Just Intonation and Locating Pitches

[klasaine]

You mean the beta side?
I don't know, something that featured an instrument with 6 strings tuned in 4th's and a major 3rd ... it never really caught on.

[BigDaddyLH]

Just intonation -- doesn't that require one of these?

[warmingtone]

Actually you need the "blues" version of the TT frets...with 2 extra frets...and you can't play with other guitarists in tune!



Still some interesting reading (if you put aside the hype and take a bit of it with a grain or two of salt).

http://www.truetemperament.com/site/...php?go=4&sgo=0

I've followed some of this and been in such conversations before elsewhere and in my own ideas. But in the end everything is a compromise...the key thing is to make the best of what is at hand and perhaps understand what is going on, especially with the guitar.

Generally, thirds and lower frets are going to be problematic (sharp, so you cant bend to correct them except from a fret below), distortion amplifies the harmonics below notes and brings them to the fore and increases the 'problems'...etc...

There are ways to set up a guitar to minimize the effects and different ways of compensating with tuning methods, or to the extreme of moving the frets...but all these are compromises too...but you get the benefit of other keys and playing with other like tuned instruments!

...

As the diatonic semitone reaches the size of the whole tone, you arrive at 7-tone equal temperament (or 5-tone if the chromatic semitone is made the size of the whole tone). It'll sound strange, but the melody won't really disappear. You'll most likely have no problem identifying this (tuned in 7-tet)...

The importance, at least what I take away from such theoretical work, is that of ratios and intervals. It is not "the notes" that are crucial but the ratio of distance between them, the intervals between notes, that music really works with. Such "extreme" theory brings this home considerably.

Worthless theorizing for other theorists? So what?

So, not my reaction to it though I don't want to 'live' purely in this 'theoretical world', but the lessons can be important to your average person and how they approach things, perhaps spark a little enlightenment and have subtle influences on approach. Not necessary to do the theory to benefit from it after all!

It has had a fair influence on me in the desire to be able to bend both up from and below a note for instance, it does influence me in the preferred way I will form chord voicings and notes sequences, incorporating harmonics and even the way I set up my guitars to minimize some of these worse effects...

But I think it has a profound if unwitting influence on a lot of music, such as the power chord to minimize the problematic 3rds especially with distortion.

...

Hmmm...ancient music, always problematic...old doesn't mean "good"...hahaha...at least to my ears.

I did hear an interesting thing related on an episode of "Radio Lab" regarding a guy who was given the task in a classical radio station of going through all the records and listening and categorizing them for play. So, he hid away in the basement and started, not illogically, with the earliest stuff...so historically. So, after weeks of listening to nothing but "gregorian chant" and not wanting to hear any music after hours, he came up to the booth and heard some music and was shocked at how discordant and chaotic it sounded. Turned out to be a beautiful if non offensive piece of Bach!

This just shows how much 'conditioning' applies to what we understand and makes appealing to individuals, how with all the science that is "true" there is still a huge part of subjectivity and perception and conditioning on the part of the listener.

So, if all we hear and play is country or blues, perhaps some jazz that modulates can sound 'too weird' or to another just wash over one...or music from other cultures or that which appeals to our kids that might be working on texture over harmony perhaps, or rhythm. Perhaps hugely complicated classical music is just something pleasant to hear in an elevator! Stravinsky causes a riot one year, is entertainment the next!

I imagine that we are conditioned into equal temperament in much the same way...I know there are people who find the "blues third" to be kind of seasick and out of tune! If you immerse yourself in it though, the subtleties will become ever more important I guess.

I was trying this last night and asking myself...do I sometimes go "too far" with playing with 'tuning' s that although I can hear it is more 'sonorous' or even justify a technique with hard data about the conflicting harmonic overtones, the average person will hear it as being "out of tune" compared to their conditioning and expectations...one always needs to tune ones ear to the audience I suppose.

[LeopoldPlumtree]

Originally Posted by BigDaddyLH

Just intonation -- doesn't that require one of these?

The TT necks aren't really intonated justly. Their meantone blues neck will give you a pure major third, but other than its inverse and the octave there aren't any more Just intervals to be found. The well temperaments they offer will nudge you closer to Just in select keys.

[Larry F]

Here's a composition I wrote using 15- and 20-equal note tunings. The orchestra part was done by using pitch bend values for the notes. Done in the late 80s-early 90s without a computer, this took a lot of time to do. But fun.

http://www.lawrencefritts.com/tetraktys.html

[Budda]

That was kind of cool!

Sounded like something from a Movie Score. Very cinematic.

[Budda]

You know, if you keep playing those Harmonics, you'll hit a "b7" type tone. It's a Septimal 7th. Just a little flat of the Fretted b7.

So now, that sure seems to make a lot of sense to me.

Seems like it makes a good case as to whay a I7 Chord sounds so right. Doesn't need to go anywhere. Sounds good right where it is.

[ryokan]

Check out Harry Partch, he composed in a 43 tone to the octave Justly tuned scale. Wonderful music, and early in his career he used slide guitars...very interesting stuff...

Here are his adapted guitars:

[Budda]

Yeah, Partch was an interesting guy for sure!

Besides Jeff Beck, Derek Trucks and Bill Frissell, I really enjoy Steve Kimock's playing.

Here's some of his stuff:

http://www.youtube.com/watch?v=sn4K4DakGlM

http://www.youtube.com/watch?v=Dwkbu...eature=related

http://www.youtube.com/watch?v=AN1qC...eature=related

http://www.youtube.com/watch?v=0diKv...eature=related

http://www.youtube.com/watch?v=V2c9J...eature=related

[Thorpey]

...

It is safe to say that this thread is wayyyyyy over my head , that isn't to say it isn't interesting... it is in fact fascinating, way to go guys

[Budda]

Thorpey,

Glad you're digging it!

Don't stress too much about it all. Like I said before, it's stuff we all, already do! (Most of us, anyways!).

This is just a way to describe what might be going on.

Just try playing those Harmonics on the 12th. Fret, 7th. Fret, 5th. Fret, and just short of the 4th. Fret (A little closer to the Nut).

For "Bonus Points" you could add the Harmonic just short of the 3rd. Fret, also!

These Pitches will probably sound familiar.

Rock On, Brother!

[Thorpey]

Originally Posted by Budda

Thorpey,

Glad you're digging it!

Don't stress too much about it all. Like I said before, it's stuff we all, already do! (Most of us, anyways!).

This is just a way to describe what might be going on.

Just try playing those Harmonics on the 12th. Fret, 7th. Fret, 5th. Fret, and just short of the 4th. Fret (A little closer to the Nut).

For "Bonus Points" you could add the Harmonic just short of the 3rd. Fret, also!

These Pitches will probably sound familiar.

Rock On, Brother!

Hey budda, thanks for the info on those harmonics, probably only hit the one just short of the 3rd fret by accident

[LeopoldPlumtree]

Originally Posted by Budda

Just try playing those Harmonics on the 12th. Fret, 7th. Fret, 5th. Fret, and just short of the 4th. Fret (A little closer to the Nut).

For "Bonus Points" you could add the Harmonic just short of the 3rd. Fret, also!

Don't forget the one just ahead of the third fret, too (sixth harmonic).

[Thorpey]

Originally Posted by LeopoldPlumtree

Don't forget the one just ahead of the third fret, too (sixth harmonic).

Hey that's cool , but how is it the sixth? I mean like, why is it name the sixth harmonic? I am very much a theory nub

Thanks again

[LeopoldPlumtree]

Originally Posted by Thorpey

Hey that's cool , but how is it the sixth? I mean like, why is it name the sixth harmonic? I am very much a theory nub

No problem! It's the sixth harmonic because it's a sixth of the string's length, and multiplies its frequency by six (which is two octaves plus a pure fifth).

[Thorpey]

ahhhhhhh right, now i'm with you!!! Where abouts did you guys learn all of this stuff?

[warmingtone]

It's probably worth learning a little about the physics of how a string moves to understand what people are talking about and to see through a lot of the mojo and hype about things like "tone"...and of course, the physics of things is how the frets are spaced and the guitar works and essential for really grasping what is being discussed by terms such as Just Intonation...

It's not really music theory at all, but basic physics, but these are the things that we use and goes someway to understanding and using things at a deeper level.

ok...so...google harmonic motion, standing waves, string motion, and the like to your hearts content...I used the first I came across to lift this diagram....

http://www.physics247.com/physics-tu...armonics.shtml

There will be far better ones of course...but very basically....

The string vibrates in a complex way. The biggest 'mode of vibration' is the one from one end to another, this is the fundamental and the 'tuned frequency' (eg A = 440 Htz)....



All these waves and more are happening when a string vibrates, you have the first primary wave happening that will be loud and make up the name of the note, then you will have all these others higher in frequency vibrating within the note.

When we gently damp a string at the 12 fret we are 'stopping' the fundamental wave but allowing the smaller higher harmonic waves to continue to ring. So, at the twelfth fret, we are stopping the fundamental and 'revealing' the others and we perceive the lowest loudest one to now be the naming note and pitch...so, damp the A string at the half way point (12th fret) and you kill off the fundamental and the 2nd order harmonic will be twice the speed and so twice the pitch and so an octave above...

Cut it in thirds at the 7th or 16th fret and the harmonic will sound an octave and a fifth above the open string. At the fifth fret it will cut it into 4 equal parts giving you a pitch two octaves above the open string pitch. Just behind fret 4 is the 4th harmonic, 5 sections of string and a pitch roughly two octaves and a major third above the open string. At the 3 1/2 fret-ish you are cutting the strings vibrations into six parts, giving you 2 octaves and a fifth above...and so it goes, getting ever higher, less in tune with our intonation system (the way the guitar is fretted, the way we organize music in the west to allow different keys and instruments to work together, etc)

So...the thing to know is that behind the primary "note" are all these other higher notes all the time.

Now, these are also important in why we make chords (roots, 3rds and fifths) and many other things.

It greatly affects the idea of "tone". You will notice that if you use a neck pickup, it will hear (generally) the broadest vibration, and except at the highest frets, this will be the fundamental note. So, it sounds smoother and more 'true'. It will be harder to get these real high harmonics to sound though they are there, the pickup and amp are just not amplifying them well enough to hear, switch to the bridge pickup and you will hear them as the harmonic series gets closer to the end of the string and closer together and will always 'pickup' these smaller vibrations (just as the harmonic points got closer and higher as you move towards the nut).

So...there are a complex of things that can effect the vibration of the string and the amplitude, or strength of the higher order harmonics, the mix of these is largely what people refer to as "tone" of an instrument. So, some woods will dampen some harmonics and accentuate others, some people will get a 'jazzy tone' by using a neck pickup and sound that has few harmonics, an acoustic guitar will be rich in jangly harmonics. Some pickups will bring out more of the higher harmonics, distortions will bring everything up and squash them into a rich goop of sound. Some distortions will sound "better" because they accentuate harmonic content that is more 'in tune'...so, a guitar or distortion or amp or whatever that accentuates "even order harmonics" may sound "better as these will be primarily octaves...so, tube amps are notorious for this, solid state more even or even accentuating slightly out fifths and way out major 3rds (odd order harmonics) and worse in the harmonic sequence. So, there is a science in a lot of the "mojo", valve amps do 'naturally' sound better.

But, if you get a feel for what is actually going on, you will understand how to judge things for yourself and to manipulate things to your liking.

A wide HB pickup will be sampling a bigger area of sting, it will generally produce a warmer midrangy kind of sound as a consequence as an example. Adjust a single coil pickup too close to a string and the magnetism can dampen harmonics..."stratitis"

Wher you pluck the string will affect the "tone"...so strike the string closer to the bridge, and you will get a brighter harmonically rich sound, perhaps more acoustic like maybe. An acoustic guitars vibrating top will itself affect the way a string vibrates and can be "tuned' to bring out pleasing harmonics and an even response from all notes. So, an expensive acoustic say, is not just about woods, but the way materials and design work together.

You can see also, that much of this kind of thing can explain why one players equipment will sound great for him, but perhaps not so magical if he were to hand it straight over. It's the details of the way and force and placement of plucking and even fretting strings for instance that can affect 'tone'.

"harmonics" as a technique has many variations of course, there are the natural harmonics of the open strings, and the same for any fretted note if you can calculate where these are...so any note damped 12 frets above that will p[roduce an note an octave higher.

There are of course "pinch harmonics" where you can pinch out higher notes, Roy Buchanan made a big feature of this but more famous is perhaps the 'solo in ZZ tops "la grange" where different notes are produced just by pinching them off at different points along the string. Jeff Beck is another that plays melodies with harmonics, a player like Tommy Emmanuel or a Lenny Breau will feature cascades of alternate harmonic and fretted notes, some will produce them by 'slapping' the strings 12 frets or another harmonic point above a note or chord (EVH or Tuck Andress)...there are countless ways of getting these notes to "ring"...

Now...obviously there is far more complexity and ramifications...but in relation to some of this 'thread'...

Within the sound of any note are all these other 'notes' or harmonics all the time making up the 'tone' and the mix of these will vary the sound and harmonic content.

Long ago, and stil in other cultures and in many music, we tuned instruments to a more 'just intonation', every key would have a distinct character, guitars had movable frets even. You can see from those fretboards how much you need to move frets to be more 'in tune' with the natural order of harmonics. But, over time equal temperament became more acceptable with all it's compromises to our ears dispite the mis-match between it and the harmonic content of any note and the complexity that arises from many notes played together. Music could be come more harmonically and melodically complex for instance. In some cultures, things stayed more 'true' and harmonically 'simple' but rhythmically far more complex, just as an example, but this is just scratchign the surface or the implications here.

However, some might feel that a flattened maj3rd is more 'in tune' with the natural order of things, and it is tempting to use 'blue notes' as being more 'tuneful' and 'right' and co-opt the natural order of things in support of it. I think this is far too superficial really, but for sure some of it holds a little truth.

Major thirds typically do sound "sharp" because they are! But, physically we know that in any single note on a string instrument, there are 4th harmonics that are a JI major third above a given note. Play an A minor chord and the third within the note A will be 'sharp'...use distortion and it will sound "bad" as well and turn to "mush with the complexity...hence "power chords". Or, adopt a 'jazz tone' and go nuts with extensions and harmony and avoid a lot of these harmonic conflicts. Or perhaps, re-fret a guitar in some weird way and only play in certain keys in tune and not with others, or have no frets at all like a violin!

Anyway, a bit off the top of my head, but it really isn't so much "music theory" as the "physics of music" and vibrations (its much the same with wind instrument waves or even the way our ear drum works)...

[Thorpey]

Jeez Louise... Thanks for this wealth of information warmingtone, I can honestly say that I didn't even consider the physics behind the guitar. Obviously I knew that there is physics involved but never considered it to the level of harmonics and just intonation...

...I'm still pottering around learning the CAGED system

This stuff will sure make for some interesting bed time reading, by the way, is there a book available that would encompass most of this stuff? I see that Doug mentioned a book earlier, is this a good book, 'The Physics of Music', or are there more specific pieces written on what seems like a very specific topic/subject?

Once again thanks guys, especially budda and warmingtone, this site once again proves to be an inspiration

[warmingtone]

well...much of the basics could be found on line about the way that music and the guitar works. Looking at a book like "the guitar handbook' by denyer has the basics of harmonics, string motion and stuff like tube amps in a couple of pages.

It would be perhaps a little too easy to get bogged down with this kind of stuff, how far does one really have to go. In first year music, we had to do some physics, but you know, when are you really going to need to have at hand the formulas to work out the reverb qualities of a room in mathematical precision?

But, the text we had was called something like, 'the physics and psychoacoustics of music'...

Psycho acoustics is a fascinating area and there are lots of tricks that can be created that can 'trick the ear' exactly the way optical illusions can fool the eye...

But, just a basic understanding of string motion, what a note is made of (a fundamental string motions and a background of harmonic overtones) should be enough. As for tuning, an awareness that in most western music, we have evolved towards a compromise 'equal temperament' tuning, that this is a little at odds with the natural order of the overtone series of harmonics but that we benefit in huge ways in the complexity and flexibility as a result.

But, even there, the guitar is necessarily a bit of a compromise. As you move on with the guitar, these things will probably become apparent and with a little understanding, work around it naturally.

It is a good thing to know if you are confronted with a bit of BS about 'tone' and such...what do people mean by that, is it just hype in advertising pickups or whatever or is there some science behind these things. If you hear someone with a great "tone", check out to see what the guy is doing that makes it sound good and why it is in a real way that you can learn from.

We for instance will often hear about a players 'touch' and this is a vital ingredient with getting a sound out of an instrument. However, we are confronted by and naturally gravitate towards 'gear' and the idea that we can buy such things. The reality is that the really great players generally sound great on any guitar or set up, so there is lots to consider in what they are doing, how they voice chords, the kind of settings they use on equipment, pickup selections and such, but mostly the way the evoke sounds out of the thing as much as anything. The way you pick a string will greatly effect harmonic content as an example, even the fretted had affects 'tone' to some degree, damping is a crucial element.

But you know...most of the physics stuff is a bit extra curricula, don't get to bogged down, learn that caged stuff and work on some of the 'music theory', this puts the background 'whys' like this physics stuff into action after all.

[Budda]

Like has been said, I think you need a working understanding of the "Basics" of Diatonic Theory and Harmony. If for no other reason, than to know the common language of Musicians.

However, if you are feeling fairly solid in those areas, here's another way to look at things:

http://www.amazon.com/Harmonic-Exper...8692851&sr=8-3

It's a more comprehensive approach than most others I have explored. And it works on the idea of actually doing the work for yourself. There is really no way to get the stuff in this book, without work.

I am finding it a very rewarding trek.
That's my .02