7-limit temperaments and the blues scale

I am currently really interested in the 7-limit. For example, take the
blues scale (0,3,5,6,7,10) Some interested facts: If C=0, then what you
have is a pentatonic scale on Eb with added minor third (Gb over Eb).
So we are working with C minor pentatonic or Eb pentatonic. Also,
(0,3,5 and 7,10,12) are the top halves of dominant seventh chords F7
and C7. So this relates to the 7-limit. Also, if you take the Z-related
complement of (0,3,5,6,7,10) you get (1,2,4,8,9,11) which is E7 and A
major triad superimposed. When one considers all the music based on the
blues scale and variants (blues, jazz, rock etc) I think this angle
might be worth pursuing. One gets (36, 42, 48, 49, 54, 63, 72) as one
possible just intonation version of the blues scale. You get a C minor
triad of (6,7,9) and an Eb minor triad of (6,7,9 - the simplest form for
a minor triad. Thoughts anyone?

One of the primary aspects of your pitch-set is the lack of "5" -- you are
dealing with simply "3" and "7" (a la LaMonte)

P

__________________________________________

"Paul G Hjelmstad" <paul.hjelmstad@us.ing.com>
Sent by: tuning@yahoogroups.com
05/27/2005 11:18 AM
Please respond to tuning

To: tuning@yahoogroups.com
cc:
Subject: [tuning] 7-limit temperaments and the blues scale

I am currently really interested in the 7-limit. For example, take the
blues scale (0,3,5,6,7,10) Some interested facts: If C=0, then what you
have is a pentatonic scale on Eb with added minor third (Gb over Eb).
So we are working with C minor pentatonic or Eb pentatonic. Also,
(0,3,5 and 7,10,12) are the top halves of dominant seventh chords F7
and C7. So this relates to the 7-limit. Also, if you take the Z-related
complement of (0,3,5,6,7,10) you get (1,2,4,8,9,11) which is E7 and A
major triad superimposed. When one considers all the music based on the
blues scale and variants (blues, jazz, rock etc) I think this angle
might be worth pursuing. One gets (36, 42, 48, 49, 54, 63, 72) as one
possible just intonation version of the blues scale. You get a C minor
triad of (6,7,9) and an Eb minor triad of (6,7,9 - the simplest form for
a minor triad. Thoughts anyone?

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--- In tuning@yahoogroups.com, "Paul G Hjelmstad"
<paul.hjelmstad@u...> wrote:

>Thoughts anyone?

Here are some:

(1) The scale is a no-fives scale, ie {2,3,7}

(2) It can be transposed to 1-8/7-7/6-9/7-3/2-12/7

(3) It contains a pentatonic scale in the Scala archives
called slendro5_2, which leaves off the 49/36

(4) I tried forcing in a little 5-limit harmony by projecting to
the breed plane, with generators 49/40 and 10/7, and taking the convex
closure, a game I've been playing lately. This expanded the scale to
1-7/6-49/40-4/3-49/36-10/7-3/2-49/30-7/4-40/21, which can be used as
is or tempered by 441 or 612 so that the 2401/2400 relationships
between some of the notes go away. This now has a 1-7/6-7/5 chord and
(via 2401/2400) a 1-6/5-7/5 chord, they fit together in a
1-7/6-7/5-49/30 chord, which is an interesting chord I don't have a
name for: it has intervals 7/6-6/5-7/6-60/49, so two 7/6 subminor
thirds, a minor third, and a neutral third making up the octave. If we
consider the neutral third to be an 11/9, we now want to temper out
540/539, which we could do in miracle, or in 130 or 171, or in the
130&171 temperament I called "sesquiquartififths" at one point, a
horrible name someone may want to suggest an alternative for. The
generator is 1/4 of a schismatic tempered fifth.

(5) Here are some Scala scl files:

! slendro5_2.scl
!
A slendro type pentatonic which is based on intervals of 7, no. 2

5
!
7/6
4/3
3/2
7/4
2/1

! hjelm.scl
Paul Hjelmstad's "blues" scale tuning@yahoo May 27, 2005
6
!
7/6
4/3
49/36
3/2
7/4
2

! hjelmconv.scl
convex closure in breed plane of hjelm.scl
10
!
7/6
49/40
4/3
49/36
10/7
3/2
49/30
7/4
40/21
2

Paul G Hjelmstad wrote:

> I am currently really interested in the 7-limit. For example, take the
> blues scale (0,3,5,6,7,10) Some interested facts: If C=0, then what you
> have is a pentatonic scale on Eb with added minor third (Gb over Eb).
> So we are working with C minor pentatonic or Eb pentatonic. Also,
> (0,3,5 and 7,10,12) are the top halves of dominant seventh chords F7
> and C7. So this relates to the 7-limit. Also, if you take the Z-related
> complement of (0,3,5,6,7,10) you get (1,2,4,8,9,11) which is E7 and A
> major triad superimposed. When one considers all the music based on the
> blues scale and variants (blues, jazz, rock etc) I think this angle
> might be worth pursuing. One gets (36, 42, 48, 49, 54, 63, 72) as one
> possible just intonation version of the blues scale. You get a C minor
> triad of (6,7,9) and an Eb minor triad of (6,7,9 - the simplest form for
> a minor triad. Thoughts anyone?

Who came up with the idea that the Blues are in the 7-limit? (No, this is really a question, since "the literature" says that the blue third is between the major and minor third, old recordings have the blue notes between the major and minor degrees, and guitarists bend up the minor third and not the major third.

But I use the 7-intonation myself, although in a different scale structure. 12-et people generally raise an eyebrow, but tolerate it.

klaus

klaus schmirler wrote:
> Paul G Hjelmstad wrote:
> > >>I am currently really interested in the 7-limit. For example, take the
>>blues scale (0,3,5,6,7,10) Some interested facts: If C=0, then what you
>>have is a pentatonic scale on Eb with added minor third (Gb over Eb).
>>So we are working with C minor pentatonic or Eb pentatonic. Also,
>>(0,3,5 and 7,10,12) are the top halves of dominant seventh chords F7
>>and C7. So this relates to the 7-limit. Also, if you take the Z-related
>>complement of (0,3,5,6,7,10) you get (1,2,4,8,9,11) which is E7 and A
>>major triad superimposed. When one considers all the music based on the
>>blues scale and variants (blues, jazz, rock etc) I think this angle
>>might be worth pursuing. One gets (36, 42, 48, 49, 54, 63, 72) as one
>>possible just intonation version of the blues scale. You get a C minor
>>triad of (6,7,9) and an Eb minor triad of (6,7,9 - the simplest form for
>>a minor triad. Thoughts anyone?
> > > Who came up with the idea that the Blues are in the 7-limit? (No, this > is really a question, since "the literature" says that the blue third > is between the major and minor third, old recordings have the blue > notes between the major and minor degrees, and guitarists bend up the > minor third and not the major third.

major second, as I'm sure everyone realized way before me.

> > But I use the 7-intonation myself, although in a different scale > structure. 12-et people generally raise an eyebrow, but tolerate it.
> > > klaus