Basing a 7-note system on pentatonic

   I made a "beta version" program designed to optimize the distance between overtones and root tones on higher octaves so they don't fall within a range between about 1.03 and 1.07 times each other (IE they avoid the approximate ratio of 1.05, which my ears detect as being maximally rough from the middle C.
  It uses a "brute force" method of trying every possible combination of interval ratios 1.07 to 1.2 to separate each of seven possible tones per octave.
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  And what the program basically gave as ideal for 7-tone scale intervals was within about 5-7 cents of a perfect pentatonic scale with the 6th and 7th notes (E and B) highly skewed from their original values (more like 1.22 and 1.82 than the usual 1.25 and 1.875).  And, case in point, playing the
pentatonic scale as a chord sounds quite good in 5-limit JI...but add either the E or the B and it sounds horribly dissonant.
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  Both the above programmatic and "by ear" tests seem to say that while our pentatonic system is dead-on our diatonic system (including 5-limit JI) may well need some work.

  Opinions or advice on these observations?  This time around I am not working on 8+ note scales with PHI/Silver-ratio basis...but instead trying to optimize 7-tone scale consonance...which seems to me to be clearly based on simply extending the pentatonic scale in a careful fashion.

-Michael

--- In tuning@yahoogroups.com, djtrancendance@... wrote:
>
>
>    I made a "beta version" program designed to optimize the distance between overtones and root tones on higher octaves so they don't fall within a range between about 1.03 and 1.07 times each other (IE they avoid the approximate ratio of 1.05, which my ears detect as being maximally rough from the middle C.
>   It uses a "brute force" method of trying every possible combination of interval ratios 1.07 to 1.2 to separate each of seven possible tones per octave.
> > - - - - - - - - - - - - - - - -
>   And what the program basically gave as ideal for 7-tone scale intervals was within about 5-7 cents of a perfect pentatonic scale with the 6th and 7th notes (E and B) highly skewed from their original values (more like 1.22 and 1.82 than the usual 1.25 and 1.875).  And, case in point, playing the
> pentatonic scale as a chord sounds quite good in 5-limit JI...but add either the E or the B and it sounds horribly dissonant.
> > - - - - - - - - - - - - - - - - - - - -
>   Both the above programmatic and "by ear" tests seem to say that while our pentatonic system is dead-on our diatonic system (including 5-limit JI) may well need some work.
>
>   Opinions or advice on these observations?  This time around I am not working on 8+ note scales with PHI/Silver-ratio basis...but instead trying to optimize 7-tone scale consonance...which seems to me to be clearly based on simply extending the pentatonic scale in a careful fashion.
>
> -Michael

How about 8:9:10:11:12:13:14?

--George

George> how about "8:9:10:11:12: 13:14"?

    I don't know if I'm the only one here whose ears jump at this...but having so many notes from a straight harmonic series in a row seems to create (to me, at least) so much "periodicity buzz" that it actually sounds more tense than playing all 7 tones from diatonic JI at once.  Not because it's a-tonal (actually since it points to the root tone of the harmonic series it's 'ultra-tonal'), but because the excessive periodicity buzz begins to sound mechanical and forced to my ears.

  The other problem is the harmonic series itself does not work past the 2/1 octave IE it ends up with more tones per octave than 7 (harmonics 15-28 have 13 notes instead of 7).
   It's a good suggestion as a test, though; in fact, I had tried that trick before.

-Michael

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@...> wrote:
>
> How about 8:9:10:11:12:13:14?
>
> --George
>

Even before I started studying just intonation, I came up with this very scale, (known by some as the "accoustic" scale), since it is the first one that shows up in the harmonic series. I couldn't for the life of me figure out how the major scale was formed and what basis it had in the harmonic series. I even did a small presentation in a music class using a small melody based on this scale. I never did well in the class. This probably was not why.

The major scale is actually based on a union of I, IV and V triads. If you stuck to harmonizing with those three chords, there would be no comma-pumping and head-scratching with the 5-limit JI scale. The accoustic scale, however, is based on only one chord, the harmonic 13th. The melodies played on this scale would have the quality of "being" music, which doesn't have the feeling of progress or going places. Rather than progressing between chords in cadences, it just sits on one chord (albeit an extended one) and be's a melody.

In actual practice, the melody would probably linger on this scale for awhile, and then modulate to another fundamental and continue from there. Then you would have something akin to the Bartok style.

It may be worth noting that the 5th mode of this scale is the melodic minor.

Billy