Steps Between Strings-A6 Tuning

[Steve Duke]

I've been following the music theory thread so I dove into it trying to learn. The question I have is: If you pick the strings: 4.F#,A,C#,E and then pick the strings 1.E,C#,A,F#, what is the number of steps between strings. Does it change when you reverse the order of picking?

[Mike Neer]

No, the notes are still the same distance from each other regardless of direction.

F# to A, minor 3rd
A to C#, major 3rd
C# to E, minor 3rd
E to F#, major 2nd etc.

[Steve Duke]

Thanks Mike. Sometimes this stuff makes my eyes cross. Thanks

[Danny Peters]

It depends on if you're talking about intervals alone or notes within a harmonic context.

Maybe this is a good time to talk about the "Everything equals 9" rule.

When reversing intervals:

2nds become 7ths.
3rds become 6ths.
4ths become 5ths.

Perfect stays perfect (4th/5th), majors become minors, and minors become majors.

So if you play a C and then an E, that's a major 3rd. But if you play an E and then a C, that's a minor 6th. Major became minor and 3 + 6 = 9.

If you play an F and then a G, that's a major second. If you play a G and then an F that's a minor 7th.

I once read in a guitar magazine that Ritchie Blackmore played the lead riff of "Smoke on the Water" in 4ths. Of course if he did, it would sound like crap. He was playing inverted 5ths, the difference being that when the bass player played an A, Blackmore wasn't playing an A and a D. He was playing an E and an A, which is a 4th interval by itself, but which is an inverted 5th when the bassist is playing an A.

Of course Mike can probably say all that a lot clearer and cleaner than I can.

[Steve Duke]

Danny: Now I know why my eyes are crossed but I think you said something my little peanut brain was trying to cypher. How do you guys know so much? I think I need to forget about theory and just move up 5 frets and then 2. Thanks, you all do help us that don't know this stuff out a lot and I appreciate your responces.

[Mike Harris]

Danny,

I don't agree with your Smoke on the Water example. E up to A ( or A down to E) is a fourth independent of whether or not there is a lower (or higher) note being played.

[Mike Neer]

....
So if you play a C and then an E, that's a major 3rd. But if you play an E and then a C, that's a minor 6th. Major became minor and 3 + 6 = 9.

If you play an F and then a G, that's a major second. If you play a G and then an F that's a minor 7th.
....

I think Steve was talking specifically about the intervals between adjacent strings.

Your example here might be confusing to Steve because you didn't specify that "if you play an E and then a C, that's a minor 6th" means that you are playing C higher in pitch or above the E. Again, the same with the F and G example--F to G is a major second--G back to the F below it is still a major second. G to the F above it is a minor 7th.

[Steve Duke]

Mike: My question was based on a coment I saw that said "Buddy E" looked at the steel when he practiced as the intervals between the strings. It got me to thinking, if you know the number of steps between strings you could move up and down the neck with some sort of logic, one string related to another. Then I got to wondering if you played them in reverse order would the concept be the same. I think I was thinking about what Danny was talking about. If you play the notes in a different order they don't go together. So,am I correct Mike, you and Danny are talking about two different things?

[Mike Neer]

Yes, you are correct. I was referring strictly to the intervals between strings in a tuning.

[Steve Duke]

Thanks Mike. Do you have anything in A6. I didn't see it on your web-site. I know I could take some formal instruction but I tried that in high school. Because I couldn't tell the teacher how many #'s there were in a given scale he said I was wasting his time and mine. That's after two weeks in class. Spent the rest of the year writing a report on composers of classical music. I've got books, CD's, TAB etc. I'm just looking for a compass not a road map. Thanks for help guys.

[Danny Peters]

Danny,

I don't agree with your Smoke on the Water example. E up to A ( or A down to E) is a fourth independent of whether or not there is a lower (or higher) note being played.

Sorry for the confusion. I didn't mean playing an E and then an A. I meant playing them at the same time. The person was claiming it was a 4th, but as the overall sound being playing is an A chord, he's not playing a 4th interval, which would be an A and a D. Instead he's playing a root-fifth diad.

You're correct, of course, that if he played an E and then moved up five frets he'd be playing a 4th above the E.

[J D Sauser]

Thanks Mike. Sometimes this stuff makes my eyes cross. Thanks

I think, that as our instrument represents music in a very graphical manner, one could consider investigating what's going on between those "notes" in a similarly graphical way.

I'd suggest physically making three (3) rulers:

#1)

[tab]
C C# D D# E F F# G G# A Bb B C C# D D# E F F# G G# A Bb B C C# D D# E F F#
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [/tab]

As you can see, we are graphically showing each of the 12 half steps as equal value intervals (same distance).

#2)

[tab]| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
1 | 2 | 3 4 | 5 | 6 | 7 1 | 2 | 3 4 | 5 | 6 | 7 1 | 2 | 3 4 |
b2 m3 sus/b5 aug b7 b2 m3 sus/b5 aug b7 b2 m3 sus/b5
[/tab]

Now that you have your two rulers (physically, printed, drawn and cut), you can SLIDE ruler #2 BELLOW ruler #1. You can start (positioning "1") at ANY note or semi-tone and see what degree the others become relative to the "1": flat second, second, minor third, third, fourth... etc.
We are now effectively transposing keys and/or scales.
Obviously, the Do, Re, Mi, Fa, Sol... positions became 1, 2, 3, 4, 5... PLUS the distances (intervals) between them become more graphically obvious.... which in turn relates to your fret board (only that the fret board is obviously tapered using an algorithm).



Lets take this a little further and build HELPER ruler(s) #3a, #3b and #3c (broken up in "a", "b" & "c" for lack of space to show all intervals in ONE ruler):

#3a)

[tab]| | : | : : | : : : | : : : : | : : : : : | : : : : : : |
|1/2| full | minor 3rd | 3rd | 4th | suspended 4th | 5th |
|b2 | second| b3/m3/-3 | Major 3rd |4th (oppos. to 5th)|sus 4th/b5th (1/2 oct.)| 5th (opposite to 4th) |
| | : | : : | : : : | : : : : | : : : : : | : : : : : : |[/tab]

#3b)

[tab]| : : : : : : : | : : : : : : : : | : : : : : : : : : |
| augmented (5th) | 6th | b7th |
| #5th/b6th (opposite to M3rd) | 6th (opposite to m3rd)/"bb7th" | "dominant 7th" (opposite to 2nd) |
| : : : : : : : | : : : : : : : : | : : : : : : : : : |[/tab]

#3c)

[tab]| : : : : : : : : : : | : : : : : : : : : : : |
| M7th | OCTAVE |
| Major 7th (opposite to m2nd (half note) | 1 or 8th (totaling 12 semi-tones) |
| : : : : : : : : : : | : : : : : : : : : : : |[/tab]

You can SLIDE and compare the #3 rulers against BOTH, the #1 and #2 rulers and discover the intervals in between ALL numbers of notes (#1) or degrees (#2).


What one may additionally try, is to gain awareness of what intervals (besides the evident number of half-note-intervals) larger intervals may be constructed of.
E. g: A minor 3rd consists of 3three half-note intervals OR a full note interval + a half note interval.
A major 3rd of 4 half note intervals, OR 2 full note intervals, or a minor 3rd + a half note interval.

Obviously, the larger the analyzed intervals become, the more the possibilities of interval groups inside... which is synonymous of discovering intervals not only between adjacent strings but also of wider grips.
Similarly, one can stumble across interesting facts like:
An octave, can be broken up in 3 equal M3rd intervals, or 4 equal minor 3rd intervals (1, m3, sus4/b5, 6th, 1). An octave is also made up of two sus 4th/b5th intervals... etc.

This ought not only to show that ALL 6th-chords -to swing back to the original question- have the exact SAME interval build up (obviously, TUNINGS may look different as they may not start at the same degree and may or may not include ALL the 4 notes of a 6th-chord in a chronological order) but also explain the very foundations of how notes, degrees and interval follow an ever repeating scheme.

One may also seem well served to seek to gain awareness of the principles of what Danny Peters suggested and and investigate the details:

...

Maybe this is a good time to talk about the "Everything equals 9" rule.

When reversing intervals:

2nds become 7ths.
3rds become 6ths.
4ths become 5ths.
...

Evidently, what makes most our eyes cross, is the fact that while everything repeats 12 times over in the exact same way, even the numeral system is based on the concept of the one Major scale (Do, Re, Mi... / C, D, E... en hence 1, 2, 3...) which however an irregular interval progression (half note intervals between degrees M3 to 4 and M7 to 1/8 vs. full note intervals between the rest of degrees).
Therefore, I would theorize that it may behoove at least some of us to consider the chromatic scale FIRST (12 equal distant semi tones) and look at larger intervals as multiples of these half-note-intervals (Eg: a minor 3rd consisting of 3 half note intervals, a 6th of 9 half note intervals... etc.) in order better understand, organize and handle the issue at hand. Really, the goal may be to learn to associate heard distances (intervals) to visual distances back and forth. We move our bar along strings or over to other strings (which are musical distances apart), visually, based on what we hear or want to hear.


The next step obviously, once one has understood this and studied it so to have made it second nature, is to learn to "HEAR" and assign the sounds of these intervals, as sequences (note for note), harmonies and chords (two or more notes ringing simultaneously/at the same time) and as progressions (sequences of chords) and also explore on memorize the tuning and thus layout of intervals available on the instrument's "neck.

I hope this may prove of some help to some.

... J-D.

[Steve Duke]

J D: You are suggesting constructing a slide rule (which I still have two Picketts') with TAB #1&#2? My question is TAB#3a,b,c, is that one rule or 3 separate rules? If separate rules then are they stacked as a log scale on a slide rule? If stacked, do they operate off TAB#1 or TAB#2? Can I apply the information in Mike, Mike & Danny's responses to one or more of these rulers? Thanks for your help J D.

[J D Sauser]

J D: You are suggesting constructing a slide rule (which I still have two Picketts') with TAB #1&#2? My question is TAB#3a,b,c, is that one rule or 3 separate rules? If separate rules then are they stacked as a log scale on a slide rule? If stacked, do they operate off TAB#1 or TAB#2? Can I apply the information in Mike, Mike & Danny's responses to one or more of these rulers? Thanks for your help J D.

My computer just broke down and I am writing from a net book. I have just come to realize that these "tabs" can be affected by the screen resolution.
I HOPE you DO see them as intended.

Ruler #1 depicts the major scale in chromatic (half note) increments. The equal distant markers should face down. THAT's one INDEPENDENT ruler.

Ruler #2 depicts the same major scale in chromatic (half note) increments, but this time using numbers instead of names. It is a secon INDEPENDENT ruler.
It's equal distant markers should face up, so that once you have #1 and #2 physically built, you can slide #2 back and forth bellow #1.
This should help you explore the same scale in different keys (all 12).

Ruler group #3 are just a set of intervals, intended to be understood like gauges. There is NO importance of the which interval sits next to the other.
You could cut a ruler for EACH interval independently... like they'd be independent gauges.
As these have their marker facing BOTH to the top and to the bottom, you can use them against EITHER, ruler #1 or #2.
It is the sole intent of the #3 rulers (in one or sections) to learn to recognize common (all) intervals up to an octave along rulers #1 and #2 starting at ANY note or half note of the scale.

I should get a new computer next week, and I will try to remember to make up a PDF (downloadable) version of these rulers, if there is interest.


Thanks! ... J-D.

[Alan Brookes]

It's the intervals between the strings rather than their pitch which separates one tuning from another. For instance, if you took the C6 tuning and tuned it down to A6, all your licks would still work ...they'd just be higher up the neck.

The C6 tuning and the open G tuning used on Dobros for bluegrass only differ by the additional string. Otherwise the intervals are the same.

[Steve Duke]

Alan: or anybody else: A6 tuning: Open strings 1,2 & 3 (A Chord). Can I play the notes in any combination at the 5th and 7th frets on these three strings and be musically correct? I'm trying to find a method to my madness.

[Joe Snow]

JD, I'm interested in pdf's of your rulers.

[J D Sauser]

JD, I'm interested in pdf's of your rulers.

Thanks for your interest.
But please bear with me, as I said, I just lost my work lap top and am presently playing around with my daughter's NetBook(let). I am flying into Florida next week and hopefully find a brand new computer I ordered today waiting there for me... I'll work something nice up the next week.

... J-D.

[Steve Duke]

J D: Looking forward to your PDF's of the rulers.Be safe.

[J D Sauser]

Sorry for the delay.
I just finished a version for those interested to try.
It's in PDF (so it should be paper format proof (Letter/A4) and should be downloadable here:

http://pdfcast.org/pdf/musical-interval-rulers
scroll down and hit the big "DOWNLOAD" button.

You will need scissors or even better, a razor blade and metal ruler to cut out the 5 rulers.

Rulers #1) & 2) may help experiment with the conversion from name notes to the number system (degrees, as it is called in traditional theory).
One can slide the numeric ruler against the name ruler, setting "1" against ANY of the 12 semitones available.

Then next 3 rulers are numeric and break up the interval pairs, helping to better understand and visualize larger intervals in a chromatic manner (your key board IS chromatic, frets come in semi tones!).
These 3 rulers can be used against both, rulers #1) & 2) as well as against each other... the goal being, to discover what intervals a larger interval can be made/seen of (some with repetitive patterns are hinted already).

Let me know if you see mistakes... it's not an easy task to make these (especially with the upside down lettering on some).

... J-D.

[Warren Pederson]

The C6 tuning and the open G tuning used on Dobros for bluegrass only differ by the additional string. Otherwise the intervals are the same.

Alan, could you explain this a little? I'm having trouble seeing this.

[J D Sauser]

The intervals found in a straight up C6th are the same as in any other 6th chord (A6th, Bb6th, B6th etc.), the pitch only changes and for the player, effectively the position of adjacent intervals moves up or down across the strings from a higher pitched tuning to a lower and vice versa.
Comparing a plain major tuning (Eg: "G") to a slightly more complex one (Eg: "C6th"), while the later will have the basic 1, 4, 5 degrees just like any other "plain" major chord (lacking additional tensions) may obviously somewhat cloud the thinking described above.

Personally, I tend to be more interested into the layout (chronology) of intervals between the strings.
I think it "says" more about a tuning that just his name chord, especially once you are beyond playing the I-chord on a fret, the IV-chord 5 frets above it and the V-chord another 2 frets further. Obviously, good Dobroists don't let that detract them from playing way beyond that, by using slants, pulls and open stings.
The more "complex" a base tuning, the more chords it contains in the same fret (the tuning could be called many different names, depending on which string is considered the root).

13th players don't just have a big fat swinging 13th chord but a larger array of CLOSE intervals across their tuning from the 9th, 6th and even b7th degrees thrown in between the basic 1, 3, 5.

... J-D.

[Alan Brookes]

The C6 tuning and the open G tuning used on Dobros for bluegrass only differ by the additional string. Otherwise the intervals are the same.

Alan, could you explain this a little? I'm having trouble seeing this.

Certainly.
C6 tuning is C E G A C E G
The intervals between the strings are 4 3 2 3 4 3.
G tuning is G B D G B D. The intervals between the strings are 4 3 5 4 3.
When you compare the intervals, in the G tuning there's a 5 semitone jump between the 4th and 3rd strings, whereas in the C6 tuning that's split between a 2 semitone and 3 semitone jump. In other words there's an extra string in there.

Looking at it another way...
If you look at the C6 tuning at the 7th fret, it's
G B D E G B D.
Compare that to G tuning..
G B D G B D.
There's an extra E string in there.

What that means is that anything you can play in G tuning you can play exactly the same in C6 tuning if you ignore the 4th string.

[Warren Pederson]

Thanks Alan, for your email too. I'm struggling some getting used to the concept, but it is enlightening.