Music Tuned to 440 Hz versus 432 Hz and the Health Effects
sciencedirect.com
sciencedirect.com
"Not significant" means that "a slight decrease" is not supported by the data in the conventionally accepted way. By convention, authors should not make claims either way if the effect is not statistically significant, even if they believe the effect is real. So the sentence above is declaring that the authors aren't following the norms of scientific claims.
You're writing like you disagree, but in the sentence after that the actual "claim" says to do exactly what you suggest(get more data).
I’ve sort of changed my mind about this, from the discussion here. It’s not wrong. But I still would not write it this way myself.
We've settled as a community on a convention that we don't claim an effect is real until it is supported by data ("statistically significant") ie. <5% likely to be explained by chance in your results.
"Significant" does not mean big or important in this context. It means better than 5% unlikely to be (un)lucky data.
But if "result [was] lower but not in a significant way" means "result was not proven to be lower", how does saying "lower but not really lower" make ever any sense? It seems to me that such nonsensical formulation ought not to be ever used by anyone.
By convention, this means "indistinguishable from", so reporting that it is lower is an unsupported claim. They would be equally justified in reporting that it was higher, ie. not at all.
Perhaps I’m too zealous about it, and maybe the conventions vary, but I was trained to avoid using words like ‘lower’ here.
The 5 % number you mention is completely arbitrary and often woefully inappropriate.
Look at it from a betting perspective. Can you earn more than 10 × your investment if the null hypothesis is false? Then anything less likely than 10 % is significant.
The parameter value is not arbitrary. It's a convention arrived at after hundreds of years. If it were arbitrary, p=0.999 or p=0.00001 would be just as good. We've settled on p=0.05 being usefully convincing but not crazy demanding to obtain by experiment with noisy measurements.
Though it has now indeed become conventional to test with p=0.05, there is nothing wrong with reporting an effect that fails the null hypothesis test. At least that is the position of the American Statistical Association [1].
[0] https://www.cantorsparadise.com/what-is-the-meaning-of-p-val...
On the value itself, we are quibbling about the meaning of ‘arbitrary’: Fisher certainly could have chosen another value, but not all values would be considered useful. Some expertise about the nature of real world data and the minds of statisticians is encoded in the chosen value.
If I propose that we change the convention to use 1e-12 instead and you think ‘that’s too small, I prefer it the way it is’, then it’s not arbitrary in the sense I mean.
What probability you accept as significant should depend entirely on how you plan to use the results. Something with a p value of a staggering 70 % (i.e. it's more likely not true than true) is significant if the payoff is good when it's true, and the cost is small when it's not true.
And 70 % is very far from 5 %!
Then again, if the payoff is tiny compared to the cost, you might ask for a p-value of less than 0.01 %, in order for it to make sense to take the chance on it.
Think like a poker player: a hand that has 1/4 chance of winning needs better than a 3-to-1 payout when it wins to be playable. Conversely, when the pot offers you a 3-to-1 payout, you better make sure your hand has more than a 1/4 chance of winning.
Ackchually... p-value represents the probability that results like these would be observed even if there was no difference between the two choices, simply due to chance.
Who picks the null hypothesis? How is it picked, i.e. why does that specific hypothesis get favourable treatment? What level of randomness should one allow? What does it even mean for an experiment to be a single, isolated trial? How can anything be?
Those are critical questions to understand the concept, and your explanation just pretends they don't exist.
In real life, to borrow your description, we can hold varying levels of belief in statements depending on how strong the evidence is, and the magnitude of the payoff in the various cases.
Maybe the probability of the result in the study in question is 51 %. That's still more than 50 %. Whether that difference is meaningful to you is not something someone else can decide.
You badly misunderstand
Honest scientists who use statistics do not make such a claim that an effect does not exist. Rather than the experiment that was conducted did not produce sufficient evidence (to a numerically defined standard) which justifies believing in the effect.
That is to say, that the existence of the effect, given the results of the experiment, has a low likelihood, and that low likelihood can be statistically quantified.
What that means is that exactly the same results as were observed will, or would, with a high probability, also be observed if the experiment occurs in the null hypothesis universe: the world in which the effect is absent.
So even if we are not in that universe (the effect is real), the experiment didn't show it.
The experiment simply doesn't discriminate between the null hypothesis and its negation to a level that could convince one to hold a probabilistic belief in the existence of the effect.
Say that given the evidence there's a 9 % chance the null hypothesis is true. A frequentist used to a 10 % significance level would then say the effect is true. A frequentist trained on a 5 % significance level would say it is false.
But that's just an arbitrary cutoff that by itself means nothing.
If instead we look at a practical scenario where we would use this result, we understand the problem space better. Maybe we have figured out how to get limited rights to the transpositions of famous music to other A4s, and this would cost a lot to do, but earn us some money if we do it and the effect is real.
Should we acquire those rights or not? Ask the 5 % frequentist and they would say "there's no significant difference, so you shouldn't." Ask the 10 % frequent and they say the opposite. Who do we listen to?
Let's ask the poker player. They will ask "What exactly does it cost to do this, and how much will you earn if it works out? That matters!"
So let's say it costs us $100 per song to get the rights to the transposed version, and we think it will earn us $102 per song if the effect is true. Now we can just plug in, remembering that there's a 9 % chance the null hypothesis is correct:
-100 + 102 * 0.91 = -7.18 per song
Not good. What if we made $127 per song with the same cost?
-100 + 127 * 0.91 = +15.57 per song
Worth doing, at the same probability of the null hypothesis!
In other words, you can't determine what's significant until you know how you will use the result.
Statistics by itself is meaningless. It gains meaning only when it's used to choose between actions.
That's a binary decision, which is bad, so we shouldn't.
In accordance with the confidence probability, we should buy into a percentage of the rights, and transpose the music to an interpolated value between A=432 and A=440 Hz.
You have this completely backwards. It means that the likelihood of the null hypothesis was not below some threshold such that it can be "ruled out". It says absolutely nothing about the likelihood of the data if the effect exists.
The obvious and only possible null hypothesis in this situation that tuning from 432 to 440 does absolutely diddly squat to the listener's physiology.
Authors are making an extremely serious mistake here and you shouldn't be pushing back
> "432 Hz tuned music was associated with a slight decrease of mean (systolic and diastolic) blood pressure values (although not significant)"
I can see why this line is fine to some and bothersome to others.
Strictly, it's just describing their results. No problem. The numbers are what they are.
On the other hand, why draw attention to the difference in means, when they are about to tell you not to take it very seriously?
This version avoids that:
"432 Hz tuned music was not associated with a significant difference in mean (systolic and diastolic) blood pressure values"
Maybe it's my age, origin, or personality, but I prefer this version.
For me, the difference between 57 and 62 beats per minute (with all other conditions being more or less equal) is a difference between me being healthy and having a light cold or enterovirus. E.g., it is a difference of "everything alright" and "some suspicious metabolic activity is there".
Our experiment consisted of throwing a dice twice.
Our data shows that on average result of second throw is lower than first one hower this result is not statistically significant.
> The current reference frequency for tuning musical instruments is 440 Hz
More accurately, the current most popular frequency for note A4 (the A above middle C) is 440 Hz. The article brings up the 432 Hz tuning but completely fails to mention that it isn't just an arbitrarily-selected frequency, but a frequency proposed by Verdi. He also proposed Scientific Pitch, which is tuning middle C to 256 Hz, making all C notes integer frequencies, and taking A4 to about 430.54 Hz.
I'm a fan of scientific pitch, and I tend to just use it as a default when I'm doing any audio programming because it makes it very easy to calculate all the pitches using C-4 as a base with frequency of 1 Hz.
Realistically, the "correct" reference pitch for a given performance is going to depend on environmental conditions, since temperature and humidity will affect the "normal" pitch for an instrument (and will do so in different ways depending on the type of instrument). Most pragmatic approach would be to base it on the hardest-to-retune instrument in a given ensemble (i.e. take a tuner to it while it's playing some octave of A, do the requisite multiplication/division to get to A4, and there you have your reference pitch). Speaking from experience in marching music, the resulting reference pitch tended to vary between 438Hz and 442Hz, with very rare exceptions.
You're only looking at the abstract. (Weirdly the abstract has separate sections. I haven't seen that before.)
> good information
Heh.
I’ve seen some interesting stuff (mostly Jacob Collier) where the tuning standard is actively manipulated during a song. Definitely convinces me we have not yet even begun to touch the boundaries of what’s possible in music.
Yeah, but we're drifting in the opposite direction. Grid, 4/4, 440Hz and 12ET are the game if you publish anything these days in the western world and it's probably harder to do something different than it would be centuries ago.
I can't wait to hear something popular in 13ET, but probably won't happen in my lifespan.
First the most nitpicky but easiest to solve: They tried lowering the music by tiny amount. Will lowering it more be even stronger? In particular will lowering it by a semitone work even better? Then it would suggest it's about the pitch rather than the tuning.
Second, they did first 440 and then 436. There will be a familiarisation effect. 2nd time in the same situation with the same music could likely less stressful. But yeah they mention they want to do randomization next.
Third, music is a deeply cultural thing. It may be that it's not objectively soothing, but rather subjectively soothing for people that grew up in certain culture and learned certain subconscious assocations. Some people like music that other people hate. This could quite plausible apply to even the tuning.
I basically rewrote the whole thing in an edit so yeah.
While possible, it's not what the link says:
> 440 Hz on one day and 432 Hz on the other
Those days could be in any order.
Also, the way they lowered the pitch was to slow the music. So the change in tempo could also have an effect.
> Second, they did first 440 and then 436. There will be a familiarisation effect. 2nd time in the same situation with the same music could likely less stressful. But yeah they mention they want to do randomization next.
They had two groups, one which did 432 Hz first and one which did 440 Hz first.
Edit: I watched the second one again, and it actually gives some reason why 432Hz may be preferred in some way in this test.
Given 440 is what we’re all used to on an everyday basis, the effects of the OP experiment might be explained by the “novelty” of how 432 sounds to us.
1. Some people say X.
2. We tested X.
3. Actually, it looks like X might be true.
4. So it would be worth doing a more powerful study.
They are testing a shitton of variables so it's highly likely that by pure chance something "statistically significant" would appear. But not even that happened (there was NO significant change at all), so the recommendation of a "more powerful study" is absolutely baseless.
If anything, the conclusion should be "we wasted our time so you don't have to waste yours in the future". Nothing to be ashamed of.
Otherwise this is how you start another bunch of "science reproducibility crisis!".
Maybe because its familiar but different at the same time.
Or maybe because so many things sound better when pitched down.
I would bet on this. That's why a lot of people like the concerts versions, instead of just listening to the studio version. It's the same... but feels new again, thanks to those small variations and imperfections from a live performance.
Still, I find it interesting they did the research for this, I love myth-busting, to know if urban legends are true or false with the foundations of data.
I wonder if for people with Absolute pitch this tuning could mess with them.
You also have the variable of whether the string instruments simply are retuned before testing alternate standards, or if the full reselection of string gages optimized for the instrument dimensions & current pitch have been accomplished for each particular tuning standard before testing.
Keep in mind that this is quite a task on a full 88-key piano where more than one identical string is hammered per note so there are over 200 strings to replace after 88 optimizations for any given tuning pitch standard. And you will need to have all posible string gages indivdually stocked in abundance, not merely commercially available standard replacement string sets.
To a point, the higher the string tension can produce higher decibel output from equivalent instrument operation techniques, and this is what musicians really notice most even on piano when their fingers and/or bows are not in direct contact with the strings.
And imagine if you will, the look on the face of a Stradivarius owner when the first set of proper steel strings arrive and are set up correctly. Then again you wouldn't want to tighten the stings too much and break the irreplaceable fiddle.
Seems to me the pitch inflation over the centuries follows the technology of manufacturing higher-tension strings gradually more reliably over time, this was a slow multi-generational process but it seems shockingly fast when the advances are applied to established instruments which are considered far more static and fully standardized already.
Eventually if you push the limits to the max you are going to exceed the sweet spot, maybe not for every instrument but the whole orchestra may not benefit, and if you have a good idea of how sweet it was you would know what to go back to.
And this is disregarding vocalists (or soloists sometimes with a Stradivarius) who are often divas that must be catered to at the expense of everyting else.
Remember perfect pitch today would be badly imperfect in any non-440 environment.
And you can only imagine how someone "born with perfect pitch" in a pre-440 world felt after the standard got away from them.
Edit: to highlight the problems of non-randomizing: it's not just the frequency that changed between experimental conditions. The conclusion could just as well have been "heart rate drops on second hearing" or "everyone's heart rate drops 4.8bpm in one day". I think that especially that last conclusion will make you think it can't be true, but as a hypothesis, it has the same status as the 440/432 manipulation.
Then there's a multitude of ways to split the octave.
As far as ET is concerned, a change in key is simply shifting the register by a number of semitones. In non ET tunings, the interval configurations change with the keys.
With some mean tone tunings, you retune some strings to accommodate different keys.
I very strongly suspect that people’s reactions to music can vary based on many factors, but the least of which involves familiarity vs newness.
Did they have control groups that listened to the same frequency tuned music on both days?
My expectation is that regardless of the tuning, people would be more relaxed listening to the same music on the second day.
I have a soprano sax which was tuned for the pitch system that didn't win out. It was called "low tone" if memory serves.
It's a fun antique which you can play out of tune to your hearts desire.
Those frequencies are for the A above middle C.
https://www.saxontheweb.net/threads/what-is-meant-by-low-pit...
They seem to think "low pitch" is 440Hz and "high pitch" is the one that lost out, 457Hz (sounds like a semitone higher to me).
432Hz is better, plus it has a cool name based in powers of two [1][2].
[1]: https://en.wikipedia.org/wiki/Scientific_pitch
[2]: https://archive.schillerinstitute.com/fid_91-96/fid_911_jbt_...
> Because of this harmonic misalignment, listening to 440 Hz music would seem to make people anxious, nervous, or aggressive, because it is not in harmony with the natural frequency of the planet earth.
> These same effects would have repercussions on human health since our DNA is sensitive to frequencies, as stated by the Professor Carlo Ventura’s team.
> Human DNA is sensitive to music and its relative frequencies to the point that it can even be reprogrammed through them. In fact, by subjecting stem cells to various frequencies it has been possible to modify their natural organic function.
and, in conclusion: "If we arbitrarily changed the "tuning" of the solar system in a similar way, it would explode and disintegrate! God does not make mistakes: Our solar system functions very well with its proper tuning, which is uniquely coherent with C=256. This, therefore, is the only scientific tuning."
The ramblings of a madman. Utter garbage.
[1]: https://roelhollander.eu/en/432-tuning/the-scale-of-fifths/#...