Yahoo Tuning Groups Ultimate Backup tuning Generalizations and extensions of modality, 2-octave repeating scales

I was just thinking about the diatonic scale modes... This is sort of
an extension into JI from diatonic theory, a lot of it incorporating
Paul Erlich's ideas on the matter.

All of the diatonic modes blend into one another, and yet they all
have their own sound which uniquely identifies them in pitch space. In
12-tet, if you temper out 81/80, there is a definite and real pattern
existing in the circle of fifths that ends up generating all of the
modes, and correlates so well with the feeling of each one that you
might actually think that the modes really ARE generated entirely by
meantone fifths. So how can we apply this to a JI context, where other
intervals than the perfect fifth can be used as well?

Let's roll with D dorian for a second.

D E F G A B C D

That B has two distinct uses that differ by a syntonic comma, and the
two uses are very, very, very musically different. Having the B down a
comma (B\) leads to progressions like ||: Dm7 G7 :|| and having the B
comma-neutral (B|//|) leads to progressions like ||: Dm7 Em7 Fmaj7#11
Em7 :||. That is to say, that having the B up a comma makes it a
beautiful and haunting consonance which is usually explored as being 3
fifths above the B, and having the B down a comma leads to a more
mellow kind of relaxed sound. But they are both a part of what most
people would term "Dorian mode."

Furthermore, there are plenty of times when other notes will have to
differ by a comma as well for various reasons, in all of the diatonic
scale modes. So I was thinking that in order to get a really
"extended" mode that can be used to get all sorts of feelings and
flavors, perhaps it might be best to describe dorian just in terms of
the JI intervals corresponding to the notes D E F G A B C D, and allow
any of the commas be adjusted as they will. Let the B go up or down a
comma, as well as the E; hell, let the D even go up or down a comma if
needed. Furthermore, if we allow septimal comma drift as well, it's
possible to let the generic dorian template "drift outward" into
7-limit space in a very natural and intuitive manner.

(Is this the same thing, using tuning-math terminology, as declaring
the mode to be whatever JI equivalent intervals D E F G A B C D work
out to be, and then treating it as a periodicity block with 81/80 and
64/63 as unison vectors?)

It's almost like the modes are just a focusing in of a lens on some
kind of a pitch mapping continuum; they are not isolated, discrete
units, but rather the lines are blurry. In the sense that the modes
are used in modern music, they just seem to be baseline generators in
which any of the notes can drift by a comma to produce different
effects.

One interesting thing to note is that this ability of the notes in the
modes to drift by commas extends to larger intervals as well. For
example, take the chord progression Fm9 Gbmaj9 Fm9. Having the Fm9 as
a minor ninth chord means there's a G in there, whereas the next chord
has a Gb, so in terms of "diatonic scale theory," it does seem like
the mode is switching. And yet, this chord progression sounds
completely diatonic, so you could view it as a larger type of "comma
adjustment" given the context that these notes are used.

If you aren't content allowing notes in a mode to differ by a full
semitone, then note the following: the G and the Gb differ by a
135/128 chroma, which is not quite the same thing as a chromatic
semitone. If you construct a scale that repeats every 2 octaves, you
can stick that interval in there to get an expanded version of an
existing mode. It's just like you're defocusing the lens on the modal
spectrum slightly, and increasing the scope of what you're looking at.
In this way, you can derive the following "expanded modal" scale for
Phrygian:

C Db Eb F G Ab Bb C D Eb F G A Bb C

Note this scale repeats every 2 octaves, and was generated by taking
this tetrachord:

| C Db Eb F |

And tiling it like so:

Which contains all of the intervals in the Fm9 Gbmaj9 chord
progression above. I haven't come up with an exact science for these
2-octave scales yet, generally doing them by ear and finding patterns
along the way, but maybe they'll be musically interesting when the
concept is applied to microtonal scales.

-Mike

Interesting ideas Mike;

You have prompted (inspired?) me to add more scales to my ScaleCoding database to cover what you are suggesting:

I have put a pdf of the new version (680) into this folder:

http://www.lucytune.com/scales/

Or directly as:

http://www.lucytune.com/scales/ScaleCoding680UniqueScales.pdf

I'll update it in the other formats, when I get time;-)

Here is how I visualise what you are proposing:

For your selected notes of:

> C Db Eb F G Ab Bb C D Eb F G A Bb C

scalecoding is"

Db-Ab-Eb-Bb-F-C-G-D-A

all used in two octaves:

i.e. 8/0/6

> Note this scale repeats every 2 octaves, and was generated by taking
> this tetrachord:

> | C Db Eb F |

tetrachord is:

Db-x-Eb-x-F-C

i.e.

5/24/6

> And tiling it like so:

All notes used is:

Db-Ab-Eb-Bb-F-C-G-D-A

i.e. 8/0/6 if C is tonic

8/0/8 is D is tonic

first octave is;

C Db Eb F | G Ab Bb C

Db-Ab-Eb-Bb-F-C-G

6/0/6

second octave is:

C | D Eb F G | A Bb C |

Eb-Bb-F-C-G-D =

5/0/6 if D is tonic

5/0/4 if C is tonic.

On 2 Jul 2008, at 19:34, Mike Battaglia wrote:

> I was just thinking about the diatonic scale modes... This is sort of
> an extension into JI from diatonic theory, a lot of it incorporating
> Paul Erlich's ideas on the matter.
>
> All of the diatonic modes blend into one another, and yet they all
> have their own sound which uniquely identifies them in pitch space. In
> 12-tet, if you temper out 81/80, there is a definite and real pattern
> existing in the circle of fifths that ends up generating all of the
> modes, and correlates so well with the feeling of each one that you
> might actually think that the modes really ARE generated entirely by
> meantone fifths. So how can we apply this to a JI context, where other
> intervals than the perfect fifth can be used as well?
>
> Let's roll with D dorian for a second.
>
> D E F G A B C D
>
> That B has two distinct uses that differ by a syntonic comma, and the
> two uses are very, very, very musically different. Having the B down a
> comma (B\) leads to progressions like ||: Dm7 G7 :|| and having the B
> comma-neutral (B|//|) leads to progressions like ||: Dm7 Em7 Fmaj7#11
> Em7 :||. That is to say, that having the B up a comma makes it a
> beautiful and haunting consonance which is usually explored as being 3
> fifths above the B, and having the B down a comma leads to a more
> mellow kind of relaxed sound. But they are both a part of what most
> people would term "Dorian mode."
>
> Furthermore, there are plenty of times when other notes will have to
> differ by a comma as well for various reasons, in all of the diatonic
> scale modes. So I was thinking that in order to get a really
> "extended" mode that can be used to get all sorts of feelings and
> flavors, perhaps it might be best to describe dorian just in terms of
> the JI intervals corresponding to the notes D E F G A B C D, and allow
> any of the commas be adjusted as they will. Let the B go up or down a
> comma, as well as the E; hell, let the D even go up or down a comma if
> needed. Furthermore, if we allow septimal comma drift as well, it's
> possible to let the generic dorian template "drift outward" into
> 7-limit space in a very natural and intuitive manner.
>
> (Is this the same thing, using tuning-math terminology, as declaring
> the mode to be whatever JI equivalent intervals D E F G A B C D work
> out to be, and then treating it as a periodicity block with 81/80 and
> 64/63 as unison vectors?)
>
> It's almost like the modes are just a focusing in of a lens on some
> kind of a pitch mapping continuum; they are not isolated, discrete
> units, but rather the lines are blurry. In the sense that the modes
> are used in modern music, they just seem to be baseline generators in
> which any of the notes can drift by a comma to produce different
> effects.
>
> One interesting thing to note is that this ability of the notes in the
> modes to drift by commas extends to larger intervals as well. For
> example, take the chord progression Fm9 Gbmaj9 Fm9. Having the Fm9 as
> a minor ninth chord means there's a G in there, whereas the next chord
> has a Gb, so in terms of "diatonic scale theory," it does seem like
> the mode is switching. And yet, this chord progression sounds
> completely diatonic, so you could view it as a larger type of "comma
> adjustment" given the context that these notes are used.
>
> If you aren't content allowing notes in a mode to differ by a full
> semitone, then note the following: the G and the Gb differ by a
> 135/128 chroma, which is not quite the same thing as a chromatic
> semitone. If you construct a scale that repeats every 2 octaves, you
> can stick that interval in there to get an expanded version of an
> existing mode. It's just like you're defocusing the lens on the modal
> spectrum slightly, and increasing the scope of what you're looking at.
> In this way, you can derive the following "expanded modal" scale for
> Phrygian:
>
> C Db Eb F G Ab Bb C D Eb F G A Bb C
>
> Note this scale repeats every 2 octaves, and was generated by taking
> this tetrachord:
>
> | C Db Eb F |
>
> And tiling it like so:
>
> | C Db Eb F | G Ab Bb C | D Eb F G | A Bb C | (D)
>
> Which contains all of the intervals in the Fm9 Gbmaj9 chord
> progression above. I haven't come up with an exact science for these
> 2-octave scales yet, generally doing them by ear and finding patterns
> along the way, but maybe they'll be musically interesting when the
> concept is applied to microtonal scales.
>
> -Mike
>
>
Charles Lucy
lucy@...

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Generalizations and extensions of modality, 2-octave repeating scales

🔗Mike Battaglia <battaglia01@...>

🔗Charles Lucy <lucy@...>

🔗Mike Battaglia <battaglia01@...>

🔗Charles Lucy <lucy@...>

🔗Dave Keenan <d.keenan@...>