8-tone scales and Dim7/dom7 b9 chords

[ashbyanderson]

Originally Posted by Bob Pearce

Here's something that may be of interest to some.

There are two 7 note scales which are subsets of the Octatonic scale. They seem to be little documented possibly because they offer too little sonic difference from the full scale

Hi Bob, your Augmented Minor looks like C Harmonic Minor as a subset of the D HW Diminished Scale or (C WH Diminished Scale) to me... and the C Diminished Minor is also a subset of the DHW Diminished Scale or( C WH Dim Scale)

Seems we are viewing the same scale with different perspectives. Looks like your chart outlines 10 of the 48 modes I listed for the D HW Diminished Scale ( C WH Dim.) in my Jazz Composition Blog.

Based on your chart , Along with the Eb Maj7 Sus 4, you can actually get a C Major 7 sus 4 in your Augmented minor scale and and A Major 7 Sus 4 too. Since this scale is a subset of the D HW Diminished Scale ( C WH Dim.) , the Chord qualities still repeat at minor third intervals. The Gb Maj7 sus 4 is also present in the D HW Diminished Scale( C WH Dim) but not a part of the Augmented Minor subset you listed.

Interesting stuff!

[ashbyanderson]

Originally Posted by jazz oud

Hi Bob, thanks for the graphic, but it's a bit impenetrable, perhaps you'd like to offer some notes on it?

Hi Jazz Oud not impenetrable- from my perspective, Bob's chart outlines the C WH diminished Scale. His 7 tone Augmented Minor subset of this octatonic scale is C,D,Eb,F,G#,A,B and his 7 tone Diminished Minor Subset is C,D,Eb,F Gb,A B.

The Chords that Bob listed are the modes/Chords that can be developed form the subsets that he outlines. I have outlined 48 modes on my Jazz Composition Blog from the same scale D HW Diminished which is the same as C WH Diminished.

[jazz oud]

Originally Posted by ashbyanderson

Hi Jazz Oud not impenetrable- from my perspective, Bob's chart outlines the C WH diminished Scale. His 7 tone Augmented Minor subset of this octatonic scale is C,D,Eb,F,G#,A,B and his 7 tone Diminished Minor Subset is C,D,Eb,F Gb,A B.

The Chords that Bob listed are the modes/Chords that can be developed form the subsets that he outlines. I have outlined 48 modes on my Jazz Composition Blog from the same scale D HW Diminished which is the same as C WH Diminished.

I see now how the chart is supposed to work. It wasn't clear that the chord names are supposed to be indicative of the scale steps included. I assumed that his subsets were the same as mine, but this makes the orientation clearer. Essential a diminished scale is like a melodic minor scale with the 5th degree split (i.e., b5 and #5 and no 5)

C D Eb F (G) A B
C D Eb F (Gb G#) A B

Michaelsorg has brought this up before, I believe. So by omitting one or the other you arrive at melodic minor #5 or melodic minor b5, which is where the "augmented minor" and "diminished minor" terms come in.

It's certainly a worthwhile perspective, and may help some connect the dots (notably, both diminished and melodic minor may be related to the b2 of a dominant chord and differ only in the noted area).

[Bob Pearce]

Originally Posted by jazz oud

Hi Bob, thanks for the graphic, but it's a bit impenetrable, perhaps you'd like to offer some notes on it?

Sure. The first 3 lines simply show the key headings. The fourth and fifth lines show intervals in music terms and Romans. These are all there for no better reason than that's how my spreadsheet template works, they're just headers.

The scales are normalised to C but include the scale degrees from the Fifth below the Root.

The individual lines for the scales show the characteristic chords which can be built upon each scale degree (they're all pretty standard except, maybe, the Maj7sus4). This provides for more information than if I just entered R, m2, 2 etc.

Originally Posted by jazz oud

I understand that Forte 7-31 is (0 1 3 4 6 7 9), or in standard terminology (1 b2 b3 3 #4 5 6), which is indeed clearly a subset of the H/W diminished scale.

I'm confused that you are calling Forte 7-31 both "diminished minor" and "augmented minor" and referring to "two scales" which are subsets of the octatonic diminished scale, but you only list one such pitch set.

I called the scales "diminished minor" and "augmented minor" as an aide memoire for myself. Apologies if it seems vain to arbitrarily name scales but I can find no prior nomenclature and I never expected to make this public.

The reason there are two scales but one pitch class set is that they (the scales) are mirrors of one another. Allen Forte considered mirrors as manifestations of the same pitch class set and named them accordingly. This may be useful from a mathematical point of view but is less so from a musical one. Many researchers in PC Set analysis have come to the same conclusion (it's difficult not to unless you consider the minor and major triads the same thing. Forte names them both as 3-11).

Originally Posted by jazz oud

From my perspective, there are two overall heptatonic sets that can be subsets of the octatonic diminished, most simply considered as:
0 (1) 3 4 6 7 9 10 (or 1 #2 3 #4 5 6 b7) I'll call this form "A"
and
0 1 (3) 4 6 7 9 10 (or 1 b2 3 #4 5 6 b7) I'll call this form "B"

The question being whether there which of the following intervallic structures are contained within the scale:
M2 A2 m2 ("A")
or
m2 A2 M2 ("B")

It appears that in the Forte system that both of these would indeed be rearranged as
0 1 3 4 6 7 9 (7-31)
But I confess that I don't understand how that works, since the intervallic structure is clearly different.

Since in jazz practice, the root of the chord is relevant to the structure of the scale, there are actually 8 viable heptatonic diminished subsets:

C7(b9)
octatonic: C Db Eb E F# G A Bb (1 b2 b3 3 #4 5 6 b7)
h1: C Db Eb E F# G A (1 b2 b3 3 #4 5 6) "A"
h2: C Db Eb E F# G Bb (1 b2 b3 3 #4 5 b7) "B"
h3: C Db Eb E F# A Bb (1 b2 b3 3 #4 6 b7) "A"
h4: C Db Eb E G A Bb (1 b2 b3 3 5 6 b7) "B"
h5: C Db Eb F# G A Bb (1 b2 b3 #4 5 6 b7) "A"
h6: C Db E F# G A Bb (1 b2 3 #4 5 6 b7) "B"
h7: C Eb E F# G A Bb (1 b3 3 #4 5 6 b7) "A"
h8: Db Eb E F# G A Bb (b2 b3 3 #4 5 6 b7) "B"

As you suggested, these tend to sound so much like the full scale that there is not much use in specifically selecting the heptatonic version.

However, there are some advantages to h2 and h4 in particular: the omission of the 6th allows some major-minor ambiguity and the omission of the #4 retains a closer relationship to the key.
h5 and h8 and sort of charmingly weird in their omission of the 3rd of the chord and the root, respectively.

There are, indeed, two (and only two) heptatonic subsets of the Octatonic scale (and by Octatonic scale I mean the one we're all familiar with). In PC Set notation they are (0,1,3,4,6,7,9) and [0,2,3,5,6,8,9]. As stated before, they are mirrors of one another and thus share the same Forte number, 7-31.

Each of these subsets (scales) has 7 unique modes, as opposed to their Octotonic parent which only has 2. I've arbitrarily arranged the modes so as to look like they do in the spreadsheet. Whilst it adds a certain symmetry and allows me to name them as minor scales there's no good reason to assume that the root is where I've put it.

[Bob Pearce]

Originally Posted by ashbyanderson

Hi Bob, your Augmented Minor looks like C Harmonic Minor as a subset of the D HW Diminished Scale or (C WH Diminished Scale) to me... and the C Diminished Minor is also a subset of the DHW Diminished Scale or( C WH Dim Scale)

Seems we are viewing the same scale with different perspectives. Looks like your chart outlines 10 of the 48 modes I listed for the D HW Diminished Scale ( C WH Dim.) in my Jazz Composition Blog.

Based on your chart , Along with the Eb Maj7 Sus 4, you can actually get a C Major 7 sus 4 in your Augmented minor scale and and A Major 7 Sus 4 too. Since this scale is a subset of the D HW Diminished Scale ( C WH Dim.) , the Chord qualities still repeat at minor third intervals. The Gb Maj7 sus 4 is also present in the D HW Diminished Scale( C WH Dim) but not a part of the Augmented Minor subset you listed.

Interesting stuff!

I'm sorry Ashby, but we clearly have very different understandings of what a mode is. Until we can come to some agreement we're talking a different language and I can't help you.

[Bob Pearce]

Originally Posted by jazz oud

I see now how the chart is supposed to work. It wasn't clear that the chord names are supposed to be indicative of the scale steps included.

Absolutely.

[ashbyanderson]

Originally Posted by Bob Pearce

I'm sorry Ashby, but we clearly have very different understandings of what a mode is. Until we can come to some agreement we're talking a different language and I can't help you.

I disagree there Bob you're definitely speaking my language- As I would not have been able to decode your chart and explain it to Jazz Oud ( see above posts) The chords listed in your chart are modes of the scales you described- or simply chords that can be developed from the scale (your Augmented Minor and your Diminished Minor). Maybe that can help you see my perspective- I definitely see yours.

In Jazz we would call your augmented minor a C harmonic minor chord or C Minor Major 7 with a #5 or b6. As for the Diminished Minor chord. A jazz musician would generally look at it as a Diminished Major 7 chord.

So that we don't drift to far from this post , which is to describe the use of 8-tone scales and Dim7/dom7 b9 chords- typically a frequent approach used by improvising musicians like myself, I propose that you relate your posts about how to use the Octatonic/Diminished scale and it's use in Jazz. My perspective is that the Octatonic Scale( HW Diminished Scale or the WH Diminished Scale ) described in these posts have 48 or more modes or chords that can be developed from the Scale as I listed in my Jazz Composition Blog. The whole point here is that the diminished scale can be substituted over any chord or mode that is a subset of one of the three diminished scales-put simply, if I find a chord or mode in a jazz standard, 2,5,1 progression, Modal tune ect. I can substitute the diminished scale in place of the standard scale if the chord or mode can be derived from any of the three diminished scales. The task as Michael stated is

Originally Posted by michaelsorg

The hardest thing about the scale is resolving it to the following chord in a way that makes sense

Basically the Dim7 and the Vb9 chords are modes or chords that can be developed from the diminished scale. The scale can be substituted over Minor 7 chord, Minor Major 7 chord, Sus Major 7 chord, and Half diminished chords and more because all of these chords can be derived from the Diminished Scale. Your chart only list a few of the chords or modes of the Diminished Scale.

[Bob Pearce]

Originally Posted by ashbyanderson

I disagree there Bob you're definitely speaking my language- As I would not have been able to decode your chart and explain it to Jazz Oud ( see above posts) The chords listed in your chart are modes of the scales you described- or simply chords that can be developed from the scale (your Augmented Minor and your Diminished Minor). Maybe that can help you see my perspective- I definitely see yours.

In Jazz we would call your augmented minor a C harmonic minor chord or C Minor Major 7 with a #5 or b6. As for the Diminished Minor chord. A jazz musician would generally look at it as a Diminished Major 7 chord.

So that we don't drift to far from this post , which is to describe the use of 8-tone scales and Dim7/dom7 b9 chords- typically a frequent approach used by improvising musicians like myself, I propose that you relate your posts about how to use the Octatonic/Diminished scale and it's use in Jazz. My perspective is that the Octatonic Scale( HW Diminished Scale or the WH Diminished Scale ) described in these posts have 48 or more modes or chords that can be developed from the Scale as I listed in my Jazz Composition Blog

Like I said Ashby, so long as you can find 48 or more modes in the Octotonic scale, we're talking a different language.

[ashbyanderson]

Originally Posted by Bob Pearce

Like I said Ashby, so long as you can find 48 or more modes in the Octotonic scale, we're talking a different language.

May be from your point of view but I have the advantage of being able to see yours, I enjoyed your post. Your chords(modes of the scale) of the scales you listed line up with 10 of the 48 chord( modes) that can be developed from the Octatonic Scale-More may be possible!

For the Readers who are ready to see 48 chords that can be derived from the diminished scale view my discoveries about the scale at the Jazz Composition Blog

I'll post the Chords/Modes in List form for those interested. See the Jazz Composition Blog for all 48 specific chords of the D HW DIMINISHED SCALE in notation form.They are all transpositions in Minor thirds from modes 1 and 2 listed below. 12 chords/modes of the DHW Diminished SCALE are listed. Once transposed up in Minor thirds 48 chords will have been derived from the scale with out using any notes other than those in the DHW DIMINSHED SCALE. This method can be transposed to the remaining Diminished Scales;GHW DIMINSHED and CHW DIMINISHED.

1.D: possible Chord/Modes D Phrygian, D-7,D-7b5,D7,D7b5,D7b9 and Do7
2.Eb: possible Chords/Modes Ebsus4#5Maj7, EboMaj7, EbMin-Maj #5, EbsusMaj7, Ebo7
3.F
4.Gb
5.Ab
6.A
7.B
8.C

[michaelsorg]

Originally Posted by Bob Pearce

Like I said Ashby, so long as you can find 48 or more modes in the Octotonic scale, we're talking a different language.

Bob and Ashby, I too think of a mode as one entity - whether it's C dorian or F# dorian, it's one mode. For practice purposes I have to concieve of that as 12 scales x 7 modes = 84 elements to practice. But for conceptualizing and theoretical purposes, it's one scale, 7 modes. Ashby, do you have perfect pitch? That would explain why you conceive of them as different things...

Bob, I can see why breaking down to a heptatonic scale helps to build a set of "normal" chords. I find it interesting and useful when dealing with different scales (or pitch class sets) to make charts of all possible chords, at least those that could be considered useful in a functional way. Especially when dealing with nine- or ten-tone scales there are lots of possibilities and combinations that arise, so a "diatonic" approach to building chords is not complete (that is, taking every other tone to build 7th chords ).

As far as the meaning of chords like (C) Eb Ab B and (C) Eb F# B, I think that's pretty open. I mean, if I'm in C minor and I play the chord (C) Eb F# B D, I intend that as Cm9(maj7#11). But if I'm in C major, it's probably a diminished 7th with maj7 and 9 added. (C) Eb Ab B in the key of G maj is some inversion of an Ab7#9(7 omitted) or a D13(#11b9). But in C minor it could be a C minor chord in need of some resolution. It could also be G7b13b9/C. I've got a tune which uses exactly these chords, I'll try to get a snippet of it up soon and post it.

[Bob Pearce]

Originally Posted by michaelsorg

Bob, I can see why breaking down to a heptatonic scale helps to build a set of "normal" chords. I find it interesting and useful when dealing with different scales (or pitch class sets) to make charts of all possible chords, at least those that could be considered useful in a functional way. Especially when dealing with nine- or ten-tone scales there are lots of possibilities and combinations that arise, so a "diatonic" approach to building chords is not complete (that is, taking every other tone to build 7th chords ).

Oh, I agree. A classic case is, of course, the "Altered" scale. The diatonic approach leads to a min7b5 but the scale is almost invariably associated with a dominant 7.

[ashbyanderson]

Originally Posted by michaelsorg

Bob and Ashby, I too think of a mode as one entity - whether it's C dorian or F# dorian, it's one mode. For practice purposes I have to concieve of that as 12 scales x 7 modes = 84 elements to practice. But for conceptualizing and theoretical purposes, it's one scale, 7 modes. Ashby, do you have perfect pitch? That would explain why you conceive of them as different things.

Thanks Michael,now that's exactly what I'm saying. But the concept is just expanded from the standard concept of one scale, 7 modes. If you can perceive of one scale using each scale step as a mode, then what about all the other possibilities for the same scale step- that's my point of view. Since the diminished scale is a symmetrical scale that has 3 transpositions. it makes sense to look at multiple possibilities for each mode of this 8 tone scales because these 3 transpositions now support all 12 keys for improvisation and compositional purposes. Generally jazz musicians are taught that the Diminished scale supports 4 keys i.e. DHW Diminshed = Do7,Fo7,Abo7 and Bo7. but the same DHW Diminshed scale supports Ebo7,Gbo7, Ao7 and Co7. The diminished scale is a Multiple Mode Scale- no doubt about it.

lets look at the different heptatonic scales( 7 tone scale) the can be used with the chords I previously outlined - you should find this interesting
because they all can be developed from one scale- in this instance the D HW diminished Scale. After doing all the transpositions of these scales in minor 3rd intervals you'll begin to see that the Diminshed scale has many modes for the specific chords I've listed. Notice that I have not included any of the minor 3rd transpositions in this example. Just doing one set of minor 3rd transpositions for the scales listed below will give you 16 Scales by transposing the scales and chords listed below in minor 3rd intervals. Notice also that each scale has a minor 3rd leap within each scale- I love this sound! For all 48 chords that can be found in one diminished scale, visit my jazz composition blog.

1.D: D-7 = D,Eb,F,Ab,A,b,C voiced as D,F,A,C
2.Eb: Ebsus4#5Maj7, = Eb,F,F#Ab,A,B, D voiced as Eb,Ab,B,D
3.F: F7 b9 = F,Gb,Ab,A,B,C,Eb voiced as F,A,C,Eb,Gb
4.Gb: Gb sus Major7= Gb,A,B,C,D,Eb,F voiced as Gb,B,F ( quartal voicing)
5.Ab: Ab phrygian = Ab,A,C,D,Eb,F,Gb voiced as Ab,A,Eb,Ab(quartal voicing)
6.A: Ao7= A,B,C,D,Eb,Gb,Ab voiced as A,C,Eb,Gb
7.B: B7#9= B,C,D,Eb,Gb,Ab,A voiced as B,Eb,A,D
8.C: C Min-Maj #5 = C,D,Eb,F,Ab,A,B ( C harmonic Minor) ( C Augmented Minor) Voiced as C,Eb,Ab,B

[ashbyanderson]

Originally Posted by michaelsorg

(C) Eb Ab B in the key of G maj is some inversion of an Ab7#9(7 omitted) or a D13(#11b9). But in C minor it could be a C minor chord in need of some resolution. It could also be G7b13b9/C.

Are you saying the that C Eb Ab B could be a G7b13b9/C Chord? without the Tonic(G) or the Seventh (F)? Hmmm!

[michaelsorg]

Originally Posted by ashbyanderson

Generally jazz musicians are taught that the Diminished scale supports 4 keys i.e. DHW Diminshed = Do7,Fo7,Abo7 and Bo7. but the same DHW Diminshed scale supports Ebo7,Gbo7, Ao7 and Co7. The diminished scale is a Multiple Mode Scale- no doubt about it.

Ashby, you touch on something that I've mentioned in a few posts on this and other forums: that the diminished scale is more flexible than is usually recognized. You mention D H/W over Do7, Fo7, etc., that means also over Bb7b9, Db7b9, E7b9, and G7b9. But of course, none of those roots are in the scale. That means you have to add a ninth tone not in the scale. But this is a very effective scale to use , since it gives you tensions from the half step above the chord tones rather than below.

And say, you use it over G7b9 going to C minor. Descending from the added G, you have:
(G) F# F Eb D C B A Ab

This is 5th mode of harmonic minor plus tensions Maj7 and Maj 9. If you stay with this over C minor, you've got bebop melodic minor, plus the blue note #4/b5. But we're talking a nine-tone scale, so I'm getting off topic on my own thread! I'll make a new post regarding the 8-tone version following this post.

1.D: D-7 = Anyway, Ashby, back to your post, I'm not getting your method here:

Originally Posted by ashbyanderson

1. D,Eb,F,Ab,A,b,C voiced as D,F,A,C
2.Eb: Ebsus4#5Maj7, = Eb,F,Ab,A,B,C, D voiced as Eb,Ab,B,D
3.F: F7 b9 = F,Gb,Ab,A,B,C,Eb voiced as F,A,C,Eb,Gb
4.Gb: Gb sus Major7= Gb,A,B,C,D,Eb,F voiced as Gb,B,F ( quartal voicing)
5.Ab: Ab phrygian = Ab,A,C,D,Eb,F,Gb voiced as Ab,A,Eb,Ab(quartal voicing)
6.A: Ao7= A,B,C,D,Eb,Gb,Ab voiced as A,C,Eb,Gb
7.B: B7#9= B,C,D,Eb,Gb,Ab,A voiced as B,Eb,A,D
8.C: C Min-Maj #5 = C,D,Eb,F,Ab,A,B ( C harmonic Minor) ( C Augmented Minor) Voiced as C,Eb,Ab,B

So in 1., you left out F#
in 2. you left out F#
in 3. D
4. Ab
5. B
6. F
7. F
8. F#

I'm not following the logic...and I'm not finding the chords or modes at your linked composer blog...

[michaelsorg]

So far I've posted about 3 different 8 tone scales: the diminished scale, the bebop major (of which the Spanish Phrygian is the 3rd mode), and the harmonic major with added #2, which turns out to also be a melodic minor with added #4.

The fourth scale that can be used the same way as all of these (outlining a diminished seventh chord with every other note in an 8-tone scale) is the bebop melodic minor. And that's all four possibilities, unless I've missed something (????)

This scale has been used very often in arranging, because it pivots so perfectly between the dim7 chord and the min6 chord. In C min: Bo7 to Cm6, which of course, is also G7b9 to Cm6. It's also great for an unaltered F9 chord (especially as IV7), for a B7 altered, for Am7b5, or D7susb9. In short, just about anywhere that you'd use C melodic minor. One exception would maybe be Eb maj7#5. There you're better off with Eb maj bebop, or for more tension, C melodic minor with added #4.

That 2 of the 4 possibilities contain the melodic minor shows the close relationship of this to the diminished scale. Some people refer to 7th mode of melodic minor as the "Diminished-Whole Tone" scale.

An interesting (if off-topic) aside: If you combine a C melodic min with an F# mel mi, you get C Db D Eb F F# G Ab A B (C) (spellings adjusted to reflect C minor tonality)
This is the symmetrical 10-tone scale, one of the modes/scales discovered and used by Oliver Messaien. It's a lot of fun to use over most minor tunes where the desired sound leans on minor(maj7) more than on minor 7th. I've written several compositions with it. It's basically a C whole-half diminished scale plus Db and G, or a C melodic minor adding Db F# and Ab. I like to call it the Neapolitan Hungarian melodic minor.