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I've never really had a clear understanding of why we have 9ths, 11ths, and 13ths, but never hear about 10th, 12th, 14th, & 15th intervals. Anyone know why these intervals are almost never mentioned?
- Perfect Unison
- Minor 2nd
- Major 2nd
- Augmented 2nd
- Minor 3rd
- Major 3rd
- Augmented 3rd
- Diminished 4th
- Perfect 4th
- Augmented 4th
- Diminished 5th
- Perfect 5th
- Augmented 5th
- Minor 6th
- Major 6th
- Augmented 6th
- Minor 7th
- Major 7th
- Augmented 7th
- Diminished Octave
- Perfect Octave
- Augmented Octave
- Minor 9th
- Major 9th
- Augmented 9th
- Minor 10th
- Major 10th
- Augmented 10th
- Diminished 11th
- Perfect 11th
- Augmented 11th
- Diminished 12th
- Perfect 12th
- Augmented 12th
- Minor 13th
- Major 13th
- Augmented 13th
- Minor 14th
- Major 14th
- Augmented 14th
- Diminished 15th
- Perfect 15th
- Augmented 15th
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12-14-2014 09:18 AM
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Maybe because in chord construction, the 9th, 11th and 13th are extensions of the basic chord tones (root, 3rd, 5th and 7th), whereas the 10th, 12th, and 14th are the same as the 3rd, 5th and 7th (one octave up) and the 15th is the root (two octaves up). I have seen 10ths used in musical discussions; for example, I remember reading an article about Freddie Green's rhythm playing explaining that his three note chords were voiced in 10ths (for example, root, 7th, 3rd + octave), which is a nice fat sound that cuts through in a big band. I think it was Bucky Pizzarelli saying this. Late 1980's, around when Freddie died? Now it seems the thinking is that he only really sounded one or two notes of those voicings. Anyway, that's where I remember the term 10ths used to describe chord construction.
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Chords are most often constructed in 3rds
1 3 5 7 9 11 13
Harmonic intervals are named in the same fashion.
This covers all 7 notes of the common scale reference.
9 11 13 could equally be 2 4 and 6 but that is a scale context, not the harmonic one.
6 is the exception sometimes, generally when the 7th is not present.
10 12 14 and 15 are notes that have already made an appearance.
10ths are sometimes discussed as an interval.
Some things in the musical naming systems could have gone down different.
Post tonal theorists use numbers 0-11 because their starting reference is intervals and not a scale.
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Probably would make a lot of sense visually to see note names written stacked out. You'll see where things repeat. C E G Bb = 1 3 5 b7 etc
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Also, regarding spelling out scale degrees which repeat notes already present in a different octave , like 10ths, usually you don't get into that much detail for a chord symbol. I would imagine it kind of defeats the purpose of its basic simplicity. Especially for jazz, chord symbol gives you something to improvise harmony and melody around , imply tonal centers which you can improvise over etc.
As stated above, a 10th is just the 3rd in a different octave. you can double 3rds, 5ths, 7ths etc., but that's very specific voicing information , and would usually be reserved for spelling out in notation if you wanted to express that beyond being "open"/ "closed" or inversions etc.
You very commonly see 10ths, 6ths and 3rds talked about as INTERVALS for harmonizing a melody or improvised line , like double stops.
In that case, it's a very handy short hand for describing what you're doing with other musicians. When you hear players/teachers talking about 10ths they are usually talking about double stop intervals. You usually don't talk about 10ths with CHORDS as much.
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In some circles, voicings are very important, and those intervals are used regularly. Especially in terms of altered qualities (you want a triadic chord tone altered in the upper register, for instance). I just saw Jerry Bergonzi playing and in the instructions he gave to the piano player when he called the tune he specified tensions that I'd never heard mentioned, that the piano player picked up on right away. The sound was one I'd never heard either. Short hand for sound required the use of a "non conventional" language and for them the tensions you mentioned were a given.
Also in some scales that don't repeat within the octave, the use of higher numerical names is kind of a necessity. But now we're talking chord and scale construction a step outside of what many traditional theories teach.
David
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I seem to recall, as a kid, being irritated at not being able to find #9 chords in my hal Leonard incredible chord finder. It only had flat tens. Took me a little while to figure that one out. :-)
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I look at it as the basic chord tones 1,3,5,7 have strong identities no matter what octave they are in. People indication inversion to move them around. The other notes are all color tones that tend to be used up an octave, they can be used in low voices carefully.
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Sorry, a little off topic, but I always kinda irritated at 7#11 chords in charts. Why not just say 7b5 ? You sure dont want the 5th and augumented 4th in the same chord? I automatically assume its b5, am I wrong? Maybe pianists do play #11 and 5th at the same time?
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Yeah with guitar it's more often b5 because of limitations. :-)
Originally Posted by Hep To The Jive
Probably more important though, different implications for what to improvise over b5 vs #11
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David,Also in some scales that don't repeat within the octave, the use of higher numerical names is kind of a necessity. But now we're talking chord and scale construction a step outside of what many traditional theories teach.
What is the common thinking or methodology to construct such scales?
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Well you probably use several right now. Symmetrical scales fit into that category. Running consecutive 4ths, for instance, you will pass the octave in 3 scale steps. But a more useful philosophy of scale construction can be seen in the Schillinger system of symmetrical scales. For these scales, they may often not be coincident with an octave tone in the first iteration. You would find, however that using these scales in sequence, your sound gets more "outside" with each generation. They're really useful that way. And how about a scale that is built on 5th intervals? It has an internal shape to it but juxtaposed, you've got to go above the octave and C G D A E... by the time you hit that E, it's in the upper register, not a 3rd anymore. Originally Posted by bako
Schillinger scales are a great topic on their own, though. I started a thread and discussion on them ages ago, I think. Great way to take melodic phrases and repeat their sounds in diatonic and non diatonic ways. The moment you start thinking of scales who's tonics don't end on the octave, it gets really interesting. They play off of the tension between the scale's logic and the diatonic structure they don't belong to. You need a nomenclature that takes order and placement into account.
David
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Thanks, I know there is some kind of Schillinger group that streams a discussion Thursday nights I'll try and check out.
Meanwhile, here's a few interval structures in a cycle till it yields 12 tones, arranged in a ascending scale like way.
C Gb / G Db / D Ab / A Eb / E Bb / B F //
C E G# / A C# F / Gb Bb D / Eb G B //
C Eb Gb A / B D F Ab / Bb Db E G //
C D E F# G# Bb / B C# Eb F G A //
C Db F# G / Bb B E F / G# A D Eb //
Or a major scale with it's negative space pentatonic
C D E F G A B / Db Eb Gb Ab Bb //
Or an alternating major and minor 3rd sequence
C E G B D F# A C# E G# B D# F# A# C# E# G# B# D# G Bb D F A C
Are these in any way similar to what you have observed?
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Surprise Schillinger System isn't mentioned a lot. Berklee originally was a school teaching Schillinger system and school I worked at Dick Grove School of Music, Dick started teaching Schillinger system at an earlier West Coast Jazz school. So roots of modern Jazz education evolved from Schillinger. Originally Posted by TruthHertz
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Hell yeah! When you get these down and you use them as the basis for linear improvisation (particularly at speed), they turn out to be very beautiful and out sounds. An entirely overlooked colour set overlooked by most improvisors. The Schillinger stuff was surprisingly elusive, at least for me, in my experience at Berklee, with the exception of Norm Zocher, who's a scale monster. I got this stuff from Roland Wiggins, who taught in Philly and who was the go-to guy at the time for everyone including Coltrane. Schillinger system of symmetrical scales is deep exploration of atonal sound through multi tonal scales over a diatonic framework. That's how jazz uses it anyway. It's also a powerful compositional principle in its own right. Originally Posted by bako
It does seem strange, doesn't it? But this is an entire approach that guitarists have not embraced, excepting maybe the tritone transposition used a lot. I think because it is well on the other side of the "traditional" divide (not something Joe Pass would have used), and it doesn't fit conveniently into a strictly diatonic based framework, at lease for short term analysis, it's invisible. Originally Posted by docbop
The very substance of this thread points to that. The numerical system that is necessary to conceive and implement these sounds somewhat requires the use of things like lower structure chord tones named for their initial appearance in the upper structure regions. Who, outside of a modern composition class, thinks that way?
It's not the common knowledge. Shame.
Enough of this derailment though. I think this line of thought has gone "out" enough.
(Back to gear talk!)
David
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Or maybe because we mostly talkin',playin',hearin' in equal temparament.But there is and Just intonation.
I remember Bergonzi and Liebman(maybe) talking about 'tonal expansions' or stacking major 7th chords on top of
each other - 1 3 5 7 9 #11 13 #15 17 #19 21 #23 - where 17 and 23 repeats 3 and 7 but just in equal temp.
W.A.Mathieu ,Harmonic Experience is a interesting book on this subject.One quote from it:
"Tonality in just intonation is an open system whose limits are defined by the capacity of the individual ear to
relate compound tones to e generating tone.Tonality in equal temperament is an open system whose limits are
defined by our sensitivity to the symmetric affect inherent in tuning, which, at a certain point, becomes
greater than the affect generated by the reference norms."
I think that both systems have some limits but also beauty that deserves attention.
For hearin' just intonation music some recordings of early european music, some beautiful world music (Africa,
Central Asia,Balkans) and for sure Easley Blackwood , Ben Johnston and other contemporary composers.
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Ted Green uses "17" to indicate a 3rd played above an 4.
There is usually, I think, a difference between a #4 and a b5. It's about which scale tone is altered and the scale implied by the chord. A (Maj 7) #4 implies a lydian scale, while a 7#11 implies a lydian dominant (mixolydian with a raised four), although other choices could be made.
The #4 (11) usually reflects a melody note, while the b5 can often be a harmonic choice.
In contrast, a b5 implies or allows a #5. It might call for a tritone scale or an altered dominant, or whole tone scale.
There are also differences when it comes to comping, I think. In Freddie Green style comping, I think the #4 would be ignored. A b5 would imply a descending chromatic line, usually in the bass.
Using a more modern comping style, I would look for rootless voicings with the #4 on top.
You can move around either a #4 or b5 voicing by whole tones and it will retain an altered dominant sound. But as above, this might be less appropriate for a #4 chord.
Another thought, a #4 (11) chord in post bop tunes may function modally rather than in a tritone/fifth cycle.
Well, that's my thinking about the #4(11) vs. b5 issue.
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George van Epps used some of that notation in his work..Ted Greene knew this type of thinking and expanded upon it in an explanation of the "overtone series" ..which as Ted pointed out..you would need a 40 or 50 fret guitar to really make use of it..and to communicate to most musicians-saying something like "..its a flat 17th" may get you in a fight rather then a turnaround.."
there is something about mixing numbers and letters that most folks don't like..blame it on algebra perhaps..but as I have observed from teaching..getting 12 tones mixed with 7 letters and a flat and sharp sign..is about all they want to handle..
I'm happy to play altered chords all day long..but if I need a calculator to remember what a #28th is ..
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Don't most of us think of scales as spanning two octaves in order that note and chord extensions and their alterations can differentiate themselves from their like pitch class siblings in the lower octave...?
What I mean is that the "same note / pitch class" sounds different functionally depending on whether it is in the lower or upper octave of the scale. Conceptually, it makes sense to "unfold" the wrapped octave scale and let the scale naturally assume a full linear two octave range.
The whole purpose of calling a note the 13th rather than the 6th is to draw out, distinguish, and indicate that the role and functional sound of that note is different depending on its placement within the lower or upper octave.
I'm assuming that when musicians practice soloing they think in terms of two octave spans so that they can make phrases that comprise chord tones in the lower octave and extensions in the upper octave to outline melodic lines that span enough width to encompass the range of notes in a complex chord...
My wording is kind of clumsy, but does anyone NOT think of it this way?
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Originally Posted by pauln
C E G Bb D sounds like C9 even if it's in different inversions where the 9 isn't on top Especially if it's not in a low voicing etc. Traditional western tonal music is built on stacked thirds. What makes us think of a note as 2 vs a 9 has to do with the presence or absence of the 7th (third below in the spelling of it). Without the Bb we can't stack the D above in thirds. So it's a 2. Without the 7th, 11th s sound like 6ths etc...
Of course in modern jazz there's a whole lot that falls outside of "traditional", "tonal", or "western".Last edited by matt.guitarteacher; 12-19-2014 at 07:39 AM.
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As you superimpose chord structures, they take on identities as their stacked forms but also in reference to the original chord. You can see and hear this with Jerry's vid.
David
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