Why do we tune in 5ths? | Hacker News Reader

Why do we tune in 5ths?

violinist.com

83 pointsofou108 comments

If the instrument is tuned in fifths then, indeed, a diatonic scale pattern that proceeds perpendicularly across the finger board at the same position has four notes on each string.

However, these four notes are sometimes spaced differently: different patterns of tones and semitones.

When an instruent is tuned in fourths, scales use three notes. There are ways to conform to many of the string-to-string pattern variations by leaving out fingers:

   a - b c'  # index ring pinky
   e f - g   # index middle pinky
   - c - d

It seems that the fifths tuning is quite tyrannical in this regard.

Now when it comes to the major scale, that scale is actually a stack of two identical tetrachords, which are a fifth apart. These tetrachords have identical fingerings:

   # tuning in fifths now:

   g - a - b c
   c - d - e f

So now if you have your fingers spread out in the right way to play the C-F tetrachord, all you have to do is preserve that when going to the next string.

I suspect violinists must be exploiting this sort of relationship; favoring fingerings that show tetrachord symmetries.

The Dorian mode (D to D mode of C major) also has two identical, stacked tetrachords, so if we slide one position down that pattern, we are still good:

   g - a - b c - d
   c - d - e f - g
      [  Dorian box ]
  [ Ionian box ]

But, having observed that, these fingering patterns are not easy even in isolation, regardless of whether there is a change in the pattern going to another string.

To some extent they should have some similar properties since a fourth is basically the inverse of a fifth (modulo an octave). In theory you should also be able to shift a tetrachord on an instrument tuned in fourths you'll just go the other way and be off by an octave.

Being off by an octave is pretty important for melodic lines, which is usually how the violin is used… so while you can translate chords from tuning in fifths to fourths or vice versa, in my experience, you need to relearn to play if you're doing melodies.

If you go the other way, the tetrachords share a note:

     C D E F, G A B C

Swap these:

     G A B {C} D E F

So, tuning by fourths, it lines up, indeed, when we take into account the shared note, e.g. these two L-shaped tetrachord patterns:

     D - E F                         D - E F
           C    +    A - B C    =    A - B{C}
                           G               G

Or:

     E F                             E F
       C - D    +     B C       =    B{C}- D
                        G - A          G - A

Excellent information here! For something a little more unusual, you can see guitar players in the experimental realm (think John Coltrane, not Thurston Moore) use four finger per string technique in standard/fourths tuning via the work of Ollie Halsall and Allan Holdsworth. Highly nimble and skilled, these guys were the 60s/70s inspiration for later shred-monsters like Eddie Van Halen (who worked to get Holdsworth a record deal). Something must have been in the water around Cambridge during the late 60's for two completely different oddballs to emerge with nearly identical techniques, especially considering that they both played in the same band for a brief moment. (Allan Holdsworth played with Tony Williams, Jean Luc Ponty, and Soft Machine. Ollie Halsall played in Patto, a band that Queen opened for and Led Zeppelin could barely keep up with, along with gigs with Brian Eno and Kevin Ayers. Rumor has it Ron Wood was the next choice after Ollie during the Rolling Stones' mid 70s lineup change).

Fouths tuning is all right for chromatic runs. You can play five notes per string with a slide legato, or go diagonally:

      x x x x
        x x x x
          x x x x

The major third between the G - B strings in standard tuning provides relief from the diagonal

      x x x x
        x x x x } maj 3rd
        x x x x }
          x x x x
          ...

It seems like chromatic runs would be a source of difficulty for the violinist tuning in standard fifths.

Ah. My favorite guitarist's name dropped.

It should be noted that Holdsworth actually played a bit of violin (you can hear it on Temporary Fault off I.O.U.; Karzie Key off the infamous Velvet Darkness album; and recordings of Tempest, Soft Machine, w/ Gordon Beck, and Gong).

Holdsworth even experimented with fifths tuning on his SynthAxe (since you could just do that in software), most notably for the song Non Brewed Condiment[1] off Atavachron, and the solo in In the Mystery, I believe, and had a separately tuned guitar for the live performance of the aforementioned song[2].

There's an interview from the 90s where he talks about his thoughts on fourths vs fifths[3].

He later said at a clinic (in the 2000s) that if he were to relearn the guitar, he would've used all-fourths tuning[4].

[1] https://www.youtube.com/watch?v=1yTCQ1-GzIg

[2] https://www.youtube.com/watch?v=qO3o484Z2OU

[3] http://www.fingerprintsweb.net/ah/press/gui0585b.html

[4] https://streamable.com/njyj8

This article, and the comments, made me realize why some friends that I tried to teach coding just couldn't grasp it yet for me it seems kinda obvious.

I don't understand music one bit, none, zero. I can read descriptions and even understand what different notes are, and the symbols for them but it's a very dry knowledge. Nothing I do make it 'click' for me and it feels so disjointed and foreign that I just got overwhelmed and I know it will never make any sense to me

I can read a math paper, and even though I might not understand it at first, at least I know that if I just take a book that explains the terminology then I'll be able to grasp it. With music it's a complete opposite - nothing no matter what I do will make it understandable for me

Edit: To give you and example, I have been studying the famous clip [0] about the rhythmic displacement. I have watched it thousands times, read tons of analysis etc. and I know exactly what was done and when. I just don't hear it being done - I know people aren't lying to me but I just cannot hear whatever happened at that famous point and what changed after

[0] https://www.youtube.com/watch?v=UinRq_29jPk

I actually don't like this attitude. In every case it's a mostly a matter of interest and effort. If you have those you can learn something.

I agree, that's what I told my friends, to just keep learning because if I could why wouldn't you. The point of my post is that I have realized how unhelpful that comment is because if someone told me that about music today... all I see is an insurmountable mountain ahead even though I've read quite a bit about it already

Mind you it's different with for example fluid dynamics or functional programming or even chemistry or biology, I have zero knowledge of it (nor interest) and all I know is that it's hard... but I know that if I spend years learning it I will succeed. I don't know how to explain this feeling I have with music - it's just foreign on another level

It's because they treat music like a math problem -- something that only necessitates reading and writing. That's how you play math, after all, but that's not how music is played.

It can be very frustrating when someone you are trying to instruct just bails out on something that appears, at least to you, very simple to understand just by following some easy, clearly defined steps, and they exclaim: "No, I can't do this. It's just too complicated!"

In some cases, perhaps even most, this is due to an aggressive indifference to learning something new, but maybe it is not always the case that this is the explanation? It could be that the mechanism for understanding this one particular matter is genuinely missing or undeveloped in that person's brain.

To me learning music is very similar to learning programming concepts. In the beginning it can all be very abstract and you don't immediately see how new concepts fit into the bigger picture. Until at one point along the way it suddenly "clicks" and it all comes together.

I've witnessed several people experience their "aha" moment in programming and in music. Before that moment they struggle hard and some even lost motivation. After that moment they all started making progress fast.

Having an instrument available helps and if you're interested in learning music I suggest starting to play and experiment. Don't think too much about the theory and the details. Just have fun, play along to your favorite songs. Dig deeper here and there when a subject piques your interest. And then someday that "aha" moment will arrive and a new world will open up.

Learning piano as an adult gave me a new sense of humility about people in fields other than mine

> I just cannot hear...what changed after

Tap your foot along to the people clapping in the video. They're clapping on 1 and 3 at the beginning, so you should count "1 2 3 4" as you tap your foot, with their claps being on "1" and "3". At/by the one-minute mark of the video, you'll realize that the claps are now on 2 and 4.

This is somehow related to why I hated introduction to programming at Uni. They would teach you the print function in python, and then ask you to do a full Pacman. Same with C ("why str1 == str2 doesnt work?"), they would treat it as a magical black box and answer questions that would have easily been answered by reading the language's manual or bible (K&R).

Then some of the students would say "I dont know where to start" and type random code, because they didnt teach nor the syntax nor the semantics...

Meanwhile the other ones who understood just went forward with it (they even made harder tests to comp. engineers!). Full brute-force practice (or work) doesnt equals good learning! With a good theory or methodology you can do a better learning.

With apologies in advance, because you probably have already done this...

Just count: 1 2 3 4 along with the pulse. First you hear the audience clap on 1 and 3, then some instrumental magic, and the audience is clapping on 2 and 4.

Is it possible that you are not hearing where the 1 begins? That can happen to the most experienced musicians sitting in on a complicated session and groaning "Where's the 'one' at, dude?"

The trick for you might be to become adept at locating the '1' beat. Start with toy problems, like children's rhymes, or even counting to four rhythmically.

Maybe your brain just doesn't work that way, as you have stated above, in which case you have an advantage over me in being aware of a perceptual lacuna and having a good analytical understanding of it.

Oh I have done this many times, when I said I've been studying this clip I really meant it because I truly want to hear it. LambdaComplex also mentioned tapping foot and counting and suddenly the count should change.

The result of my many experiments is that it is super hard to count 1 2 3 4 when they only clap twice. Most of the times, within seconds, I'm 'rhythmically' counting claps. Be it 'one three one three' or whatever numbers I chose, but the number only changes with the next clap so, well, that won't work because the audience doesn't change how they clap and I'm only using two different numbers.

I'm forcing myself hard to count to 4, basically saying another number in-between claps and if it works for an extended period of time I'm so focused on keeping my own momentum and keeping the 4-count going that I don't even hear the music just the claps and I try to remember to say the other number in between 1 and 3. That also absolutely fails because I'm already checked out of whatever I'm trying to hear

I also did experiments with my friends and some of them just hear when it happens without any counting or whatever. So I tried that as well - I would listen to this with my eyes closed and mark the point when I thought the clapping has changed. I think the results were statistically as good as my internal approximation of how long 40second is until I learned to hear the exact part of music I have to hear before I say 'yeah, it's that' - but it has nothing to do with my understanding of it.

So it looks like a perceptual thing, the result of how your physical brain has been wired, where you cannot perceive the phenomenon directly despite having a solid analytic understanding of the matter.

This reminds me of Frank Jackson's famous Knowledge Argument for Qualia

https://plato.stanford.edu/entries/qualia-knowledge/

It might help to know that the "instrumental magic" is that he literally adds a beat. Each bar has 4 beats and he switches where they're clapping by giving one bar 5 beats. You kind of have to stop/restart counting to intellectualize it.

Of course, but he adds the beat so smoothly and unobtrusively that the ordinary listener hears no glitch in the matrix. That is where the magic comes in.

To endorse your perspective - I love music, play an instrument to a reasonable standard, enjoy a wide variety of different types of music, have an acute sensibility of tuning - can easily tell if something is out of tune.

Yet, can I recognise a chord? No chance. I’ve tried for years to train myself. Just can’t do it. It never clicks.

It took me about 3-4 separate attempts over the last 15 years to get music, and only this last couple of years I was finally able to crack the music notation, music theory, and music production nut. I'm by no means pro-level, but I can follow along and have a mostly intelligent conversation about anything musical and audio-related now, and also put out my own tracks that are based on this shockingly broad set of concepts that you can pick up as you're learning the world of music.

I had to attack this from every possible angle because I had practically the same experience as you. What ultimately worked for me was a combination of a piano teacher, going through the Adult Piano books, doing a few music production programs (including some online university ones) and surrounding myself (virtually) with people writing music regularly. Eventually, although through many ups and downs, it all made sense.

IMO the hardest part is having to scale the massive wall of terminology and basic concepts you have to grasp in order to speak music theory. Notes, durations, keys, chords, intervals, scales, modes, music notation, meter, various modifiers you would find on a sheet of music, etc.. in addition to being able to actually play those physically in the real world... It's a ton. You don't need any of it to actually write music that people will like, but if you want to feel like you can at least communicate about it to other humans, it really helps.

I think it's mostly just that 5ths give you a good balance between ergonomics and range, and 5ths are relatively easy to tune by ear.

Something interesting about violin tuning: if you tune by ear, you get a 3:2 ratio between the frequency of adjacent strings. If we're in the key of G, we can call the G string 1/1 in just intonation notation. The next string is D, or 3/2. Then we have A at 9/4. That's an octave and a just major second. The interesting thing is that when you get to E, it's 27/8. It's an octave and a major sixth, sort of. If we ignore the octave, it becomes 27/16 which is close to the more commonly used just major 6th which is 5/3.

If a violin is tuned to 12-tone equal temperament then the distinction is moot. But in a just tuning, that open E may well be a wrong note depending on what you're playing.

Violins don't have frets.

They didn't mention frets... Tuning the open strings relative to each other, at least for non perfectly pitched people, results in tuning the strings justly rather than to equal temperament.

The 5th is the least tempered interval in 12 equal temperament (excluding the untempered octave and unison), with less than 2 cents difference from the just interval, and the violin only has 4 strings, so in practice it's probably close enough.

Yes, it would be hard to be less tempered than octave and unison :)

The errors stack, so you get about 6 cents error between the G and E string. That's enough to be a perceptible difference.

True, but how often are you going to play an open G and an open E together?

It seems like there are some practical difficulties with that :)

If you have a video of somebody who managed it, please share the link!

You don't, but you might play them sequentially. It's just something to be aware of, whether the strings were tuned to equal temperament or just intonation: if you're in the key of G, that open E might be a little off from the note you want.

In practice, I think experienced violinists tend to avoid the open strings. This may be one of the reasons why.

Of course it does. But, because violins don't have frets, that's only relevant when you're playing a string open.

Or playing partial tones, which is often used to get those very high notes.

Yes and probably fair to say that open strings are often avoided in practice - e.g. because no vibrato on an open string.

Vibrato also helps a lot to obscure the difference between, for example, just intonation and equal temperament, although of course that's not why we do it.

Just to clarify, by "we" I mean "humans", not "violinists". I don't play violin.

On multiple occasions, I've stumbled upon really old high school physics textbooks and they usually had a chapter on the physics of musical frequencies. It seems to be a weirdly forgotten subject.

The octave is a doubling/halving of frequencies, and so is very recognizable. The fifth is the next lowest whole number frequency ratio 3/2, 2/3. So liberal use of fifth interval makes notes often end up low whole number ratio frequencies of each other which sounds harmonious.

Also, if I remember correctly, every note in the major scale is a 3/2,2/3 ratio from a note in the lower or higher octave following the standard order of key signatures as you jump across consecutive octaves, which, I assume, is how they arrived at that standard order.

That’s called “Pythagorean tuning” and it’s possible but it’s not especially common. The system we use is a compromise derived from that system. If you use pure 3:2 ratios you get the so-called “wolf tones”, but we don’t get those any more.

The current most common system is equal temperament, which is a type of meantone tuning, where you take the 3:2 ratio and alter it. Equal temperament alters it to 2^(7/12) ≈ 1.4983, and it has the nice property that you get twelve notes and it’s all perfectly symmetrical, it doesn't matter which note you start on.

Before equal temperament, there were various other systems. One popular one was quarter-comma meantone, which took four stacked 3:2 ratios (81:16) and squashed them to equal two octaves and a 5:4 ratio (80:16), which results in a value of 5^(1/4) ≈ 1.4953. You see it in some old organs—which may have, say, separate keys for G# and Ab.

Then there are various non-meantone tunings, various “just” intonations, etc. In just intonation, a chord like C E G will have a 4:5:6 ratio. You can’t do this with all major triads, though, so you end up with some major triads that sound correct and others that sound out of tune. Our modern system is a compromise where all major triads are equally out of tune, rather than having some better and some worse.

Wolf tones are certain notes which don't sound very well which vary between instruments due to their construction. I think you mean the Pythagorean comma.

You are talking of the same thing. The typical wolf tone in quarter comma meantone was G#-Eb, which sounded so bad that some instruments added a separate key for Ab.

Actually, "wolf interval".

Pythagorean comma is the difference between enharmonic notes in Pythagorean tuning, e.g., difference between Ab and G#. Not what I was talking about.

With any 12-tone system, you might have eleven fifths which are 700-x cents wide, on average... and then a diminished sixth (rather than a fifth), which is necessarily 700+11x cents wide as a result. The "wolf interval" is the diminished sixth (commonly G# to Eb, or C# to Ab). In equal temperament, the diminished sixth is equal to a fifth. You might also call something other than a fifth a wolf interval. Basically, an interval which normally sounds good, except you chose an enharmonic version of it, which sounds bad.

"The" wolf interval is the quarter-comma meantone diminished sixth, which is 2^7 / 5^(11/4) = 1.5312. The Pythagorean wolf interval is 2^7 / (3/2)^11 = 1.4798. It's equal to a perfect fifth, minus the Pythagorean comma.

I see. I was confused because string players talk a lot about our wolf notes/wolf tones (especially violists and cellists), but I hadn't come across the term wolf interval.

That's because these tuning systems have been out of favor since about 1700. You might encounter some organists who know about it, but even then, there are only a handful of organs tuned this way in North America.

https://en.wikipedia.org/wiki/Meantone_organs_in_North_Ameri...

It was Werckmeister who popularized and advocated systems which don't have wolf intervals (so-called "well temperament", as in "Bach's well-tempered clavier". The composers who cared about wolf intervals generally predate Bach, to give you an idea.

Nowadays (since the 1980s) I can press a button and put my synthesizer or electronic piano in whatever tuning I want, so I can play with quarter-comma meantone temperament without finding one of the organs on the list, and experience it myself.

> The octave is a doubling/halving of frequencies

Side note: Except when in praxis you have to accord for non-perfect masses, then you have to stretch the tuning.

https://en.wikipedia.org/wiki/Stretched_tuning

> It seems to be a weirdly forgotten subject.

I was fortunate to have had the opportunity to take a Physics of Music course in college that counted as the physics requirement.

It was really nice to have the mysteries what makes music appealing be an academic focus for the summer. We even had a project at the end where we built an instrument. I made a fairly rudimentary xylophone with some pipes and a hand pipe cutter.

The physics of music comes up a bunch in music production. When working with different waveforms, filter types and specific bass frequencies, you always have to make sure you know what your spectrum looks like, or you'll have phase issues, or you won't hit the desired levels for each instrument and so on. You end up staring at fundamentals and harmonics a lot in order to get the timbres and the mix you have in mind.

Fiddlers don't always tune in fifths. There's a couple of tunes I play in DDAD, my favorite for its three octaves of awesome resonance. Classical violinists tend to sneer at such tunings, outside of rather esoteric baroque players, I believe. It's a shame, because different tunings can really change the tone of the instrument in interesting ways.

As the comments allude, fifths make it easy to play a large range of harmonious music. And, no doubt. A lot of fiddle tunes are written for cross-tuning, and they're tortuous to play at speed in GDAE.

>It's a shame, because different tunings can really change the tone of the instrument in interesting ways.

I find this with guitar, but guitarists on the whole aren't snobbish about alternate tunings. DADGAD is my favourite guitar tuning for similar reasons.

DADEAE is another tuning that is good for resonant melodic playing without straining the neck. As you can see you have the D,A,E strings tuned in 5ths like a banjo or fiddle.

According to my dad, guitarists were more snobbish about tunings in the past. By the late 60s it was cool to experiment with tunings (at least for rock guitarists), but he says there definitely was a point where you were looked down on, particularly for open tunings

A tangent: I’m learning piano and musical notation finally clicked for me.

Musical notation is a high level language. It gives you a program that you can run on any instrument. And it gives you the ability to modify it with relative ease.

When playing clarinet in high school I felt that notion is this archaic thing that we’re stuck with because of the morons in the past. But I’m realizing it’s this beautifully refined language, developed over centuries.

It might be refined and developed over centuries, but it's also the expression of overwhelmingly a single culture.

Western musical notation is not useless for denoting the music of other cultures, but it's also not very good and is frequently quite bad. If you think of western musical notation as "the system", you're at risk of remaining ignorant of the beautifully refined languages, developed over centuries, in other cultures.

It's also a highly abstract language that seems to frequently, somewhat like Javascript, lead its users to have very little familiarity with what is going on at lower levels.

As a classical guitarist, western notation is not particularly good at expressing the music our own culture. The high open E string can be and is regularly played on the other 5 strings too, potentially at the same time! Natural and artificial harmonics, which string to play on and which fingers to use, and all sorts of right hand notation all feel very much bolted on cluttering the actual score. The continual coming and going of voices due to technical limitations means that music has to be experimentally decoded with much backtracking.

They tried to teach me various instruments when I was a boy. I didn't mind the playing, but Lord Almighty how I hated the notation stuff. It simply made no sense whatever, and was - as you describe it - clearly invented by morons. Only when I ventured into tech-land in my teenage years did any of it finally click: So that's what they mean by 'octave' - a doubling of frequency. Why couldn't they just have said so? Harmonies, chords, what have you - it was all just frequencies and sine waves. Didn't musicians know anything?

These many years later, I still don't quite get it, but do of course realise there must be some sort of point to it all. High level language? Yes, I get it. Bach wrote in Python, not C. Time to revisit.

You can’t quite run it on different hardware: unlike on a piano, the note does not uniquely determine how something is played on, say, a guitar.

What are some troubles guitarists are having with musical notation?

The same note can be found on different strings. Sheet music doesn’t tell you which one to play. That just one example that makes it hard

On a piano, musical notation doesn't tell you which finger or hand you should use. This seems similar.

Just for clarification, I asked because GP said:

> You can’t quite run it on different hardware: unlike on a piano, the note does not uniquely determine how something is played on, say, a guitar.

It’s not similar, because it doesn’t even tell you where to put the finger of your choice in a guitar, whereas that is uniquely specified on a piano. Of course, on top of that, you also have a wide range of ways to modify how you play on a guitar.

I still don't see the point. If you practice a piece, you have to practice how to put which finger where, on a piano or a guitar. It's part of practicing to figure this out.

> Of course, on top of that, you also have a wide range of ways to modify how you play on a guitar.

Yeah, same with the piano. And I think, with most of all instruments.

You can easily build a robot that you feed sheet music, and that robot will then be able to press the right buttons on a piano keyboard.

This is not possible for a guitar (and others) because there is no unique mapping between the note on the sheet and the position on the instrument.

This sounds needlessly antagonistic, but I hope I’m just reading nuance wrong.

You probably do. I play two instruments (not guitar obviously) and I want to know why musical notation is a problem for guitarists.

I know it's not really suited for e.g. non-western or modern quarter-tone music. But since I don't play the guitar I would like to understand the reasoning behind your qoute:

> You can’t quite run it on different hardware: unlike on a piano, the note does not uniquely determine how something is played on, say, a guitar.

Is that more clear?

It’s still antagonistic because sheet music is not ‘a problem’ for guitarists.

I never said it's a problem. I asked what's the problem that "You can’t quite run it on [...] say, a guitar."

You specifically refer to guitarists’ problem with notation, not the mathematical non-uniqueness. You ask you want to know why “musical notation is a problem for guitarists.”

It’s not.

Am I missing something, or are you directly contradicting your original comment?

https://news.ycombinator.com/item?id=28725817

If you actually read my comment (try it!) you will see that I make a statement about sheet music not uniquely specifying where on a guitar a specific note is to be played. I make no statement whatsoever about guitarists.

You seem to have trouble with the concept that the vast majority of instruments does not yield a recognizable melody simply by pressing the right button at the right time. All of those musicians are doing just fine, thank you very much.

There's a different thing for that: tabulatures.

Tabulatures come with their own limitations though. They're mostly a far less portable way to express western music. They also lose a lot of meaning. Is a note part of a particular chord or melody line? A lot of this is not visible in tabulatures.

The point of OP was that sheet music is general and portable, but it really is not. Tabulatures make the Position you play on a guitar unique, but, again, are not portable.

On the clarinet you’ve got that awkward break at the twelfth so the registers have different fingering patterns. Piano notation seems to be mocking you.

Now I play the banjo, where a number of open tunings are commonly used, which allows fast rhythms with minimal fretting.

I have an electric guitar with 5 strings tuned fifths (C G D A E), and a tenor guitar with 4 strings in fifths (currently D A E B). I've been mucking around with both for a few years.

Conceptually, they're nice. You get a great set of movable bar shapes, giving you spread chords with the first, fifth, and easy access to a 9th (2nd), minor third, major third, or 4th (11th). So it's super easy to get the common chord "colors" (sus2, maj, min, sus4).

Similarly, you can add the next string to get a maj 6th, min 7th, and maj 7th with a 4 string movable chord. However, it all sounds a little thin if you're playing in an acoustic style. Bar chords in standard guitar tuning sound better to my ear, so I'm not sure I believe any of the responses talking about better overtones. Maybe that's different with a violin and the music that's played, dunno. If it was overtones, why wouldn't the "double bass" violins use it?

Even with the shorter length of the tenor guitar (23 inches), playing diatonic scales is unpleasant. My pinky finger feels week when it has to stretch that distance for 4 notes per string. And I really don't like the stretched out (three notes per string) pentatonics. Because of this, I think the answer to the link above really is about the scale size and ergonomics.

I'll probably leave the tenor guitar alone (it's a novelty for me anyways), but I'm thinking I'll switch to CGDGBE or go back to Drop D on the electric guitar. All fifths just isn't that enjoyable for me.

There was a King Crimson link on HN the other day. I should mention Robert Fripp's "New Standard Tuning" is all fifths up the point where the highest string would be way too thin or way too tight (CGDAEG). Even as is, that high G seems unhappy, but he makes it work :-)

I think someone used to sell string sets for that, but I can't find it on Amazon atm.

I pretty much only play guitar in nonstandard tunings. Not all of them are oriented around fifths, but they often are at least in part.

Repetition of finger positions across strings is one motivation. While some of the linked comments suggest reachability, the standard guitar tuning affords a lot more for many common guitar styles. But nonstandard tunings open up a lot of other styles because you can use partial fifths on open strings more readily than with standard.

Two things I think (particularly) guitarists miss:

1. If you’re not doing chord/scale/mode transitions standard tuning is optimized for, you’re putting a lot of cognitive load either on your playing or your practice.

2. Translating guitar tuning to fifths tuning is a lot easier than vice versa if you’re reading tabs or standard sheet music.

I've often wondered what guitarists are thinking about when they use alternate tunings. I'm sure if you play in one tuning long enough you can conceptualize how all the notes related to chords and keys, etc. But if you frequently change tunings, when you learn a song does it just become a matter of memorizing finger patterns, or do can your brain actually figure out the mapping such that you are thinking in terms of chords and intervals?

A lot of guitarists have no problem with playing open tunings because they can pretty seamlessly transcribe the notes along one string to the whole tuning, like how the 2nd fret of the low D string in open D is an E note so thus a finger across the whole fret is an "E chord".

It's once you get into alternate tunings that are outside the "open tuning" norm that it becomes, at least for me, memorizing finger patterns and getting fine coordination locked in. The theory gets thrown out for "what sounds good" and "hmm that sounded about right".

For me, once I’m playing it’s almost entirely muscle memory. Writing or learning, the tuning doesn’t matter at all it’s just developing that muscle memory.

The thing nonstandard tunings does for me is it gives me a base state to work from that lets me use patterns and techniques suited to it. Drop D is very good for bass-heavy fifth chord stuff. CGD--- is really good for fingerstyle techniques. Other weirder tunings like some used by Michael Hedges let you rethink whole chord relationships.

Pat Metheny noted recently (0) that although he loves to use alternate tunings, he feels that it takes at least 10 years to really know your way around a given tuning, and thus changing them around impairs your ability to really get deep into your performance/compositional process.

(0) https://www.youtube.com/watch?v=QEgalcH_-b4

Other players such as Nick Drake, composed on piano, and tuned the guitar to accommodate the composition.

When I was a kid, I played cello and bass, which were tuned in 4ths and 5ths. I could go back and forth between the two instruments without batting an eye, including sight reading.

I think you just develop two parallel mental circuits, and there are enough sonic and tactile clues that you don't forget which instrument you're playing.

After high school I played bass exclusively for almost 40 years, and during the pandemic I got my cello out again. After several weeks, the old circuits started to re-attach themselves again. In my case I'm trying to play jazz on both instruments, which includes improv soloing. Let's just say that's a work in progress. There is still a lot of stuff I can play on bass, that I can't approach on the cello.

Non standard tunings can be very interesting for song writing, in particular the use of droning notes, or when using playing styles like travis picking. Some of the American primitive players like Fahey, or Rose, and more recently players like Nathan Salsburg, put together really great sounding stuff.

> If you’re not doing chord/scale/mode transitions standard tuning is optimized for, you’re putting a lot of cognitive load either on your playing or your practice.

I actually find that once you learn something in standard that there is relatively little cognitive load involved. It's more about refining very fine motor skills and coordination between shapes/fingerings. At a certain point the motions become instinctual and the "cognitive load" simply disappears. You just play. It's when I transition between tunings that I feel (initially) very uncomfortable, because I'm relearning those fine motor skills in new patterns to fit the tuning.

With regard to songwriting specifically, I've found that strange tunings are an easy way to knock myself out of my comfort zone. I think a lot of guitarists find themselves in a rut where they're accidentally writing stuff that sounds very similar over and over.

All of a sudden it's a bit difficult for me to predict what a chord will sound like before playing it, and as I'm getting aquatinted with the new tuning I run into little happy accidents that might not have been terribly ergonomic (or even possible) in a standard guitar tuning.

So much this. The most absurd tunings I’ve worked with have helped me rethink even familiar progressions and explore new ideas that wouldn’t occur to me.

> I actually find that once you learn something in standard that there is relatively little cognitive load involved. It's more about refining very fine motor skills and coordination between shapes/fingerings.

This is actually the cognitive load I’m talking about. I can do that, and I have, but playing the music I want to play is really challenging because I have to adapt free strings or polyharmonic positions to positions my hands can and will do (and can adapt to do better) but still keep me focused on whether I’m getting the sound out of my instrument the way I want.

(Thanks for the name drops, I have a couple artists to check out! Since I’m here talking tunings, my biggest influences are Kelli Rudick and Kaki King)

Probably my favorite example of non-standard guitar tuning is the way Luca Stricagnoli tunes his guitar in his Sweet Child O' Mine cover[1]. He starts with a capo covering half the strings on fret 3, and a SpiderCapo on fret 1, with a spare capo. At 3:45 or so he removes the half capo, and puts the spare capo onto fret 2, transitioning from Major to Minor key.

[1] https://www.youtube.com/watch?v=Ok5d8nXAngw

Music/math nerds: "The Science of Harmony", from 2019, has some major breakthroughs. Enjoy.

https://spj.sciencemag.org/journals/research/2019/2369041/

I've thought about this a fair bit myself, and I think it's a combination of a couple of the reasons stated.

First, it's a reasonable range in which every other note can be played within the string before.

But more importantly, I think it's just because it's incredibly easy to hear a fifth for tuning. Humans are fairly adept at hearing minute differences between two of the same frequency (i.e. a few hertz or cents off) when two notes are exactly the same, a fifth above share the most harmonics within that reasonable fingering range.

Although it's typical to tune orchestral strings using harmonics to match the pitches. For the cello, viola and violin, this is done by comparing the 2nd and 3rd harmonics (at the octave and twelfth). For the bass, tuned in fourths, one compares the 3rd and 4th harmonics (at the 12th and second octave).

What is the music history version of HN where you can get a drive-by answer from one of the (probably many) musicologists who have devoted their lives to studying the history of the violin?

> What is the music history version of HN

In the 11 hours since you commented, the answer appears to be... HN :)

A lot of speculation but no real answers. I find the argument about resonances between strings to be spurious since it really only applies to notes played on open strings which are a distinct minority of the notes played (not to mention that there are distinct advantages to avoiding open strings, such as the lack of the ability to apply vibrato on an open string).

Ultimately, it's a matter of string length, I think. It's worth noting that in the cello, viola and violin, all four fingers are used independently in fingering notes, but on the double bass (unless you're Joel Quarrington), you finger 1, 2, and 3+4 together since the littlest finger doesn't quite have the strength to press the string down on its own and the ring finger doesn't have the reach of the little finger.

But, like all the respondents in the discussion, I don't really know either.

Also, bass is most commonly tuned in fourths unless you're Red Mitchell.

Your point about resonances isn't really true. The other strings can resonate "sympathetically" even when you play a fingered note. For example, vibrato can be achieved on open strings by vibrating on the finger position that corresponds to the note an octave higher than the open string. This is mostly used for the open G string, since as the lowest note, it can't be played anywhere else on the instrument. But its also used on other strings for different colors.

Sympathetic resonance is also why some keys sound better on a violin than others. Violinists tend to like the keys with sharps: G D A E

But that's not connected to fifths tuning. It can happen with any tuning (one “trick” with a dual neck 6/12 string electric guitar is to tune the strings on the 12-string neck to each of the diatonic pitches so they resonate with whatever note is played on the 6-string neck, and then of course there are the sympathetic strings on Indian stringed instruments which have a similar function).

Curiously, while orchestral strings tend to be more comfortable in the sharp keys, as a double bass player, I was equally at home (if not more so) in the flat keys that tend to be favored by winds.

There’s probably a PhD length answer that involves the transition from Renaissance to Baroque music, the plagues of the mid 17th century and the Little Ice Age.

Violins have always been identified as being tuned in 5ths to the best of my knowledge, but the features mentioned above helped them out-compete other stringed instruments over a century when the fashion in music favoured those features.

Some of them are - the construction favours better projection over the kind of mellow sound of a viol, the rounded bridge allows for better virtuosic playing rather than chords. Music from the late 16th to the time of Monteverdi had a tradition of florid embellishments (diminutions) which favour a more responsive instrument, like cornetto, recorder or violin. The plague of 1630 in Venice is thought to be a major factor in the decline of the cornetto, so the violin had an opportunity to fill that gap then.

There’s also a change in the theory of harmony around this time from the Guidonian hand and hexachords to a more complete chromaticism. As someone’s already pointed out, fifths make for a very convenient arrangement of tones and semitones in order to play a scale. I suspect hexachords fit more naturally (!) across strings tuned to fourths - you would have ut-re—mi on the hard, soft and natural hexachords at your fingertips. As music theory moved away from this understanding of harmony, it would have also been more suited to the violin over the similar instruments tuned to fourths and thirds.

Just don't use a guitar tuner. Or a piano. Your open C won't be C, it will be 440 * pow(sqrt(2,12),7) which is ~0.75Hz flat.

(Does this mean guitars and pianos are out of tune? Yes.)

It may be of interest that even in classical music there are occasional exceptions to the normal GDAE violin tuning. In Mahler’s 4th symphony the violin solo is played on an instrument tuned to AEBF# which gives it a very distinct quality.

https://www.violinist.com/blog/stormviolin/20173/21062/

That has to be one of the more civil examples of online discourse I’ve ever seen.

To be fair, you’re the first commenter. But I applaud you setting a good (sorry) tone!

They may have been talking about the comments in the posted link.

They were, I was trying to bring some of that good tone here.

A lot of people seem to be answering by explaining what 5ths are. That isn't really the question. The question IMO is why they tune to 5ths rather than something else like 4ths, as a guitar often is.

4ths are really just 5ths backwards, but I've always wondered that about violin, too.

edit: Ah, the last answer is very clear and good.

I always hum the first two notes of the Dallas opening theme to remember what a fifth is.

Make your life simpler and memorize SOAD's Toxicity intro.

We don't. :) https://hubguitar.com/music-theory/why-the-guitar-is-tuned-i...

All this music theory stuff is not the answer. The answer is because the typical male hand can play the fourth with the pinky finger. So tuning in fifths gives the instrument the most range.

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