Seventh Heaven

Here's a 7 prime limit just scale cramming in as many 7's as possible.

Seventh Heaven
1/1
54/49
9/8
6/5
60/49
4/3
72/49
3/2
81/49
12/7
90/49
96/49
2/1

With the version I posted earlier the tonic was the fourth note in the scale. I transposed the numbers so that 1/1 is now the tonic.

John.

   Actually quite a nice scale...especially if you don't mind the 14/9 variety of fifth or the occasional 15/11 type of fourth and 22/15 diminished fifth and the 11/9-ish neutral second.  Everything else in this scale, so far as I can see, is amazingly low-limit.

--- On Mon, 2/14/11, john777music <jfos777@...> wrote:

From: john777music <jfos777@yahoo.com>
Subject: [tuning] Seventh Heaven
To: tuning@yahoogroups.com
Date: Monday, February 14, 2011, 10:28 AM

Here's a 7 prime limit just scale cramming in as many 7's as possible.

Seventh Heaven

1/1

54/49

9/8

6/5

60/49

4/3

72/49

3/2

81/49

12/7

90/49

96/49

2/1

With the version I posted earlier the tonic was the fourth note in the scale. I transposed the numbers so that 1/1 is now the tonic.

John.

Very interesting scale...how did you derive it, John?

-Igs

--- In tuning@yahoogroups.com, "john777music" <jfos777@...> wrote:
>
> Here's a 7 prime limit just scale cramming in as many 7's as possible.
>
> Seventh Heaven
> 1/1
> 54/49
> 9/8
> 6/5
> 60/49
> 4/3
> 72/49
> 3/2
> 81/49
> 12/7
> 90/49
> 96/49
> 2/1
>
> With the version I posted earlier the tonic was the fourth note in the scale. I transposed the numbers so that 1/1 is now the tonic.
>
> John.
>

Hi Igs,

just for fun I decided to create a scale with as many 7's as possible. I looked at all the 7 prime limit notes that relate to 1/1 which belong to the list on page 26 of my book. I selected 11 notes (after 1/1) from the list that contained a 7 or a multiple of 7 in the numerator or denominator. Here's what I got..

1/1
15/14
8/7
7/6
9/7
21/16
7/5
10/7
14/9
12/7
7/4
27/14
2/1

Playing the scale on my keyboard it was clear that 1/1 did not sound like a tonic (or a resolved sounding note). Playing around with the scale it seemed to me that 7/6 (the fourth note) sounded like a better choice of tonic. So, starting with 7/6 I multiplied each note by 6/7 to get the scale you have below. Some of the intervals are only 35 cents wide but I must say the scale sounds (to me at least) exotic and intriguing.

Have you tried it yourself?

John.

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> Very interesting scale...how did you derive it, John?
>
> -Igs
>
> --- In tuning@yahoogroups.com, "john777music" <jfos777@> wrote:
> >
> > Here's a 7 prime limit just scale cramming in as many 7's as possible.
> >
> > Seventh Heaven
> > 1/1
> > 54/49
> > 9/8
> > 6/5
> > 60/49
> > 4/3
> > 72/49
> > 3/2
> > 81/49
> > 12/7
> > 90/49
> > 96/49
> > 2/1
> >
> > With the version I posted earlier the tonic was the fourth note in the scale. I transposed the numbers so that 1/1 is now the tonic.
> >
> > John.
> >
>

John,

I improvised this and had a nice edit and then Sonar crashed and I had
family business to attend to. Soooooo this is much rougher but essentially
as performed. I hope you feel it does your tuning a bit of justice.

http://micro.soonlabel.com/just/7th-heaven/daily20110214-7th-heaven.mp3
or online play
http://notonlymusic.com/board/viewtopic.php?f=23&t=794&start=0

As I told you in email

"I just finished the composition. Oddly enough traditional tertiary triads
didn't sound too good. So I wrote a piece that revolved around minor 7th
dyad as the consonant resting point.
Let me edit a few bum notes and I will post it."

Chris

On Mon, Feb 14, 2011 at 1:28 PM, john777music <jfos777@...> wrote:

>
>
> Here's a 7 prime limit just scale cramming in as many 7's as possible.
>
>
> Seventh Heaven
> 1/1
> 54/49
> 9/8
> 6/5
> 60/49
> 4/3
> 72/49
> 3/2
> 81/49
> 12/7
> 90/49
> 96/49
> 2/1
>
> With the version I posted earlier the tonic was the fourth note in the
> scale. I transposed the numbers so that 1/1 is now the tonic.
>
> John.
>
>
>

Thanks Chris,

your piece demonstrates that the scale "works" but it seems a bit slow and moody. I think the scale is worthy of further exploration if you want to have another crack at it.

I'm going to post my own melodic Seventh Heaven piece which is simply using all the notes going from 1/1 to 2/1 and back again.

You said <Oddly enough traditional tertiary triads didn't sound too good.>

I think this is to be expected. I suspect that a lot of the *good* chords that occur in Seventh Heaven sound like crap in 12TET. i.e. there are unexpected good chords that would not occur in 12TET. You might have to "find" these good chords.

Thanks again for trying the scale.

John.

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> John,
>
> I improvised this and had a nice edit and then Sonar crashed and I had
> family business to attend to. Soooooo this is much rougher but essentially
> as performed. I hope you feel it does your tuning a bit of justice.
>
> http://micro.soonlabel.com/just/7th-heaven/daily20110214-7th-heaven.mp3
> or online play
> http://notonlymusic.com/board/viewtopic.php?f=23&t=794&start=0
>
> As I told you in email
>
> "I just finished the composition. Oddly enough traditional tertiary triads
> didn't sound too good. So I wrote a piece that revolved around minor 7th
> dyad as the consonant resting point.
> Let me edit a few bum notes and I will post it."
>
> Chris
>
>
> On Mon, Feb 14, 2011 at 1:28 PM, john777music <jfos777@...> wrote:
>
> >
> >
> > Here's a 7 prime limit just scale cramming in as many 7's as possible.
> >
> >
> > Seventh Heaven
> > 1/1
> > 54/49
> > 9/8
> > 6/5
> > 60/49
> > 4/3
> > 72/49
> > 3/2
> > 81/49
> > 12/7
> > 90/49
> > 96/49
> > 2/1
> >
> > With the version I posted earlier the tonic was the fourth note in the
> > scale. I transposed the numbers so that 1/1 is now the tonic.
> >
> > John.
> >
> >
> >
>

John(to Chris)>"You said <Oddly enough traditional tertiary triads didn't sound too good."

     I think this is to be expected. I suspect that a lot of the *good* chords that occur in Seventh Heaven sound like crap in 12TET."

   The real difference to me...is there are a lot of 14/9 "fifths" where the perfect fifths would normally be.  So if you like 14/9, that's fine, but if you are expecting 3/2 for your cookie-cutter meantone-style triads, tough...(lol) 
   This type of double standard I hate.  When people use a fair deal of 3/2-like fifths people complain "hur hur...that's just meantone, nothing special"...and if they use anything else around that area IE 22/15, 13/9, 14/9...they complain "ugh, all the traditional 3/2 triads sound bad, this scale is no good".
  Seems like people aren't happy either way...so what's the goal here?

--- On Mon, 2/14/11, john777music <jfos777@...> wrote:

From: john777music <jfos777@...>
Subject: [tuning] Re: Seventh Heaven
To: tuning@yahoogroups.com
Date: Monday, February 14, 2011, 5:22 PM

Thanks Chris,

your piece demonstrates that the scale "works" but it seems a bit slow and moody. I think the scale is worthy of further exploration if you want to have another crack at it.

I'm going to post my own melodic Seventh Heaven piece which is simply using all the notes going from 1/1 to 2/1 and back again.

You said <Oddly enough traditional tertiary triads didn't sound too good.>

I think this is to be expected. I suspect that a lot of the *good* chords that occur in Seventh Heaven sound like crap in 12TET. i.e. there are unexpected good chords that would not occur in 12TET. You might have to "find" these good chords.

Thanks again for trying the scale.

John.

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:

>

> John,

>

> I improvised this and had a nice edit and then Sonar crashed and I had

> family business to attend to. Soooooo this is much rougher but essentially

> as performed. I hope you feel it does your tuning a bit of justice.

>

> http://micro.soonlabel.com/just/7th-heaven/daily20110214-7th-heaven.mp3

> or online play

> http://notonlymusic.com/board/viewtopic.php?f=23&t=794&start=0

>

> As I told you in email

>

> "I just finished the composition. Oddly enough traditional tertiary triads

> didn't sound too good. So I wrote a piece that revolved around minor 7th

> dyad as the consonant resting point.

> Let me edit a few bum notes and I will post it."

>

> Chris

>

>

> On Mon, Feb 14, 2011 at 1:28 PM, john777music <jfos777@...> wrote:

>

> >

> >

> > Here's a 7 prime limit just scale cramming in as many 7's as possible.

> >

> >

> > Seventh Heaven

> > 1/1

> > 54/49

> > 9/8

> > 6/5

> > 60/49

> > 4/3

> > 72/49

> > 3/2

> > 81/49

> > 12/7

> > 90/49

> > 96/49

> > 2/1

> >

> > With the version I posted earlier the tonic was the fourth note in the

> > scale. I transposed the numbers so that 1/1 is now the tonic.

> >

> > John.

> >

> >

> >

>

Perhaps I will tomorrow. I think your evaluation of what I did is pretty
fair.

On Mon, Feb 14, 2011 at 8:22 PM, john777music <jfos777@...> wrote:

>
>
> Thanks Chris,
>
> your piece demonstrates that the scale "works" but it seems a bit slow and
> moody. I think the scale is worthy of further exploration if you want to
> have another crack at it.
>
> I'm going to post my own melodic Seventh Heaven piece which is simply using
> all the notes going from 1/1 to 2/1 and back again.
>
> You said <Oddly enough traditional tertiary triads didn't sound too good.>
>
> I think this is to be expected. I suspect that a lot of the *good* chords
> that occur in Seventh Heaven sound like crap in 12TET. i.e. there are
> unexpected good chords that would not occur in 12TET. You might have to
> "find" these good chords.
>
> Thanks again for trying the scale.
>
> John.
>
>
>
> --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
> >
> > John,
> >
> > I improvised this and had a nice edit and then Sonar crashed and I had
> > family business to attend to. Soooooo this is much rougher but
> essentially
> > as performed. I hope you feel it does your tuning a bit of justice.
> >
> > http://micro.soonlabel.com/just/7th-heaven/daily20110214-7th-heaven.mp3
> > or online play
> > http://notonlymusic.com/board/viewtopic.php?f=23&t=794&start=0
> >
> > As I told you in email
> >
> > "I just finished the composition. Oddly enough traditional tertiary
> triads
> > didn't sound too good. So I wrote a piece that revolved around minor 7th
> > dyad as the consonant resting point.
> > Let me edit a few bum notes and I will post it."
> >
> > Chris
> >
> >
> > On Mon, Feb 14, 2011 at 1:28 PM, john777music <jfos777@...> wrote:
> >
> > >
> > >
> > > Here's a 7 prime limit just scale cramming in as many 7's as possible.
> > >
> > >
> > > Seventh Heaven
> > > 1/1
> > > 54/49
> > > 9/8
> > > 6/5
> > > 60/49
> > > 4/3
> > > 72/49
> > > 3/2
> > > 81/49
> > > 12/7
> > > 90/49
> > > 96/49
> > > 2/1
> > >
> > > With the version I posted earlier the tonic was the fourth note in the
> > > scale. I transposed the numbers so that 1/1 is now the tonic.
> > >
> > > John.
> > >
> > >
> > >
> >
>
>
>

Beautiful scale John !
To my eyes it explores interesting bridges between the 49/40 or 60/49 hemififths (which can be heard as 11/9 or 27/22 variations, the difference being 540/539), and the 7th limit (only) present with 12/7.
The hemifiths brings Mohajira flavors here. It has at least one perfect Mohajira tetrachord :
[90/49 1/1 9/8 60/49]
and a strange Rast-Mohajira hybrid scale :
[1/1 54/49 60/49 4/3 3/2 81/49 90/49], that would be a full Mohajira with 80/49 instead of 81/49.

Note that the reason that the scale is in fact, not so "7th-limit" but sounding rather "11th-limit" (hear for example the "11/8" between 6/5 and 81/49) is because you started from, except for 1/1, ONLY with ratios including 7. So obviously 12/7 is your former 1/1 and perhaps too much isolated now. I suppose that introducing a little more ratios non-including 7 from the beginning would make it in fact more 7th-limit (and "7th Heaven" ?, this I can't tell...)

ex. of such variation with 8/5 :
1/1
54/49
9/8
6/5
60/49
4/3
72/49
3/2
8/5
81/49
12/7
90/49
2/1

or 15/8, with a 56/45 as a tempered "turkish" third :
1/1
54/49
9/8
60/49
56/45
4/3
72/49
3/2
81/49
12/7
90/49
15/8
2/1

or 7/6, with perhaps 7/4 and 80/49 :
1/1
54/49
9/8
7/6
60/49
4/3
72/49
3/2
8/5
80/49
7/4
90/49
2/1

??
- - - - - - -
Jacques

John wrote :

> Hi Igs,
>
> just for fun I decided to create a scale with as many 7's as > possible. I looked at all the 7 prime limit notes that relate to > 1/1 which belong to the list on page 26 of my book. I selected 11 > notes (after 1/1) from the list that contained a 7 or a multiple of > 7 in the numerator or denominator. Here's what I got..
>
> 1/1
> 15/14
> 8/7
> 7/6
> 9/7
> 21/16
> 7/5
> 10/7
> 14/9
> 12/7
> 7/4
> 27/14
> 2/1

Thanks Jacques,

I didn't know that approximate 11 limit intervals occurred in the scale and this is a bonus.

Do you want to try composing a piece using the scale?

John.

--- In tuning@yahoogroups.com, Jacques Dudon <fotosonix@...> wrote:
>
> Beautiful scale John !
> To my eyes it explores interesting bridges between the 49/40 or 60/49
> hemififths (which can be heard as 11/9 or 27/22 variations, the
> difference being 540/539), and the 7th limit (only) present with 12/7.
> The hemifiths brings Mohajira flavors here. It has at least one
> perfect Mohajira tetrachord :
> [90/49 1/1 9/8 60/49]
> and a strange Rast-Mohajira hybrid scale :
> [1/1 54/49 60/49 4/3 3/2 81/49 90/49], that would be a
> full Mohajira with 80/49 instead of 81/49.
>
> Note that the reason that the scale is in fact, not so "7th-limit"
> but sounding rather "11th-limit" (hear for example the "11/8" between
> 6/5 and 81/49) is because you started from, except for 1/1, ONLY with
> ratios including 7. So obviously 12/7 is your former 1/1 and perhaps
> too much isolated now. I suppose that introducing a little more
> ratios non-including 7 from the beginning would make it in fact more
> 7th-limit (and "7th Heaven" ?, this I can't tell...)
>
> ex. of such variation with 8/5 :
> 1/1
> 54/49
> 9/8
> 6/5
> 60/49
> 4/3
> 72/49
> 3/2
> 8/5
> 81/49
> 12/7
> 90/49
> 2/1
>
> or 15/8, with a 56/45 as a tempered "turkish" third :
> 1/1
> 54/49
> 9/8
> 60/49
> 56/45
> 4/3
> 72/49
> 3/2
> 81/49
> 12/7
> 90/49
> 15/8
> 2/1
>
> or 7/6, with perhaps 7/4 and 80/49 :
> 1/1
> 54/49
> 9/8
> 7/6
> 60/49
> 4/3
> 72/49
> 3/2
> 8/5
> 80/49
> 7/4
> 90/49
> 2/1
>
> ??
> - - - - - - -
> Jacques
>
>
>
> John wrote :
>
> > Hi Igs,
> >
> > just for fun I decided to create a scale with as many 7's as
> > possible. I looked at all the 7 prime limit notes that relate to
> > 1/1 which belong to the list on page 26 of my book. I selected 11
> > notes (after 1/1) from the list that contained a 7 or a multiple of
> > 7 in the numerator or denominator. Here's what I got..
> >
> > 1/1
> > 15/14
> > 8/7
> > 7/6
> > 9/7
> > 21/16
> > 7/5
> > 10/7
> > 14/9
> > 12/7
> > 7/4
> > 27/14
> > 2/1
>

--- In tuning@yahoogroups.com, "john777music" <jfos777@...> wrote:
>
> Thanks Jacques,
>
> I didn't know that approximate 11 limit intervals occurred in the scale and this is a bonus.

Definitively, it can even be an interesting temperament if you temper 540/539

> Do you want to try composing a piece using the scale?
>
> John.

At this moment Chris I am sure will do a better job than me (and has better keyboard technique ;-)
Some parts of the harmonies he did are actually very beautiful.

But do you want to try to improve this scale by making it more 7th-limit balanced ? I think it's worth it to try. You can use any of the variations I suggested of course, there are others. Forget about the chromatic scale and try adding different real 7th-limit ratios first (like with "7" in the denominator, or numerator).

> --- In tuning@yahoogroups.com, Jacques Dudon <fotosonix@> wrote:
> >
> > Beautiful scale John !
> > To my eyes it explores interesting bridges between the 49/40 or 60/49
> > hemififths (which can be heard as 11/9 or 27/22 variations, the
> > difference being 540/539), and the 7th limit (only) present with 12/7.
> > The hemifiths brings Mohajira flavors here. It has at least one
> > perfect Mohajira tetrachord :
> > [90/49 1/1 9/8 60/49]
> > and a strange Rast-Mohajira hybrid scale :
> > [1/1 54/49 60/49 4/3 3/2 81/49 90/49], that would be a
> > full Mohajira with 80/49 instead of 81/49.
> >
> > Note that the reason that the scale is in fact, not so "7th-limit"
> > but sounding rather "11th-limit" (hear for example the "11/8" between
> > 6/5 and 81/49) is because you started from, except for 1/1, ONLY with
> > ratios including 7. So obviously 12/7 is your former 1/1 and perhaps
> > too much isolated now. I suppose that introducing a little more
> > ratios non-including 7 from the beginning would make it in fact more
> > 7th-limit (and "7th Heaven" ?, this I can't tell...)
> >
> > ex. of such variation with 8/5 :
> > 1/1
> > 54/49
> > 9/8
> > 6/5
> > 60/49
> > 4/3
> > 72/49
> > 3/2
> > 8/5
> > 81/49
> > 12/7
> > 90/49
> > 2/1
> >
> > or 15/8, with a 56/45 as a tempered "turkish" third :
> > 1/1
> > 54/49
> > 9/8
> > 60/49
> > 56/45
> > 4/3
> > 72/49
> > 3/2
> > 81/49
> > 12/7
> > 90/49
> > 15/8
> > 2/1
> >
> > or 7/6, with perhaps 7/4 and 80/49 :
> > 1/1
> > 54/49
> > 9/8
> > 7/6
> > 60/49
> > 4/3
> > 72/49
> > 3/2
> > 8/5
> > 80/49
> > 7/4
> > 90/49
> > 2/1
> >
> > ??
> > - - - - - - -
> > Jacques
> >
> >
> >
> > John wrote :
> >
> > > Hi Igs,
> > >
> > > just for fun I decided to create a scale with as many 7's as
> > > possible. I looked at all the 7 prime limit notes that relate to
> > > 1/1 which belong to the list on page 26 of my book. I selected 11
> > > notes (after 1/1) from the list that contained a 7 or a multiple of
> > > 7 in the numerator or denominator. Here's what I got..
> > >
> > > 1/1
> > > 15/14
> > > 8/7
> > > 7/6
> > > 9/7
> > > 21/16
> > > 7/5
> > > 10/7
> > > 14/9
> > > 12/7
> > > 7/4
> > > 27/14
> > > 2/1
> >
>

Jacques,

as regards tweaking the scale by introducing more just 7 limit dyads I think the tonic might change from 1/1 to another note and I would possibly end up where I started. i.e....

1/1
15/14
8/7
7/6 tonic
9/7
21/16
7/5
10/7
14/9
12/7
7/4
27/14
2/1

I could temper the scale to yield more sevens but I'm not sure if more sevens can be found (within 6.776 cents accuracy or 256/255). This tempering would take me a long time to program and I can't be bothered.

I could also temper it to yield the maximum number of good intervals (e.g. 3/2, 4/3 etc) overall but I imagine the number of sevens might decrease.

So I'll leave it to others if they want to *improve* the scale.

John.

--- In tuning@yahoogroups.com, "Jacques Dudon" <fotosonix@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "john777music" <jfos777@> wrote:
> >
> > Thanks Jacques,
> >
> > I didn't know that approximate 11 limit intervals occurred in the scale and this is a bonus.
>
> Definitively, it can even be an interesting temperament if you temper 540/539
>
> > Do you want to try composing a piece using the scale?
> >
> > John.
>
> At this moment Chris I am sure will do a better job than me (and has better keyboard technique ;-)
> Some parts of the harmonies he did are actually very beautiful.
>
> But do you want to try to improve this scale by making it more 7th-limit balanced ? I think it's worth it to try. You can use any of the variations I suggested of course, there are others. Forget about the chromatic scale and try adding different real 7th-limit ratios first (like with "7" in the denominator, or numerator).
>
> > --- In tuning@yahoogroups.com, Jacques Dudon <fotosonix@> wrote:
> > >
> > > Beautiful scale John !
> > > To my eyes it explores interesting bridges between the 49/40 or 60/49
> > > hemififths (which can be heard as 11/9 or 27/22 variations, the
> > > difference being 540/539), and the 7th limit (only) present with 12/7.
> > > The hemifiths brings Mohajira flavors here. It has at least one
> > > perfect Mohajira tetrachord :
> > > [90/49 1/1 9/8 60/49]
> > > and a strange Rast-Mohajira hybrid scale :
> > > [1/1 54/49 60/49 4/3 3/2 81/49 90/49], that would be a
> > > full Mohajira with 80/49 instead of 81/49.
> > >
> > > Note that the reason that the scale is in fact, not so "7th-limit"
> > > but sounding rather "11th-limit" (hear for example the "11/8" between
> > > 6/5 and 81/49) is because you started from, except for 1/1, ONLY with
> > > ratios including 7. So obviously 12/7 is your former 1/1 and perhaps
> > > too much isolated now. I suppose that introducing a little more
> > > ratios non-including 7 from the beginning would make it in fact more
> > > 7th-limit (and "7th Heaven" ?, this I can't tell...)
> > >
> > > ex. of such variation with 8/5 :
> > > 1/1
> > > 54/49
> > > 9/8
> > > 6/5
> > > 60/49
> > > 4/3
> > > 72/49
> > > 3/2
> > > 8/5
> > > 81/49
> > > 12/7
> > > 90/49
> > > 2/1
> > >
> > > or 15/8, with a 56/45 as a tempered "turkish" third :
> > > 1/1
> > > 54/49
> > > 9/8
> > > 60/49
> > > 56/45
> > > 4/3
> > > 72/49
> > > 3/2
> > > 81/49
> > > 12/7
> > > 90/49
> > > 15/8
> > > 2/1
> > >
> > > or 7/6, with perhaps 7/4 and 80/49 :
> > > 1/1
> > > 54/49
> > > 9/8
> > > 7/6
> > > 60/49
> > > 4/3
> > > 72/49
> > > 3/2
> > > 8/5
> > > 80/49
> > > 7/4
> > > 90/49
> > > 2/1
> > >
> > > ??
> > > - - - - - - -
> > > Jacques
> > >
> > >
> > >
> > > John wrote :
> > >
> > > > Hi Igs,
> > > >
> > > > just for fun I decided to create a scale with as many 7's as
> > > > possible. I looked at all the 7 prime limit notes that relate to
> > > > 1/1 which belong to the list on page 26 of my book. I selected 11
> > > > notes (after 1/1) from the list that contained a 7 or a multiple of
> > > > 7 in the numerator or denominator. Here's what I got..
> > > >
> > > > 1/1
> > > > 15/14
> > > > 8/7
> > > > 7/6
> > > > 9/7
> > > > 21/16
> > > > 7/5
> > > > 10/7
> > > > 14/9
> > > > 12/7
> > > > 7/4
> > > > 27/14
> > > > 2/1
> > >
> >
>