Symmetrical Diminished Scale

For "symmetrical" I think one can only mean what some call octatonic: tone-semitone, or semitone-tone. Its normal environment is that of diminished seventh chords, but it can be used on various occasions (even just to give a modal character to a chord that, enharmonically, is perceived as a major triad). In practice, you can play C-Fb-Abb on one side and, on the other, play the scale C-Db-Eb-Fb-Gb-Abb-Bbb-Cbb.

... or, on a triad perceived as minor, you play the other one (A-C-F♯: semitone-tone starting from A).

P.S. I am expressing myself in a somewhat improper way, but I am still studying them and it is only to make things clear, before others much more competent than me and capable of delving deeper into the subject respond (since they haven't done so yet).

In addition to using tone-semitone on diminished seventh chords, you can use semitone-tone on dominant seventh chords.

Relative to the seventh chord, the semitone-tone contains: root, b9, #9, 3, #11, 5, 13, 7. It works well on chords such as 13b9, 7b9#11, 13#9 etc.

There are two symmetric diminished scales:

- Auxiliary diminished scale, which is equivalent to the octophonic tone-semitone

- Blues diminished scale, which is equivalent to the octophonic semitone-tone

both constitute an enrichment of the basic diminished scale.

Their use in tonal harmony is to replace the basic diminished scale to obtain a more lively harmonic coloration.

Note that both, unlike other non-diatonic synthetic-symmetric scales, having the 6th degree, consequently possess the relative minor (correction: they can replace the relative minor).

For example, to a chord containing the A-C-E minor triad, I can pair the A Blues Auxiliary Diminished scale.

...this argument doesn't quite add up for me... the doubts are: what is the basic diminished scale? If they are symmetrical, what purpose does a relative minor serve?

The structure of the symmetrical diminished scale is 1, 2, b3, 4, b5, #5, 6, 7. Practically 8 sounds where whole tones and semitones alternate. This symmetry means that every 3rd note can be the tonic of another diminished scale containing the same notes (4 possible tonics per scale). Obviously, the resulting chords are the diminished triad and the diminished seventh chord. The available tensions are the ninth, the eleventh, the minor thirteenth, and the major seventh (it does not present Avoid Notes).

DrJellyfish wrote:

If they are symmetrical, what is the point of a relative minor?

... indeed...

Talentuoso wrote:

The structure of the symmetric diminished scale is 1, 2, b3, 4, b5, #5, 6, 7.

Exactly. Since Modale mentioned a blues diminished scale, an auxiliary one, and a base one, I was wondering what the latter was.

I will try to clarify some doubts that were understandably the consequence of my previous laconic statement.

First of all, I will not speak in the abstract, but I believe it is useful to refer to a practical example.

Diminished Scale (basic): C-D-Eb-F#-G-A-B-C

Auxiliary Diminished Scale: C-D-Eb-F-F#-G#-A-B-C

Blues Auxiliary Diminished Scale: C-Db-Eb-E-F#-G-A-Bb-C

The Auxiliary Diminished Scale is the keeper of pure diminished tonal color because it does not possess the minor triad of the VI mode and the major triad of the I.

This means that it is a scale in its purest symmetrical state; the absence of a VI minor triad and a I major triad makes it unsuitable for diatonic-tonal situations.

The Blues Auxiliary Diminished Scale possesses the I major triad and the VI minor triad unaltered.

This means that although it is technically a symmetrical scale, the presence of the aforementioned triads denies it pure diminished tonal color and makes it usable in tonal harmony, for example instead of a C maj or A min scale. Therefore, it can also replace the relative minor. And this is what I wanted to say in my previous article.

The Auxiliary Diminished Scale introduces the fourth degree (IV) into its whole/half step structure. It is a HYBRID SCALE, containing both the fourth degree, which is typical of horizontal harmonies, and the +IV, which is typical of vertical harmonies. This scale is therefore suitable for use both in horizontal tonal situations, teleologically oriented, and in verticalizing and modal tonal situations with a tendency toward harmonic and tonal expansion. The presence of the +IV neutralizes the horizontal force of the natural fourth, allowing the latter to blend into the vertical aspect of a chord. The presence of the natural fourth gives it an exotic flavor and a certain tonal elasticity.

For completeness, I want to say that the "diminished" color is nonetheless completed by the "augmented" color.

The diminished scale (basic) is: C-D-E-F#-G#-A-B-C-. The scale that holds pure augmented color is the Auxiliary Diminished Scale, also called the whole-tone scale. The pure diminished color of this scale is due to the absence of the I major triad and the VI minor triad. It was used extensively and wonderfully by Debussy, to the point that O. Messiaen in his "Technique de mon langage musical" gave up treating it, stating precisely that after Debussy, there was nothing else to say or give regarding this scale.

I hope I have cleared up some doubts.... perhaps I have created others. ...

I have dusted off a live performance from my archive that uses the first mode of the C Blues Auxiliary Diminished Scale. I think it is interesting to listen to.

http://www.pianoconc...-lydian-n1-dwm/

I didn't know this scale. Any reference texts?

http://www.jazzitali...simmetriche.asp

thnx JamSession, but I was looking for the basic diminished chord mentioned above.

And indeed, it is not a symmetrical scale and, now that I think about it, it is the fourth mode of the so-called harmonic major scale (of G).

I would like to express what I think regarding Dr. Jellyfish's statement: "And it is, in fact, not a symmetrical scale and, now that I think about it, it is the fourth mode of the so-called harmonic major scale (of G)".

The PRIMORDIAL COLORS of Harmony are two: Augmented and Diminished; they are brought by augmented and diminished scales which are therefore structural scales of harmony, progenitors of such colors.

the G harmonic major scale is produced by the V of the C diminished scale (C-D-Eb-F#-G-A-) , thus a secondary color born from a primary color is produced. It is not possible for a scale that does not carry a fundamental color to originate on its own degrees a scale that carries a fundamental color. Besides, the harmonic major scale is a terminal product; it is an ionian scale and this can be deduced from the presence of the perfect IV in the scale. If we want to improvise on such a scale, we always remain there on those notes. If instead we view it as the fifth degree of the C diminished scale, the horizon opens up because this is a color of the C lydian scale; therefore, in improvisation, starting from the C lydian scale, we can veer towards the augmented or diminished color, also using the auxiliary diminished scales and the auxiliary augmented one. We can also veer towards the C blues scale, which is also a color born from the C lydian scale, or even towards the C flat 7 color, which is also a product of the C lydian scale (C-D-E-F#-G-A-Bb-C). As you can see, all the main families of chords in "Western harmony" contain the +IV, so how can one say that the ionian scale originates chords and scales, given that it does not contain the +IV! Given a scale on which to improvise or compose, it is important to identify the original scale because it is totipotent and only from it can we then improvise moving towards one color or another; if we take a peripheral scale, nothing starts from it.

modale wrote:

the G harmonic major scale is produced by the V of the C diminished scale (C-D-Eb-F#-G-A-)

Have patience, Modale, but is this type of diminished scale your own invention or from which pre-existing theory does it derive?

modale wrote:

THE PRIMORDIAL COLORS of Harmony are two: Augmented and Diminished

but also no... ;-)

modale wrote:

It is not possible that a scale not carrying a fundamental color originates on its own degrees a scale carrying a fundamental color.

... but then again... it is neither mathematics nor religion. Strictly speaking, "it is not possible" that one of the main instruments of our time is structured in such an asymmetrical way, privileging the key of C major etc...

instead, it is possible...

The diminished scale is a lydian scale to which we give the lowering of the 3rd by a half tone. Furthermore, the symmetric diminished whole-half and half-whole scales are defined as auxiliary; evidently, there is a basic one.

"Lydian Chromatic Concept of Tonal Organization", by G. Russell - page 15.

Ok. Now I'll take a look. Thanks for the report.