Jonah Dempcy

Overtone Series and Western Harmony

Harmonics and tuning

If the first 15 harmonics are transposed into the span of one octave, they approximate some of the notes in what the West has adopted as the chromatic scale based on the fundamental tone. The Western chromatic scale has been modified into twelve equal semitones, and in relation to that scale, many of the harmonics are slightly out of tune, and the 7th, 11th, and 13th harmonics are significantly so. In the late 1930s, composer Paul Hindemith ranked musical intervals according to their relative dissonance based on these and similar harmonic relationships.

Below is a comparison between the first 20 harmonics and their equivalent frequencies in the 12-tone equal-tempered scale. Orange-tinted fields highlight differences greater than 5 cents, which is the "just noticeable difference" for the human ear. (Because physical characteristics of musical instruments cause significant variations from these theoretical values, they should not be used for tuning without adjusting for those variations.)

Some theorists believe that the overtone series is the basis of the experience of consonance and dissonance, for example, one writer states that

"If two different notes are played simultaneously, the composite sound includes the harmonics of both notes. In musical intervals, one or more of those harmonics are common to both notes. For example, if C3 and G3 are sounding together, their harmonic series intersect at G4 (2nd of G3, 3rd of C3) and G5 (4th of G3, 6th of C3). If these common harmonics are at the same frequency or nearly so in both notes, the composite sound will seem harmonious. If their frequencies differ significantly, we tend to hear the notes as "out of tune" with each other. Tuning involves changing the fundamental pitch of one of the notes to control the relationship between these common harmonics"

However, this theory neglects the fact that several intervals made up of electronically generated pure sine waves (with no overtone content) are still perceived as consonant or dissonant. The frequencies of the overtone series, being a range of integral multiples of the fundamental frequency, are naturally related to each other by small whole number ratios and it is these small whole number ratios that are the basis of the consonance of musical intervals, for example, a perfect fifth, say 200 and 300 Hz (cycles per second), produces a combination tone of 100 Hz (the difference between 300 Hz and 200 Hz) that is, an octave below the lower note. This 100 Hz first order combination tone then interacts with both notes of the interval to produce second order combination tones of 200 (300-100) and 100 (200-100) Hz and, of course, all further nth order combination tones are all the same, being formed from various subtraction of 100, 200, and 300. When we contrast this with a dissonant interval such as a tritone (not tempered) with a frequency ratio of 7:5 we get, for example, 700-500=200 (1st order combination tone)and 500-200=300 (2nd order). The rest of the combination tones are octaves of 100 Hz so the 7:5 interval actually contains 4 notes: 100 Hz (and its octaves), 300 Hz, 500 Hz and 700 Hz. All the intervals succumb to similar analysis as been demonstrated by Paul Hindemith in his book, The Craft of Musical Composition.

From Wikipedia

Free Jazz Mix (2001)

Great Info on Jazz Standards

1	1930	Body and Soul		C		J	R	S	A	O
2	1939	All the Things You Are		C	M	J	R	S	A	O
3	1935	Summertime		C		J	R	S	A	O
4	1944	'Round Midnight		C	M	J	R	S	A	O
5	1935	I Can't Get Started (with You)		C	M	J	R	S	A	O
6	1937	My Funny Valentine		C	M	J	R	S	A	O
7	1942	Lover Man (Oh, Where Can You Be)		C	M	J	R	S	A	O
8	1930	What Is This Thing Called Love?		C	M	J	R	S	A	O
9	1933	Yesterdays		C	M	J	R	S	A	O
10	1946	Stella By Starlight		C		J	R	S	A	O

Different Lands

Press Release Submission on All About Jazz

• All About Jazz press release submission form

Listen to the Real Book:

1   A Call For All Demons Sun Ra 2   A Child Is Born Thad Jones 3   A Fine Romance Jerome Kern 4   A Family Joy Michael Gibbs 6   A Foggy Day George Gershwin 7   A Night In Tunisia Dizzy Gillespie / Frank Paparelli 8   African Flower Duke Ellington 9   Afro Blue Mongo Santa Maria 10   Afternoon In Paris John Lewis 11   Airegin Sonny Rollins

etc...

Expected vs. Unexpected

Labels: philosophy

Jazz Picante

Rune Grammofon

Rune Grammofon is a record label dedicated to releasing work by the most adventurous and creative Norwegian artists and composers.

Being music enthusiasts almost to the point of absurdity, we don't want to limit ourselves to certain genres, as long as there's real heart and personality. With an increasing number of indifferent records bombarding the market place, we modestly aim to recapture the magic connected to the discovery of new artists and buying their records. Our aim is to put love and care into each release, giving it the best possible design and packaging. No plastic, ever. All releases come in the digipak format with exclusive design by brilliant designer Kim Hiorthøy. 

Jeff Ballard

Roy Hargrove - Nothing Serious

Subs for V7 - I-vi-ii-V7 practice

Kurt Rosenwinkel - Zhivago

Rhythm Changes Piano Solo

Shell Voicings on Piano

Root Position Shell Voicings

2nd Inversion Shell Voicings

3-7 Voicings

Adapting Shell Voicings For Extended and Altered Chords

Giant Steps Played by Robot

You won't believe this video that Dan Gaynor just turned me on to. I've
heard tons of guys play Giant Steps like this at Berklee but this guy
takes the cake. Here is the next generation of young unswinging tenor
players. Things are looking pretty grim for the future, but at least
we'll have live Jazz in space.



Link: Giant Robot Steps

Barry Harris Subs - Clarification

Bobby said...

I see how all the final chords resolve to Cmaj except the last. G7 to C, V7 to I; Bb7 to C , fine bVII7 to I; Db7 to C , ok bII7 to I; and I'm fine with adding a II chord before each dominant, but E7 resolving to C? This I don't really get, either theoretically or aurally.

I responded...

You can think of E7 resolving to C in a number of ways.

For one thing, E7 regularly resolves to A-7 which is an inversion of C6. Also, the chord E7 can be played along with a shell G7 to yield the G13b9 chord.

You could play the 5th mode of A Harmonic Minor over this chord (E F G# A B C D) and it would sound quite fine.

But, I'm guessing you don't have a problem this kind of E7b9 -> C transition, but rather E7#11 -> C. E7#11, to which you would play 4th mode of B Melodic Minor as a scale (E F# G# A# B C# D), is somewhat difficult to make work. E7#11 to C is "out there" in the same way that E7#11 to A-7 sounds a bit odd.

However, you can still make it work. Here's an example of a lick in 8th-notes that uses this substitution:

Chord changes:
E7#11 | C

Descending 8th notes:
A# F# D C# B A# G# F# | G

Another way to look at it would be as an Ab-7b5 or Bb7sus4b9 chord, since both of those share the key of B Melodic Minor with E7#11. Bb7->C is quite common and sus4b9 chords are often substituted for unaltered dominant7 chords so it's not unheard of ...

On the topic of why this could work theoretically, it's because E7#11 shares 2 of the 4 notes comprising the diminished 7th "backbone" of the C major key. According to Barry Harris, a major key is comprised of a major 6 chord from the root and a diminished 7 chord from the leading tone. Hence, the key of C is comprised of C6 and Bdim7. This yields an 8-note scale, C D E F G G# A B, which Barry Harris considers superior to the 7-note scale taught in mainstream music theory.

It also accounts for a second tritone that resolves. Whereas conventional music theory only examines the resolution of the tritone of the 4-7, Barry Harris' theory includes the resolution of the tritone of the 2-b6 as well.

In conventional music theory, it is said that the 4 resolves to the 3 while the 7 resolves to the 1. Barry Harris' theory simply states that any of the 4 tones of the diminished backbone of a key will resolve to a neighboring tone from the major 6 chord from the tonic. Here's a table showing this:

Dim7 from 7th | Maj6 from root

B | A, C

D | C, E

F | E, G

G# | G, A


This table is for the key of C. The left column consists of the notes of the Bdim7 chord and the right column has notes from the C6 chord. This table illustrates how notes from the Bdim7 chord resolve to neighboring tones from the C6 chord.

To tie this back in to the discussion of E7#11 resolving to C, we simply say that it is not as strong of a resolution as E7b9 to C, because only 3 of the 4 notes from the diminished backbone are present. In the case of E7b9 (or G7b9, et al.) the notes B, D, F and G# are present, so it resolves strongly to C. In the case of E7#11, only B, D and G# are present, so the resolution is weaker. But, it is still possible to make it work. Just experiment at home first before trying it on the fly at a gig!

Also, of course, you would probably not want to use this reharmonization while accompanying someone. It would clash if they played F or G, both of which are commonly played over G7. So, I would only play E7#11 as a sub for G7 resolving to C when playing a solo.

Dick Hyman Lesson on Art Tatum

Art Tatum's lessons (introduction)
00:57

Art Tatum's lessons (G turn)
00:57

Art Tatum's lessons (descending pentatonic scales)
01:31

Art Tatum's lessons (displaced pentatonic scales)
00:44

Art Tatum's lessons (neighbor tone devices in Db)
02:48

Art Tatum's lessons (diatonic devices)
03:31

Portland Jazz Jams

This is a good resource for NW jazz artists, as well as having a Jazz Knowledge Wiki that aims to provide a repository for jazz education. Check it out!

Art Tatum - Humouresque (video)

Art Tatum - Yesterdays (video)

Barry Harris Substitutions

The Geometry of Harmony

Composer reveals musical chords' hidden geometry

by Chad Boutin · Posted July 6, 2006; 02:00 p.m.

Composers often speak of fitting chords and melodies together, as though sounds were physical objects with geometric shape -- and now a Princeton University musician has shown that advanced geometry actually does offer a tool for understanding musical structure.

In an attempt to answer age-old questions about how basic musical elements work together, Dmitri Tymoczko has journeyed far into the land of topology and non-Euclidean geometry, and has returned with a new -- and comparatively simple -- way of understanding how music is constructed. His findings have resulted in the first paper on music theory that the journal Science has printed in its 127-year history, and may provide an additional theoretical tool for composers searching for that elusive next chord...

Making graphical representations of musical ideas is not itself a new idea. Even most nonmusicians are familiar with the five-line musical staff, on which the notes that appear physically higher represent sounds that have higher pitch. Other common representations include the circle of fifths, which illustrates the relationships between the 12 notes in the chromatic scale as though they were the 12 hours on a clock's face.

"Tools like these have helped people understand music with both their ears and their eyes for generations," Tymoczko said. "But music has expanded a great deal in the past hundred years. We are interested in a much broader range of harmonies and melodies than previous composers were. With all these new musical developments, I thought it would be useful to search for a framework that could help us understand music regardless of style."

Traditional music theory required that harmonically acceptable chords be constructed from notes separated by a couple of scale steps -- such as the major chord, whose three notes comprise the first, third and fifth elements in the major scale, forming a familiar harmony that most audiences find easy to enjoy. Many 20th-century composers abandoned this requirement, however. Modern chords are often constructed of notes that sit right next to one another on the keyboard, forming "clusters" -- dissonant by traditional standards -- that to this day often challenge listeners' ears.

"Western music theory has developed impressive tools for thinking about traditional harmonies, but it doesn’t have the same sophisticated tools for thinking about these newer chords," Tymoczko said. "This led me to want to develop a general geometrical model in which every conceivable chord is represented by a point in space. That way, if you hear any sequence of chords, no matter how unfamiliar, you can still represent it as a series of points in the space. To understand the melodic relationship between these chords, you connect the points with lines that represent how you have to change their notes to get from one chord to the next."

Patterns Using Stowell's Dom.7 Reharmonizations

• G melodic minor- one tension (#11) = C7#11
• F melodic minor- one tension (b13) = C7b6
• Bb melodic minor- two tensions (b9, #9) = C7sus4b9
• Eb melodic minor- three tensions (#9, #11, b13) = C-7b5
• C# melodic minor- four tensions (b9, #9, #11, b13) = C7Alt.

John Stowell Dominant 7 Harmonizations

Major mode       |  Mel. minor mode

D Dorian         |         D Mel. minor
E Phrygian       |         E Phrygian Nat.6
F Lydian         |         F Lydian #5
G Mixolydian     |         G Lydian Dominant (eg: the chord G7#11)
A Aeolian        |         A Mixolydian b6
B Locrian        |         B Locrian Nat.2
C Ionian         |         C# Altered

Barry Harris ii-V7 Substitutions

Esoteric Music Theory

David Valdez' Jazz Forum

David Valdez' Jazz forum: Jazz resources, musician features, Jazz harmony and improvisation lessons, streaming Jazz videos, Jazz links, Jazz interviews, Jazz saxophone articles, Bebop masters, esoteric music philosophy, and David Valdez' upcoming gigs.

Jazz Resource Center

Variations on Diatonic Arpeggio Exercise

Arpeggios to the Third, Diatonic Exercise

Continuous Triplets Exercise

4-Note Motif Added as 16ths to an 8th-note line

1 e + a 2 e + a 3 e + a 4 e + a
C   B   A   G   F   E   D   C

1 e + a  2 e + a 3 e + a 4 e + a 1
C D C A# B   A   G   F   E   D   C

1 e + a 2 e + a  3 e + a 4 e + a 1
C   B   A B A F# G   F   E   D   C

1 e + a 2 e + a 3 e + a  4 e + a 1
C   B   A   G   F G F D# E   D   C

1 e + a 2 e + a 3 e + a 4 e + a 1
C   B   A   G   F   E   D E D B C

4-Note Motif Played as Continuous 16th-Notes