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.

the beat makes a difference

The idea of a beat (or a "tactus") -- that is some regularly recurring accent that sets up a meter -- is interesting. Without such an accent or focal point there's no way of telling where the downbeat is needless to say, which means, consequently that determining where any given rhythmic pattern starts and ends is made impossible. Take the following rhythm which recurs ad infinitum:

Without a downbeat there's no real way to distinguish what the rhythm really is. For instance any of the 3 notes could be thought of as beginning the pattern:

Which would produce the following (the gray area encloses the same notes which look different due to beaming).
Actually one good benefit of this is that if you can play the first one you can play all of them (for me #2 was always very, very hard to play...it's not!).

some creepy chords

I've always associated the minor-major 7th chord with jazz tunes, South American (mainly Brazilian) music and cliff-hanger moments in James Bond movies and 70s TV shows like Charlie's Angels. But I just watched The Machinist (2004) a Spanish made film with Christian Bale and Jennifer Jason Leigh and it turns out that they can be used to convey creepiness, too (which I guess, after all, is an extension of tension). The moment I'm talking about here occurs at ca. 40min 37sec.


Note also that the 2nd "creepy" chord (1st chord in the 2nd measure) is an augmented triad with a major 7th. (You could also look at this as a C/Ab, which could easily come from the Harmonic Major mode.) From the first chord to this one the only changing part is the middle two voices: a major third that rises a half step. The last chord in that measure is also an augmented triad: really just the "upper" part of the Ab min/Maj7th.

Other elements which add to the creepiness (which seem to be universal): a slow tempo -- somewhere around a quarter note equaling something in the 50s -- and a lot of reverb.

Music by Roque Baños.

yankee rose + heaven tonight

Two different tunes from the 80s when guitar was king, by kings of the guitar: David Lee Roth's Yankee Rose with Steve Vai handling the guitar chores and Yngwie J. Malmsteen's Heaven Tonight. Though done by masters of technique the songs (and videos) are in that vein of true rock 'n roll fun. And who wouldn't rejoice at playing these tunes to thousands of fans?

Yankee Rose
(1986)




Heaven Tonight
(1988)

Actually Steve and Yngwie represent 2 different approaches to shredding, and here are representative short licks from the above tunes. Steve seems to like sliding around the neck, especially when arpeggiating. The picking isn't so rough but the shfting is in this one (this occurs at 2:38 in the video -- subtract out 1:41 if you're listening to some form of the audio):


And Yngwie -- Mr. "Neo-Classical" -- is all about sweeping arpeggios and alternate picking, the latter of which is featured here in a very nice harmonic minor passage (at 0:36):



N.B. I've transcribed this at pitch -- Yngwie (with band in tow) tunes down a half-step, so he's really playing in F# minor, though it sounds in F minor.

the naked women project at abc no-rio

The Naked Women Project will be kicking off the annual ABC No-Rio Gala fundraiser event tonight starting at 6pm. $5 gets you in (but they'll take more: remember this is to help them raise money so that they can stay open all year and have great, awesome music every Sunday).

The lineup:

T-bone
bass
The Law
trumpet
Swirly
electronic winds
M'tazz
guitar
Polashek
sax
Father Todd
'bone + words
Thabit
drums

ABC No-Rio is located at 156 Rivington Street (between Suffolk and Clinton Streets) on the Lower East Side. The F/J/M/Z station at Essex-Delancey is just 2 blocks away.

new york city pop band live again

A trio incarnation of the New York City Pop Band will be supplying some music for the opening reception of the art show "Dance, Sing and Eat" by Yori Hatakeyama and Sawaka Norii. That's at New Century Artists, Inc which is located at 530 West 25th Street, Suite 406. We start at 4pm, the opening proper at 3pm (and goes until 6pm).

The trio is:
Charles M'tazz Ramsey on guitar,
Tom T-bone Blatt on bass,
Nick Thabit on drums.

duo fortuna

I'm really happy that I'm back with Duo Fortuna, a piano guitar duo in which I have the great pleasure of playing with Leslie Purcell Upchurch. I think of Electric Bartok, maybe with some more Eastern elements thrown in.

It's rare for me when this amount of rapport just happens. The pieces are (except for one or 2 examples) completely imrpvoised, but generally with some parameter(s) in place. E.g. "chromatics" where the dominant idea is chromatic, half-step movement. Or "Hirajoshi" where we stick to that Japanese scale (actually it's a koto tuning, but roughly a scale).

Check out the myspace for some audio.

the naked women project at the tank

The Naked Women Project take to the Tank's stage tonight at 9:30 pm. Tickets are $7. There might be a mad, crazed priest out front ere the show's beginning, so don't come too late.


As always we'll be presenting a wonderful exciting blend of high-energy experimental jazz, free improvisation, afro-pop, psychedelia and spoken word.

The personnel:

T-Bone
bass
Big Matt
sax
The Law
trumpet
M'tazz
guitar
The Mad Priest
'bone + spoken word
Swirly
wind synths

Zebra

drums

The Tank is located at 354 West 45th Street between 8th and 9th Avenues.

sine waves graphically

The sine wave is a "pure" tone, i.e. it is only a fundamental with no other overtones. All other sounds (musical or otherwise) are composites of sines (sinusoids according to Benade). Since doing the post on FirstSounds I became interested in how sines and other sounds looked so I started systematically doing some recordings with sine waves from a software synth (the Dreamstation).

The following images are from the editing software Cakewalk. Basically these pictures are telling us how the ear moves back and forth in response to sound waves. The interesting thing, of course, is how in compound sounds the ear is able to perceive more than one tone (or in other cases how it assembles one tone from many partials...more on that in a later post).

The first is of an A4 (the A above middle C).

Then a C5#.

And an E5 (now a major 10th above middle C).

Next are composites...First the major 3rd resulting from the A and C#.

Then the minor 3rd of C# and E.

Then the perfect 5th resulting from the A and E.

And finally the whole A major triad.


And one other interesting thing to note: these are time - amplitude graphs with the x-axis representing time and the y-axis amplitude (the middle horizontal line indicates the point where there is no sound, where the eardrum is in between being moved in and out). These images are small so it isn't evident in all of them, but by comparing the last one (the complete triad) with that of any of the single tones it is extremely easy to see that the triad is louder, exactly what one would expect (more sound = more volume).