8 ms·

I am hoping someone can answer the following genuine question(s) from a mystified layman: Is our perception of sound really so sensitive to precise ratios ? Is

I am hoping someone can answer the following genuine question(s) from a mystified layman: Is our perception of sound really so sensitive to precise ratios ? Is a frequency ratio of 1.5000 somehow inherently more pleasing than 1.5001, or is it more the case that appropriately trained or gifted individuals can detect the difference ?

acadien 12y ago
I suspect we are very sensitive to the introduction of beats which form when incommensurate frequencies are combined. That is to say when you add a frequency of 1KHz to 1.1KHz you get beats at 0.1KHz with an internal frequeqncy of 2.1KHz. This isn't the precise effect that takes place since the two frequencies are offset by some fixed amount, but a similar effect will take place for an offset that is not quite a perfect fifth.
Tloewald 12y ago
I suspect that the problem is not just the subtle problem of pitch but the way waves phase in and out of sync with each other (especially on sustained notes) rather than remaining in consistent relation, so it should be possible for almost anyone to notice the effect if they know what to listen for. Not my area of expertise -- just an educated guess.
cynicalkane 12y ago
I met a composer of minor note (pun intended) who avoided writing major 10ths in the melody, because the ratios in standard tuning were wrong enough to cause major discomfort for him. This interval is about 14 cents sharp, where a cent is defined as 1/1200 of an octave on a logarithmic scale, so 14 cents is about an 0.8% difference in pitch. Curiously, major 3rds did not bother him, even though they have the same ratio problems.
- pmiller2 12y ago
  To put that in perspective, pretty much anybody can distinguish a pitch difference of 25 cents. People with perfect pitch can distinguish differences of less than 10 cents. Anecdotally, when I was taking lessons with my old cello teacher (who has perfect pitch), if he and I played a note on an open string simultaneously, I could always tell if we were in relative tune by the way the notes interfered. I don't think I'm particularly special in that regard. Edit: Also, once I have one string tuned, I can tell if a neighboring string is correctly tuned because neighboring strings differ by fifths. Again, I don't think I'm particularly special; it's just a matter of learning what to listen for.
  - ArkyBeagle 12y ago
    People with relative pitch can also discern < 10 cent differences. 10 cents is pretty obvious in the right context. People with perfect pitch don't need a reference; people with relative pitch do. I play pedal steel, and string 6/G# drops a whacking 10 ten cents when press my A pedal and boy howdy can I hear it - and I don't have perfect pitch, just reasonably good relative pitch.
    - williamcotton 12y ago
      Pedal steel! Do you live in the Bay Area and like playing country music? If so, wanna jam sometime? I've got a rehearsal space in SF.
      - ArkyBeagle 12y ago
        I live in Texas. It's a bit of a haul :)
        williamcotton 12y ago
        As you could guess it's pretty tough to find pedal steel players around here!
        ArkyBeagle 12y ago
        I would actually think that to be untrue - NorCal has lots of pickers of many instruments. The process of finding musicians is just one of those hard problems. It might be worth joining the (web-based) Steel Guitar Forum. Membership is $5.00 per year. There may also be a local steel guitar association. If you play another instrument, you may be able to volunteer to sit in backing other players at meetings. Also, find The Guy in the area who does steel guitar repair. Good luck in your search!
        scarecrowbob 12y ago
        Here's a second vote for the steel guitar forum-- they are quite helpful. Greets from Fredericksburg :D If it is any consolation to your williamcotton, I'm also having trouble finding a band, but I haven't been at it so long so I usually end up playing bass....
- tprice7 12y ago
  It makes sense that major 3rds didn't bother him. With major tenths the fifth harmonic of the lower note is beating against the second harmonic of the upper note. With major thirds it is beating against the fourth harmonic of the upper note. The second harmonic is generally louder than the fourth, and so the effect is more noticeable.
- juliangregorian 12y ago
  But between neighboring notes (half-steps) it would be a 14% difference, which is noticeable to almost anyone with ears.
awkward 12y ago
Yes, because frequencies that don't fit together precisely produce 'beats', where the wavelengths align, and sound quieter when they don't. You're adding two waves, so an in tune one looks regular: http://www.wolframalpha.com/input/?i=sin%28x%29+%2B+sin%28x+*+3%2F2%29 http://www.wolframalpha.com/input/?i=sin%28x%29+%2B+sin%28x+... And an out of tune one has very audible dips and troughs in intensity: http://www.wolframalpha.com/input/?i=sin%28x%29+%2B+sin%28x+*+305%2F200%29 http://www.wolframalpha.com/input/?i=sin%28x%29+%2B+sin%28x+... There's a degree to which it doesn't matter (either it's below what we're sensitive to or it's drowned out by overtones) but the beating sound is very audible.
- munificent 12y ago
  Right. Sort of the audio equivalent of Moiré patterns. Two overlaid frequencies that differ very slightly are actually more noticeable than ones that differ by a greater amount because the size of the least common multiple—which determines how the pattern perceptually repeats—is larger in the former. http://en.wikipedia.org/wiki/Moir%C3%A9_pattern http://en.wikipedia.org/wiki/Moir%C3%A9_pattern
- KyleBrandt 12y ago
  Also there is sympathetic vibrations. So for example if the rest of the orchestra is playing a note that is an open string on your instrument, that string will vibrate even though you are not touching it. You also get a similar impact from overtones. So what happens is at a certain point is that you might not perceive the pitch difference, but you can detect a change in the timbre of sound (quality, tone, resonance).
cperciva 12y ago
Some people are more sensitive than others. As an experienced orchestral violinist with perfect pitch, I can hear the difference between 440 and 440.2 Hz; and I avoid attending concerts from orchestras which tune to A=442 because it sounds horribly wrong to me. (My preferred A is 438 Hz, in part because that works best with my violin's natural resonances.)
- pmiller2 12y ago
  I used to take cello lessons, and my teacher had perfect pitch as well. I used to tune beforehand to A=440hz, but he kept having me tune higher. I was puzzled as to why until I asked and he said he tuned to A=445. One of the lessons I learned was that it's better to be relatively in tune than absolutely in tune (i.e. tune to the soloist no matter what), and it's moderately better to be sharp than flat if you're going to be out of tune.
  - cperciva 12y ago
    445? Ouch! tune to the soloist no matter what Not necessarily. Some soloists (particularly violinists) deliberately tune slightly sharper than the orchestra they're playing with, because the difference in tone allows them to cut through more easily.
    - haberman 12y ago
      You may be aware that baroque instruments tune to A=415 -- even worse! :) But it's a half-step lower than A=440 so maybe it wouldn't sound wrong to you. Also, apparently pitch used to vary quite a lot during the baroque period. I've even heard claims of pitch varying by as much as a minor third, though that seems rather extreme: http://en.wikipedia.org/wiki/Historically_informed_performance#Tuning_and_pitch http://en.wikipedia.org/wiki/Historically_informed_performan...
      - gtani 12y ago
        this one was tuned down a whole step, Bb-F-C-B but they DMCA's his yotube vid: http://www.telegraph.co.uk/culture/music/classicalcdreviews/9602631/Pieter-Wispelwey-Bach-Six-Cello-Suites-Classical-Music-CD-review.html http://www.telegraph.co.uk/culture/music/classicalcdreviews/...
s-phi-nl 12y ago
I have experience of performers, when not accompanied by a piano, choose to perform intervals closer to 1.50000 than 1.50001, so it seems they prefer them. However, the answer is more complicated than that. Quoting directly from my acoustics textbook: "Research on the intervals played or sung by skilled musicians shows substantial variability in the intonation from performance to performance. These variations are frequently larger than the differences between the various tunings. Studies of large numbers of performances have shown that deviations from equal temperament are usually in the direction of Pythagorean intervals (Ward 1970). "Several investigators have found that performers tend to stretch their intervals (including octaves), even when unaccompanied by a piano. Many choral conductors prefer the third in a chord slightly raised, especially in sustained chords or cadences, to avoid any suggestion of 'flatting' the chord, a particular nemesis of choirs. How much of the apparent preference for sharpened intervals is due to constant exposure to pianos with stretched turning is difficult to determine." The Science of Sound, Third Edition, by Rossing, Moore, and Wheeler, p. 187. (Ward 1970) is "Musical Perception" by W.D. Ward, in Foundations of Modern Auditory Theory, Ed. J. Tobias.
- the_duck 12y ago
  > Several investigators have found that performers tend to stretch their intervals Johan Sundberg has excellent examples of this "stretched" tuning in some of his talks. He claims that musicians stretch intervals intentionally in order to add excitement to particular passages. The link below contrasts equally tempered and "stretched" versions of the same musical phrases. http://www.youtube.com/watch?v=CxFVjKMsaTc&t=50m32s http://www.youtube.com/watch?v=CxFVjKMsaTc&t=50m32s To my ears the stretched versions are far more engaging, especially the example with the tenor Jussi Bjorling around 52:50.
cormullion 12y ago
It does depend on the style of music, but it's easy to notice the clash between piano and violin tuning in, say, a slow movement of a Beethoven or Mozart piano concerto. In particular, it's the sharpness of the major third on the piano that can makes a noticeable contrast with what the string players are doing. (string players know all about this, pianists have to put up with it): (http://www.violinmasterclass.com/en/masterclasses/intonation http://www.violinmasterclass.com/en/masterclasses/intonation) Perfect (absolute) pitch can sometimes be a blessing, sometimes a curse. I don't have it, but my partner did, and she struggled to enjoy some concerts that I enjoyed, simply because the notes from the various players weren't aligned well enough...
- jstanek 12y ago
  > she struggled to enjoy some concerts that I enjoyed, simply because the notes from the various players weren't aligned well enough... Hmm, it depends from listener to listener. Obviously I can't comment for your partner, but I too have perfect pitch. Bad alignment of players isn't really a problem for me unless the players are dramatically out of tune. I'm not the greatest at determining tunings by ear either, as this kind of thing varies.
  - jessaustin 12y ago
    ...I too have perfect pitch... I'm not the greatest at determining tunings by ear either... Sorry I'm relatively ignorant when it comes to these topics; what does this mean? What are you able to do, upon listening to a particular musical performance?
    - TheLoneWolfling 12y ago
      Perfect pitch means knowing absolute versus relative frequency. Most people have no (or very little) sense of absolute pitch - if you get asked to sing / hum / whistle a song, you'll start on any random old note. You'll get the relative pitches right - the change in pitch between notes - but not the absolute. (To be pedantic, you'll get the ratio of the frequencies approximately right) Someone with perfect pitch can identify "that note is the A# below middle C", for instance. But not necessarily that accurately. " not the greatest at determining tunings by ear " just means that he's not very good at it. So he may identify that A# as a C or something.
tim333 12y ago
The discrepancies mentioned in the article are rather larger than 1 part in 15000 and can be heard quite easily. I'm not sure what the lowest difference the ear can detect is but with two notes played simultaneously you can get odd beat effects as the notes go in and out of phase. Say the two notes produce harmonics at about 5kHz, then if they are out by 1/15000 then they will go in and out of phase every three seconds and vibrate the ear drum more when in phase than when not so you may well notice.
VLM 12y ago
Wanna see a cool visualization of the question you propose? Google "Lissajous Pattern" and the like. Youtubes and images and wikipedia articles. This is NOT what your eardrum looks like when you hear notes in tune, but it does provide a certain visual simulation of why simple integer-ish ratios sound better than random ratios.
arh68 12y ago
You're fighting a lot of imperfections here. Even a well-tuned piano isn't going to be in tune lowest C to highest C, steel strings just don't allow for perfection [1]. Guitar gets even worse, as you have to deform the string to fret it, leading to strange bridges and nuts like Earvana to compensate. If you want perfect notes, stick to synths. [1] https://en.wikipedia.org/wiki/Stretched_tuning https://en.wikipedia.org/wiki/Stretched_tuning
- kazinator 12y ago
  At least in their piano patches, synths are programmed to replicate, or at least imitate, this inflation in tuning in order to sound like a proper piano. My mid-90's vintage Alesis QuadraSynth plus has a setting for this which basically applies a function to detune the pitch, across the keyboard range, by a programmable amount.
  - TylerE 12y ago
    That's just changing the reference pitch, a different thing.
    - kazinator 12y ago
      No, it the pitch change is different for each note. That's why it's a function (of the pitch number).
    - gtani 12y ago
      I don't know about that particular synth, but having a menu of temperaments is not uncommon on digital pianos, see p 41: http://download.yamaha.com/api/asset/file/?language=no&site=no.yamaha.com&asset_id=61387 http://download.yamaha.com/api/asset/file/?language=no&site=...
gtani 12y ago
the difference in a fifth between JI and Equal Temperament can be over 20 cents in at least 1 key, i.e. almost a quarter tone, or a lot, which i think most people can hear. So, yes, it can be a big difference. And that's not accounting for the tuning peculiarities that every instrument has. A lot of older, perfectly playable pianos were always tuned below A=440 and can't be brought up now. When i started playing woodwinds, my band teacher specifically told me not to tune against piano in higher registers, which would have made the flute sharp, which is exactly what you don't want. This thread did remind me to try Werkmeister and Kimberger tunings on my digital piano, p 41: http://download.yamaha.com/api/asset/file/?language=no&site=no.yamaha.com&asset_id=61387 http://download.yamaha.com/api/asset/file/?language=no&site=... I shd practice viola, also
ArkyBeagle 12y ago
The rough lower limit of pitch discernment is about one "cent" - the ratio 1.501/1.500. That's ten times the 1.5001 figure you gave. I am not sure that one tenth of a cent is perceptible. Ten cents is a big difference, at least to me, but I'm somewhat trained.
kazinator 12y ago
If two notes are played simultaneously and are off from that ratio a little bit, you can clearly hear "beats": a fluttering in the volume. This is audible not only for unison notes that are off, but for other intervals like fifths. The beats are faster (and easier to hear, and more annoying) the higher the note. For instance if you play 1000 Hz against 1001 Hz (0.1% error), you will hear a 1 Hz beat. 100 Hz against 101 Hz also produces a 1 Hz beat, but the error is a lot greater at 1%.
ogig 12y ago
During history what it was perceived as consonant for most then became disonant, and the other way around. 6ths were the perfect 5th of their time. Musics of the world uses different afination schemes, and thus different ratios than western musc. As a jazz enthusiast I hear consonance in pieces that most people catalog as noise. (Abert Ayler comes to my mind). My point is that, while there is an underlaying physics explanation for sound and harmony, the ultimate "perception of sound", specially music, is a human trait, where emotion and culture play a much more relevant role than the precision of any ratio between sounds. http://en.wikipedia.org/wiki/Harmony http://en.wikipedia.org/wiki/Harmony (Historial rules, and Perception of Harmony sections are both relevant)
nemetroid 12y ago
I made two example audio files in Matlab for a previous discussion. Both are of a major chord (root, major third and perfect fifth) made up of three sine waves. One is in equal temperament (frequencies f, f * 2^(4/12) and f * 2^(7/12)) and the other is in "just intonation" (f, 5f/4 and 3f/2). Here's equal: http://vocaroo.com/i/s1a539BsTA8F http://vocaroo.com/i/s1a539BsTA8F Here's just: http://vocaroo.com/i/s1bLClEDtLsO http://vocaroo.com/i/s1bLClEDtLsO The most apparent difference is the wobbliness in the first one. (try opening both at the same time!) EDIT: I mixed them up previously, now correct.
- vacri 12y ago
  I hear more wobbliness in the second one (...TA8F) Great example, though - and playing them both at once is an interesting exercise in aliasing.
  - nemetroid 12y ago
    You heard it right, the second one was the equal temperament (i.e. the wobbly one). I had mixed them up by accident, but now they are labelled correctly.
protonfish 12y ago
I've been playing music all my life and even took theory courses in college and this whole thing is blowing my mind so I got out Excel and did a little math and discovered that the adjustments of equal temperament are significantly larger that 1.5000 to 1.5001. Here's my data: A 55.00 55.00 55.00 E 82.50 82.41 110.00 B 123.75 123.47 220.00 F# 185.63 185.00 440.00 C# 278.44 277.18 880.00 G# 417.66 415.30 1,760.00 D# 626.48 622.25 3,520.00 A# 939.73 932.33 7,040.00 F 1,409.59 1,396.91 C 2,114.38 2,093.00 G 3,171.58 3,135.96 D 4,757.37 4,698.63 A 7,136.05 7,040.00 Starting with A1 (55Hz) the first column of numbers is simply multiplied by 1.5 12 times through the circle of fifths to get to an alleged A8. The last column I simply multiplied 55Hz by 2 7 times to get to the A8 to see the discrepancy. The middle column of numbers I used to tweak the ratio for perfect fifths. I had to use 1.498307 to get the A8s to match up.

acadien 12y ago

I suspect we are very sensitive to the introduction of beats which form when incommensurate frequencies are combined. That is to say when you add a frequency of 1KHz to 1.1KHz you get beats at 0.1KHz with an internal frequeqncy of 2.1KHz. This isn't the precise effect that takes place since the two frequencies are offset by some fixed amount, but a similar effect will take place for an offset that is not quite a perfect fifth.

Tloewald 12y ago

I suspect that the problem is not just the subtle problem of pitch but the way waves phase in and out of sync with each other (especially on sustained notes) rather than remaining in consistent relation, so it should be possible for almost anyone to notice the effect if they know what to listen for. Not my area of expertise -- just an educated guess.

cynicalkane 12y ago

I met a composer of minor note (pun intended) who avoided writing major 10ths in the melody, because the ratios in standard tuning were wrong enough to cause major discomfort for him. This interval is about 14 cents sharp, where a cent is defined as 1/1200 of an octave on a logarithmic scale, so 14 cents is about an 0.8% difference in pitch. Curiously, major 3rds did not bother him, even though they have the same ratio problems.

pmiller2 12y ago
To put that in perspective, pretty much anybody can distinguish a pitch difference of 25 cents. People with perfect pitch can distinguish differences of less than 10 cents. Anecdotally, when I was taking lessons with my old cello teacher (who has perfect pitch), if he and I played a note on an open string simultaneously, I could always tell if we were in relative tune by the way the notes interfered. I don't think I'm particularly special in that regard. Edit: Also, once I have one string tuned, I can tell if a neighboring string is correctly tuned because neighboring strings differ by fifths. Again, I don't think I'm particularly special; it's just a matter of learning what to listen for.
- ArkyBeagle 12y ago
  People with relative pitch can also discern < 10 cent differences. 10 cents is pretty obvious in the right context. People with perfect pitch don't need a reference; people with relative pitch do. I play pedal steel, and string 6/G# drops a whacking 10 ten cents when press my A pedal and boy howdy can I hear it - and I don't have perfect pitch, just reasonably good relative pitch.
  - williamcotton 12y ago
    Pedal steel! Do you live in the Bay Area and like playing country music? If so, wanna jam sometime? I've got a rehearsal space in SF.
    - ArkyBeagle 12y ago
      I live in Texas. It's a bit of a haul :)
      - williamcotton 12y ago
        As you could guess it's pretty tough to find pedal steel players around here!
        ArkyBeagle 12y ago
        I would actually think that to be untrue - NorCal has lots of pickers of many instruments. The process of finding musicians is just one of those hard problems. It might be worth joining the (web-based) Steel Guitar Forum. Membership is $5.00 per year. There may also be a local steel guitar association. If you play another instrument, you may be able to volunteer to sit in backing other players at meetings. Also, find The Guy in the area who does steel guitar repair. Good luck in your search!
        scarecrowbob 12y ago
        Here's a second vote for the steel guitar forum-- they are quite helpful. Greets from Fredericksburg :D If it is any consolation to your williamcotton, I'm also having trouble finding a band, but I haven't been at it so long so I usually end up playing bass....
tprice7 12y ago
It makes sense that major 3rds didn't bother him. With major tenths the fifth harmonic of the lower note is beating against the second harmonic of the upper note. With major thirds it is beating against the fourth harmonic of the upper note. The second harmonic is generally louder than the fourth, and so the effect is more noticeable.
juliangregorian 12y ago
But between neighboring notes (half-steps) it would be a 14% difference, which is noticeable to almost anyone with ears.

awkward 12y ago

Yes, because frequencies that don't fit together precisely produce 'beats', where the wavelengths align, and sound quieter when they don't. You're adding two waves, so an in tune one looks regular: http://www.wolframalpha.com/input/?i=sin%28x%29+%2B+sin%28x+*+3%2F2%29 http://www.wolframalpha.com/input/?i=sin%28x%29+%2B+sin%28x+... And an out of tune one has very audible dips and troughs in intensity: http://www.wolframalpha.com/input/?i=sin%28x%29+%2B+sin%28x+*+305%2F200%29 http://www.wolframalpha.com/input/?i=sin%28x%29+%2B+sin%28x+... There's a degree to which it doesn't matter (either it's below what we're sensitive to or it's drowned out by overtones) but the beating sound is very audible.

munificent 12y ago
Right. Sort of the audio equivalent of Moiré patterns. Two overlaid frequencies that differ very slightly are actually more noticeable than ones that differ by a greater amount because the size of the least common multiple—which determines how the pattern perceptually repeats—is larger in the former. http://en.wikipedia.org/wiki/Moir%C3%A9_pattern http://en.wikipedia.org/wiki/Moir%C3%A9_pattern
KyleBrandt 12y ago
Also there is sympathetic vibrations. So for example if the rest of the orchestra is playing a note that is an open string on your instrument, that string will vibrate even though you are not touching it. You also get a similar impact from overtones. So what happens is at a certain point is that you might not perceive the pitch difference, but you can detect a change in the timbre of sound (quality, tone, resonance).

cperciva 12y ago

Some people are more sensitive than others. As an experienced orchestral violinist with perfect pitch, I can hear the difference between 440 and 440.2 Hz; and I avoid attending concerts from orchestras which tune to A=442 because it sounds horribly wrong to me. (My preferred A is 438 Hz, in part because that works best with my violin's natural resonances.)

pmiller2 12y ago
I used to take cello lessons, and my teacher had perfect pitch as well. I used to tune beforehand to A=440hz, but he kept having me tune higher. I was puzzled as to why until I asked and he said he tuned to A=445. One of the lessons I learned was that it's better to be relatively in tune than absolutely in tune (i.e. tune to the soloist no matter what), and it's moderately better to be sharp than flat if you're going to be out of tune.
- cperciva 12y ago
  445? Ouch! tune to the soloist no matter what Not necessarily. Some soloists (particularly violinists) deliberately tune slightly sharper than the orchestra they're playing with, because the difference in tone allows them to cut through more easily.
  - haberman 12y ago
    You may be aware that baroque instruments tune to A=415 -- even worse! :) But it's a half-step lower than A=440 so maybe it wouldn't sound wrong to you. Also, apparently pitch used to vary quite a lot during the baroque period. I've even heard claims of pitch varying by as much as a minor third, though that seems rather extreme: http://en.wikipedia.org/wiki/Historically_informed_performance#Tuning_and_pitch http://en.wikipedia.org/wiki/Historically_informed_performan...
    - gtani 12y ago
      this one was tuned down a whole step, Bb-F-C-B but they DMCA's his yotube vid: http://www.telegraph.co.uk/culture/music/classicalcdreviews/9602631/Pieter-Wispelwey-Bach-Six-Cello-Suites-Classical-Music-CD-review.html http://www.telegraph.co.uk/culture/music/classicalcdreviews/...

s-phi-nl 12y ago

I have experience of performers, when not accompanied by a piano, choose to perform intervals closer to 1.50000 than 1.50001, so it seems they prefer them. However, the answer is more complicated than that. Quoting directly from my acoustics textbook: "Research on the intervals played or sung by skilled musicians shows substantial variability in the intonation from performance to performance. These variations are frequently larger than the differences between the various tunings. Studies of large numbers of performances have shown that deviations from equal temperament are usually in the direction of Pythagorean intervals (Ward 1970). "Several investigators have found that performers tend to stretch their intervals (including octaves), even when unaccompanied by a piano. Many choral conductors prefer the third in a chord slightly raised, especially in sustained chords or cadences, to avoid any suggestion of 'flatting' the chord, a particular nemesis of choirs. How much of the apparent preference for sharpened intervals is due to constant exposure to pianos with stretched turning is difficult to determine." The Science of Sound, Third Edition, by Rossing, Moore, and Wheeler, p. 187. (Ward 1970) is "Musical Perception" by W.D. Ward, in Foundations of Modern Auditory Theory, Ed. J. Tobias.

the_duck 12y ago
> Several investigators have found that performers tend to stretch their intervals Johan Sundberg has excellent examples of this "stretched" tuning in some of his talks. He claims that musicians stretch intervals intentionally in order to add excitement to particular passages. The link below contrasts equally tempered and "stretched" versions of the same musical phrases. http://www.youtube.com/watch?v=CxFVjKMsaTc&t=50m32s http://www.youtube.com/watch?v=CxFVjKMsaTc&t=50m32s To my ears the stretched versions are far more engaging, especially the example with the tenor Jussi Bjorling around 52:50.

cormullion 12y ago

It does depend on the style of music, but it's easy to notice the clash between piano and violin tuning in, say, a slow movement of a Beethoven or Mozart piano concerto. In particular, it's the sharpness of the major third on the piano that can makes a noticeable contrast with what the string players are doing. (string players know all about this, pianists have to put up with it): (http://www.violinmasterclass.com/en/masterclasses/intonation http://www.violinmasterclass.com/en/masterclasses/intonation) Perfect (absolute) pitch can sometimes be a blessing, sometimes a curse. I don't have it, but my partner did, and she struggled to enjoy some concerts that I enjoyed, simply because the notes from the various players weren't aligned well enough...

jstanek 12y ago
> she struggled to enjoy some concerts that I enjoyed, simply because the notes from the various players weren't aligned well enough... Hmm, it depends from listener to listener. Obviously I can't comment for your partner, but I too have perfect pitch. Bad alignment of players isn't really a problem for me unless the players are dramatically out of tune. I'm not the greatest at determining tunings by ear either, as this kind of thing varies.
- jessaustin 12y ago
  ...I too have perfect pitch... I'm not the greatest at determining tunings by ear either... Sorry I'm relatively ignorant when it comes to these topics; what does this mean? What are you able to do, upon listening to a particular musical performance?
  - TheLoneWolfling 12y ago
    Perfect pitch means knowing absolute versus relative frequency. Most people have no (or very little) sense of absolute pitch - if you get asked to sing / hum / whistle a song, you'll start on any random old note. You'll get the relative pitches right - the change in pitch between notes - but not the absolute. (To be pedantic, you'll get the ratio of the frequencies approximately right) Someone with perfect pitch can identify "that note is the A# below middle C", for instance. But not necessarily that accurately. " not the greatest at determining tunings by ear " just means that he's not very good at it. So he may identify that A# as a C or something.

tim333 12y ago

The discrepancies mentioned in the article are rather larger than 1 part in 15000 and can be heard quite easily. I'm not sure what the lowest difference the ear can detect is but with two notes played simultaneously you can get odd beat effects as the notes go in and out of phase. Say the two notes produce harmonics at about 5kHz, then if they are out by 1/15000 then they will go in and out of phase every three seconds and vibrate the ear drum more when in phase than when not so you may well notice.

VLM 12y ago

Wanna see a cool visualization of the question you propose? Google "Lissajous Pattern" and the like. Youtubes and images and wikipedia articles. This is NOT what your eardrum looks like when you hear notes in tune, but it does provide a certain visual simulation of why simple integer-ish ratios sound better than random ratios.

arh68 12y ago

You're fighting a lot of imperfections here. Even a well-tuned piano isn't going to be in tune lowest C to highest C, steel strings just don't allow for perfection [1]. Guitar gets even worse, as you have to deform the string to fret it, leading to strange bridges and nuts like Earvana to compensate. If you want perfect notes, stick to synths. [1] https://en.wikipedia.org/wiki/Stretched_tuning https://en.wikipedia.org/wiki/Stretched_tuning

kazinator 12y ago
At least in their piano patches, synths are programmed to replicate, or at least imitate, this inflation in tuning in order to sound like a proper piano. My mid-90's vintage Alesis QuadraSynth plus has a setting for this which basically applies a function to detune the pitch, across the keyboard range, by a programmable amount.
- TylerE 12y ago
  That's just changing the reference pitch, a different thing.
  - kazinator 12y ago
    No, it the pitch change is different for each note. That's why it's a function (of the pitch number).
  - gtani 12y ago
    I don't know about that particular synth, but having a menu of temperaments is not uncommon on digital pianos, see p 41: http://download.yamaha.com/api/asset/file/?language=no&site=no.yamaha.com&asset_id=61387 http://download.yamaha.com/api/asset/file/?language=no&site=...

gtani 12y ago

the difference in a fifth between JI and Equal Temperament can be over 20 cents in at least 1 key, i.e. almost a quarter tone, or a lot, which i think most people can hear. So, yes, it can be a big difference. And that's not accounting for the tuning peculiarities that every instrument has. A lot of older, perfectly playable pianos were always tuned below A=440 and can't be brought up now. When i started playing woodwinds, my band teacher specifically told me not to tune against piano in higher registers, which would have made the flute sharp, which is exactly what you don't want. This thread did remind me to try Werkmeister and Kimberger tunings on my digital piano, p 41: http://download.yamaha.com/api/asset/file/?language=no&site=no.yamaha.com&asset_id=61387 http://download.yamaha.com/api/asset/file/?language=no&site=... I shd practice viola, also

ArkyBeagle 12y ago

The rough lower limit of pitch discernment is about one "cent" - the ratio 1.501/1.500. That's ten times the 1.5001 figure you gave. I am not sure that one tenth of a cent is perceptible. Ten cents is a big difference, at least to me, but I'm somewhat trained.

kazinator 12y ago

If two notes are played simultaneously and are off from that ratio a little bit, you can clearly hear "beats": a fluttering in the volume. This is audible not only for unison notes that are off, but for other intervals like fifths. The beats are faster (and easier to hear, and more annoying) the higher the note. For instance if you play 1000 Hz against 1001 Hz (0.1% error), you will hear a 1 Hz beat. 100 Hz against 101 Hz also produces a 1 Hz beat, but the error is a lot greater at 1%.

ogig 12y ago

During history what it was perceived as consonant for most then became disonant, and the other way around. 6ths were the perfect 5th of their time. Musics of the world uses different afination schemes, and thus different ratios than western musc. As a jazz enthusiast I hear consonance in pieces that most people catalog as noise. (Abert Ayler comes to my mind). My point is that, while there is an underlaying physics explanation for sound and harmony, the ultimate "perception of sound", specially music, is a human trait, where emotion and culture play a much more relevant role than the precision of any ratio between sounds. http://en.wikipedia.org/wiki/Harmony http://en.wikipedia.org/wiki/Harmony (Historial rules, and Perception of Harmony sections are both relevant)

nemetroid 12y ago

I made two example audio files in Matlab for a previous discussion. Both are of a major chord (root, major third and perfect fifth) made up of three sine waves. One is in equal temperament (frequencies f, f * 2^(4/12) and f * 2^(7/12)) and the other is in "just intonation" (f, 5f/4 and 3f/2). Here's equal: http://vocaroo.com/i/s1a539BsTA8F http://vocaroo.com/i/s1a539BsTA8F Here's just: http://vocaroo.com/i/s1bLClEDtLsO http://vocaroo.com/i/s1bLClEDtLsO The most apparent difference is the wobbliness in the first one. (try opening both at the same time!) EDIT: I mixed them up previously, now correct.

vacri 12y ago
I hear more wobbliness in the second one (...TA8F) Great example, though - and playing them both at once is an interesting exercise in aliasing.
- nemetroid 12y ago
  You heard it right, the second one was the equal temperament (i.e. the wobbly one). I had mixed them up by accident, but now they are labelled correctly.

protonfish 12y ago

I've been playing music all my life and even took theory courses in college and this whole thing is blowing my mind so I got out Excel and did a little math and discovered that the adjustments of equal temperament are significantly larger that 1.5000 to 1.5001. Here's my data: A 55.00 55.00 55.00 E 82.50 82.41 110.00 B 123.75 123.47 220.00 F# 185.63 185.00 440.00 C# 278.44 277.18 880.00 G# 417.66 415.30 1,760.00 D# 626.48 622.25 3,520.00 A# 939.73 932.33 7,040.00 F 1,409.59 1,396.91 C 2,114.38 2,093.00 G 3,171.58 3,135.96 D 4,757.37 4,698.63 A 7,136.05 7,040.00 Starting with A1 (55Hz) the first column of numbers is simply multiplied by 1.5 12 times through the circle of fifths to get to an alleged A8. The last column I simply multiplied 55Hz by 2 7 times to get to the A8 to see the discrepancy. The middle column of numbers I used to tweak the ratio for perfect fifths. I had to use 1.498307 to get the A8s to match up.