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I have noticed that a sixth, particularly a harmonic sixth, sounds very harsh when the lowest note is below C3 and especially harsh if the sixth is minor. In fact, a minor sixth below C3 sounds to my ears, more like an augmented fifth than a minor sixth. Below C2, the sixth might as well be as harsh as the tritone. But why? Why is it that a very consonant interval becomes harsh below C3? Thirds become muddier, but they don't become more harsh. Fourths and fifths also don't become more harsh. And of course the octave isn't going to become harsh unless that octave turns into a false relation.

Now, if that sixth is part of a consonant triad, it doesn't become harsh, just muddy. But by itself, the sixth becomes harsh below C3. Even if upper voices in the treble clef add harmony, if the sixth is below C3, it still sounds harsh, though not as much as it does unharmonized. It is only when the harmony is added within the same register that I don't hear a harshness from the sixth. But why is the sixth so harsh in the low register? Here is the harmonic series:

enter image description here

And here is where the consonant intervals show up in the harmonic series:

enter image description here

As you can see, in the harmonic series, both the major and minor thirds and the major and minor sixths overlap at the fifth harmonic. The major sixth is between the third and fifth harmonics and the minor sixth is between the fifth and eighth harmonics. So, this might explain why the minor sixth sounds like an augmented fifth in the low register. But, according to this, the major sixth should be more consonant than the major third because the major third uses the fourth harmonic whereas the major sixth uses the third harmonic. But in the low register, even this major sixth sounds harsh, whereas the thirds just sound muddy.

So what gives? Why is it that below C3, all sixths sound harsh whereas thirds just sound muddy in that register and all sixths above C3 sound like a very consonant sixth? Harmonics alone doesn't seem sufficient to explain this harsh sixth in the low register.

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    Does this answer your question? Why do low chords sound muddier than high chords? – Richard Jan 18 at 21:53
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    But, I don't hear a muddy sound to the sixth, but rather a harsh sound. – Caters Jan 18 at 22:29
  • It's really hard to say why this sounds harsh to you. The linked question explains why chords may sound muddier, but telling you exactly why something may sound harsh to you and not to others will be opinionated because it's in the ears of the beholder. – Dom Jan 19 at 2:13
  • It's quite possibly just your ears and/or your brain. I've read other questions of yours where the minor sixth interval consistently sounds primarily like an augmented fifth to you, while it doesn't to many of us (quite possibly most of us). – Dekkadeci Jan 19 at 9:45
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The main reason you think higher-pitched 6ths sound consonant is because you have spent all your life listening to them played in equal temperament, and that you may not be listening very critically because you are hearing what you are accustomed to.

In fact, in equal temperament tuning, thirds and sixths are all grossly out of tune compared with just intonation intervals, but most people never get to hear the difference, so they just accept that that is what "music" sounds like.

In a different tuning system, for example 53-EDO which divides an octave into 53 equal parts not 12, thirds and 6ths sound very much more consonant, and don't sound "harsh" even at very low pitches. 53EDO is not exactly the same as just intonation, but it is much closer than standard Western equal temperament.

Incidentally, 53EDO it is not just a theoretical tuning system - it has been the basis for Turkish music for centuries.

This is a demo of the difference, made using the Steinway D Classical piano in Pianoteq, playing the same scale of 6ths first in conventional equal temperament (12EDO) and then in 53EDO tuning.

https://www.dropbox.com/s/ppp9qumqjo3w0a8/53%20EDO%206ths%20-%20Flow%201.wav?dl=0

Here is the scale in staff notation:

enter image description here

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  • Is there a way to tune Pianoteq in 53EDO? – Pyromonk Jan 19 at 21:44
  • @Pyromonk you'd need 52 keys per octave to do that. – phoog Jan 21 at 17:05
  • @phoog, that's not a problem. But I don't remember any microtonal settings for it (perhaps I just didn't look enough into it). Thank you, I'll try to consult the manuals. – Pyromonk Jan 23 at 23:39
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    @Pyromonk having looked at Pianoteq a bit, I see that it's a MIDI controller, so it does not have 53 keys per octave, only 12. You ought to be able to use MIDI pitch bend to change the pitch, but using 53-EDO with a 12-tone keyboard puts you in the same position you'd be in if you were trying to use acoustically pure just intonation: you have to use different pitches for certain notes depending on the harmonic context. The A is the 39th division if you go down a fifth and up a major third, but it's the 40th division if you go up three perfect fifths. – phoog Jan 24 at 2:58
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    @Pyromonk having looked at Pianoteq a bit more, I see that it supports custom tuning through an "advanced tuning" panel (apparently not available in the basic version). It still only supports 12 pitches per octave, though, as far as I can tell, so if you assign each of the 12 pitches to one of the 53-EDO pitches, you're going to have one wolf fifth somewhere (because 12 * 31 = 372 and 7 * 53 = 371). Furthermore, 8 of the major thirds will be closer to equal-tempered than to just; only 4 will be closer to just. – phoog Jan 24 at 4:05
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Disclaimer: I am not a professional musician or a physicist.

Since you do not specify the instrument which you experience problems with, I am going to presume we are dealing with "pure" (sine) sound waves and no overtones.

As one gets lower and lower in terms of octaves, the wave length of any given note increases. Now, as far as my understanding goes, the more often the crests of the waves created by playing notes coincide, the more consonant we perceive the intervals between the notes.

Since the wave lengths for low-register notes are greater, there is a chance that their crests do not "meet" before the wave "dies", which would explain why intervals become more dissonant in the low register and more consonant - in the upper one, especially for percussive instruments like the piano or the xylophone. The wave length becomes shorter for higher notes, which allows the crests to coincide more often when travelling for the same distance.

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  • I didn't say that sixths were perfectly consonant, because I know that perfect consonances only include unisons, fourths, fifths, and octaves. I just said that sixths are a very consonant interval in higher registers. – Caters Jan 19 at 0:44
  • @Caters, thank you for clarifying. Could you please let us know what orchestration you are experiencing problems with? I assumed you were dealing with piano and even tried to create some wave image comparisons to show you what's happening, but the sounds were too impure to serve as an example of what's happening. – Pyromonk Jan 19 at 0:46
  • I am indeed getting this harsh sixth in the low register on the piano. – Caters Jan 19 at 1:16
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    "There's a chance the crests do not 'meet' before the wave dies": the frequency with which the crests coincide is found by subtracting the frequencies of the pitches. So for a very low third, say A=55.00 Hz and C=65.41 Hz, they will meet more than ten times a second. Unless the wave dies in 50 milliseconds, they will definitely meet before the wave dies. More generally, the proposition that the frequency of coinciding crests determines consonance seems flawed. – phoog Jan 24 at 3:07
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    Well I think it's more about the density of overtones, more of which are audible in lower notes, of course. One consequence of this is, I think, that amateur male singers are more likely than amateur female singers to be able to sing acoustically pure thirds -- at least that's the case in the group I'm in at the moment. I think this is because an out-of-tune third sounds a lot worse in the male vocal range than an equally out-of-tune third in the female vocal range, so the men have had more incentive to learn to sing them in tune. – phoog Jan 24 at 20:10

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