Easy ways to build/"sneak" microtonalism into common music: follow up to "the kiss of death"

Chris> "I see here a progression - in general western music has progressed towards greater and greater chromatic usage in harmony - melodic usage is not nearly as big of a deal - microtonality is the next logical step in harmony yes - but how long before that is accepted would depend on micro-tonal composers making something compelling enough for the average listener to make average musician make the effort all of us do now."

  Indeed...
Once upon a time virtually the only thing considered consonant was 3-limit IE 1/1 3/2 2/1.  Then came 5-limit and pentatonic scales.  And then 5-limit. 
And finally full-blown chromatic although even the most of the time we sadly end up stuck playing 5-limit type scales like the 7-tone c-major scale and various major-minor modes which usually end up containing exactly the same intervals, just in different orders. 

Now we ask the question...what if we could make more complex chords A) that go beyond 5-limit type scales and are still able to be played on today's instruments...or B) even leave the chromatic system behind entirely?

    To answer a possible solution for B)...recently I derived a scale that fits fairly closely into chromatic 12TET which is derived from the formula (1/octave)^x + 1 and features the tones:

---C4 D4 E4 F#4 G4 (g is the period) A4 B4 C#5 D5 (d = period) E5 F#5 G#5 A5 (a = period) B5 C#6 D#6 E6 (e = period) F#6 G#6 A#6 B6 (b = period) C#7 D#7 F7 F#7 (f# = period) G#7 A#7 C8 C#8 (c# = period)---

   It turns out Daniel Forro on the tuning list had derived the scale about 20 years ago.  And any musician can play it on any 12TET-capable instrument while preserving a majority of the micro-tonal feel and increase in degrees of tonal color and number of chords possible.

>>----------------------------
   So far as the question B) "what about leaving the
chromatic scale behind entirely"...I have found one possible solution in "re-gearing" the (1/octave)^x + 1 formula which generates the chromatic scale above to take advantage of other symmetries.
  For example: (1/PHI)^x + 1 (golden ratio sections) and (1/2.414)^x +1 (silver-ratio sections).

  Of course using those scales in the most consonant ways would require special timbres: but thanks to Sethares' and other algorithms to find ideal timbres and computer-based synthesizers with adjustable timbres...not to mention the possibility of, say, using a DSP-type effect to alter the timbres on notes played by a guitar...a whole new world of beautifully skewed timbre music may become readily accessible to the public.

   And of course, there are many other options (IE 7-limit, 9-limit, 11-limit...instead of 5-limit JI, decatonic scales in 22TET, and MOS scales to name a few)...I find the above particularly amusing because it is very hard to make sour chords with them (and thus learning the music theory for them would likely prove much easier than for, say, decatonic scales).

-Michael

> Now we ask the question...what if we could make more complex chords A) that
> go beyond 5-limit type scales and are still able to be played on today's
> instruments...or B) even leave the chromatic system behind entirely?
>
>     To answer a possible solution for B)...recently I derived a scale that
> fits fairly closely into chromatic 12TET which is derived from the formula
> (1/octave)^x + 1 and features the tones:
>
> ---C4 D4 E4 F#4 G4 (g is the period) A4 B4 C#5 D5 (d = period) E5 F#5 G#5 A5
> (a = period) B5 C#6 D#6 E6 (e = period) F#6 G#6 A#6 B6 (b = period) C#7 D#7
> F7 F#7 (f# = period) G#7 A#7 C8 C#8 (c# = period)---
>
>    It turns out Daniel Forro on the tuning list had derived the scale about
> 20 years ago.  And any musician can play it on any 12TET-capable instrument
> while preserving a majority of the micro-tonal feel and increase in degrees
> of tonal color and number of chords possible.

I made a post about this very same scale last year. Kind of a
pan-modal scale, if you will. I do like the way it sounds quite a bit.
Another one for you:

C D E | F G A | Bb C D | Eb F G | Ab Bb C

Kind of the utonal complement of the other one, in a way.

-Mike

>"I had the same question as you -- why is a 12-ET scale in

a thread about sneaking micro-tonalism into common music?"

I agree, it's confusing.
     The idea is about discussing the uses of periods other than the octave...using chromaticism as a simple example and then evolving into discussion of micro-tonal use.

   Mike B's example uses the circle of 4ths, the one I brought up used the circle of 5ths.  And, actually, the scale it is based on, (1/octave)^x + 1, is in fact micro-tonal...only it's close enough to chromaticism that it can be imitated with 12TET pretty well, thus making it more accessible to most people.  Note: the same theory can also be morphed into something distinctively not 12TET sounding at all, such as the scale generated by (1/PHI)^x + 1 or (1/sqrt(2))^x + 1 and beyond. 

   The point is using chromatic scales to explain the use of periods near chromatic tones which can also be extended into distinctively micro-tonal scales.

-Michael

[Non-text portions of this message have been removed]

Slonimsky's Thesaurus of scales and melodic patterns charted out quite a bit of this 12 tone territory. Which i think he would have enjoyed being taken into this territory.

Since i had 22 tone 11 limit just instruments . i explored non octave scales in much the same fashion which results in a bi-level set of intervals. Even after the sequence is determined, where one starts in the sequence on an instrument will produce quite different results. Usually i could play through them all and narrow it down by purely empirical methods. This would take some time as often the whole sequence would not repeat till way beyond the range of the instrument.

Besides the music of Georgia, another non octave language we can find in the field are Africa Ballophones (more of the 5 tone as opposed to the 7 tone) will have different intervals in the base. This has much to do with their language where they will speak in different ranges depending on both the subject and the emotional tone. Pretty much it was along this line that i attempted to line up my scale. Making it flaw from top to bottom is some reasonable way . As a whole i enjoyed the results of periods less than the octave more than those larger.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Mike Battaglia wrote:
>
>
> > Now we ask the question...what if we could make more complex chords > A) that
> > go beyond 5-limit type scales and are still able to be played on today's
> > instruments...or B) even leave the chromatic system behind entirely?
> >
> > To answer a possible solution for B)...recently I derived a > scale that
> > fits fairly closely into chromatic 12TET which is derived from the > formula
> > (1/octave)^x + 1 and features the tones:
> >
> > ---C4 D4 E4 F#4 G4 (g is the period) A4 B4 C#5 D5 (d = period) E5 > F#5 G#5 A5
> > (a = period) B5 C#6 D#6 E6 (e = period) F#6 G#6 A#6 B6 (b = period) > C#7 D#7
> > F7 F#7 (f# = period) G#7 A#7 C8 C#8 (c# = period)---
> >
> > It turns out Daniel Forro on the tuning list had derived the > scale about
> > 20 years ago. And any musician can play it on any 12TET-capable > instrument
> > while preserving a majority of the micro-tonal feel and increase in > degrees
> > of tonal color and number of chords possible.
>
> I made a post about this very same scale last year. Kind of a
> pan-modal scale, if you will. I do like the way it sounds quite a bit.
> Another one for you:
>
> C D E | F G A | Bb C D | Eb F G | Ab Bb C
>
> Kind of the utonal complement of the other one, in a way.
>
> -Mike
>
>

i thought the point was also mapping onto a 12 tone keyboard

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Michael Sheiman wrote:
>
>
> >"I had the same question as you -- why is a 12-ET scale in
>
> a thread about sneaking micro-tonalism into common music?"
>
> I agree, it's confusing.
> The idea is about discussing the uses of periods other than the > octave...using chromaticism as a simple example and then evolving into > discussion of micro-tonal use.
>
> Mike B's example uses the circle of 4ths, the one I brought up used > the circle of 5ths. And, actually, the scale it is based on, > (1/octave)^x + 1, is in fact micro-tonal...only it's close enough to > chromaticism that it can be imitated with 12TET pretty well, thus > making it more accessible to most people. Note: the same theory can > also be morphed into something distinctively not 12TET sounding at > all, such as the scale generated by (1/PHI)^x + 1 or (1/sqrt(2))^x + 1 > and beyond. >
> The point is using chromatic scales to explain the use of periods > near chromatic tones which can also be extended into distinctively > micro-tonal scales.
>
> -Michael
>
>
>
>
>
>
>
>
>
>
> [Non-text portions of this message have been removed]
>
>

http://anaphoria.com/7-9then7-12.gif
here is one i ended up using where first i had a 9 tone scale that repeated at the 'fifth' and then treated 12 of these as a scale and then took 7 out of those. then it modulations.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Michael Sheiman wrote:
>
>
> >"I had the same question as you -- why is a 12-ET scale in
>
> a thread about sneaking micro-tonalism into common music?"
>
> I agree, it's confusing.
> The idea is about discussing the uses of periods other than the > octave...using chromaticism as a simple example and then evolving into > discussion of micro-tonal use.
>
> Mike B's example uses the circle of 4ths, the one I brought up used > the circle of 5ths. And, actually, the scale it is based on, > (1/octave)^x + 1, is in fact micro-tonal...only it's close enough to > chromaticism that it can be imitated with 12TET pretty well, thus > making it more accessible to most people. Note: the same theory can > also be morphed into something distinctively not 12TET sounding at > all, such as the scale generated by (1/PHI)^x + 1 or (1/sqrt(2))^x + 1 > and beyond. >
> The point is using chromatic scales to explain the use of periods > near chromatic tones which can also be extended into distinctively > micro-tonal scales.
>
> -Michael
>
>
>
>
>
>
>
>
>
>
> [Non-text portions of this message have been removed]
>
>