably the "chosing mechanism" for reference units - will be related to our voice, our vocal possibilities. The rest of this story becomes generally easy and clear.

Whoopee, another puzzle is solved!
(-;
Just some thoughts on Christopher's post:

In my practical experience perfect tuning frequencies depend on the way instruments are built.
E.g: I've got a saxophone which was built in 1947 and after years of experimenting with it I came to the conclusion that it sounds best in its own natural resonance at the pitch of a=438 Hz. I think most of the saxophones built at that time were designed for this kind of tuning. Today's standard tuning pitch for the music I use to play is a=442 Hz, so I always get into trouble when playing whith large ensembles or instruments that are in fixed tune ('classically' high pitched pianos).
My other saxophone (newer, maybe from the 1980s) sounds great at a=440 Hz. On both instruments, when played at their perfect natural resonance pitch, I can develop a complex and controled spectrum of overtones, which lacks when I have to tune them in another way. Eventually, this leads to music that is more emotional (in my ears) because it's easier to form the sound I want from the instrument. I just have to understand and respect the entity of it, in a way.
Same goes for overtone singing (for me at least). I mostly use a 440 tuning fork for practicing and quite often when having finished an exercice I find that my 'inner pitch' has fallen. When I start from a lower tuning (437 or 438) I don't get this phenomenon and the quality of overtones is much better while it's independent from the absolute pitch of the root.
So, I guess my perfect natural resonance pitch is a=437, although I was built in 1982... strange!

Any thoughts?
regards,
Johannes
...but another question arises. (-:

Let's forget for a while about "seconds" and "cycles per seconds" as concrete "number" related phenomenons. These numbers - whatever they are - in essence - have been created to describe something. One of such "things" to describe and compare with each other - are the "resonances". Are there any natural (or somehow signifficant) peak resonances, to which the tuning systems are attracted?

Hi Christopher,

Well let us begin from the top with your first point, then I may come back to the others - it is getting late!
I wouldn't say Pythagorean tuning is a system of 'easy ratios' it would be more correct to say that it as tonal system with a simple GENERATOR (the 3:2 proportion) - and it does make quite a difference.
Neither I think it would be correct to characterize Pythagorean tuning as 'more sharp'.
I have made a diagram with a comparison of the 12 TET, the Pythagorean tuning system and Just tuning (which I would call the system of easy ratios).
Legend
Blue: 12 TET, the octave divided in 12 equal proportions. It looks extremely pleasant to the eye but what is visually pleasant may not be harmonic to the ears - just think of the paper A format which is very harmonic to the eyes but in music the proportion 1: squareroot 2 is extremely dissonant.
The axises are found at 0-100-200-300-... etc. cent.
Red: Pythagorean tuning, it is symmetrical (apart from the tritone) around the vertical line.
Green: Just tuning, elements from the harmonic series, 2 (octave), 3 (perf. fifth) and 5 (maj. just third) combined.

Finally the intervals from the harmonic series is our common deepest reference when it comes to defining it pure or not - also among music theorists. So for example the Pythagorean major third is far from just and both the 12 TET and Pyth. tuning fail to render just thirds and sixths.
That is one of the reasons that during the renaissance with the oral polyphony where the thirds were very important (they still are but we seem to have forgotten) they used a fourth and different system (or series of systems): meantone temperament - where the thirds are just.
On a more practical level just tuning is not very suitable for polyphonic music as the chords become to diverse - they tend to contain many different intervals.
One thing you may say about Pythagorean tuning is that it has two and only two semitone intervals.
Hi Johannes,

I always suspected you were a 437! ;-)
"easy ratios" = "average english"in this area. ;-)

Nice picture, I did similar comparisons in excel and for frequency values; comparing the "exchange" between 12-TET and pythagorean - I found, that the "A" was in the "center" of this pattern. But I don't remember details, it was 2 years ago or more, I would have to reconstruct the pattern again.

But I'd like to add a few words. Some time ago, when I was experimenting with micro-chords for binaural-beat applications (I explored some topics related to Bob Monres' hemi-sync technology - you find it via google) - I was creating multioctave-chord based "fractal" drones (the chords were present both - tonal, and in a special setting as binaural beats). To find out which kind of drones would be appropriate for such complex soundscapes, I created 3 versions of it: 12-TET based, pythagorean type and harmonic one. Pythagorean drone was the "sharpest" sounding one. 12-TET was soft. I don't remember why I didn't liked the harmonic one as a solution, but all I can say - harmonic chord does not have harmonic vibratio within; sounds rather "electrical". From these experiments came my conclusion.

Yep, definitely is late, after 3 a.m., it's time to go sleep.
@ Marco:
Halleluja for your not accepting anything - we need to question the fundament!
I think the answer was decent enough: the second is a second because of subdivisions - subdivisions of the apparently only handy constant within the rhythmic phenomena spectrum - one day. So the old boys divided the day in a way which would be convenient. I already did argue for the convenience of a sexigesimal division. And we are still missing some good universal reference time unit within the range of time shorter than a day. Scientist need to go to the atomic level to find constants they can use as actually days are becomming longer with the age of our planet. See Wikipedia article.
The division of the day in 12 (24) is probably a loan from another area were a lot of tempering is needed because ultimately the set pieces do not fit: calendars. I suppose you would agree with me that a division of a year or a day in four is universal (two culminations, two balance points). Like when dealing with time units shorter than a day, it was basically necessary to find smaller subdivisions of the year and here the moon came in to the picture which is basically why we have 12 months (and 12 hours).
It is somewhat ironic that in a subculture dealing with planets, frequencies and 'star wisdom' if you ask people of the length of the lunar month, they tend to reply 28 days (they are thinking within a 7 based system) whereas the more correct answer would be 29½ days.
What is fascinating is the point that ultimately the lunar month does NOT fit with the solar year and the solar day does not fit with the lunar month... very much like the problems we have with tuning in music!
Like I wrote to Chistopher I am very curious to hear any suggestions for time units shorter than a day which have a universal basis. The problem is that the overall rule of nature seem to carry the headline 'Variance' so it would be risky to try to establish a 'standard heart beat rate' or 'standard respiration rate' etc.
In my reply to Christopher i refered to my own quest for a references based in nature and only succeded to find a length measure but as it can be converted to time (frequency) by the formula fxλ=c (frequency multiplied with wawelength = constant, 340 m/s) there may be something to begin with (I am aware that talking about constant refering to this very useful formula brings us into another problem as this particular constant varies according to temperature).
You may find my reflections at this link. I am sorry, it is in danish but I suppose you may get most of the meaning by using a translator tool.

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