keys that don't sound good

[PhilGox]

Hello!

As I was working major pentatonic scales I noticed something strange:

I play G major pentatonic in closed position (start on D string fret 5) and no problem.
I play the same position on G# or Gb and it sounds flat and a little out of tune.
I checked all my instruments, banjo, barytone uke, banjolélé and mandolin. (all tuned in fiths.)
They are all perfectly tuned all along the neck.
(I'm very maniac with tuning)
G key gives a rich sound, full of harmonics.
Gb or G# gives a poor and flat sound.
It nearly sounds out of tune.
Although if I check the notes one by one with a tuner they are all ok.
The phenomenon is less perceptible on mandolin than on the other instruments but is here anyway.
Puting a capo on first fret to play in G# restaures good sound.

It makes me feel that fith tuning instruments don't suit all keys.
For the same closed position G# doesn't sound as good than G.
The same with C and C#.
I know jazz players like to play in all keys.
Theory says it works.
But in practice does fith tuning really allow all the keys with the same rich sound?
Is a capo the only solution?
Or is it better to transpose the tunes to the keys that sounds the better?
What do fith tuning players usually do?

Thanks in advance and happy sunday.

[Andy Hatfield]

There are definitely keys that ring better on the mandolin, due to factors like overtones, and the resonating frequency the instrument body is tuned to. I've recently begun practicing a couple tunes in Ab, and frankly the instrument doesn't sound as good in that key.

Andy

[T.D.Nydn]

If your playing in G ,and then go to Gb,yes,that would sound flat,,just play in any key for awhile and that key begins to sound normal...

[Simon DS]

The unfretted open strings will all resonate to a certain extent with what ever notes you play up the neck. This adds a colour to the notes you play -sometimes the colour's a bit muddy, sometimes it's great. The size/acoustics of room you play in can also have a similar effect.

[Jim Broyles]

My guess is that the nut slots are too shallow. If they are not deep enough, the strings will pull sharp in the first position. I don't have the link handy, but if you go to frets.com, there is a section about intonation at the nut.
Actually, here it is:
http://frets.com/FretsPages/Musician/GenSetup/NutAction/nutaction.html

[Willie Poole]

Well with my 50+ years of playing mandolin I have found a way to keep that from happening...JUST DON`T PLAY IN THOSE KEYS...Amen...

Willie

[allenhopkins]

In my observation, such as it is, playing a scale that includes open strings, as opposed to one where every note must be fretted, produces a "fuller" sound.

Also: no instrument's fretboard is perfect, and the frets are placed in a "tempered" scale, which includes some pitch compromises to make every note sound "close enough," as opposed to a "perfect" scale, which unfortunately will only work in one key. (I recall the classical guitarist who played an instrument with detachable fretboards, so he could get a "non-tempered" scale for whatever key he played in; the frets were located with subtle differences, so he had his "C" fretboard, his "G" fretboard, etc., etc.)

Assume that the tempered scale is computed from the nut, and starts with the unfretted string. If you then start a scale from the first fret, might it not sound slightly "off?"

I yield to the more knowledgeable among us, to tell me I'm totally off base,,

[MikeZito]

In my observation, such as it is, playing a scale that includes open strings, as opposed to one where every note must be fretted, produces a "fuller" sound.


+1 with Allen on this one.

I developed the the habit of using open/droning strings as a guitar player, because I always performed as a solo on stage, and needed a 'bigger sound' than what I would normally get playing more traditional chords. In later years I noticed that Bill Bolick of the Blue Sky Boys used a similar style in his mandolin playing, so when I eventually took up the mandolin, I kept (or at least attempted to) that same 'big sound' style.

[farmerjones]

Two things seems to be in play here: Temperament (perfect vs. justified). And, the Circle of Fifths.
One can Google, Temperament. It's quite a rabbit hole.
But I always have a Circle of 5ths, diagram printed out, so I can review it. (I'm doing it now)
G# is a minor key with the same notes as B. Other than having 5 sharps, it is what it is.
C# is a minor key with the same notes a E. That should be no problem either.
The notion of G# major or C# major however can create problems. Because the choice of mode, say for example Ionian, (WWHWWWH) there may not be a suitable note/tone to be achieved on the fret board.
I know Jazz players practice going around the circle of 5ths in Major and Minor, but I know of none personally, that delve into keys like G# major or C# major.
What do 5th tuning players do? I play a violin with no frets so I can essentially match what the orchestra is playing, even if it's off by a semi-tone. Fretted folk must tune to an artifact, then re-tune if the key requires it.

Maybe Jim Broyles will help me? What mode do I use when playing in C#major or G#major? Is it my choice, or is there no such thing?

[FLATROCK HILL]

G# is a minor key with the same notes as B. Other than having 5 sharps, it is what it is.
C# is a minor key with the same notes a E. That should be no problem either.
The notion of G# major or C# major however can create problems. Because the choice of mode, say for example Ionian, (WWHWWWH) there may not be a suitable note/tone to be achieved on the fret board.
I know Jazz players practice going around the circle of 5ths in Major and Minor, but I know of none personally, that delve into keys like G# major or C# major.

I guess it's because I have almost no formal training in music theory that I can't understand what you just said.

What is the difference between G major and G# major other than the half-step?
Seems like although maybe more difficult to play in certain keys, and obviously different open strings, all of the notes for any key should be available on the fretboard.

(It's probably the 'Ionian' thing that is throwing me off. Do they use that much in bluegrass?)

[sblock]

Two things seems to be in play here: Temperament (perfect vs. justified). And, the Circle of Fifths.
One can Google, Temperament. It's quite a rabbit hole.
But I always have a Circle of 5ths, diagram printed out, so I can review it. (I'm doing it now)
G# is a minor key with the same notes as B. Other than having 5 sharps, it is what it is.
C# is a minor key with the same notes a E. That should be no problem either.
The notion of G# major or C# major however can create problems. Because the choice of mode, say for example Ionian, (WWHWWWH) there may not be a suitable note/tone to be achieved on the fret board.
I know Jazz players practice going around the circle of 5ths in Major and Minor, but I know of none personally, that delve into keys like G# major or C# major.
What do 5th tuning players do? I play a violin with no frets so I can essentially match what the orchestra is playing, even if it's off by a semi-tone. Fretted folk must tune to an artifact, then re-tune if the key requires it.

Maybe Jim Broyles will help me? What mode do I use when playing in C#major or G#major? Is it my choice, or is there no such thing?

I think you have this wrong.

In 12-tone Equal Temperament (12TET), all keys are exactly the same, in the sense that all musical intervals (major/minor seconds, thirds, fifths, etc.) are the same frequency ratios, regardless of the key. So it doesn't matter whether you play something in G or G# -- the temperament (the amount that the Pythgorean ideal ratios are tuned 'off' by a bit, to close the Circle of Fifths) is identical. This is not true in Just Temperament, however.

Instruments that are designed to follow 12TET, which includes most keyboard and fretted instruments, don't tend to sound (much) different in different keys. And they don't sound different in different modes, either. Modes are like keys: they are just groups of particular notes favored by a tune. In 12TET, all semitone intervals between any given pair of notes are exactly the same. There is not any "favored" key or "sweet" key. If you are playing the proper frequencies specified by 12TET, all the keys and modes will sound the same --- they'll just have a different root frequency. So you have to look elsewhere for any perceived differences.

If your fretted instrument does sound a little different in different keys, you cannot chalk it up to the temperament. Instead, it might have something to do with the specific compensation made at the saddle. But that is only a minor effect. Or, it might just have to do with the way you're fretting the notes. Keys with lots of open strings are easier to play in, and if you have a tendency to push hard on fretted notes, these might go slightly sharp. So you might be off a tiny bit when playing in keys with few open notes. And that's what you're hearing. If some keys sound bad to you, it might just be down to your playing technique, unfortunately! Some have suggested that the natural frequencies of the mandolin (e.g., the Helmholtz air resonance, or some wooden mode frequencies) favor some keys over others. I don't quite buy that. But it's certainly possible to sound badly in some keys with an inferior instrument, especially one that's set up poorly (e.g., bad bridge position; high action; poor compensation; old strings). I would certainly not agree with the proposition that any particular keys happen to "sound bad" on a top-end mandolin with proper setup -- because they don't.

Another possibility, coming from the violin, is that you might be tuning your mandolin in perfect fifths (as violinists so often do), and not to the 12TET frequencies specified by your electronic tuner. That's a mistake, and I would avoid that, if I were you. Tuning GDAE in perfect fifths produces Just Temperament for those open strings, and these will sound a bit off in keys that happen to have lots of sharps or flats, since the open notes are compromised slightly. Do you do that, I wonder? Violinists in orchestras often avoid playing open strings, especially in pieces with many sharps or flats, because they have Just Tempered their open strings, and these are slightly off. Be sure to stick with 12TET for the open strings on anything fretted, like a mandolin. Do not tune it like a violin.

[DavidKOS]

I know Jazz players practice going around the circle of 5ths in Major and Minor, but I know of none personally, that delve into keys like G# major or C# major.


As a jazz mandolin and guitar player, I can say that yes we do play in all keys, including C#/Db and G#/Ab.

Often we have to play in multiple keys in the same song.




What is the difference between G major and G# major other than the half-step?
Seems like although maybe more difficult to play in certain keys, and obviously different open strings, all of the notes for any key should be available on the fretboard.



see the following please


I think you have this wrong.

In 12-tone equal temperament (12TET), all keys are exactly the same, in the sense that all musical intervals (major/minor seconds, thirds, fifths, etc.) are the same frequency ratios, regardless of the key.


...... Stick with 12TET for the open strings.

Great comments about tuning relationships, open strings, etc.

One other thing - I've also played a lot of folk music with non-jazzers and it is usually in a limited number of keys that are usually C, G, D, A, Am, Dm, F, etc.

When I play something that's in Eb, Ab, Db, etc., they often are just not used to hearing those keys.

One of the guys had a Bb/Eb melodeon, and it was fun to play all the same tunes we had played a few minutes earlier a half step up from the A/D melodeon.

Some of the other string players looked at me like I was from Mars or something for liking those odd keys.

We also discovered the "yodeling pickle" was in Db.

http://www.joesdump.com/wp-content/uploads/2018/01/11761-Yodelling-Pickle.jpg

[FLATROCK HILL]

see the following please

Ok David... I saw "the following". I won't claim to understand it fully, but it (and you) seem(s) to be in agreement with me.
All of the notes are available on the fretboard regardless of key... No.?.

[DavidKOS]

Ok David... I saw "the following". I won't claim to understand it fully, but it (and you) seem(s) to be in agreement with me.
All of the notes are available on the fretboard regardless of key... No.?.

Yes they should be, assuming your instrument has a properly fretted and set up neck and bridge.

Another example - I played a lot of Irish traditional session music with some friends and the keys were very limited - they would not play a tune in keys like Eb or Ab on their D whistles and Irish flutes.

The music is designed for those open string keys!

[sblock]

:popcorn:

[farmerjones]

Thanks Fellow Caf'e_ers.
This seems like de'ja vu all over again.
Obviously I misspoke, it should be Even Temperament vs. Justified Temperament, vs. Perfect Temperament.

Here's another: If there is a key of B (6 flats or sharps) how come there are only five black keys in a keyboard octave?

[blaise.douros]

Thanks Fellow Caf'e_ers.
This seems like de'ja vu all over again.
Obviously I misspoke, it should be Even Temperament vs. Justified Temperament, vs. Perfect Temperament.

Here's another: If there is a key of B (6 flats or sharps) how come there are only five black keys in a keyboard octave?

Because there is, technically, such a note as Fb, E#, Cb,and B#. E# sounds exactly like F natural, but from a pure theory perspective, one does not function exactly like the other. Let's say you're in the key of F#, and you play a I-IV-V chord progression. The V chord, which is C# major, is spelled like this: C#, E#, G#. It is NOT spelled C#, F, G#. That's because E#, from a theory perspective, is the note a half-step below F#--because you can't have two notes in a scale with the same name.

Source: I majored in music theory and composition.

[DavidKOS]

Because there is, technically, such a note as Fb, E#, Cb,and B#. E# sounds exactly like F natural, but from a pure theory perspective, one does not function exactly like the other. Let's say you're in the key of F#, and you play a I-IV-V chord progression. The V chord, which is C# major, is spelled like this: C#, E#, G#. It is NOT spelled C#, F, G#. That's because E#, from a theory perspective, is the note a half-step below F#--because you can't have two notes in a scale with the same name.

Source: I majored in music theory and composition.

Me too! MM University of New Orleans 1985

It also has to do with how the additional chromatic pitches were added to Western music in theory - and practical terms, as far as the keyboard - historically.

[sblock]

There is nothing mysterious about this. The simple answer is that the standard keyboard (in 12TET) does not require separate piano keys for notes that happen to be enharmonic, since they sound at the same pitch. Thus, although we may choose to call a note "Eb" in the key of (say) Bb, we might call that same pitch "D#" in the key of E. These tones correspond to the same black keys on the piano. And you only need five black ones, plus seven white ones, to cover all 12 possible semitones of the chromatic scale in an octave (including both octave notes). And after that, everything just repeats. Enharmonic tones serve different musical functions, though, and what you choose to call them depends very much on the musical context, as so nicely explained in earlier posts.

[blaise.douros]

Me too! MM University of New Orleans 1985

Nice! Got my BA from St. Olaf College, 2007. My theoretical knowledge greatly outpaces my chops, so at least I can feel good-ish about that while everyone else here plays circles around me.

[David L]

The biggest difference between the keys of G and G# are the open strings. Open strings vibrate sympathetically when those notes (or harmonically close) are played on other strings, as atsunrise mentioned. If capoing at the first fret lets you play clearly in G#, then that is the problem.

No one has mentioned the "fix" for that. You have to dampen the open strings, especially the bass strings. The easiest way is to lightly touch the unused strings with the fleshy part of the thumb by the palm. I find that I have to do this on my banjolin to get a purer tone. Electric guitar players do this all the time to keep the bass strings from sympathetically feeding back.

[Marty Jacobson]

I'm not as up on the theory, but if your mandolin is set up properly, no key should sound bad, or sour, or weak, or anything negative like that. Some other keys may have more sustain or sympathetic ringing from the open strings, but if it sounds bad, then your bridge is probably in the wrong place or compensated incorrectly.

[Tom Haywood]

It could be all in your head. Really. Even if the mandolin is set up and intonated perfectly (theoretically), it still plays notes in an equal tempered scale. That means that every note is equally out of tune from the pure intervals that can be played on a fretless instrument or shown mathematically. Every key will sound the same, theoretically. One commentator states that the equal tempered major third is 14 cents sharp of the pure interval. The average listener can hear a 2 cent difference, so 14 cents is quite a lot a lot. That is why we "sweeten" our tunings in different keys so they sound better. Our ears and minds get accustomed to the discrepancies on fretted instruments, at least for the notes and chords we commonly hear. Not so much for keys we rarely hear.

[DavidKOS]

It could be all in your head. Really. Even if the mandolin is set up and intonated perfectly (theoretically), it still plays notes in an equal tempered scale. That means that every note is equally out of tune from the pure intervals that can be played on a fretless instrument or shown mathematically. Every key will sound the same, theoretically. One commentator states that the equal tempered major third is 14 cents sharp of the pure interval. The average listener can hear a 2 cent difference, so 14 cents is quite a lot a lot. That is why we "sweeten" our tunings in different keys so they sound better. Our ears and minds get accustomed to the discrepancies on fretted instruments, at least for the notes and chords we commonly hear. Not so much for keys we rarely hear.

As a jazz player, I use all 12 (15 when spelled correctly) keys and am as used to hearing Ab as A or G.

"That is why we "sweeten" our tunings in different keys so they sound better"

That only works if you limit your playing to those keys.

For a jazz player that needs to play in all keys, all chords, 12 tone ET is the only workable system.

I have no problem with the 3rds in 12 tone ET; my ear is used to hearing them. I have no need to try to make them match the lower pitch 3rd of the harmonic series.

"That means that every note is equally out of tune from the pure intervals that can be played on a fretless instrument or shown mathematically."

If you want to play Just intonation music, get an oud! no frets.

[farmerjones]

I do know Jazz doesn't chase the harmonious. The dissonant tone has equal worth.
9ths, 11ths, & 13ths would get an eyebrow raise in some jams, and a smile in others. :cool:

[DavidKOS]

I do know Jazz doesn't chase the harmonious. The dissonant tone has equal worth.
9ths, 11ths, & 13ths would get an eyebrow raise in some jams, and a smile in others. :cool:

Eyebrow raised?

In some non-jazz sessions I've been at, if I played those "jazz"chords, somebody would throw a bottle or something at me to stop.:))

[sblock]

Eyebrow raised?

In some non-jazz sessions I've been at, if I played those "jazz"chords, somebody would throw a bottle or something at me to stop.:))

Sure they'd throw that bottle, but wouldn't they raise an eyebrow as they did so? :grin:

[DavidKOS]

Sure they'd throw that bottle, but wouldn't they raise an eyebrow as they did so? :grin:

Only to aim better.

[Kevin Stueve]

just tell em the 11th is really a sus4 . ;)

[Tom Haywood]

I suspect most of the jazzers hear most all keys regularly and their ears are used to the discrepancies. I'll step out on a limb and suggest that using a capo when playing in a key that many of us don't hear often, such as Gb, preserves the relative tunings and overtones of the intervals that we are used to and may sound more "normal" to the ear than playing the chords in a different form.

[Jim Broyles]

I know you're kidding, but for the uninitiated, the 11th is really not a sus4. In an 11th chord, there will be a third, thus, it isn't suspended, although the 11 is the same note as the 4. FWIW, an 11th chord will generally also have the b7 and the 9. #11 is a different animal - think Lydian feel.

[PhilGox]

Thanks all
for expalnations!

@Sblock: I don't even know how to tune it in perfect fiths :)
Possible I make so but could you explain how to tune in perfect fiths please?
I tune each string according to what says the tuner.
Sometimes I have to adjust it a little by ear to tune the strings together on 5th fret octave.

I swear I have good hear and my instruments are well tuned all along the neck.
A small amount of out of tune drives me mad! :)
I checked setup once again and no problem with this.
When I say G# is out of tune I mean it sounds so when I play music.
But the tuner tells me each independent note of the scale is ok.

@David L :
Yes! Dampening the strings is a solution for the "out of tuned effect".
Resonating G on G# tone is the problem, as logical.
I should have thought about it earlier, thanks :)

But...
I'm aware of equal temperament and the theory which says that all keys sounds the same.
It would be true if I could manage to always dampen all the simpatetic ringing.
But this way I don't have the rich resonance sound of the G scale sound.
In G# I just feel I loose all the interesting sound of the fith tuning
If you like simpathetic ringing and lot of harmonics as I do, the instrument really sounds better (for me) at some keys and more weak (or less interesting) at others.
Imagine you have an wonderful reverb pedal that warms your sound and you suddenly turn it off.
This is the best way I can explain what I feel.

Then I think I'll use a capo...

Anyway, thanks for making me learn interesting things! :)

(And sorry if I take time to answer, it takes me time to read, understand and write in english.
And I confess I spend much time playing too ;) )

[Bob Visentin]

At the weekly jam I go to we like to play in F and Bb. It keeps the banjos away.:))

[sblock]

Thanks all
for expalnations!

@Sblock: I don't even know how to tune it in perfect fiths :)
Possible I make so but could you explain how to tune in perfect fiths please?
I tune each string according to what says the tuner.
Sometimes I have to adjust it a little by ear to tune the strings together on 5th fret octave. (bold added)

OK, the way that you tune might be contributing to your problem. If you tune the strings exactly to what the tuner says, then you will get 12TET (Twelve-tone Equal Temperament). Fini! However, you ALSO wrote that you tend to adjust your tuning further, so that the note on the 5th fret of the higher string is exactly one octave above the note on the open, lower string. However, that 5th fret (on an accurately made fretboard, with the bridge in the exact right place) is designed to give a frequency that is 1.49831 times the root, which is not exactly 3/2 of it (= 1.5 times)! The fretted string will therefore tend to sound just a trifle flat (~2 cents' worth), if your ear is good enough to hear that. If you consistently raise the note on the higher string to compensate for this apparent flatness, across the board, then you will have achieved Just Intonation tuning, and not Equal Temperament tuning. You can also get Just Intonation by comparing the harmonic produced at the 7th fret of a lower, open string with the octave below sounded by the open string found just above it -- or, with the exact match to the octave harmonic of that string found at the 12th fret. This procedure does not rely on using any frets at all, and is therefore "perfect" in getting you the Pythagorean frequency of a "just" fifth interval (3/2 = 1.5 times the root) as the tuning reference. Violinists sometimes use this harmonic for Just tuning, but they're also trained from the very start to hear a perfect fifth, and especially to listen for the sympathetic resonance (i.e., the reinforcement of higher harmonics) that occurs when two adjacent strings are sounded together that happen to be exactly a fifth apart. This process produces Just Tuning for the open strings, not 12TET. On a violin, the player can adjust the fingered notes to the right 12TET tones by ear, but the open violin strings will always produce a 'wide octave' due to their non-12TET tuning. You should not tune a mandolin like a violin.

My advice would be to rely on your tuner, and not tweak it further, especially if you intend to play in a key with many sharps or flats, i.e., well "away" from the open-string notes of G,D,A,E.

Bon courage, mon vieux!

[sblock]

:mandosmiley:

[PhilGox]

Yeaaaah!!

Thanks a lot for this explanation sblock!! :)

You found the problem I was not aware of.
You made me discover I don't tune my instruments in 12TET but in Just Intonation tuning.
It's true that when I tune I look for perfect resonance between strings and octaves.
I used to tune my electric bass this way too when I played bass.
(Perfect octaves are easy to hear when you play both notes.
If they are not in perfect octaves you hear a sort of modulation that is clearly audible.
When the signal is "straight" then you have perfect octaves.)

So indeed it's logical some keys don't sound well tuned if I don't have 12TET.
Now I understand this thanks to you.
It's better to be aware of the difference between 12TET and Just Intonation tuning.

But...
I just CAN'T STAND untuned octaves as I use them a lot with open strings.
I tried perfect 12TET tuning and it really sounds odd to me.
if I hear lighty untuned octaves it drives me mad.
So I think I will make my choice to Just intonation tuning.
The instrument seems to resonate better this way, with lot of harmonics as I like.
This is just a matter of taste.
I understand someone who is not especially looking for this resonance will prefer 12TET.
Anyway It doesn't bother me to use a capo for odd keys full of sharps I don't often play.


This forum is incredible!
After 30 years of music it makes me learn I didn't tune my strings "correctly".
Today I'm glad to know this because knowledge can't hurt.

And at least if someone tells me I don't tune it correctly I will be able to answer proudly:
"Non Monsieur!*
This is called "Just Intonation Tuning":cool:

Have a good day!

*="No sir!" plus a little bit of french irony ;)

[William Smith]

After a day of being around noise, like lawn mower, busy restaurant kitchen, screaming babies etc....I pick up the mandolin and well no key sounds good! I usually have to give up for that day till my ears get right so to speak. But in generality all keys are sweet on the mandolin, I love playing in them all.

[DavidKOS]

OK, the way that you tune might be contributing to your problem. If you tune the strings exactly to what the tuner says, then you will get 12TET (Twelve-tone Equal Temperament).
...... then you will have achieved Just Intonation tuning, and not Equal Temperament tuning.
.........
My advice would be to rely on your tuner, and not tweak it further, especially if you intend to play in a key with many sharps or flats, i.e., well "away" from the open-string notes of G,D,A,E.

Thank you.

It is also gratifying to read a post by somebody that actually understands tuning systems.

[sblock]

Some folks with "great ears" can easily hear a tuned note that differs from a reference note -- or one that is simply off in frequency, in the case of perfect pitch! -- by just a cent or two. [N.B: A 'cent' is one part in 1200 of an octave, which is a factor of 2.] I am not talking about listening for beats as both notes are sounded; I am talking about playing the two notes in succession.

Most folks can't do that, however -- the notes have to be off by more like 5-15 cents to make much of a difference. I have often wondered whether having a great ear is more of a blessing, or more of a curse! My current thinking is that it is a curse, because things can never be perfect in Western, multi-key music that spans more than an octave or so.

Western music inevitably involves compromises in the frequencies of scale intervals, which we call temperament, in order to come out right over multiple octaves. Some musical intervals are going to be off by as much as 15-18 cents in tempered scales. And there is no getting around this if you allow more than one musical key to be played. And even then, you run into trouble if your musical range spans more than an octave. And so, you have to make compromises. Twelve-tone Equal Temperament is the most even-handed compromise possible, because it makes all 12 semitones in the scale have the exact same frequency ratio (namely, the twelfth-root-of-two: apply it twelve times in a row, and you wind up with a factor of two = 1 octave). And that's what nearly all modern keyboard and fretted instruments use. It gets the 5th interval fairly close (to within less than 2 cents), but the nasty thing about 12TET is that the major and minor thirds are off by about 14-16 cents -- which many of us, even those with 'normal' ears, can hear. There are other systems of tuning possible, which make various other compromises, but these don't tend to work very well with fretboards! (For some, you have to install microfrets and suchlike, or bent frets, etc.). And NO SYSTEM of temperament is without its compromises, so it really depends on what bothers your ear the least, not on what "works." No system of temperament gets everything right, at least to some ears.

If you Just tune (use perfect fifths) a mandolin or violin on its open strings, say, starting with the low G (yes, I know most folks start with the A string and go both up and down, but I am simplifying things here to make a point), the first fifth, from G to D, with be just ~2 cents high (i.e., a factor of exactly 1.5, and not 1.4983, in pitch). Going up from there, the A string will be (1.5 x 1.5), or 2.25 times the frequency. The E string will be (1.5 x 1.5 x 1.5) higher, or 3.375 times higher. But in 12TET, that E note it should be 3.364 times higher, instead. By now, you're off by a factor of 1.00327 in pitch, or 0.3%, which is significant -- the errors are starting to accumulate. Each fifth you go up adds to the existing error. Not good.

As you can see from this example, tuning a fretted instrument in perfect fifths starts to make the higher strings sound consistently 'off' with respect to the lower strings. And their fretted notes will also sound consistently off, too, because their unfretted pitches are off in the first place, even if the frets give 12TET intervals. So you haven't really fixed any problem. And that's why it's not a good idea to Just tune a mandolin!

Put another way, there is nothing particularly "just" (in the sense of 'correct'. In French, "juste" means correct, n'est-ce pas?!) about Just Intonation. It is not more perfect in some sense: on the contrary, it starts accumulating bigger and bigger errors with every octave you go up, until these become so bad that anyone, even those of us blessed with less sensitive ears (!), can hear them.

P.S. Thanks for the kind words and thanks to my earlier posts! :redface:

[DavidKOS]

Twelve-tone Equal Temperament is the most even-handed compromise possible, because it makes all 12 semitones in the scale have the exact same frequency ratio (namely, the twelfth-root-of-two: apply it twelve times in a row, and you wind up with a factor of two = 1 octave). And that's what nearly all modern keyboard and fretted instruments use. It gets the 5th interval fairly close (to within less than 2 cents), but the nasty thing about 12TET is that the major and minor thirds are off by about 14-16 cents -- which many of us, even those with 'normal' ears, can hear. There are other systems of tuning possible, which make various other compromises, but these don't tend to work very well with fretboards!


And thanks for another post that makes musical and logical sense about tuning systems.

[PhilGox]

+100!

No one had never made things so clear to me before about tuning system than sblock!
I always thought I used 12TET but you proved me I was wrong.
And I thank you for this :)

I understand clearly why you say that 12TET is the best compromise.
And I agree it's true in most cases.

But since I understand things I realised something:
If I play jazzy, bluesy, funky or rock things, a little off note doesn't bother me.
I mean I can sometimes hear it but it seems to suit the music well.
I don't play bluegrass but I suppose it must be the same.
As someone who plays fast things with mostly shorts freted notes don't really mind for the very slight out of tune of 12TET.

But depending on the style of music, you might hear the difference more:
I also love to play sort of slow ethnic things that sounds like arab or spanish or medieval.
To give an idea, it sometimes makes my friends think of an indian sitar or a oud.
In this case the sound and ambiance is nearly more important than the notes you play.
Then Just Intonation is better than 12TET.
Because the instrument have to resonate perfectly with open strings to give this ambiance.
(I use mostly fiths banjos for this but also mandolin or nylon GDAE baryton uke, and it's the same effect for all).
I've just tried both systems with all my instruments and I swear it's not imagination from me.


As you said any tuning system is a compromise, if I understand well:
-12TET: All keys allowed but not exactly perfect fiths. (pas très juste, ou un peu faux ;) )
-Just Intonation: Perfect fiths, sounds great in a few keys but awful in some others.
Cruel dilemma!

So my personal compromise is:
1-Do I really want to play in twelve keys?
2-Or do I want my instruments to resonate like a sitar and give the ambiance I love so much? Even If I'll have to use only G D A keys and capo for others?

Now l will knowingly choose n°2.
I did so for too long without knowing my tuning method was not 12TET and I'm not ready to compromise the sounding it gave me.
Sometimes errors can be good :)