creepy chords addendum

I was reading through Ponce's fabulous Guitar Sonata no. 3 last night and realized that in measures 39 and 40 (of the first movement) there is the same chord progression as mentioned in the post on creepy chords. Ponce is in Bb, but the chords qualities are the same: Major 7th +5 and a Minor(Major) 7th:



In this context I wouldn't say that the chords are "creepy", though they are tense. More creepy -- or at least menacing -- are the chords immediately preceding the 2 above (actually starting in measure 35: the structure is repeated):


Here we're really only dealing with one chord per measure: Ponce simply "flips" the outer voices (the 7th and root exchange places) giving him a very nice stepwise-ascending bass line.

And lest we think that these are just contemporary harmonic structures, or something born of jazz, keep in mind that this piece was written in 1927 -- and it's probably a safe bet that Ponce didn't invent this all on his own, so one might be able to trace it back at least to Debussy (maybe even Liszt???)...worthy of investigation.

intervals on the guitar ii

So now we come to the part of tuning the guitar that makes life interesting...the B string. In our last post we conquered the first four strings of the guitar (which are the same as the bass except that the bass being a bass has its strings an octave lower). Check out this diagram: I've made the B string red here to call attention to it:



Under each string is listed the number of frets that that string is distant from its neighbor to the left. If you wanna check this for accuracy consider the following: the low E and high E strings are 2 octaves apart (E2 and E4 respectively). Now look at the numbers: if we simply add up them up we get 5 + 5 + 5 + 4 + 5 = 24 frets. What's the interval corresponding to 24 frets? It's 2 x 12, which is the same as 2 octaves.

So let's take an example: what is the following interval?

We've traveled down the neck 2 frets and laterally 1: but this lateral move has brought us onto the B string. Checking our chart up above we see that that means we've moved the equivalent of 4 frets down the neck. Consequently our interval is (2 + 4 = 6 frets which we know from the last post's first chart is) a tritone. You'll see this show up in A-form dominant chords.

Here's one more:


In this case we've moved laterally 2 strings, one of which is the B string, and backwards 1 fret. The B string is 4 frets, the E is 5 and our "backwards" move is -1, and all of that adds up to 8 frets, a minor 6th.

That really wraps up our discussion. One loose end, though: we've always considered our intervals from lowest to highest, but this may not be the order in which they occur melodically. Just keep in mind that from C up to G is the exact same as from G down to C (a perfect 5th). You can always measure from the bottom up even if you want to know the interval starting from the higher note.

intervals on the guitar/bass

The last post here dealt with seeing the intervals on the piano. This time we're going to look at the intervals on the guitar/electric bass.

If we stick with a single string it's a very straightforward affair: every fret up or down is a semi-tone, aka a minor 2nd. Here's a chart that shows all of the intervals up to (and including) the octave. The left side of the vertical line -- which represents the string, any string -- is how many frets one is measuring from any starting point; to the right side is listed the corresponding interval.

In this chart m = minor, M = major, P = perfect and TT = tritone (augmented 4th/diminished 5th).

So let's take an example: say we're interested in knowing what the interval is when we play a note on the 4th fret and (on the same string) the 11th. Just subtract the lower number from the higher -- which gives us 7 -- and consult that number on the left hand of the chart. Then look at the right hand side for the interval, which in our case is a P5.

Now, an interval like the P5 on the guitar is usually much easier to play using 2 strings. The following will apply completely to the bass and almost completely to the guitar. "Almost" because one of the strings (the B string) is not tuned like the others. For now let's just stick with the first 4 strings on the guitar (E, A, D, G).

The strings are tuned in Perfect 4ths. Consulting our chart that means that if we move from one string to the next (from left to right) we're moving 5 frets. Let's call this movement lateral movement. If we moved laterally 2 strings away we would have moved 10 frets. Actually we all know this because this is how we first started tuning the guitar/bass.

So take the following example:


What is this interval? We've gone up 2 frets and over laterally one string. That lateral move is equivalent to 5 frets, so we've actually gone up in pitch 2 + 5 = 7 frets, which according to our chart way up above is a P5.

Here's another example:


Again, this isn't hard to determine. We've traveled "up" 1 fret and laterally 2 strings, each string being equal to 5 frets. So our total distance is 1 + 5 + 5 = 11. And that corresponds to a M7.

Now let's throw a little wrench in the gears. Consider this interval:


Here we actually have to employ the concept of negative numbers, which really means that we subtract instead of add. Why? Because relative to our starting position we're going in the opposite direction. Here we've moved laterally one string and down the neck (up in the diagram) 2 frets. That is numerically 5 frets + -2 (or just 5 - 2) = 3 frets. Our chart tells us that 3 frets is a minor 3rd.

Let this sink in: next time we'll tackle that B string...

intervals

The keyboard offers a nice way of visualizing intervals (and many other relationships) which is helpful if you're ever having any trouble trying to remember and internalize what they are.

In the following I've taken the basic keyboard, rotated it 90° counter-clockwise (thanks to Photoshop) so that now "up" in pitch is now "up" vertically. What we're going to do is look at all of the intervals of a C major scale as they relate to C. One cool feature of this is that if we look at the intervals ascending from C they are all either perfect or major. If we measure descending from C all of the intervals are either perfect or minor. On the keyboard I've colored blue the reference C. Since we're measuring always from C I've just indicated to the right of the note name the interval. Go ahead, click on the image...it'll enlarge.


So let's see how the keyboard can make the intervals easy to "see" by examining the minor and major 2nds. The minor 2nd is the least amount of distance you can travel on the keyboard without remaining on the same note: there are no keys in between the 2 in question (here in our example C and B). In the major 2nd there is one key in between the notes (C and D). If you know any Latin you'll recall that minor and major are comparative adjectives: they mean "smaller" and "bigger" respectively. And we can easily see why the major 2nd is the "bigger" interval: it takes up more space in terms of keys. On a guitar it will take up more frets. And acoustically the note of the major 2nd will always be a bigger number (in Hertz -- i.e. it will vibrate more times a second) than a minor 2nd related to the same reference note.

One last thing: If you examine and really absorb all of the above intervals you'll notice that almost all of the possible number of keys are covered. E.g. from C up to B is a major 7th, which is 11 keys away from C; from C down to D is a minor 7th, 10 keys. From C up to E is a major 3rd (4 keys distant) and from C down to A is a minor 3rd (3 keys distant). On our chart there is no interval that corresponds to being 6 keys away from C. This is actually a famous interval, and will complete all of the intervals within an octave, and it has several names. If you are thinking about C to F# it is called an Augmented 4th (sometimes +4 or #4) ; C up to Gb is called a Diminished 5th (sometimes b5). It is also known as a tritone because it is made up of 3 (tri) whole steps (tones). Just using the white keys of the piano this interval is found in F - B (because six keys is exactly half of the octave's 12 it is symmetric: from F up or down you'll land on a B if you travel six keys).

put a lyd on it (flat-7, that is...)

The Lydian flat-7 (aka the "Overtone" scale) is the 4th mode of the melodic minor scale. One mood that it is able to evoke (for me, at least) is one of "mechanization". Here are 3 examples, and they're all cartoon related.

The first one is called "Powerhouse" by Raymond Scott. No, it wasn't written for the cartoons, but it got used by Warner Bros. in some Bugs Bunny things, and that's where I heard it as a kid and forever have those 2 things linked in my brain. This is just the first theme (clicking on the images will enlarge them a bit):



The second one is the theme song from the Jetsons.



(The first lick above is instrumental and the theme proper -- "Meet George Jet-son" -- starts on the downbeat of the 2nd measure.)

And the third is from the Simpsons.


Of course there's more going on here than just a certain mode: the rhythm of the melody and the underlying accompaniment have a lot do with projecting that mechanized, futuristic feel. On the other hand, all things being equal (like the rhythm), this does seem to be a good mode to use for those occasions.

By the way, in improvisation one can see a rationale for the Lydian b7 (even if it weren't a mode that existed all on its own, anyway) by looking at the regular old Lydian. That is, the Lydian is used somewhat in place of the Ionian to get a raised 4th; similarly in the Mixolydian one might also desire a raised 4th...et voila! the Lydian flat-7.

Oh, yes, you can easily find all of the above tunes on youtube, etc, if they aren't a permanent part of your memory yet.

once again back at the yippie museum

Tonight The Naked Women Project will congregate and return to the Yippie Museum/Cafe. Check it out! The Yippie is located at 9 Bleecker Street (between Elizabeth and Bowery).


Tonight's offering is the usual, sans any performance art.

personnel:
T-Bone Blatt
bass
M'tazz the Great
guitar
Zebra
drums
Samu the Law
trumpet
Swirly
ewi
Father Todd
words
Matt
sax

blues, high-energy experimental jazz, funk,
psychedelic afro-pop...

the neapolitan sixth chord

The Neapolitan Sixth chord (usually N⁶) is a major triad built on the lowered 2nd degree of a major or minor scale/key. The sixth, as you'll recall from this post, meaning that the triad is in first inversion. It still functions as a II chord: that is it is usually followed by the dominant (or I⁶₄), and like any II chord it can occur in either major or minor settings.

Here's an example from Coste's Quadrille No. 2, op. 3 -- this one's in E minor, meaning that the Neapolitan chord is an F major, and since it's in first inversion it has an A as its lowest note. (click on the image to make it bigger):


And here's a nice extended usage from the end of Tárrega's Maria (Gavotte).


The key here is A minor, so the Neapolitan sixth is a B-flat major triad (with D in the bass).

Here's another example which uses the Neapolitan as a pivot chord in modulating. Because the Neapolitan is a major triad it is found in other keys diatonically. The following is from Carcassi's Etude no. 9 op. 60. It's in A minor and goes to the N⁶ chord, but instead of going on to cadence in A minor it pivots here to D minor (B-flat is the sixth degree of D minor).


(N.B. In the above Roman numeral analysis both of the VII chords are diminished and probably should have little circles next to them, too, to help call attention to that fact.)

So these are some uses of the Neapolitan: they are, in fact, widespread, and even though the above examples don't illustrate it they are used also in major keys. Also they aren't always used in the first inversion: Segovia in his Remembranza (Etude II) uses the Neapolitan in 2nd inversion (i.e. N⁶₄). Molino in his first Guitar Sonata (2nd movement) uses the Neapolitan in root position (the N/V...an F major chord going to E major, overall in the key of A major).

That appellation of Neapolitan has no significance, btw...just like the augmented sixth chords which are called Italian, German and French. More on those in a later post.