October 26, 2012

7-Limit Harmonies in the Bohlen Pierce Scale

The most consonant harmonies in the Bohlen Pierce scale (to my ear) are those that fall within the gamut of Harry Partch's 7-limit just intonation system. The BP intervals 9/7 and 7/5 (steps 3 and 4) seem to be the most pleasing, and their equal temperament counterparts are less than 4 cents from just.

The step 2 interval 25/21 is 302 cents, an acceptable minor third to western ears, but equal temperament changes it to a flat-sounding 292 cents.

The step 12 interval 25/9 (B note) is totally outside of the western 12-tone system.

This chart shows the intersection between the Bohlen Pierce scale and the 7-limit just intonation system.  The D and B notes (in blue) suffer the problems mentioned above.  The difference between cents and round hundreds is a rough indicator of how alien the interval will sound compared to traditional western harmony.

steps name ratio cents cents ET 12-tone name
0 C 1/1 0 0 Unison
2 D 25/21 302 293 Minor 3rd
3 E 9/7 439 435 Dim 4th
4 F 7/5 582 585 Tritone
6 G 5/3 884 877 Major 6th
7 H 9/5 1018 1024 Minor 7th
9 J 15/7 1319 1316 Dim 9th
10 A 7/3 1467 1463 Aug 9th
12 B 25/9 1769 1755 none
13 C 3/1 1902 1902 12th

August 01, 2011

More 7th Chords on C6th

Last year I posted about positions for 7th chords on C6th.  To recap, here are the handy positions for playing I, IV and V 7th chords in the key of E, using the the A to Bb lever, the C to C# lever, and P5 which lowers G to Gb.


A7   E7   B7     A7   E7   B7
1   __________________________________
2 E ___3____4____5______9____10___11__
3 C ___3#___4____5#_____9____10#__11__
4 A ___3#___4#___5#_____9#___10#__11#_
5 G ___3b___4____5b_____9____10b__11__
6 E ___3____4____5______9____10___11__
7 C ___3#___4____5#_____9____10#__11__
8 A ___3#___4#___5#_____9#___10#__11#_
9   __________________________________
10  __________________________________
Let's call the A to Bb lever "A", the C to C# lever "C", and the G to Gb pedal "G".  We can then use this shortcut notation:

A7 = 3 ACG
E7 = 4 A
B7 = 5 ACG

A7 = 9 A
E7 = 10 ACG
B7 = 11 A

Now here's the other half of the puzzle.  You may already know that the C lever (C to C#) makes an A7 chord on strings 2 through 8.  If you add the E to Eb pedal P6 into the mix, you can create another complete set of 7th chords.

Let's call the E to Eb pedal "E".  In our shortcut notation, the new scheme looks like this:

A7 = 0 C
E7 = 1 CAE
B7 = 2 C

A7 = 6 CAE
E7 = 7 C
B7 = 8 CAE

Pedal 6 doesn't lower string 2 (it raises it to F) so we do lose that string in those CAE positions.  Here's the tab:


A7   E7   B7     A7   E7   B7
1   __________________________________
2 E ___0_________3___________7________
3 C ___0#___1#___3#_____6#___7#___8#__  C lever (C to C#)
4 A ___0____1#___3______6#___7____8#__  A lever (A to Bb)
5 G ___0____1____3______6____7____8___
6 E ___0____1b___3______6b___7____8b__  E pedal (E to Eb, P6)
7 C ___0#___1#___3#_____6#___7#___8#__  C lever (C to C#)
8 A ___0____1#___3______6#___7____8#__  A lever (A to Bb)
9   __________________________________
10  __________________________________

 
So again we have this handy thing going on where the I7, IV7 and V7 chords are all clustered together on 3 frets.  Now here's the mindblower.  When you combine these two systems, you have one of the three seventh chords in the key of E at every fret on the neck!


A7 = 0 C
E7 = 1 CAE
B7 = 2 C
A7 = 3 ACG
E7 = 4 A
B7 = 5 ACG
A7 = 6 CAE
E7 = 7 C
B7 = 8 CAE
A7 = 9 A
E7 = 10 ACG
B7 = 11 A

Amazing, isn't it?

July 19, 2011

Reading Music in the E9 neck by Mike Perlowin

Has this ever happened to you? You've just heard a great piece of music, and you know it would lend itself perfectly to the steel and you want to learn it, but there is no tab available. What do you do? Well, you've got three choices. One- you can painstakingly try to figure it all out by ear, two- you can wait for somebody else to tab it out, or three- you can go out and buy the sheet music and read it.

To borrow a line from Shakespeare, "To read or not to read-that is the question." Actually it shouldn't be a question at all. If you define "not reading" as playing by ear, learning and hearing all your chords and positions and doing all the things that we all do anyway, than the quote should be to read and not to read.

Anybody who has seen any of the installments of my music theory series will already know that I'm a strong advocate of learning to read standard notation. Let me make an even stronger statement. In my opinion reading notation is easier than reading tablature. It is also a more accurate way of communicating musical ideas, and since it is applicable to all instruments, a player who reads can adapt music for other instruments to the steel.

Unfortunately, written music has gotten a bad rap, along with those musicians who rely on it. The problem is that traditional classical music training teaches people only how to read music, and not how to use their ears and brains. Who among us hasn't met some monster technician who can play anything they see, but who hasn't the slightest idea how to play by ear. To these people the written note isn't so much a tool as a crutch. The problem though isn't what they know, it's what they don't know.

Learning to play by ear, which presumably everybody who reads this magazine has all already done, is a different science than learning to play by notes. For some reason, advocates of each school of thought tend to dismiss each other as insignificant or unimportant, but the truth is that these two styles of learning music are not mutually exclusive. In fact, they compliment each other very well.

The real problem with notation is that with it's emphasis on the individual note, it doesn't tell us whether to play with the pedals up or down, or what string to use. This makes it useless as a tool to learn how to play the steel if you are just starting out, which is one of it's major uses with other instruments. We must learn the complexities of our instrument first, and then learn how to read music on it later.

This is where a knowledge of key signatures and chord spellings* becomes necessary. (You've all learned how to spell all the important chords, right?) Lets look at the following example.



The first thing you see is the key signature. One flat, specifically, B flat. This tells us that the song is in the key of F (This of course corresponds to the phrase "One down" or the hand signal of one finger pointing downward.) Now look at the notes. C, A, G, and F. Three of these four notes, C, A, and F, are found if the F major chord. Therefore, if you get into a some sort of F chord position, 3 of the 4 notes will already be there for you. Then you have to manipulate your guitar in such a way as to play the remaining note, either by moving your bar; or lifting a pedal if you're on the 8th fret with the pedals down, or if you're on the 13th fret with the pedals up, playing the 7th string.

Now this is a little convoluted, compared with the usual method of just looking at the note and playing it, but it works. The fact is that nothing about the pedal steel guitar is simple or easy, so why should reading be any different, but the system does work.

Recently I sat down at my steel with the sheet music to Dave Brubeck's "Blue Rondo A La Turk." Not exactly a typical steel guitar tune. I looked at the music, recognized the chords that were outlined in the melody, got into the proper pedal and bar position, and I was able to play the song almost immediately.

Even with all it's inadequacies, and even with the rather convoluted method used to make it work, I still say that conventional notation is a better way to communicate a musical idea than tablature. With tab, one- you learn by rote without gaining any kind of knowledge, and two- you can't learn a new song until somebody else tabs it out for you. With notation, you can learn a piece of music that is written for piano, or harp, of brass choir.

Conventional notation is the universal written language of musical ideas. Learning how to use this useful tool won't make you forget what you already know. It will expand your knowledge and make you a better player.



*Just as all words have their correct spellings, so do all chords. Here are all the spellings of the primary major, minor and 7th chords that are commonly used. These spellings should be memorized. Remember the chord name (A, C etc.) is the same as the root.

Major Chords:

Root Third Fifth

AC# E

Bb D F

B D# F#

C E G

D F# A

E G# B

F A C

G B D

Minor chords

Root Third Fifth

A C E

Bb Db F

B D F#

C Eb G

D F A

E G B

F Ab C

G Bb D

Seventh Chords

Root Third Fifth Seventh

A C# E G

Bb D F Ab

B D# F# A

C E G Bb

D F# A C

E G# B D

F A C Eb

G B D F