7-note scales split into pentatonic scales by octave to maximize consonance

Lately I've been trying to find out the best compositional way to split apart pentatonic scales to form huge chords...since it seems so far 5-note-per-octave chords are approaching the limit of the size of a chord consonant within an octave space so far as diatonic tunings.

One trick I have found that really seems to work well is splitting your usual 7-tone scales into multiple pentatonic scales and then distributing those in their own octave spaces IE

#1) a#4,c#5,d#5,f#5,g#5
#2) a#6,c6,d#6,f6,f#6

(Note: together these form the entire 7-tone scale (c,c#,d#,f,f#,g#,a#)...but they still retain a sort of pentatonic lower level of tension/higher level of consonance)
**************************************************************

Try writing two individual melodies...one only using notes in scale #1 and the other only using notes in scale #2. Now try playing them together. Note how just about everything sounds more pure than you'd expect (or at least it does by far to my ears).

On the side, I wonder if there is any special mathematical reason why this works and/or possible applications to other tunings...

Michael

As I wrote before and showed examples, this bimodal/trimodal etc. compositional technique is very good, I've been using it for years to split 12-tone terrain into more distinguished and characteristic modes where each has different intervallic structure, mood and its own melodic and harmonic potential. I personally prefer when each of modes has different notes (the most simple example is diatonics on white keys against pentatonics on black keys), but anything is possible. Five years ago I have combined in one work Chinese and Japanese pentatonics this way.

But I don't think your resulting scale is C Phrygian which you wrote, because note C is there only one times. I would say some of the octave doubled notes with tend naturally to be considered root note (candidates are Bb, Eb, Gb), just statistically it's more probable we will hear them more often.

And the last thing: I would write all notes as flats to make it more easy to read, as it's more natural to combine unaltered notes with flats than with sharps. Therefore Bb Db Eb Gb Ab and Bb C Eb F Gb.

Daniel Forro

On 21 Apr 2009, at 2:51 AM, djtrancendance wrote:

>
>
> Lately I've been trying to find out the best compositional way to > split apart pentatonic scales to form huge chords...since it seems > so far 5-note-per-octave chords are approaching the limit of the > size of a chord consonant within an octave space so far as diatonic > tunings.
>
> One trick I have found that really seems to work well is splitting > your usual 7-tone scales into multiple pentatonic scales and then > distributing those in their own octave spaces IE
>
> #1) a#4,c#5,d#5,f#5,g#5
> #2) a#6,c6,d#6,f6,f#6
>
> (Note: together these form the entire 7-tone scale > (c,c#,d#,f,f#,g#,a#)...but they still retain a sort of pentatonic > lower level of tension/higher level of consonance)
> **************************************************************
>
> Try writing two individual melodies...one only using notes in scale > #1 and the other only using notes in scale #2. Now try playing them > together. Note how just about everything sounds more pure than > you'd expect (or at least it does by far to my ears).
>
> On the side, I wonder if there is any special mathematical reason > why this works and/or possible applications to other tunings...
>
> Michael
>

Daniel> "But I don't think your resulting scale is C Phrygian which you wrote,

because note C is there only one times."

   What I meant...was the combination of the two pentatonic scales forms the 7-notes...not that there is any designated order to them.

   In other words it could be
Db,Eb,F,Gb,Ab,Bb,C
or
Eb,F,Gb,Ab,Bb,C,Db
or
C,Db,Eb,F,Gb,Ab,Bb (what I wrote originally)...in other words the order isn't important and neither is symmetry in this technique.  It's not C-Phygian...it's simply the use of the same notes that exist in that scale spread as diatonic scales with the notes following no particular order.

    The point is that I limit my use of certain notes to certain octaves, making it the equivalent of using 5 of 7 possible notes per octave to make a relaxed "pentatonic feel" despite using a full array of notes over the course of a 2-3 octaves.

   I guess what (if anything) perhaps seems to make it different than your method...is I am being rigid in staying to 5-note subsets of the same 7-notes rather than branching into completely different modes per octave (as you appear to do quite often).

   To me,  it's as much about the issue of production quality and hearing harmonics clearly (IE why so many orchestral composers spread their arrangements over several octaves even for, say, a triad to make it sound clearer)...as it is about hearing consonant-sounding notes.

-Michael

--- On Mon, 4/20/09, Daniel Forro <dan.for@...> wrote:

From: Daniel Forro <dan.for@...>
Subject: Re: [tuning] 7-note scales split into pentatonic scales by octave to maximize consonance
To: tuning@yahoogroups.com
Date: Monday, April 20, 2009, 5:41 PM

As I wrote before and showed examples, this bimodal/trimodal etc.

compositional technique is very good, I've been using it for years to

split 12-tone terrain into more distinguished and characteristic

modes where each has different intervallic structure, mood and its

own melodic and harmonic potential. I personally prefer when each of

modes has different notes (the most simple example is diatonics on

white keys against pentatonics on black keys), but anything is

possible. Five years ago I have combined in one work Chinese and

Japanese pentatonics this way.

But I don't think your resulting scale is C Phrygian which you wrote,

because note C is there only one times. I would say some of the

octave doubled notes with tend naturally to be considered root note

(candidates are Bb, Eb, Gb), just statistically it's more probable we

will hear them more often.

And the last thing: I would write all notes as flats to make it more

easy to read, as it's more natural to combine unaltered notes with

flats than with sharps. Therefore Bb Db Eb Gb Ab and Bb C Eb F Gb.

Daniel Forro

On 21 Apr 2009, at 2:51 AM, djtrancendance wrote:

>

>

> Lately I've been trying to find out the best compositional way to

> split apart pentatonic scales to form huge chords...since it seems

> so far 5-note-per-octave chords are approaching the limit of the

> size of a chord consonant within an octave space so far as diatonic

> tunings.

>

> One trick I have found that really seems to work well is splitting

> your usual 7-tone scales into multiple pentatonic scales and then

> distributing those in their own octave spaces IE

>

> #1) a#4,c#5,d#5, f#5,g#5

> #2) a#6,c6,d#6,f6, f#6

>

> (Note: together these form the entire 7-tone scale

> (c,c#,d#,f,f# ,g#,a#).. .but they still retain a sort of pentatonic

> lower level of tension/higher level of consonance)

> ************ ********* ********* ********* ********* ********* *****

>

> Try writing two individual melodies...one only using notes in scale

> #1 and the other only using notes in scale #2. Now try playing them

> together. Note how just about everything sounds more pure than

> you'd expect (or at least it does by far to my ears).

>

> On the side, I wonder if there is any special mathematical reason

> why this works and/or possible applications to other tunings...

>

> Michael

>

I don't think this is the main reason behind doubling of notes in the orchestral arrangements. If there are only three notes in the chord and you want to arrange it for orchestra, then of course it's necessary to use one note more times, be it in unison or in octaves.

Then composer/arranger must think how many instruments he will use, which orchestral groups will be involved, which dynamics he needs, if some note or instrument should be emphasized, how dense and wide the chord will be, if narrow/wide/mixed texture, doubling only or interpolation, considering also spectral question, length, articulation, rhythm... Too many things to decide and a lot of possibilities how to do it.

Besides there are rather strict and limiting rules for orchestral arrangements concerning good sound. From the point of the contemporary music the classical orchestra has a basic problem: all good sounding combinations were well analyzed and used by previous composers, with a peak somewhere at let's say Mahler, R. Strauss, Respighi, Holst, Stravinski, Debussy - that means Late-romantism, Impressionism, Folklorism. Contemporary orchestral music must follow these rules when composer wants such good sound (and this way music unfortunately returns back to the past time), or try new combinations and accept the fact it will never sound so well.

So in my opinion classical orchestra is good only for historical music and not so good for contemporary music. Only changes in its setting and form could help and shift it into the 21st century (like ading a lot of instruments - plucked, ethnic, electronic, using of DSP and amplification on some instruments). But tradition and prejudices work against it, as orchestra is a big institution, like a factory. Maybe economic crisis and general development of music will help to change this fossil dinosaurs and make something more flexible from it.

Daniel Forro

On 21 Apr 2009, at 11:38 AM, Michael Sheiman wrote:
>
> To me, it's as much about the issue of production quality and > hearing harmonics clearly (IE why so many orchestral composers > spread their arrangements over several octaves even for, say, a > triad to make it sound clearer)...as it is about hearing consonant-> sounding notes.
>
> -Michael

Daniel> "From the point of the contemporary music the classical orchestra has a basic >problem: all good sounding combinations were well analyzed and used by previous

>composers"

    This makes perfect sense so far as acoustic orchestral music where there are so many instruments (with many sounding very similar) that several must be played in virtually the same octave space and some overlap/conflict is virtually impossible to avoid.  

    However I'm convinced any orchestral (or any massively layered arrangement) done electronically (where you can get a massively wider range of different types of instruments involved and more different types of over-tones as well)...it often comes down to the fact problems in electronic music can be solved through very inconsistent production solutions and tons of different options, many of which can kill the organics beauty of the instrument they "clean up".

   For example, you can pan instruments with clashing frequencies on opposite sides of the spectrum when they hit nearby notes, add high-pass or band-elimination filters to avoid such conflict (tuning the middle harmonics on the bass down so they don't clash with the lower harmonics for higher instruments like flutes, for example), simply adjust the volume of instruments dynamically...

   But, even if you have, say, a single pianos playing a C major 7th chord...I figure you can have all the clever DSP filters and panning in the world and it pays to, for example, have no more than 3 notes played at once per any given octave and do things like "limit" each instrument to it's own "octave space".  Plus, this has the huge advantage of not adding the nasty phasing and lack-of-fullness artifacts DSP all too often leaves behind.

    Personally I compose enough electronic music to know how badly filters can make instruments sound overly artificial...especially when you do things like use a high-pass filter at 250hz+ on melodic instruments (which, sadly, people do a lot).   And thus my motto for production quality tuning...has become, solve as much as you can by arrangement alone before you resort to using DSP as a crutch.

-Michael

--- On Mon, 4/20/09, Daniel Forro <dan.for@tiscali.cz> wrote:

From: Daniel Forro <dan.for@...>
Subject: Re: [tuning] 7-note scales split into pentatonic scales by octave to maximize consonance
To: tuning@yahoogroups.com
Date: Monday, April 20, 2009, 8:12 PM

I don't think this is the main reason behind doubling of notes in the

orchestral arrangements. If there are only three notes in the chord

and you want to arrange it for orchestra, then of course it's

necessary to use one note more times, be it in unison or in octaves.

Then composer/arranger must think how many instruments he will use,

which orchestral groups will be involved, which dynamics he needs, if

some note or instrument should be emphasized, how dense and wide the

chord will be, if narrow/wide/ mixed texture, doubling only or

interpolation, considering also spectral question, length,

articulation, rhythm... Too many things to decide and a lot of

possibilities how to do it.

Besides there are rather strict and limiting rules for orchestral

arrangements concerning good sound. From the point of the

contemporary music the classical orchestra has a basic problem: all

good sounding combinations were well analyzed and used by previous

composers, with a peak somewhere at let's say Mahler, R. Strauss,

Respighi, Holst, Stravinski, Debussy - that means Late-romantism,

Impressionism, Folklorism. Contemporary orchestral music must follow

these rules when composer wants such good sound (and this way music

unfortunately returns back to the past time), or try new combinations

and accept the fact it will never sound so well.

So in my opinion classical orchestra is good only for historical

music and not so good for contemporary music. Only changes in its

setting and form could help and shift it into the 21st century (like

ading a lot of instruments - plucked, ethnic, electronic, using of

DSP and amplification on some instruments) . But tradition and

prejudices work against it, as orchestra is a big institution, like a

factory. Maybe economic crisis and general development of music will

help to change this fossil dinosaurs and make something more flexible

from it.

Daniel Forro

On 21 Apr 2009, at 11:38 AM, Michael Sheiman wrote:

>

> To me, it's as much about the issue of production quality and

> hearing harmonics clearly (IE why so many orchestral composers

> spread their arrangements over several octaves even for, say, a

> triad to make it sound clearer)...as it is about hearing consonant-

> sounding notes.

>

> -Michael