Diatonic 8-Tone Scales:

[Melody Droid]

Yesterday I found what I consider to be the most important single
article on pitch class set (12TET scale structure) analysis: Voice
Leading In Early Stravinsky, by Allen Forte, in the book Confronting
Stravinsky.
In there he talks about what he calls the "diatonic octachord", which
has the scale step pattern of 1-1-1-2-2-1-2-2, which in relation to
the C Major scale would mean the addition of F# to that scale.
I wasn't aware of any 8-tone scales that included the diatonic major
other than the 8-tone blues mode 1-2-2-1-2-1-1-2, so I'll have to
diagram out all of the 5 possible 8-tone diatonic scales and see
which ones aren't duplications of each other, and report back on that.
The Forte diatonic 8-tone scale has the same number of tritones (4)
as the 8-tone blues mode, so it should be similar in terms of
consonance/dissonance.
The 8-tone octatonic scale 1-2-1-2-1-2-1-2 is extremely dissonant,
containing 8 tritones.
I'll get back to you on my results later.
Bill Flavell

[Joey Goldstein]

Yesterday I found what I consider to be the most important single
article on pitch class set (12TET scale structure) analysis: Voice
Leading In Early Stravinsky, by Allen Forte, in the book Confronting
Stravinsky.
In there he talks about what he calls the "diatonic octachord", which
has the scale step pattern of 1-1-1-2-2-1-2-2, which in relation to
the C Major scale would mean the addition of F# to that scale.
I wasn't aware of any 8-tone scales that included the diatonic major
other than the 8-tone blues mode 1-2-2-1-2-1-1-2, so I'll have to
diagram out all of the 5 possible 8-tone diatonic scales and see
which ones aren't duplications of each other, and report back on that.
The Forte diatonic 8-tone scale has the same number of tritones (4)
as the 8-tone blues mode, so it should be similar in terms of
consonance/dissonance.
The 8-tone octatonic scale 1-2-1-2-1-2-1-2 is extremely dissonant,
containing 8 tritones.
I'll get back to you on my results later.
Bill Flavell

There is a concept in jazz theory circles known as the "bebop scales".

Their archetypical use is as a scale that is applied to chord, a
chord-scale, by which a player can run scalar passages in duple rhythm
wher there are alwaays chord tones on strong beats. But there are many
other usages of these scales as well, including harmonic usages.
Eg. The C6 bebop scale consists of the 4 tones of a Cmaj6 chord with a
passing tone stuck between eacch chord tone. 3 of the passing tones are
diatonic to the C major scale but one passing tone is chromatic.

C E G A C chord tones
D F G# B passing tones

1 & 2 & 3 & 4 & 1
C D E F G G# A B C chord tones on strong beats

1 & 2 & 3 & 4 & 1
C B A Ab G F E D C

(Note: That these 4 passing tones happen to form a Ddim7 chord. This
scale is often used harmonically to create passing dim7 chords between
the 4 inversions of C6.)

The G7 bebop scale has a chromatic passing tone between G and F.
G B D F G
A C E F#
It appears to be the same scale that Forte discusses in his Stravinsky book.

[Jerry Kohl]

Yesterday I found what I consider to be the most important single
article on pitch class set (12TET scale structure) analysis: Voice
Leading In Early Stravinsky, by Allen Forte, in the book Confronting
Stravinsky.
In there he talks about what he calls the "diatonic octachord",

Actually, he calls it the "master diatonic octad".

which

has the scale step pattern of 1-1-1-2-2-1-2-2, which in relation to
the C Major scale would mean the addition of F# to that scale.

Or Bb. This is in fact the scale of "musica recta" (without the
complication of having nly B-natural in the lowest octave), dating
back to the early medieval period.

--
Jerry Kohl <***@comcast.net>
"Légpárnás hajóm tele van angolnákkal."

[Joey Goldstein]

Yesterday I found what I consider to be the most important single
article on pitch class set (12TET scale structure) analysis: Voice
Leading In Early Stravinsky, by Allen Forte, in the book Confronting
Stravinsky.
In there he talks about what he calls the "diatonic octachord", which
has the scale step pattern of 1-1-1-2-2-1-2-2, which in relation to
the C Major scale would mean the addition of F# to that scale.

F F# G Ab Bb C C# D# F
1- 1-1- 2- 2-1- 2- 2

The diatonic scale plus F#, starting on F gives the intervallic pattern:

F F# G A B C D E F
1 1 2 2 1 2 2 1
Is that what you meant?

I wasn't aware of any 8-tone scales that included the diatonic major
other than the 8-tone blues mode 1-2-2-1-2-1-1-2,

Really? But it's so simple.

so I'll have to

diagram out all of the 5 possible 8-tone diatonic scales and see
which ones aren't duplications of each other, and report back on that.
The Forte diatonic 8-tone scale has the same number of tritones (4)
as the 8-tone blues mode, so it should be similar in terms of
consonance/dissonance.

How does the presence of tritones in a scale moderate the scale's dissonance?
There are intervals that are more dissonant than tritones; min 2nds, min
9ths, maj 7ths.

The 8-tone octatonic scale 1-2-1-2-1-2-1-2 is extremely dissonant,

Or consonant depending on how it is being used.
There are 4 major triads found within that scale. Are major triads
dissonant somehow?

containing 8 tritones.
I'll get back to you on my results later.

[Buster Mudd]

Post by Joey Goldstein
How does the presence of tritones in a scale moderate the scale's dissonance?
There are intervals that are more dissonant than tritones; min 2nds, min
9ths, maj 7ths.

It's been ages since I studied Forte, but IIRC his whole concept of
Interval Vectors was based on the notion that the presence of *any*
interval...and specifically, how many instances of each
interval...determined a salient quality of that pitch class
collection. Dissonance being just 1 such quality.