Blue Temperament Chords

Here's my Blue Temperament tuning again but this time with a list of good chords that are an octave or less wide.

BT in cents...

0.0c, 121.6c, 200.7c, 313.5c, 388.4c, 501.2c, 580.4c,
702.0c, 816.9c, 889.4c, 1012.5c, 1085.1c, 1200c.

BT in frequencies...

1.0, 1.072740, 1.122938, 1.198533, 1.25153, 1.335782,
1.398289, 1.5, 1.602938, 1.671566, 1.794724, 1.871563, 2.0.

Adjustments...

1st note 0.0 cents
2nd note +21.6 cents
3rd note +0.7 cents
4th note +13.5 cents
5th note -11.6 cents
6th note +1.2 cents
7th note -19.6 cents
8th note +2.0 cents
9th note +16.9 cents
10th note -10.6 cents
11th note +12.5 cents
12th note -14.9 cents

List of good chords if tonic (1/1) is E...
Use fixed width font.

E1 F#1 A#1 C1
E1 F#1 A#1 D1
E1 F#1 B1 D1
E1 G1 A#1 C1 E2
E1 G1 A#1 C#1 E2
E1 G1 A#1 D1
E1 G1 B1 D1
E1 G1 B1 E2
E1 G#1 B1 D1
E1 G#1 B1 E2
E1 G#1 C1 E2
E1 G#1 C#1 E2
E1 A1 B1 E2
E1 A1 C1 E2
E1 A1 C#1 E2

F1 G#1 B1 D1 F2
F1 G#1 B1 D#1 F2
F1 G#1 B1 E2
F1 G#1 C1 D#1 F2
F1 G#1 C1 E2
F1 A1 B1 D#1 F2
F1 A1 B1 E2
F1 A1 C1 D#1 F2
F1 A1 C1 E2

F#1 A#1 C1 D#1 F#2 *
F#1 A#1 D1 F#2
F#1 B1 D1 F#2
F#1 B1 D#1 F#2
F#1 A#1 C1 F#2 (subset of *)
F#1 A#1 D#1 F#2 (subset of *)
F#1 C1 D#1 F#2 (subset of *)

G1 A#1 C1 E2 G2 *
G1 A#1 C#1 E2 G2 **
G1 A#1 D1 G2
G1 B1 D1 G2
G1 B1 E2 G2
G1 A#1 C1 G2 (subset of *)
G1 A#1 E2 G2 (subset of *)
G1 C1 E2 G2 (subset of *)
G1 A#1 C#1 G2 (subset of **)
G1 A#1 E2 G2 (subset of **)
G1 C#1 E2 G2 (subset of **)

G#1 B1 D1 F2 G#2
G#1 B1 D1 F#2
G#1 B1 D1 G#2
G#1 B1 D#1 F2 G#2
G#1 B1 D#1 F#2
G#1 B1 E2 F#2
G#1 B1 E2 G#2
G#1 C1 D#1 F2
G#1 C1 D#1 F#2
G#1 C1 E2 F#2
G#1 C#1 E2 G#2
G#1 C#1 F2 G#2

A1 B1 D#1 F2
A1 B1 E2 G2
A1 C1 D#1 F2 A2
A1 C1 D#1 G2
A1 C1 D#1 A2
A1 C1 E2 G2
A1 C1 E2 A2
A1 C1 F2 A2
A1 C#1 E2 G2
A1 C#1 E2 A2
A1 C#1 F2 A2
A1 D#1 F2 A2

A#1 C1 D#1 F#2 A#2
A#1 C1 D#1 G2 A#2
A#1 C1 E2 F#2 A#2
A#1 C1 E2 G2 A#2
A#1 C#1 E2 G2 A#2
A#1 D1 F#2
A#1 D1 G2

B1 D1 F2 G#2 B2
B1 D1 F#2 B2
B1 D1 G2 B2
B1 D1 G#2 B2
B1 D#1 F2 G#2 B2
B1 D#1 F#2 A#2
B1 D#1 F#2 B2
B1 D#1 G2 A#2
B1 D#1 G2 B2
B1 E2 F#2 A#2
B1 E2 F#2 B2
B1 E2 G2 A#2
B1 E2 G2 B2
B1 E2 G#2 B2

C1 D#1 F2 A2 C2
C1 D#1 F#2 A#2 C2
C1 D#1 G2 A#2 C2
C1 E2 F#2 A#2 C2
C1 E2 G2 A#2 C2
C1 E2 A2 C2

C#1 E2 G2 A#2 C#2
C#1 E2 G2 B2
C#1 E2 G#2 B2
C#1 E2 G#2 C#2
C#1 E2 A2 B2
C#1 E2 A2 C#2
C#1 E2 A#2 C#2
C#1 F2 G#2 B2
C#1 F2 A2 B2

D1 F2 G#2 B2 D2 *
D1 F#2 B2 D2
D1 G2 B2 D2
D1 G2 C#2
D1 G#2 C#2
D1 F2 G#2 D2 (subset of *)
D1 F2 B2 D2 (subset of *)
D1 G#2 B2 D2 (subset of *)

D#1 F2 G#2 B2 D#2
D#1 F2 G#2 C2 D#2
D#1 F2 A2 B2 D#2
D#1 F2 A2 C2 D#2
D#1 F#2 A#2 C2 D#2
D#1 F#2 B2 D#2
D#1 G2 A#2 C2
D#1 G2 B2

The best chords are generally those where the lowest and highest notes are exactly one octave apart and the key of these chords will in most, if not all cases, be the lowest or highest note or both.
For dense chords (with four or five notes) most will sound sweeter when one or two notes are omitted. In the case of a five note chord where the lowest and highest notes are one octave apart, keep the lowest and highest notes and omit one or two of the other three notes in any combination you like. For four note chords where the lowest and highest notes are one octave apart then keep the lowest and highest notes and omit either one of the other two notes.
All subsets of the chords listed here should be good. All good intervals are within plus or minus 6.776 cents (256/255) accuracy of a good JI interval.
For chords less than an octave wide play each note alternately with the whole chord and the note that sounds most similar to the chord is the key of the chord.

For more on Blue Temperament and how I worked it out go to
http://www.johnsmusic7.com
and click on the region you live in. The link will take you to the nearest Amazon site to you where you can buy the book.
There are also three Blue Tuning tunes you can play on the web site, one is my own and the other two are by Chris Vaisvil.

John.

--- In tuning@yahoogroups.com, "john777music" <jfos777@...> wrote:

> All subsets of the chords listed here should be good. All good intervals are within plus or minus 6.776 cents (256/255) accuracy of a good JI interval.

Which good JI intervals does it actually approximate? I'm seeing 9-limit, which means a reasonable comparison would be to the marvel-tempered duodene. That does 9-limit chords far more accurately, so I'm not seeing any bang for the buck. Which is why I want to know what its target consonances are.

! dwarf12marv.scl
Marvelous dwarf: 1/4 kleismic tempered duodene
12
!
131.309694
200.054240
315.641287
431.228334
515.695527
631.282574
700.027120
815.614167
900.081360
1015.668407
1131.255454
1200.000000
! four tetrads/pentads representible by
! [[-1, 1, 2], [-1, 2, 2], [-1, 1, 1], [-2, 1, -1]]

Here are the target JI intervals that I consider *good*...
9/8, 8/7, 7/6, 6/5, 5/4, 9/7, 4/3, 7/5, 10/7, 3/2, 8/5, 5/3, 12/7, 7/4, 9/5, 13/7 and 2/1. All these occur in Blue Temperament.
I also think that 11/8, 11/7 and 11/6 are *good* but they do not occur in Blue Temperament.

John.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "john777music" <jfos777@> wrote:
>
> > All subsets of the chords listed here should be good. All good intervals are within plus or minus 6.776 cents (256/255) accuracy of a good JI interval.
>
> Which good JI intervals does it actually approximate? I'm seeing 9-limit, which means a reasonable comparison would be to the marvel-tempered duodene. That does 9-limit chords far more accurately, so I'm not seeing any bang for the buck. Which is why I want to know what its target consonances are.
>
> ! dwarf12marv.scl
> Marvelous dwarf: 1/4 kleismic tempered duodene
> 12
> !
> 131.309694
> 200.054240
> 315.641287
> 431.228334
> 515.695527
> 631.282574
> 700.027120
> 815.614167
> 900.081360
> 1015.668407
> 1131.255454
> 1200.000000
> ! four tetrads/pentads representible by
> ! [[-1, 1, 2], [-1, 2, 2], [-1, 1, 1], [-2, 1, -1]]
>

--- In tuning@yahoogroups.com, "john777music" <jfos777@...> wrote:
>
> Here are the target JI intervals that I consider *good*...
> 9/8, 8/7, 7/6, 6/5, 5/4, 9/7, 4/3, 7/5, 10/7, 3/2, 8/5, 5/3, 12/7, 7/4, 9/5, 13/7 and 2/1. All these occur in Blue Temperament.
> I also think that 11/8, 11/7 and 11/6 are *good* but they do not occur in Blue Temperament.

This is 9-limit plus the interval 13/7. The scale I gave does the 9-limit stuff much more accurately, and also does 13/7 more accurately but has only two instead of three 13/7s inside of the specified bounds. All of this leads me to suspect you have not really found the minimax tuning for your target intervals. That could be done, or with greater ease, least squares optimum could be found.

thanks John!

On Sun, Nov 28, 2010 at 3:09 PM, john777music <jfos777@yahoo.com> wrote:

>
>
> Here's my Blue Temperament tuning again but this time with a list of good
> chords that are an octave or less wide.
>
> BT in cents...
>
> 0.0c, 121.6c, 200.7c, 313.5c, 388.4c, 501.2c, 580.4c,
> 702.0c, 816.9c, 889.4c, 1012.5c, 1085.1c, 1200c.
>
> BT in frequencies...
>
> 1.0, 1.072740, 1.122938, 1.198533, 1.25153, 1.335782,
> 1.398289, 1.5, 1.602938, 1.671566, 1.794724, 1.871563, 2.0.
>
> Adjustments...
>
> 1st note 0.0 cents
> 2nd note +21.6 cents
> 3rd note +0.7 cents
> 4th note +13.5 cents
> 5th note -11.6 cents
> 6th note +1.2 cents
> 7th note -19.6 cents
> 8th note +2.0 cents
> 9th note +16.9 cents
> 10th note -10.6 cents
> 11th note +12.5 cents
> 12th note -14.9 cents
>
> List of good chords if tonic (1/1) is E...
> Use fixed width font.
>
> E1 F#1 A#1 C1
> E1 F#1 A#1 D1
> E1 F#1 B1 D1
> E1 G1 A#1 C1 E2
> E1 G1 A#1 C#1 E2
> E1 G1 A#1 D1
> E1 G1 B1 D1
> E1 G1 B1 E2
> E1 G#1 B1 D1
> E1 G#1 B1 E2
> E1 G#1 C1 E2
> E1 G#1 C#1 E2
> E1 A1 B1 E2
> E1 A1 C1 E2
> E1 A1 C#1 E2
>
> F1 G#1 B1 D1 F2
> F1 G#1 B1 D#1 F2
> F1 G#1 B1 E2
> F1 G#1 C1 D#1 F2
> F1 G#1 C1 E2
> F1 A1 B1 D#1 F2
> F1 A1 B1 E2
> F1 A1 C1 D#1 F2
> F1 A1 C1 E2
>
> F#1 A#1 C1 D#1 F#2 *
> F#1 A#1 D1 F#2
> F#1 B1 D1 F#2
> F#1 B1 D#1 F#2
> F#1 A#1 C1 F#2 (subset of *)
> F#1 A#1 D#1 F#2 (subset of *)
> F#1 C1 D#1 F#2 (subset of *)
>
> G1 A#1 C1 E2 G2 *
> G1 A#1 C#1 E2 G2 **
> G1 A#1 D1 G2
> G1 B1 D1 G2
> G1 B1 E2 G2
> G1 A#1 C1 G2 (subset of *)
> G1 A#1 E2 G2 (subset of *)
> G1 C1 E2 G2 (subset of *)
> G1 A#1 C#1 G2 (subset of **)
> G1 A#1 E2 G2 (subset of **)
> G1 C#1 E2 G2 (subset of **)
>
> G#1 B1 D1 F2 G#2
> G#1 B1 D1 F#2
> G#1 B1 D1 G#2
> G#1 B1 D#1 F2 G#2
> G#1 B1 D#1 F#2
> G#1 B1 E2 F#2
> G#1 B1 E2 G#2
> G#1 C1 D#1 F2
> G#1 C1 D#1 F#2
> G#1 C1 E2 F#2
> G#1 C#1 E2 G#2
> G#1 C#1 F2 G#2
>
> A1 B1 D#1 F2
> A1 B1 E2 G2
> A1 C1 D#1 F2 A2
> A1 C1 D#1 G2
> A1 C1 D#1 A2
> A1 C1 E2 G2
> A1 C1 E2 A2
> A1 C1 F2 A2
> A1 C#1 E2 G2
> A1 C#1 E2 A2
> A1 C#1 F2 A2
> A1 D#1 F2 A2
>
> A#1 C1 D#1 F#2 A#2
> A#1 C1 D#1 G2 A#2
> A#1 C1 E2 F#2 A#2
> A#1 C1 E2 G2 A#2
> A#1 C#1 E2 G2 A#2
> A#1 D1 F#2
> A#1 D1 G2
>
> B1 D1 F2 G#2 B2
> B1 D1 F#2 B2
> B1 D1 G2 B2
> B1 D1 G#2 B2
> B1 D#1 F2 G#2 B2
> B1 D#1 F#2 A#2
> B1 D#1 F#2 B2
> B1 D#1 G2 A#2
> B1 D#1 G2 B2
> B1 E2 F#2 A#2
> B1 E2 F#2 B2
> B1 E2 G2 A#2
> B1 E2 G2 B2
> B1 E2 G#2 B2
>
> C1 D#1 F2 A2 C2
> C1 D#1 F#2 A#2 C2
> C1 D#1 G2 A#2 C2
> C1 E2 F#2 A#2 C2
> C1 E2 G2 A#2 C2
> C1 E2 A2 C2
>
> C#1 E2 G2 A#2 C#2
> C#1 E2 G2 B2
> C#1 E2 G#2 B2
> C#1 E2 G#2 C#2
> C#1 E2 A2 B2
> C#1 E2 A2 C#2
> C#1 E2 A#2 C#2
> C#1 F2 G#2 B2
> C#1 F2 A2 B2
>
> D1 F2 G#2 B2 D2 *
> D1 F#2 B2 D2
> D1 G2 B2 D2
> D1 G2 C#2
> D1 G#2 C#2
> D1 F2 G#2 D2 (subset of *)
> D1 F2 B2 D2 (subset of *)
> D1 G#2 B2 D2 (subset of *)
>
> D#1 F2 G#2 B2 D#2
> D#1 F2 G#2 C2 D#2
> D#1 F2 A2 B2 D#2
> D#1 F2 A2 C2 D#2
> D#1 F#2 A#2 C2 D#2
> D#1 F#2 B2 D#2
> D#1 G2 A#2 C2
> D#1 G2 B2
>
> The best chords are generally those where the lowest and highest notes are
> exactly one octave apart and the key of these chords will in most, if not
> all cases, be the lowest or highest note or both.
> For dense chords (with four or five notes) most will sound sweeter when one
> or two notes are omitted. In the case of a five note chord where the lowest
> and highest notes are one octave apart, keep the lowest and highest notes
> and omit one or two of the other three notes in any combination you like.
> For four note chords where the lowest and highest notes are one octave apart
> then keep the lowest and highest notes and omit either one of the other two
> notes.
> All subsets of the chords listed here should be good. All good intervals
> are within plus or minus 6.776 cents (256/255) accuracy of a good JI
> interval.
> For chords less than an octave wide play each note alternately with the
> whole chord and the note that sounds most similar to the chord is the key of
> the chord.
>
> For more on Blue Temperament and how I worked it out go to
> http://www.johnsmusic7.com
> and click on the region you live in. The link will take you to the nearest
> Amazon site to you where you can buy the book.
> There are also three Blue Tuning tunes you can play on the web site, one is
> my own and the other two are by Chris Vaisvil.
>
> John.
>
>
>

Gene,
the scale you posted ! dwarf12marv.scl
Marvelous dwarf: 1/4 kleismic tempered duodene
has 515.7 cents for the Perfect Fourth which should be ideally 498 cents. So it's 17.7 cents out of tune. The max deviation for me is 6.776 cents (256/255).
John.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "john777music" <jfos777@> wrote:
> >
> > Here are the target JI intervals that I consider *good*...
> > 9/8, 8/7, 7/6, 6/5, 5/4, 9/7, 4/3, 7/5, 10/7, 3/2, 8/5, 5/3, 12/7, 7/4, 9/5, 13/7 and 2/1. All these occur in Blue Temperament.
> > I also think that 11/8, 11/7 and 11/6 are *good* but they do not occur in Blue Temperament.
>
> This is 9-limit plus the interval 13/7. The scale I gave does the 9-limit stuff much more accurately, and also does 13/7 more accurately but has only two instead of three 13/7s inside of the specified bounds. All of this leads me to suspect you have not really found the minimax tuning for your target intervals. That could be done, or with greater ease, least squares optimum could be found.
>

>"Gene,
the scale you posted ! dwarf12marv.scl
Marvelous dwarf: 1/4 kleismic tempered duodene
has 515.7 cents for the Perfect Fourth which should be ideally 498 cents. So
it's 17.7 cents out of tune. The max deviation for me is 6.776 cents (256/255)."

I use similar criteria for my own scale IE that the worst possible error of
any dyad from its ideal (the ideal being one of a fixed list of dyads) defines
how bad the scale is.

I think something I've run into (especially with Gene) is that we have
different concepts of how we use "minimax" and I think it would really help if
we all concur there is more than one possible way to say what "minimax" can
mean.

Gene seems to keep sighting least squares optimization (minimizing the maximum
error of the average of all dyads)...but John and I appear to be using something
more akin to "minimizing the maximum error of the highest-error unique dyad".
Both "minimize the maximum error", but in very different ways.

Hi Michael,

I'm balancing the maximum number of notes that go with the tonic (7 prime limit) with the maximum number of dyads/intervals that occur overall (any limit) which are an octave or less wide and belong to my "list of good intervals".
My 6.776 cents (256/255) max deviation tries to minimize the error and maximize the number of good dyads available.
Have you tried Blue Temperament? Try the list of chords I posted earlier.

John.

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> >"Gene,
> the scale you posted ! dwarf12marv.scl
> Marvelous dwarf: 1/4 kleismic tempered duodene
> has 515.7 cents for the Perfect Fourth which should be ideally 498 cents. So
> it's 17.7 cents out of tune. The max deviation for me is 6.776 cents (256/255)."
>
> I use similar criteria for my own scale IE that the worst possible error of
> any dyad from its ideal (the ideal being one of a fixed list of dyads) defines
> how bad the scale is.
>
> I think something I've run into (especially with Gene) is that we have
> different concepts of how we use "minimax" and I think it would really help if
> we all concur there is more than one possible way to say what "minimax" can
> mean.
>
>
> Gene seems to keep sighting least squares optimization (minimizing the maximum
> error of the average of all dyads)...but John and I appear to be using something
> more akin to "minimizing the maximum error of the highest-error unique dyad".
> Both "minimize the maximum error", but in very different ways.
>

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:

> I use similar criteria for my own scale IE that the worst possible error of
> any dyad from its ideal (the ideal being one of a fixed list of dyads) defines
> how bad the scale is.

If that worst error is minimalim, that's minimax.

> I think something I've run into (especially with Gene) is that we have
> different concepts of how we use "minimax" and I think it would really help if
> we all concur there is more than one possible way to say what "minimax" can
> mean.

Minimax comes with only one caveat I know of: it's not necessarily unique. In that case, my recommendation is to break ties via least squares.

> Gene seems to keep sighting least squares optimization (minimizing the maximum
> error of the average of all dyads)...

Least squares is least squares and minimax is minimax, and I know of no one who is confusing them.

Gene wrote :

> Which good JI intervals does it actually approximate? I'm seeing 9-> limit, which means a reasonable comparison would be to the marvel-> tempered duodene. That does 9-limit chords far more accurately, so > I'm not seeing any bang for the buck. Which is why I want to know > what its target consonances are.

> --- In tuning@yahoogroups.com, "john777music" <jfos777@...> wrote:
> >
> > Here are the target JI intervals that I consider *good*...
> > 9/8, 8/7, 7/6, 6/5, 5/4, 9/7, 4/3, 7/5, 10/7, 3/2, 8/5, 5/3, > 12/7, 7/4, 9/5, 13/7 and 2/1. All these occur in Blue Temperament.
> > I also think that 11/8, 11/7 and 11/6 are *good* but they do not > occur in Blue Temperament.
>
> This is 9-limit plus the interval 13/7. The scale I gave does the 9-> limit stuff much more accurately, and also does 13/7 more > accurately but has only two instead of three 13/7s inside of the > specified bounds. All of this leads me to suspect you have not > really found the minimax tuning for your target intervals. That > could be done, or with greater ease, least squares optimum could be > found.

Hi Gene,
I am not certain to understand John's system (and especially the difference between the "Blue Just tuning" and his "Blue temperament") but it seems to me you are not talking about comparable objects. I am pretty sure you talk of temperaments, while what John describes as a "temperament" is more a modal tuning since his criteria is relative to a collection of intervals he considers good because consonant with 1/1, and does not cares so much of the consonances between them, which should be a criteria for a temperament.
- - - - - - -
Jacques

Jacques,

I try to do both, that is, maximize the number of notes that go with the tonic *and* maximize the number of good intervals overall. I am aiming at a balance between the two.

John.

--- In tuning@yahoogroups.com, Jacques Dudon <fotosonix@...> wrote:
>
> Gene wrote :
>
> > Which good JI intervals does it actually approximate? I'm seeing 9-
> > limit, which means a reasonable comparison would be to the marvel-
> > tempered duodene. That does 9-limit chords far more accurately, so
> > I'm not seeing any bang for the buck. Which is why I want to know
> > what its target consonances are.
>
>
> > --- In tuning@yahoogroups.com, "john777music" <jfos777@> wrote:
> > >
> > > Here are the target JI intervals that I consider *good*...
> > > 9/8, 8/7, 7/6, 6/5, 5/4, 9/7, 4/3, 7/5, 10/7, 3/2, 8/5, 5/3,
> > 12/7, 7/4, 9/5, 13/7 and 2/1. All these occur in Blue Temperament.
> > > I also think that 11/8, 11/7 and 11/6 are *good* but they do not
> > occur in Blue Temperament.
> >
> > This is 9-limit plus the interval 13/7. The scale I gave does the 9-
> > limit stuff much more accurately, and also does 13/7 more
> > accurately but has only two instead of three 13/7s inside of the
> > specified bounds. All of this leads me to suspect you have not
> > really found the minimax tuning for your target intervals. That
> > could be done, or with greater ease, least squares optimum could be
> > found.
>
> Hi Gene,
> I am not certain to understand John's system (and especially the
> difference between the "Blue Just tuning" and his "Blue temperament")
> but it seems to me you are not talking about comparable objects. I am
> pretty sure you talk of temperaments, while what John describes as a
> "temperament" is more a modal tuning since his criteria is relative
> to a collection of intervals he considers good because consonant with
> 1/1, and does not cares so much of the consonances between them,
> which should be a criteria for a temperament.
> - - - - - - -
> Jacques
>

Hi John,
Again without seeing the difference with the JI version, and only by looking at the cycle of fifths we can see its structure is not what we can expect from a "temperament". It's a modal tuning (and there is nothing wrong with that !)
- - - - -
Jacques

--- In tuning@yahoogroups.com, "john777music" <jfos777@...> wrote:
>
> Jacques,
>
> I try to do both, that is, maximize the number of notes that go with the tonic *and* maximize the number of good intervals overall. I am aiming at a balance between the two.
>
> John.
>
> --- In tuning@yahoogroups.com, Jacques Dudon <fotosonix@> wrote:
> >
> > Hi Gene,
> > I am not certain to understand John's system (and especially the
> > difference between the "Blue Just tuning" and his "Blue temperament")
> > but it seems to me you are not talking about comparable objects. I am
> > pretty sure you talk of temperaments, while what John describes as a
> > "temperament" is more a modal tuning since his criteria is relative
> > to a collection of intervals he considers good because consonant with
> > 1/1, and does not cares so much of the consonances between them,
> > which should be a criteria for a temperament.
> > - - - - - - -
> > Jacques

Hi Jacques,

if a "modal tuning" uses notes that go best with the tonic only then my scale isn't exclusively modal. I had to choose between 9/8 and 8/7. 8/7 goes better with 1/1 than 9/8 but I chose 9/8 because it goes with more notes overall. Same with 7/4 and 9/5. 7/4 goes better with 1/1 than 9/5 but I chose 9/5 again because it goes with more notes overall. Same with 15/8 and 13/7. 13/7 goes better with 1/1 but I chose 15/8 because it goes with more notes overall.
Then, when I tempered my JI scale (Blue Just) I did so to maximize the number of good intervals overall, irrespective of whether or not they contained the tonic (although I stuck to +-6.776 cents accuracy of the notes in the original just tuning).

John.

--- In tuning@yahoogroups.com, "jacques.dudon" <fotosonix@...> wrote:
>
> Hi John,
> Again without seeing the difference with the JI version, and only by looking at the cycle of fifths we can see its structure is not what we can expect from a "temperament". It's a modal tuning (and there is nothing wrong with that !)
> - - - - -
> Jacques
>
>
> --- In tuning@yahoogroups.com, "john777music" <jfos777@> wrote:
> >
> > Jacques,
> >
> > I try to do both, that is, maximize the number of notes that go with the tonic *and* maximize the number of good intervals overall. I am aiming at a balance between the two.
> >
> > John.
> >
> > --- In tuning@yahoogroups.com, Jacques Dudon <fotosonix@> wrote:
> > >
> > > Hi Gene,
> > > I am not certain to understand John's system (and especially the
> > > difference between the "Blue Just tuning" and his "Blue temperament")
> > > but it seems to me you are not talking about comparable objects. I am
> > > pretty sure you talk of temperaments, while what John describes as a
> > > "temperament" is more a modal tuning since his criteria is relative
> > > to a collection of intervals he considers good because consonant with
> > > 1/1, and does not cares so much of the consonances between them,
> > > which should be a criteria for a temperament.
> > > - - - - - - -
> > > Jacques
>

It is quite normal that a modal tuning may work for several tonics. But as long as in a continuous sequence such as a cycle of fifths, depending on the tonic it works or not for basic chords, in my sense it's not exactly a temperament. Since about your tempered version you don't give more precise explanations, you may keep it secret but what is really tempered with it I cannot say.
- - - - - - -
Jacques

--- In tuning@yahoogroups.com, "john777music" <jfos777@...> wrote:
>
> Hi Jacques,
>
> if a "modal tuning" uses notes that go best with the tonic only then my scale isn't exclusively modal. I had to choose between 9/8 and 8/7. 8/7 goes better with 1/1 than 9/8 but I chose 9/8 because it goes with more notes overall. Same with 7/4 and 9/5. 7/4 goes better with 1/1 than 9/5 but I chose 9/5 again because it goes with more notes overall. Same with 15/8 and 13/7. 13/7 goes better with 1/1 but I chose 15/8 because it goes with more notes overall.
> Then, when I tempered my JI scale (Blue Just) I did so to maximize the number of good intervals overall, irrespective of whether or not they contained the tonic (although I stuck to +-6.776 cents accuracy of the notes in the original just tuning).
>
> John.
>
> --- In tuning@yahoogroups.com, "jacques.dudon" <fotosonix@> wrote:
> >
> > Hi John,
> > Again without seeing the difference with the JI version, and only by looking at the cycle of fifths we can see its structure is not what we can expect from a "temperament". It's a modal tuning (and there is nothing wrong with that !)
> > - - - - -
> > Jacques

Jacques,

I sent you a copy of my book. Did you get it and read it? My temperament is explained in chapter 8.

John.

--- In tuning@yahoogroups.com, "jacques.dudon" <fotosonix@...> wrote:
>
> It is quite normal that a modal tuning may work for several tonics. But as long as in a continuous sequence such as a cycle of fifths, depending on the tonic it works or not for basic chords, in my sense it's not exactly a temperament. Since about your tempered version you don't give more precise explanations, you may keep it secret but what is really tempered with it I cannot say.
> - - - - - - -
> Jacques
>
>
> --- In tuning@yahoogroups.com, "john777music" <jfos777@> wrote:
> >
> > Hi Jacques,
> >
> > if a "modal tuning" uses notes that go best with the tonic only then my scale isn't exclusively modal. I had to choose between 9/8 and 8/7. 8/7 goes better with 1/1 than 9/8 but I chose 9/8 because it goes with more notes overall. Same with 7/4 and 9/5. 7/4 goes better with 1/1 than 9/5 but I chose 9/5 again because it goes with more notes overall. Same with 15/8 and 13/7. 13/7 goes better with 1/1 but I chose 15/8 because it goes with more notes overall.
> > Then, when I tempered my JI scale (Blue Just) I did so to maximize the number of good intervals overall, irrespective of whether or not they contained the tonic (although I stuck to +-6.776 cents accuracy of the notes in the original just tuning).
> >
> > John.
> >
> > --- In tuning@yahoogroups.com, "jacques.dudon" <fotosonix@> wrote:
> > >
> > > Hi John,
> > > Again without seeing the difference with the JI version, and only by looking at the cycle of fifths we can see its structure is not what we can expect from a "temperament". It's a modal tuning (and there is nothing wrong with that !)
> > > - - - - -
> > > Jacques
>

--- In tuning@yahoogroups.com, "john777music" <jfos777@...> wrote:
>
> Jacques,
>
> I sent you a copy of my book. Did you get it and read it? My temperament is explained in chapter 8.
>
> John.

I read it and I ask for more explanations because I didn't get the answer to the question of what does it tempers. In chapter 8 you say :
"Each note except the tonics 1/1 and 3/2 were raised or lowered by not more than 6.775877 cents so as to yield the maximum number of good intervals", and you say that you run a programm during 12 hours to get the result, and that's it.
I understood you have a pre-determined range of ±6.775877 cents and a pre-determined choice of "good intervals" ; I would like to believe your programm does the best job with that but I don't understand on what you got it to work, what commas it dissolves and what it improves other than for the same pre-determined intervals.
Why not showing what it changes in comparison with the "Blue Just tuning", whose structure remains unchanged ? Why not simply giving for example a table of the 12 fifths and thirds of both, like for any temperament ?

Does the following help?

Blue Temperament
|
Step size is 100.00000 cents
  1:  121.600:      1:  100.0000 cents   diff. -0.216000 steps, -21.60000 cents
  2:  200.700:      2:  200.0000 cents   diff. -0.007000 steps, -0.70000 cents
  3:  313.500:      3:  300.0000 cents   diff. -0.135000 steps, -13.50000 cents
  4:  388.400:      4:  400.0000 cents   diff.  0.116000 steps,  11.60000 cents
  5:  501.200:      5:  500.0000 cents   diff. -0.012000 steps, -1.20000 cents
  6:  580.400:      6:  600.0000 cents   diff.  0.196000 steps,  19.60000 cents
  7:  702.000:      7:  700.0000 cents   diff. -0.020000 steps, -2.00000 cents
  8:  816.900:      8:  800.0000 cents   diff. -0.169000 steps, -16.90000 cents
  9:  889.400:      9:  900.0000 cents   diff.  0.106000 steps,  10.60000 cents
 10:  1012.500:    10:  1000.0000 cents  diff. -0.125000 steps, -12.50000 cents
 11:  1085.100:    11:  1100.0000 cents  diff.  0.149000 steps,  14.90000 cents
 12:  1200.000:    12:  1200.0000 cents  diff.  0.000000 steps,  0.00000 cents
Total absolute difference  :  1.251000 steps,  125.10000 cents
Average absolute difference:  0.104250 steps,  10.42500 cents
Root mean square difference:  0.127465 steps,  12.74654 cents
Highest absolute difference:  0.216000 steps,  21.60000 cents

On Thu, Dec 2, 2010 at 6:42 AM, jacques.dudon <fotosonix@...> wrote:
>

> Why not showing what it changes in comparison with the "Blue Just tuning", whose structure remains unchanged ? Why not simply giving for example a table of the 12 fifths and thirds of both, like for any temperament ?
>
>

To have the ratios in cents, yes. Thanks Chris !
- - - -
Jacques

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Does the following help?
>
> Blue Temperament
> |
> Step size is 100.00000 cents
>   1:  121.600:      1:  100.0000 cents   diff. -0.216000 steps, -21.60000 cents
>   2:  200.700:      2:  200.0000 cents   diff. -0.007000 steps, -0.70000 cents
>   3:  313.500:      3:  300.0000 cents   diff. -0.135000 steps, -13.50000 cents
>   4:  388.400:      4:  400.0000 cents   diff.  0.116000 steps,  11.60000 cents
>   5:  501.200:      5:  500.0000 cents   diff. -0.012000 steps, -1.20000 cents
>   6:  580.400:      6:  600.0000 cents   diff.  0.196000 steps,  19.60000 cents
>   7:  702.000:      7:  700.0000 cents   diff. -0.020000 steps, -2.00000 cents
>   8:  816.900:      8:  800.0000 cents   diff. -0.169000 steps, -16.90000 cents
>   9:  889.400:      9:  900.0000 cents   diff.  0.106000 steps,  10.60000 cents
>  10:  1012.500:    10:  1000.0000 cents  diff. -0.125000 steps, -12.50000 cents
>  11:  1085.100:    11:  1100.0000 cents  diff.  0.149000 steps,  14.90000 cents
>  12:  1200.000:    12:  1200.0000 cents  diff.  0.000000 steps,  0.00000 cents
> Total absolute difference  :  1.251000 steps,  125.10000 cents
> Average absolute difference:  0.104250 steps,  10.42500 cents
> Root mean square difference:  0.127465 steps,  12.74654 cents
> Highest absolute difference:  0.216000 steps,  21.60000 cents
>
> On Thu, Dec 2, 2010 at 6:42 AM, jacques.dudon <fotosonix@...> wrote:
> >
>
> > Why not showing what it changes in comparison with the "Blue Just tuning", whose structure remains unchanged ? Why not simply giving for example a table of the 12 fifths and thirds of both, like for any temperament ?

Jacques,

I never considered "dissolving" commas in my scale, commas don't figure in my system.

How does my Blue Temperament improve on my Blue Just tuning?
With Blue Just tuning exactly 50% of all intervals (an octave or less wide and excluding the unison) are *good* and are all perfectly in tune. There's also a 13/7 in there somewhere, not perfectly in tune but within 6.776 cents.

When I tempered the Blue Just scale (to get Blue Temperament), 67% of all intervals (an octave or less wide and excluding the unison) are now *good*, not perfectly in tune, but within 6.776 cents accuracy which is close enough for me.
That's an improvement of 17% (67-50).

This is the improvement: more variety/musical possibilities.

See the list on page 37 which shows the good intervals and how often they occur in Blue Temperament.

John.

PS I don't use chains or circles of fifths or any other intervals.

--- In tuning@yahoogroups.com, "jacques.dudon" <fotosonix@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "john777music" <jfos777@> wrote:
> >
> > Jacques,
> >
> > I sent you a copy of my book. Did you get it and read it? My temperament is explained in chapter 8.
> >
> > John.
>
> I read it and I ask for more explanations because I didn't get the answer to the question of what does it tempers. In chapter 8 you say :
> "Each note except the tonics 1/1 and 3/2 were raised or lowered by not more than 6.775877 cents so as to yield the maximum number of good intervals", and you say that you run a programm during 12 hours to get the result, and that's it.
> I understood you have a pre-determined range of ±6.775877 cents and a pre-determined choice of "good intervals" ; I would like to believe your programm does the best job with that but I don't understand on what you got it to work, what commas it dissolves and what it improves other than for the same pre-determined intervals.
> Why not showing what it changes in comparison with the "Blue Just tuning", whose structure remains unchanged ? Why not simply giving for example a table of the 12 fifths and thirds of both, like for any temperament ?
>