the yearly roundup

Hard to believe but another year is looming large on the horizon. That means it's time for the yearly roundup of good stuff that I've encountered music-wise. And by encountered I also mean re-encountered, too. This stuff isn't necessarily particular to 2010, that's just when it happened my way.

Books

David Toop's Sinister Resonance. Toop does it again. This book is special for me because it has come along right at a time when I've been thinking about the peripheries of music and sound more generally as well as what's going on when we hear/perceive such.

Wallace Berry's Structural Functions in Music. Actually I'm not sure where I come down with this book. The author does penetrate deeply. I'd be interested if the book were about music and not just a small segment -- though maybe people could start writing appendices of sorts applying Berry to Indian music, R&B and free jazz, etc.

Recordings

Carolyn Hove, Ascending to Superlatives (yeah, I'm not thrilled about the title, either, but there it is...) Great English horn album starting off with a Castelnuovo-Tedesco piece entitled Eclogues (for English horn, flute and guitar) which is fantastic. All the works are terrific. This record will make you believe in 20th century music (if your faith has indeed ebbed). Also, though I went to CCM I had no idea the Gerhard Samuel was also a composer...

Not entirely unrelated is L'ensemble Pyramide's recording of Migot chamber works featuring flute, clarinet, harp, bassoon, etc. Great pieces! I'm a huge Migot fan and if you've never heard of him just go ahead and jump in with this one. The works are modal and very, well, French. If you dig on the likes of Poulenc and Dutilleux you'll like this one. There's a wikipedia thang about Migot here.

Gentle Giant's Octopus. My favorite prog album to date. Very diverse, excellent tunes.

Bill Emerson's Gold Plated Banjo. A good friend of mine always turns me onto what he considers the "best of", any genre. For bluegrass his pick is this one, and I have to agree. It's so filled with gladness that it'll make you happy that you're alive -- it'll at least put a big smile on your face!

The B-52s first album. I heard it when I was in 6th grade and loved it. I listened to it again about a month and a half ago and I still love it.

Other albums heard a long time ago and re-enjoyed: Vangelis' Albedo 0.39. That's right albedo, the reflectivity of an object, 1.00 being perfect, 0.39 being roughly the Earth's. V does all of the instruments and the tune Main Sequence is spot-on fusion (with even a great little blues lick near the end!). Of course the opening tune is great (Pulstar) as is the tune Alpha, both of which were in Carl Sagan's Cosmos.

Susanne Schoeppe's Ponce, Moreno, Dolezel & Castillo: Guitar Recital (yeah, technically any recording with the word "recital" in the title should entitle the maker(s) to a public torturing...pretend the album is called Diario, I guess). Susanne needs to be thanked, sincerely, for playing (and playing beautifully) Torroba's Sonata Fantasia. It's an absolutely exquisite work and hopefully will only grow in popularity.

Zombies: Odessey and Oracle.

Video

Scott Henderson: Jazz-Rock Mastery. This is really 2 videos in one: the first is about scale choices for given common chords (maj7, min7, min7b5, dom7 and altered dom7s -- Scott details playing both inside and outside); the second concerns phrasing and is really a breath of fresh air.

Various

The You Rock Guitar. I picked one up back at the beginning of November. A really fabulous midi controller. FINALLY a midi controller that has what I (we) really want: a midi out! No need for a 13 pin cable which then gets converted to midi then sent to the midi out. This is very inexpensive and easy to play. It's not a guitar, so there are some compromises: pulling off to open strings doesn't work, and the strings which are picked/plucked are all the same size which means that your hand doesn't get any clues as to where it is by string size. It has some onboard sounds but I go right into a Yamaha TX-7. The best feature: it doesn't EVER go out of tune...

the enigmatic scale and even some more extended triads

I made a point in the posts about extended triads of keeping only to diminished, perfect and augmented fifths because those were the only ones I could imagine happening in scales. Not so! I recently looked at the enigmatic scale and found that we need to be more inclusive still. Here is the scale along with its triads:


As you can see both the II and V chords go beyond the parameters which I naively set. Since in this scale there are three minor seconds/half steps in a row (A#-B-C-Db) we end up with doubly diminished and doubly augmented fifths. If we consider that each fifth can have four types of 3rd (diminished, minor, major and augmented) then we will end up with 20 (count them twenty) triad types! (As far as symbols go I just simply stacked either plus signs or minus signs to indicate doubly diminished.)

Once again: give the triads a go...the whole point is that hopefully they aid you in expanding your vocabulary.

By the way, check out the wikipedia article on this scale here. You can discover its history (which includes Verdi) and that it actually has a different descending form.

See also extended triads iii, extended triads ii, extended triads i, basic triad types.

puer natus est nobis

Yes, today is Christmas and so accordingly here is offered a very old Christmas song: the Introitus Puer natus est nobis. You can google it yourself, of course, but the first one here has the plainchant notation as found in the Liber usualis.

But this has organ accompaniment (which seems to be the way it's done these days...I spent several days at the Abbey of Gethsemani and they did all of their plainchant not only in English but with organ also. I guess it does help the pitch not to deviate...) so the following one may be the way you're more used to hearing it:

Also this selection is found on In Dulci Jubilo's record Salve Feste Dies, and it's worth checking out because of their approach to the rhythm (the rhythmic values in "Gregorian" chant are highly controversial: it's known that there were different rhythmic values but what's not known is what they were).

In terra pax, let's hope...

the neapolitan minor

A plug for one of my favorite scales. You can think of this as a Phrygian with a sharp 7 (i.e. a major 7th) or you can think of it as a harmonic minor with a flat 2. Here it is built on C:


Harmonically there are some interesting chords. Look at the V7 chord: it's a free-roaming dominant 7 b5 chord. Look at it in 2nd inversion...that's right, it's a French augmented sixth chord (which is also analyzable as a Fr 4/3). Here is the G7b5 and the Fr+6 with its common resolution (the +6 opening up to a P8):


There are two extended triads: the V (a maj-dim, aka the Italian augmented 6th in root position) and the VII (dim3-dim).

As for the modes they're really interesting:

[mode i: phrygian #7]
mode ii: lydian #6
mode iii: mixolydian #5 (mixolydian augmented)
mode iv: aeolian #4 (lydian-aeolian)
mode v: locrian #3
mode vi: ionian #2
mode vii: (dorian #1) locrian bb3, bb7

And here's an actual use of the aeolian #4 found in measure 11 of Manuel Ponce's fantastic Sonata III:



And for you guitarists here is the scale in five positions comparable to the five positions of major, melodic minor and harmonic minor:



Learn it, love it, live it...

extended triad types iii

In this post we're going to look at extended triads in the way in which some might believe we should have done at the beginning: analytically or simply mathematically. The reason we didn't begin this way is because I wanted to demonstrate that there are real (and not just conceptual/theoretical) reasons why one needs the idea of extended triads, viz. the fact that they are produced naturally in certain scales.

So let's consider triads this way: chords consisting of a root, 3rd and 5th (as opposed to a harmonic structure that has just any 3 tones). As for 3rds we will allow diminished, minor, major and augmented; and for 5ths we'll allow diminished, perfect and augmented. The reason for "will allow" is that these intervals are all found naturally occurring in scales (such as the whole-half diminished and ionian flat-2, etc). We aren't going to examine triads which are comprised of a quadruply diminished 3rd and a quintuply augmented 5th (which triad would produce a third lower than the root and the like -- this could be interesting in a modern physics/mathematical kind of way but it's not extremely useful to us at present.

So based on our options of intervals we can simplify the triad families based on the 5th: there are only three kinds (diminished, perfect and augmented). Each family will have 4 types of third (diminished, minor, major and augmented). You won't have to resort to your calculator to figure, then, that there are, all in all, 12 triads. Here's a 1000 words:


The 3rds in blue denote that that chord is a basic triad type (diminished, minor, major or augmented) -- for example, the min 3rd in the diminished 5th family is blue because that chord is your garden variety diminished triad. And another 1000 words follow here with actual instantiations of all of the chord types:



Finally some issues of nomenclature. A M3P5 chord is simply called a major chord, so all chords containing a major or minor 3rd could be likewise appelled (a major diminished chord for M3dim5). Also since perfect 5ths are somewhat privileged we could drop that part of the name when it occurs: a diminished 3rd chord, an augmented 3rd chord.

Lastly -- and as promised -- let's look at the °3dim chord again. It has another name and is actually an extremely common chord in common practice "classical" music. Here it is in first inversion, showing its outer voice resolution:



Yes, that's right! An It+6 chord! For our purposes, then, the It+6 chord in root position is simply an It°3 chord. More on augmented 6th chords to come.

Play through these chords: some of these triads will undoubtedly be (or become) sonically interesting to you...

see also extended triads i, extended triads ii, basic triads

extended triad types ii

In this post we're going to examine the whole-half diminished scale. It is, like the whole tone scale, a symmetric arrangement of tones, and its name is the formula of the arrangement (i.e. a whole tone followed by a half tone followed by a whole tone...). This scale is different from many, many others in that it has more than 7 tones, in fact it is octatonic (8 toned). Here it is along with its triads:



Since it's composed of more than 7 tones some problems of nomenclature occur. For instance, at some point a scale tone (degree) has to be duplicated. Above we've made it F and F#, though it could've been D and D# (which would've produced an E#, then F#), etc. A massive ramification of this is that there is not a unique, one-to-one correspondence between scale degrees and triads -- some triads will manifest in 2 different forms. Above it is II, IV and VII (because they each contain F, which scale degree also exists as F#).

In this scale there are two triads which are "extended": the I and III. But these extended triads are a bit different from the ones which occurred in the previous post, and that's because they are enharmonically equivalent to basic triads. Put another way, the first two extended triads we encountered have no sonic equivalents, whereas these two that hail from the whole-half diminished scale do. Here they are:



The I chord sounds like a 1st inversion Ab major triad; the III chord sounds like a 2nd inversion G# minor one. But even though this is the case it's still important to be able to analyze these triads as extended types, if only for consistency's sake (most likely from a performer's point of view). But there is precedent for this sort of thing. Consider the Fr+6 chord: it is enharmonically equivalent to a dominant 7th chord, but its function is quite different in common practice harmony (that is its resolution is different from that of a dominant 7th chord).

So, back to the chords at hand: the I chord can be called a minor augmented (min Aug) and the III chord a diminished 3rd augmented (°3 Aug).

extended triad types

Over the next 3 posts we're going to be discussing extended triad types, i.e. triads in addition to the 4 basic types of major, minor, augmented and diminished (which topic was covered in this post). Perhaps unexpectedly this investigation will lead us into taking up the topic of augmented 6th chords.

If we only concern ourselves with the major and minor scales (both melodic and harmonic), and even if we throw in the harmonic major as well, we'll never encounter any triads beyond the 4 basic ones already mentioned. But this isn't always the case. Take for example the Double Harmonic scale and the triads which form from the scale degrees:


There are major triads (I and II), minor triads (III and IV) and augmented triads (VI) here, but look at the V and VII chords. They don't fit the pattern of the 4 basic types. The issue is that there isn't any ready-made term for either of these, so let's simply name them according to their intervals (which are some form of 3rd and 5th). The V chord is composed of a major 3rd and a diminished 5th, so we could name it a major diminished triad. Likewise the VII chord reveals a structure of a diminished 3rd and a diminished 5th: let's nominate this one a diminished 3rd diminished. And in abbreviated format: maj dim (V) and °3 dim (VII). Here's how they look built on C:



Why are there these different triad types lurking in this scale? Because scale degress 7, 1 and 2 are 2 consecutive minor 2nd intervals, which adds up to a diminished 3rd (and not a full minor 3rd found in the major and minor scales). This accounts for the double flat in the °3 dim triad built on C.

So now armed with this new knowledge you can analyze all of the following scales and you'll find that they contain the 4 basic triad types plus these 2 new "extended" triads: Neapolitan Major, Neapolitan Minor, Double Harmonic (as above), Ionian flat-2 and the Whole Tone Leading. Next time we're going to delve into the whole-half diminished scale and find even more triad types...

noh -- live 100% improvised

Yes, back at Goodbye Blue Monday on Wednesday 1 December at 9pm:

NOH the 100% improvised spoken word free rock/blues band.

The lineup:

Mark Zebra Warshow: drums

Jesse Martin: bass

Charles Ramsey: guitar

Raymond Todd: spoken/vocals

That's at 1087 Broadway in Bushwick, Brooklyn, NYC...J train to Kosciuszko...FREE!

hidden patterns: the harmonic major

There are different ways of learning modes: one way is to look at (say) a C major scale and then see that it contains the D dorian, E phrygian, F lydian and so on. Another way to approach learning modes would be to keep the same tonic: C ionian, C dorian, C phrygian, etc. In this method we're actually moving through many (7 in fact) different keys: C major, Bb major, Ab major... If we do this with the harmonic minor modes something very interesting happens...but first let's take a look at the major and then melodic minor scales.

This table shows the major scale modes starting on C as well as the parent mode whence they come:



If we examine the roots of the parent scales we'll notice that -- when rearranged -- they form an A-flat major scale: Ab Bb C Db Eb F G.

Let's do the same thing with the melodic minor modes:


In this case the roots of the parent scales form a B-flat melodic minor scale (Bb C Db Eb F G A).

Up to this point there isn't much surprising: the roots of the parent scales both spell out major and melodic minor scales. However this situation changes when we subject the harmonic minor modes to the same investigation:


Here the roots of the parent scales form a (drum roll please...) harmonic major scale! F harmonic major to be exact: F G A Bb C Db E. And in a way this gives a nice rationale for the harmonic major: even if we'd never heard of nor conceived of it there it is, buried in the harmonic minor in a sense. File this one under how wonderously strange nature is...

See also: modes

nor gloom of night...

This Sunday, 24 October at 7 pm I'll be playing with Nor Gloom of Night at ABC No-Rio.

The show is spoken word with musical accompaniment: the music being very atmospheric and ethereal (think sound: definitely no standard harmonic progressions will be heard). I've been lax about posting gigs since the summer but Nor Gloom did do one gig about a month ago: there are no rehearsals and the lineup changes and as a result predicting the outcome of a gig is not an easy chore...that's the fun.

ABC No-Rio is located at 156 Rivington Street.

exploring modes via pentatonics

OK, so if you've been reading this blog I understand that at this point you're rolling your eyes and emitting some form of loud "arrgh!" at the thought of yet another post dealing with pentatonic scales. Well, that's just how cool and useful I think they are, so here goes.

Let's say you have a Dmin7 chord that you're going to play over (or even write a melody over, etc). By using pentatonic scales you can elicit the colors of certain modes, and can do so by using your own and perhaps already copious supply of pentatonic licks.

The pentatonics that can easily be used are the following: start with the pentatonic with with the same root, in this case D minor. We can use the pentatonics which are 2 "clicks" both clock and counter-clockwise on the circle of fifths:

C | G | D | A | E

Each pentatonic scale, when combined with the underlying chord, corresponds to one or more modes. For example, if we take an E minor pentatonic scale (e, g, a, b, d) and play that over a Dmin7 chord (d, f, a, c) our resulting conglomeration of tones will be:

d, e, f, g, a, b, c

aka the dorian mode.

Starting with the pentatonic 2 clicks to the left and moving to the right (or clockwise on the circle of fifths) we can generalize the mode relationships as:


The reason that there can be more than one mode hinted at is because not all 7 tones of a scale are present in those situations. E.g. if we play a D minor pentatonic (d, f, g, a, c) over a Dmin7 chord (d, f, a, c) we only have five tones:

d, f, g, a, c

and without knowing what the 2nd (some kinda e) and 6th (some kinda b) are we can't tell what the mode is with complete precision. For instance, if there were an eb and a b natural we would end up with a complete dorian flat-2 (or flat-9), the second mode of the c melodic minor scale.

That is how the minor pentatonics will work over minor chords. In some future post we'll explore how they work over major chords.

what chord is it?

Let's assume that you've played some sort of harmonic structure and you want to know (for some reason or another) what's the name of this thing I just played? We've discussed before that context has a lot to do with a chord's naming, but for now let's say that we're just dealing with one chord that sounds really cool and we need some kind of name for it. Here's a method which can get you in the game:

1. Write out all the chord tones and remove any duplicated tones.

2. See if there are any triads present (might have to look enharmonically). If no triads
go to step 4.
(a) If there's just one triad then this is likely your chord: go to step 3.
(b) If there is more than one triad pick the one that makes sense to you and go to step 3.

3. If there are any remaining tones they will relate in one of three ways, as:
(a) extensions
(b) additions
(c) suspensions

4. If no triads:
(a) Is one implied (e.g. a major 3rd could imply a major triad)
(b) Is it a power chord?
(c) Is it a stacked interval (stacked 5ths)
(d) Is it a tone cluster?
(e) Does the harmonic structure correspond to/imply any mode?

Needless to say for the above to work we have to have some sort of knowledge of basic triads and extensions, etc. Let's take a few examples and see what happens.

Example 1: f, g, a, c#.
Are there triads present? Yes: f, a, c# is an augmented triad.
Any remaining tones? Yes: g. This relates to f as a 2nd or 9th. Since there's no 7th present (which would be some sort of e) let's call this an F aug add 9 (or F+5 add 9).

Also example 1 can be viewed like this: f might actually be e# enharmonically spelled. That means we would have an A augmented triad: a, c#, e# (f). The remaining g is simply the 7th, so the chord could also be named: A7+5. (This kind of enharmonic spelling is quite common in music, classical or otherwise as music is really a guide for performers and not analyzers.)

Example 2: f#, g, b. Any triads? No. Any triad implied? Yes: g and b can easily give the sense of a G major triad (the perfect 5th is not needed for the ear to hear the "complete" chord). Then f# is simply the 7th which gives us a Gmaj7.

Example 3: bb, a, c, b. Again, no triads, buuut...a and c are enough for an A minor triad. The remaining bs are 9ths: we could call this structure A min add 9 add b9. Clearly, though, this is a form of a chord cluster, which will never yield very willingly to a nomenclature born of tonal music.

Also these 2 rules will help from time to time:
(1) If you ever have both a major 3rd and a minor 3rd treat the major 3rd as the actual 3rd and the minor 3rd as a(n enharmonically epelled) sharp 9th. E.g. the tones e, g#, b, d, g can be viewed as an E7#9 (g = f double sharp).
(2) Similarly in cases where you have a perfect 5th and a diminished 5th the perfect 5th is the real fifth and the diminished 5th can be seen as a sharp 11: c, e, gb, g, b = C maj7 #11 (gb = f#).

If the above is of only the slightest help then it will have served its purpose: the sound of the chord (and its emotive evocations) is the most important thing; the importance of naming it lies somewhere between a distant second and not completely a worthless endeavor.

See also: triads, seventh chords, slash chords, sixth chords.

short coryell lick (which has been seen before...)

I've been listening to a lot of Larry Coryell lately and on the tune "Wolfbane" (from his 2005 album Electric with bassist Victor Bailey and Lenny White on drums) I heard a lick which I had transcribed on this blog before...yup one from Vinnie Moore's "Morning Star". Here's the Larry phrase (which is over E7#9) and the lick under discussion begins on the 4th beat of the 2nd measure:


And if you go to the Vinnie Moore transcription it's pretty easy to find: it's the very first phrase.

So the question is: did Larry listen to Vinnie's lick? or is it the case that given the number of players and the style that this pattern is inevitable? Similarities are bound to occur: just listen to the last movement of Brahms' First Symphony...remind anyone of Beethoven?

some live video

Last Friday's gig -- which I didn't plug here on this blog because I've been too busy (read "lazy") -- was streamed live by the Yippie and then posted on USTREAM. I've linked to it here but you'll have to move the cursor around to these spots to see/hear the following:

19:45 John N. Johnson presents a great Monologue
46:13 General Slocum's Theater of Disaster
1:31:14 Naked Women Project
1:56:12 the moment where I break my high E string




Here's a link straight up if you'd prefer to see it on the USTREAM site.

The first performance is spoken word only (a great story about a man and his cat); the second mixes text with incidental music; the last music and spoken word.

naked women project at nublu

The Naked Women Project will be at Nublu tonight. Check it out: $10 for 2 sets. That's right: 2 (count them two) sets of high-energy jazz, free improvisation, afro-pop and psychedelia all strewn with spoken word.

The projected line-up is:

T-bone
bass
The Law
trumpet
M'tazz
guitar
Polashek
sax
Father Charlie
words
Zebra
drums

with special guest performance artist Jazmine...

Nublu is located at 62 Avenue C.

transforming the circle of fifths

Yesterday we looked at the circle of fifths (COF) and regarded how some scales and intervals looked when displayed on that circle. But as interesting as the COF is, it isn't the only way to display all 12 pitch classes: another intuitive way to do so would be to arrange the pitches chromatically. Here's how a circle of minor 2nds (COM2) looks:


It might not be obvious at first glance, but there's an interesting relationship between the COM2 and the COF. To start to see it let's look at how the whole tone scale -- or major 2nds -- looks when displayed on the COM2:

And let's recall how the same collection of tones looks on the COF:

They're the same shape! The two circles differ only by the tones not a part of this collection, and they differ in a very systematic way. The easiest way to see the pattern is like this:

that is, the tones not a part of the major 2nd collection simply swap places with their tritone.

Another way -- a more arithmetical way -- to understand this transformation is to use a formula:

1. Convert all the tones to numbers as in 12-tone music (C=0, Db=1, D=2 and so on).
2. Multiply all tones by 7 mod 12 (i.e. multiply by 7 and if the number is 12 or bigger subtract 12: if it is still bigger subtract 12 again, and so on until the number in question is less than 12).

Some examples:

C [0 M7 mod 12 = 0 x 7 = 0 =] C
Db [1 M7 mod 12 = 1 x 7 = 7 =] G
D [2 M7 mod 12 = 2 x 7 = 14 -12 = 2 =] D
A [8 M7 mod 12 = 8 x 7 = 56 (mod12) = 8 =] Eb

This multiplicative operation is a way of extending the basic operations of 12 tone music (retrograde, inversion, inversion retrograde), but here we have a graphic display.

Lastly we can see how some scales look when displayed on the COM2. Here's a major scale:
which is still a symmetric shape, though far different from the one it takes in the COF.

And here's how perfect 5ths look:

This shape is more visible evidence of a strong correspondence between the two circles under question...if this shape is mapped onto a COF one then has a chromatic scale:

circle of fifths and scales

We touched on the circle of fifths before in this post. The circle of fifths is just that: notes seperated by a fifth (C - G -D - A, etc) and arranged in a circle because (in equal tempered tuning, at any rate) the fifths lead back to the starting point after all 12 tones have been accounted for (...Eb - Bb - F - C).

The circle of fifths (henceforth COF) has many uses, but one I've been playing around with lately is examining how scales look -- i.e. what shapes they take when the collections of notes are joined one to another as in the sequence of a scale. E.g. here's a whole tone scale:

And a chromatic scale:

Not surprisingly the 2 scales above take symmetric shapes when graphically displayed (the scales are symmetric in terms of their construction: comprised of 1/2 steps or whole steps). Surprising -- to me, at any rate -- is that when the major scale is displayed it also forms a symmetric shape:

As does the melodic minor.

Some asymmetric shapes: the harmonic minor:

and the neapolitan minor:

You can do these on your own, of course. Some other symmetric scales: the neapolitan major, the major pentatonic, the double harmonic. Some asymmetric ones: the hungarian minor and the harmonic major.

Lastly we can observe intervals -- actually we've already done this with the chromatic and whole-tone scales (min2 and Maj2 respectively). Here in one diagram are min3, Maj3 and P5:

The remaining intervals can all be found simply by going the other way round: C to Ab can be seen as a Maj3 down or as a min6 up. C to F is a P5 down or a P4 up, and so on...

naked women at goodbye blue monday TONIGHT

Yes, TONIGHT a pared-down quintet manifestation of Naked Women return to the stage at Goodbye Blue Monday.

The lineup:

T-Bone Blatt
bass
Matthew Polashek
sax
m'tazz
guitar
Father Todd
'bone + words
Zebra aka "Tiger"
drums

The show is FREE and starts at 9pm.

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.