Perfect pitchers - equal temperament?

Edited: February 18, 2019, 4:50 PM · To start with, I don't have perfect pitch.

When a person with perfect pitch hums a, say, D, how does the D relate to the A in 440?

When a person with perfect pitch tells me that my open D is too sharp, does she mean that I am out of tune relative to the tuning fork (down a 5th), or to an ideal piano in equal temperament?

She said she doesn't know what I'm talking about. She's born with it. Can evolution equip a human with a system created in modern time?

If it is not equal temperament, what is it then?

Replies (26)

February 16, 2019, 6:56 PM · I can't directly answer your questions, but just say that the D string on the violin is a tiny bit lower than the D on the piano if the violin is tuned in perfect fifths and the A on the violin is the same as the A on the piano.

I think she must have learned it somehow very early in life since those pitches we use in music don't exist in nature. They are created by culture. But I don't know how people develop perfect pitch.

I think that she would need to learn to be flexible. Pitches can be intonated both high and low and actually be correct in the context.

February 16, 2019, 7:00 PM · The capacity is 'evolution equipped' but the ability is learned. So it's ET if the person grew up in ET environment.
Edited: February 16, 2019, 7:01 PM · The counterpart to equal temperament is called "just" intonation, and just intonation varies by key.

Without hearing the notes in question I don't know if you can tell what she means by "open D is sharp". Could be her being trained to a piano, or trained to A major, or trained to some other tempered system.

Edited: February 16, 2019, 7:04 PM · Here is an interesting article of the neuroscience of perfect pitch:

https://www.udel.edu/udaily/2019/february/pitch-perfect-hearing-recognition-student-david-krall-brain-research-identify-notes/

February 16, 2019, 7:08 PM · Most violinists have good ear due to years of experience playing in tune. So as long as you are able to play in tune (whether solo, chamber or big ensemble, or with piano) you are set, and need not worry about these matters.

You can always keep training your ears with careful scale practice. Be alert, and strive for perfection, rather than being content with "almost there" intonation.

To your question: I don't think there's an universal standard defining perfect pitch, as one of our previous threads in the matter didn't clear up this issue-for me, at least.

I agree one cannot be born knowing what an A 440 sounds like-the person must learn the system first, and then realize he/she can easily tell and sing an A 440.

And in the end, it doesn't matter if you have "perfect pitch" if you don't practice to play in tune. You can have the skill to hear all sorts of notes in different pitches (440-445, etc.), and still play out of tune. So just play in tune, and do not worry about lacking this ability.

I am supposedly a "perfect pitch" person (depending who you ask), but definitely, do hear D# relative to the scale. I hear it "in tune" depensing on the work/phrase being played. I do not ever think of notes in equal temperament terms.

(For playing so many years at 442, I often mistakenly think 440 is "too low". Perhaps my ears lack true "perfection." )

February 16, 2019, 8:41 PM · This makes me so confused - now it's like… to a perfect pitcher trained up in 440 equal tempered piano, she would feel very uneasy (or "out of tune") in other systems, such as pythagorean tuned strings quartet, or songs in baroque tuning?
February 16, 2019, 9:28 PM · How would you even tune yourself to pythagorean or just intonation? As far as I know, perfect pitch isn't that precise.
Edited: February 16, 2019, 10:34 PM · Cotton
You don't so much "tune the string" to just intonation as much as you tune the notes you play relative to other notes that you play.
The open A string at 440 is great for A Major, but is technically not in just tune for [checks notes] F sharp major.

I can't play in either tune :(

Edited: February 17, 2019, 7:35 AM · That's not what I meant. I know how temperaments work. Isn't he asking if people with perfect pitch can tell them apart note-by-note?
February 17, 2019, 12:20 PM · "When a person with perfect pitch tells me that my open D is too sharp, does she mean that I am out of tune relative to the tuning fork, or to an ideal piano in equal temperament?"
A. You're talking about two different things, relative pitch and perfect pitch.
B. Who know how her individual ear is perceiving? She probably has no idea herself. It's just a feeling, an intuition.

Since people have differing sensitivities to various senses--touch, vision, smell, hearing--wouldn't it make sense that there are varying sensitivities to pitch identification as well?

But more importantly, I think it really has nothing to do with equal temperament per se. Human senses don't operate on an "either-or" system: they are able to use fuzzy logic to determine and identify. For example, your best friend shows up one day with a mustache. Would you fail to recognize him? Your sister calls on the phone with a bad cold. Do you recognize her voice? Probably. We categorize something as "red" even though there may be thousands (or millions) of shades of red. So when is something "not red" and instead orange?

In the same way, the human ear isn't an "either this or that" system. It can deal with fuzziness or "almost this or that." If you play F3 and A3 on the piano, you can see it's wide. It's got an obvious beat, about 7 beats per second. But a typical theory student that knows their intervals would still call it a Major third.
When I taught ear training at various colleges, I used what most people do in the classroom: the piano. But there was little talk of equal temperament. If the piano was even close to being in tune, that was enough.

The other thing you don't know about the person in question is her environment in learning the pitches.
I've said it before, but the assumption that all pianos are always in tune and tuned in the same way is bunk.
A child could grow up in a household where the parents are too cheap to ever tune the piano and maybe the treble has fallen a quarter-tone relative to the middle. How will that affect the development of perfect pitch? What if the family piano was old and the local tuner refused to tune it past 435 for fear of breaking strings?

People need to remember that phenomena such as "perfect pitch" and "equal temperament" are slippery, fuzzy terms, that pitch sensitivity varies widely, and that people with perfect pitch may not even be able to describe what about a pitch sounds "flat" or "sharp" any more than they can describe what "red" means.

February 17, 2019, 5:02 PM · One sentence in the article George Huhn cites claims perfect pitchness occurs in only aboubt 0.01 per cent of people - that is one in 10,000. I knew one such person; my friend, SR, had been a Tone Master recording engineer, who lost that job in his 50s because health insurance for his family cost more than his employer could afford. SR's photo had even appeared on the cover of the recording engineering journal. Even after SR left the recording industry for a job at the research facility where I was working, Leonard Slatkin reached back and had SR travel to Moscow with the Saint Louis Symphony to record their concerts there over 20 years ago. Even though I had moved away be then I saw SR playing the bass there with some St. Louis players in Moscow on evening ABC TV news during some time the orchestra members were relaxing.

So - to get to what I learned of SR's ability - he could tell you what any note was and the frequency of A-4 for the tuning of that note. He could identify unseen propeller aircraft by the pitch of their engines and he could tell the speed of an automobile by the pitch of tire sound.

But in more practical terms, during his brief music director stint (while our community orchestra was searching for its next professional conductor) he demonstrated the power of his absolute pitch-ness by tuning 4 wind players simultaneously (not having to have any one of them play "his" part separately). I've never seen a conductor able to do that before or since.

It was pretty remarkable to be there and hear that. Unfortunately, about a year ago I tried to look up SR again, on-line, and learned he had died only a few weeks earlier.

February 17, 2019, 6:06 PM · I assume that the optimal way to tune for general purposes is in slightly tight fifths, just enough so we still cannot hear that it is not 100% pure. Could someone please tell me what the normal threshhold for humans is in terms of cents (is that what is used to measure)? So for example if I tune to A 442, can my D be +3 cents or even more? The D in equal temperament is + how much?
February 17, 2019, 7:27 PM · Piano tuners live by the beat of intervals to make it all equal.
February 17, 2019, 8:54 PM · Most musicians can hear the difference between two tones starting around 4-6 cents. Your average Joe Schmoe might be able to hear something like a difference of 7-10 cents. That's between two tones played one after another, though. It might be more obvious with harmonic intervals.
February 18, 2019, 12:57 AM · Interesting fact: Even untrained people can distinguish an 1 hertz difference.

Once I had a tuning fork manufactured to sound 440. I measured it with en electronic tuner and it reliably says 441 hz. I was interested to see if an untrained person would notice the difference and I sounded them (the tuning fork and the tuner sounding at exactly 440) to one of my non-musical colleagues. He told me the 440 was lower, with very careful listening though.

February 18, 2019, 1:04 AM · Thank you all for the advice. truly.

I was concerned about this question because I need to routinely tune to the piano and a strings ensemble. I can notice the difference between tuning in 5th and tuning using a e-tuner in equal temperament. So I think it really makes a difference in absolute or in relative terms.

And again, thank you!!

February 18, 2019, 1:13 AM · Extended reading:

https://en.wikipedia.org/wiki/Cent_(music)#Human_perception

"It is difficult to establish how many cents are perceptible to humans; this accuracy varies greatly from person to person. One author stated that humans can distinguish a difference in pitch of about 5–6 cents.[4] The threshold of what is perceptible, technically known as the just noticeable difference (JND), also varies as a function of the frequency, the amplitude and the timbre."

February 18, 2019, 7:09 AM · Cotton, so you reckon for tuning perfect fifths in double stops, 3 cents tightness is ok then?
February 18, 2019, 7:51 AM · I'm curious if people fully understand cents. I read a lot of people on a lot of forums glibly telling us how many they can hear. Food for thought - what's low G on a fiddle 215Hz? 1 cent at that frequency is 0.124 Hz. In other words the beat would occur once every 8 seconds. 3 cents would be a beat every 3 seconds, approximately.
Edited: February 18, 2019, 8:43 AM · "Could someone please tell me what the normal threshhold for humans is in terms of cents (is that what is used to measure)? So for example if I tune to A 442, can my D be +3 cents or even more? The D in equal temperament is + how much?"

It's difficult to understand the question here. Assuming you're asking - if I tune my A to 442 and D to a fifth relative to that, how much would I be off an equal temperament D tuned to 440? Why would you ask that? I suppose you're trying to understand what a standard tuner would show for that D you're playing, not that you're tuning to 442 and then playing with a piano at 440 and wondering "am I perceptibly off?" - which would be silly, because you should tune to 440 then.

But on second thought, that question wouldn't make much sense either - if you're using a tuner to tune to 442, then its D would also be tuned relative to 442, and the number of cents you'd be off it when tuning to fifths, as it's a relative frequency, would not change from the number of cents you'd be off if you had tuned to and set the meter to 440 Hz - about 2 cents (displayed flat, because the equal would be sharp).

You can find more information here, including a chart about perception at the bottom: http://www.sengpielaudio.com/calculator-centsratio.htm

Now if for some reason you did want to do a 440 to 442 comparison, with yourself tuned to 442 using relative fifths, then your D would be about 6 cents sharp relative to equal with base 440, and your E would be about 10 cents sharp relative to that, and your G about 4 cents sharp.

Edited: February 18, 2019, 9:11 AM · When a person with perfect pitch hums a note, of course they'll have to have a well trained voice to convey anything meaningful. What a person with perfect pitch hears and what they sing aren't necessarily going to be the same thing! Afaik, perfect pitch is just eidetic memory, so if they learnt it from a musical instrument, it will be ET.
A violin's D (a JI perfect fifth below A440) ought to sound flat to them because the ET perfect fifth below the A440 set by their piano tuner will be a sharp D, according to JI standards.
February 18, 2019, 10:08 AM · 'It's difficult to understand the question here. Assuming you're asking - if I tune my A to 442 and D to a fifth relative to that, how much would I be off an equal temperament D tuned to 440? Why would you ask that?'

Yes this is what I am asking, sorry I didn't make it very clear. I'm just asking because I am curious to see what my own personal cents threshold is against equal temperament. I never use a tuner for my A since I have perfect pitch, and if I am playing with piano then I just tune to that. I always tune in slightly tight 5ths (whether it's equal temperament or not I don't know) but from your answer, I see that a D with equal temperament relationship to A 442 is 2 cents higher than a D played a perfect fifth below A 442?

Edited: February 18, 2019, 2:40 PM · Horace wrote:
"To start with, I don't have perfect pitch.

When a person with perfect pitch hums a, say, D, how does the D relate to the A in 440?

When a person with perfect pitch tells me that my open D is too sharp, does she mean that I am out of tune relative to the tuning fork, or to an ideal piano in equal temperament?

She said she doesn't know what I'm talking about. She's born with it."
__________________

Horace, I don't think there's any way of nailing down what a person with perfect pitch is talking about in their evaluation of intonation, if that person doesn't know themself.

Mine is probably based on piano intonation, since I had hours of exposure to that every day from early in the womb.

February 18, 2019, 2:54 PM · "D with equal temperament relationship to A 442 is 2 cents higher than a D played a perfect fifth below A 442?"

Yes, it doesn't matter what the base frequency is - a perfect fifth below that will be about 2 cents flat relative to the corresponding equal temperament "fifth", because the measure of cents is proportional to frequency, not fixed.

February 18, 2019, 4:46 PM · David: thank you. I think I pretty much got the picture now!!!
February 18, 2019, 5:31 PM · I always learn something new here on v.com. This is the first time I have ever heard of, "cents", in music. I was a music major for several years, been around many musicians and professors and never has anyone mentioned "Cents"! I'm going to look more into this! What an amazing discussion!

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