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I have multiple times heard this claim, from very different sources.

There certainly seems to be some correlation between intonation and "loudness", in the sense that ensembles with great harmony playing/singing tend to give an impression of inherent power – without needing any brute force or particularly loud instruments.

That sounds more powerful to me than a not-so-great brass ensemble, let alone any vocal harmonies that were severed with autotune. (Please nobody tell me 12-edo is good intonation!)

However, is there really any direct way in which good tuning makes a voice louder? At least if we consider loudness as purely physical power (Fletcher-Munson weighted or not), this seems doubtful: energy is conserved, it doesn't care whether frequencies match up exactly. So if there's any such relation, I suppose it would have to be a more complex psychoacoustic kind of loudness.

Does such a thing really happen, or is it merely the case that good players will generally have, apart from better intonation, also a "better tone" – which in itself already sounds subjectively firmer/louder, regardless of intonation?

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    not any attempt to answer, however - did Robert Plant exactly hit every single note? No. Does he sound like he could break windows? Yes. QE[not at all]D – Tetsujin Jan 17 '15 at 18:15
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    Plant had an ear for the blending of sound waves, so whether or not he showed up as 'in tune' on a tuner, his pitch was always perfect for the musical context at hand. – Darren Ringer Jan 17 '15 at 18:49
  • You need to qualify your question to distinguish between perceived amplitude and actual amplitude. – jjmusicnotes Jan 18 '15 at 6:42
  • @jjmusicnotes: I don't know; as I said I just heard this claim "it makes you louder", and I'd like to know in which sense of "loud" this is true or whether it's simply bogus. – leftaroundabout Jan 18 '15 at 10:57
  • Amplitude, at any rate, is rather useless as an indicator for loudness. (Otherwise, there would be no point in compressing/limiting record masters.) If anything, you need to talk about amplitudes of some single frequency, but I also don't think that's helpful – after all, white noise sounds louder than any sine wave of the same ampliture, though it's Fourier transform is lower at every single frequency. (Do correct me if I'm thinking wrong here!) That's why I discussed power (i.e. RMS), but as I said the argument can't really be true in that sense, since energy is conserved. – leftaroundabout Jan 18 '15 at 11:00
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Intonation is certainly important, but I'd like to add an observation about other factors. 30 years ago in music school I studied operatic singing (I'm a tenor).

With regard to being "louder", first there is learning to sing with greater volume, but second, and just as important, is learning to cultivate a certain resonance in the voice that involves learning to manipulate formants and resonant frequencies in the resonant cavities of the nasal passages, the mouth, the larynx and the chest, along with the use of diaphragm-muscle breath support, and vibrato, to learn to create a sound that "projects" or "cuts through" an orchestra or instrumental accompaniment so the audience can hear the singer clearly even though the singer is not using a microphone and is not being amplified.

This is a technique developed through trial and error and guided by the experience of a voice teacher, to produce what opera singers call the bel canto vocal tone. It is not, broadly speaking, something that is learned by entirely scientific or physiological measurements or study. But students learning opera singing are certainly taught a few things about the anatomy and physiology of the parts of their bodies used to produce the voice, and how to become aware of and eventually manipulate and control those parts.

Something of the same sort applies to different styles of singing as well. You gave an example of the neo-string-band music of Nickel Creek. In this video they are crooning rather softly, but they can also sing in the "high lonesome" old-time style, which doesn't use vibrato and which is miles away from opera singing. Yet the "high-lonesome" old-time singing style was developed long before there was such a thing as singing into a microphone through an amplification system; it's a style of singing that permits singers to be heard clearly over a string band unamplified.

It's fair to say that any instrumentalist who performs unamplified learns how to do something similar with their instrument. One way or another they learn that certain techniques of creating a certain acoustic tone will "cut through" and be heard over an orchestra or band, whereas other tones will be "buried beneath" the orchestra or band and won't be clearly heard.

  • These are some psychological effects and techniques to make a sound more apparent among other sounds (eg. bringing a solo to the front). But the effect of goood intonation making the overall sound of a solo performer or an ensemble stronger is missing. Vice versa ensembles with worse intonation sound weaker over all, even though they apply such loudness techniques. – Guney Ozsan Jan 22 '15 at 19:24
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I recognize the phenomenon and I believe that - among other factors (see below) - it must have to do with the way sound waves combine, i.e. with constructive or destructive interference. I think that your argument concerning energy conservation is not valid, because e.g. in active noise control sound waves are designed to cancel each other, so there is energy in both sound waves but the total sum is small (or, ideally, zero).

So if two notes are slightly out of tune, the total energy is possibly smaller than when they're exactly in tune. The same is true if voices are in harmony because of the harmonics which form a coherent spectrum if the interval between the fundamental notes is sung/played correctly.

So far the argument was purely physical. I believe that there are other factors. One of them is the way singers articulate the vowels when singing in harmony. The total sound becomes more coherent if, apart from singing in tune, the articulation (i.e. the filtering of the sound) matches closely. In a similar manner, when instruments play in unison or in harmony, the result will sound better/louder/more coherent if the phrasing and sound quality matches well.

Yet another factor is timing. And I'm talking about small timing differences, which can make a huge difference. So if a band or choir is very tight, i.e. if their timing is very well synchronized, they will be able to produce more power than otherwise.

I know that all arguments put forth here are speculations in the sense that I have no experimental evidence to back them up, but from my experience as a musician I'm pretty sure that all of them make a difference concerning the coherence and power of the total sound of an ensemble.

  • ANC uses a known phase relation between a microphone on the outside of headphones, and the hp-speakers on the inside to always generate destructive interference at one single spot, namely the eardrum. This does (of course) not violate conservation of energy: summed over all space, the active NC actually makes the noise louder. Just because only your eardrums notice the sound at all, you feel it's made quiter. — Real musical instruments, even when played in perfect just intonation, don't phase-lock. Even if they did, room reflections would scramble the phases. So this argument doesn't work. – leftaroundabout Jan 17 '15 at 16:52
  • @leftaroundabout: I still think it does to a certain extent. ANC is of course an extreme example (BTW, there also is such a thing as global ANC). Connecting one of two stereo speakers out of phase will have a clear effect anywhere you listen. Similarly a wrong (out-of-phase) connection of one speaker of a 4x12 cab, etc. What I'm saying is that sound waves with frequencies slightly out of tune will produce some similar effect of weakening the total sound impression as opposed to sources that are coherent in pitch and timbre. – Matt L. Jan 17 '15 at 21:09
  • If you connect one of two stereo speakers with inverse polarity, the speakers are still phase-locked together. That's what never happens with instruments in an ensemble, regardless of intonation. (And FWIW, the "clear effect anywhere" of phase reversal only happens in the bass range, due to wavelength>≈separation; for treble frequencies the switching of the phase may be notable as some change in sound, but only near-field monitors make it really obvious which polarity is correct.) – leftaroundabout Jan 17 '15 at 21:42
  • @leftaroundabout: I do agree about the non-existence of 'phase-locking' of an ensemble. Yet, I don't think that's the point because, coming back to my over-simplistic example, for a true stereo signal there is no phase locking either, reversed polarity or not. – Matt L. Jan 17 '15 at 21:49
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    What do you mean by a "true stereo signal"? For an ordinary stereo-mic recording, the channels certainly are locked (at some complex, but fixed relation, for any stationary source). For a mix with signals not panned hard left/right even more so. — If you record the stereo channels as completely separate takes, then there is indeed no phase correlation, but that's almost never done (and for such a signal, you would in fact not notice a difference when reversing one channel's polarity). – leftaroundabout Jan 17 '15 at 22:00
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The short answer is "Yes" and the facts behind that are "Resonance" and "Harmonics".

  • Resonance: Resonance happens when an object sounds a note, another object tuned to the same note starts vibrating and giving sound of the same note. So we get a louder tone when there are resonating objects around.

  • Harmonics: When a note is played the base frequency and its multiples are also sounded (eg. a vibrating 440Hz A string gives sounds in 880, 1320, 1760Hz...etc frequencies as well). Base note is the first harmonic that we perceive as the name of the note. Its following harmonics are also sounded with less and less magnitude (octave, octave + perfect fifth, second octave, second octave + major third...etc.).

So, if you play a note you can make resonate and sound everything around you tuned to the same note, its octave, perfect fifth, major third, minor third, seventh, ninth...etc. resulting in a very strong sound. Harmonics and acoustic resonance is very effective on instrument boards, well tuned open strings, sounding instruments with good intonation, vocal cords, and naturally on acoustic ensembles.

This effect multiplies a lot in ensembles making resonate every instrument around. If every player has a very good intonation, chords and crossing notes will sound not only louder but better in quality and closer to the composer's imagination. Good intonation is also very helpful in playing good quality quiet tones and chords with little effort. This is one of the reasons why good players and ensembles can make the same instruments sound different and better than average players.

  • Resonance between different instruments or even voices? Seems unlikely to me, do you have any references on this? For empty strings on a single instrument this can of course have a great effect (Sitar etc.), but I can't see this working for e.g. a string ensemble (where each string is much stronger affected by the bow than by the vibrations from other instruments; after all those need to be picked up again by the body and then sent to the strings through the bridge). – leftaroundabout Jan 18 '15 at 11:06
  • Allthough... I once played with a metal band, and the bass drum literally made my bow bounce on the strings, so strongly was it picked up by the cello body. But then, I was sitting right next to the drummer and it was an estimated 30 dB louder than a string ensemble could ever get, so... – leftaroundabout Jan 18 '15 at 11:09
  • Right, resonance between instruments is just "sympathetic resonance"... – Bob Broadley Jan 18 '15 at 12:08
  • @leftaroundabout It is not just resonating strings but also instrument bodies, already playing closed strings, fingered air tubes and other overlapping harmonics being played by other players. Also take into account that all successfully overlapping harmonics will be resonating and sounding from all instrument bodies, objects and room back to you. Poor intonation in ensembles does not give that effect by first hand experience. Besides that, composer's success in writing and instrumenting a chord is also very effective acquiring chords full of sound. Vocal cords of course work mostly one way. – Guney Ozsan Jan 18 '15 at 23:31

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