Yahoo Tuning Groups Ultimate Backup tuning 2.3.5.7 system

Igs said <Honestly though, if you want a full 2.3.5.7 system with any real level of accuracy (i.e. <8 cents) in all primes, there's no good simple solution.>

Here's a complete list of good and bad (according to my taste) 2, 3, 5, 7, 11 and 13 prime limit intervals (an octave or less wide) and how often the good intervals occur over any 12 keys in my Blue Temperament.

2/1...good...12 times
3/2...good....9 times
4/3...good....9
5/3...good....8
5/4...good....8
6/5...good....8
7/4...good....2
7/5...good....6
7/6...good....3
8/5...good....8
8/7...good....2
9/5...good....4
9/7...good....4
9/8...good....2
10/7..good....6
10/9..bad
11/6..good....0
11/7..good....0
11/8..good....0
11/9..bad
11/10.bad
12/7..good....3
12/11.bad
13/7..good....3
13/8..bad
13/9..bad
all are bad IMO beyond this point.

*All* of the good 2, 3, 5, and 7 prime limit intervals occur in Blue Temperament and they are all within 6.776 cents (256/255) accuracy.

John.

🔗cityoftheasleep <igliashon@...>

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

> Here's a complete list of good and bad (according to my taste) 2, 3, 5, 7, 11 and 13
> prime limit intervals (an octave or less wide) and how often the good intervals occur over
> any 12 keys in my Blue Temperament.

Right--12 keys. That's about the smallest scale that you can use and get enough accurate 7-limit harmonies to be usable; I'm curious, though--have you done a tetradic analysis of your scale to see how many full 4:5:6:7 tetrads are possible? Because the tetrad is the basic "unit" of 7-limit harmony, and a scale that gives 7-limit dyadic harmonies but few tetrads is not desirable for the tetradic approach that Mike B. is talking about.

-Igs

🔗genewardsmith <genewardsmith@...>

🔗john777music <jfos777@...>

Hi Igs,

I don't know if there are any 4:5:6:7 tetrads in my scale but there are a lot of good chords with as many as five notes that are not more than an octave wide.

Here's my Blue Temperament scale in cents...

0.0, 121.6, 200.7, 313.5, 388.4, 501.2, 580.4, 702.0, 816.9, 889.4, 1012.5, 1085.1, 1200.0

If E is 1/1 or 0.0 cents then here are all the good chords (every possible dyad occurs in my list of *good* intervals within 6.776 cents accuracy) an octave or less wide...

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

...So, plenty of four note and five note chords here.

John.

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "john777music" <jfos777@> wrote:
>
> > Here's a complete list of good and bad (according to my taste) 2, 3, 5, 7, 11 and 13
> > prime limit intervals (an octave or less wide) and how often the good intervals occur over
> > any 12 keys in my Blue Temperament.
>
> Right--12 keys. That's about the smallest scale that you can use and get enough accurate 7-limit harmonies to be usable; I'm curious, though--have you done a tetradic analysis of your scale to see how many full 4:5:6:7 tetrads are possible? Because the tetrad is the basic "unit" of 7-limit harmony, and a scale that gives 7-limit dyadic harmonies but few tetrads is not desirable for the tetradic approach that Mike B. is talking about.
>
> -Igs
>

🔗cityoftheasleep <igliashon@...>

FWIW, I didn't say *I* wanted an accurate 2.3.5.7 temperament. There was a time when I did, but then I decided I'm not a huge fan of the otonal tetrad as a "basic harmonic unit". But that Archytas hobbit looks delicious.

-Igs

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@> wrote:
>
> > Right--12 keys. That's about the smallest scale that you can use and get enough accurate 7-limit harmonies to be usable
>
> Getting fussy about tuning accuracy all of a sudden? If not, what about this, with one major tetrad, one minor tetrad, one subminor tetrad, one supermajor tetrad, etc:
>
> ! archytas7.scl
> Archytas (64/63) hobbit in POTE tuning
> 7
> !
> 218.64253
> 393.37465
> 490.67874
> 709.32126
> 806.62535
> 981.35747
> 1200.0000
> !
> !! prearchytas7.scl
> ! Archytas[7] 5-limit transversal = hexany21a
> ! 7
> !!
> ! 9/8
> ! 5/4
> ! 4/3
> ! 3/2
> ! 8/5
> ! 16/9
> ! 2/1
>

🔗Mike Battaglia <battaglia01@...>

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> Surely you like the blues?

No, not really. Maybe really old blues, the kind played by old men who've suffered long and tortured lives and can't really express themselves any other way, but there is just so much AWFUL music out there that goes by the name of "blues", music that is trite, shallow, formulaic, macho, and downright false. As a musical form of I-IV-V with dom7 chords on all degrees, I think it's just really flat and boring. Not that I haven't played some blues in my day, but I really can't say I find it enjoyable. Really the only time I care for the dom7 chord is when it's used as...a dominant 7th chord, i.e. as part of functional harmony.

-Igs

🔗Chris Vaisvil <chrisvaisvil@...>

A question

Is the 7 note version more or less included in the 12 or 17 note versions of
Archytas?

I am being too lazy to look it up - nonetheless - I'm trying for a
generality here.

Chris

On Mon, Jan 24, 2011 at 10:00 PM, cityoftheasleep
<igliashon@...>wrote:

>
>
> FWIW, I didn't say *I* wanted an accurate 2.3.5.7 temperament. There was a
> time when I did, but then I decided I'm not a huge fan of the otonal tetrad
> as a "basic harmonic unit". But that Archytas hobbit looks delicious.
>
> -Igs
>
>
> --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>, "genewardsmith"
> <genewardsmith@...> wrote:
> >
> >
> >
> > --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>,
> "cityoftheasleep" <igliashon@> wrote:
> >
> > > Right--12 keys. That's about the smallest scale that you can use and
> get enough accurate 7-limit harmonies to be usable
> >
> > Getting fussy about tuning accuracy all of a sudden? If not, what about
> this, with one major tetrad, one minor tetrad, one subminor tetrad, one
> supermajor tetrad, etc:
> >
> > ! archytas7.scl
> > Archytas (64/63) hobbit in POTE tuning
> > 7
> > !
> > 218.64253
> > 393.37465
> > 490.67874
> > 709.32126
> > 806.62535
> > 981.35747
> > 1200.0000
> > !
> > !! prearchytas7.scl
> > ! Archytas[7] 5-limit transversal = hexany21a
> > ! 7
> > !!
> > ! 9/8
> > ! 5/4
> > ! 4/3
> > ! 3/2
> > ! 8/5
> > ! 16/9
> > ! 2/1
> >
>
>
>

🔗Daniel Nielsen <nielsed@...>

On Mon, Jan 24, 2011 at 10:09 PM, cityoftheasleep
<igliashon@...>wrote:

>
>
> --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>, Mike Battaglia
> <battaglia01@...> wrote:
> >
> > Surely you like the blues?
>
> No, not really. Maybe really old blues, the kind played by old men who've
> suffered long and tortured lives and can't really express themselves any
> other way, but there is just so much AWFUL music out there that goes by the
> name of "blues", music that is trite, shallow, formulaic, macho, and
> downright false. As a musical form of I-IV-V with dom7 chords on all
> degrees, I think it's just really flat and boring. Not that I haven't played
> some blues in my day, but I really can't say I find it enjoyable. Really the
> only time I care for the dom7 chord is when it's used as...a dominant 7th
> chord, i.e. as part of functional harmony.
>
> -Igs
>

Don't mind me - just carving that on my tombstone.

🔗akjmicro <aaron@...>

I don't care much for most blues, either. A lot of times jazz doesn't do much for me, either.

AKJ

--- In tuning@yahoogroups.com, Daniel Nielsen <nielsed@...> wrote:
>
> On Mon, Jan 24, 2011 at 10:09 PM, cityoftheasleep
> <igliashon@...>wrote:
>
> >
> >
> > --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>, Mike Battaglia
> > <battaglia01@> wrote:
> > >
> > > Surely you like the blues?
> >
> > No, not really. Maybe really old blues, the kind played by old men who've
> > suffered long and tortured lives and can't really express themselves any
> > other way, but there is just so much AWFUL music out there that goes by the
> > name of "blues", music that is trite, shallow, formulaic, macho, and
> > downright false. As a musical form of I-IV-V with dom7 chords on all
> > degrees, I think it's just really flat and boring. Not that I haven't played
> > some blues in my day, but I really can't say I find it enjoyable. Really the
> > only time I care for the dom7 chord is when it's used as...a dominant 7th
> > chord, i.e. as part of functional harmony.
> >
> > -Igs
> >
>
> Don't mind me - just carving that on my tombstone.
>

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

> On Mon, Jan 24, 2011 at 11:09 PM, cityoftheasleep <igliashon@...t> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > Surely you like the blues?
>
> No, not really. Maybe really old blues, the kind played by old men who've suffered long and tortured lives and can't really express themselves any other way, but there is just so much AWFUL music out there that goes by the name of "blues", music that is trite, shallow, formulaic, macho, and downright false. As a musical form of I-IV-V with dom7 chords on all degrees, I think it's just really flat and boring. Not that I haven't played some blues in my day, but I really can't say I find it enjoyable. Really the only time I care for the dom7 chord is when it's used as...a dominant 7th chord, i.e. as part of functional harmony.

Oh? Well when I hear this:

http://www.youtube.com/watch?v=YXBmsHk-qfA

or this:

http://www.youtube.com/watch?v=kfuHgzu1Cjg

I hear some pretty sweet functional 7-limit harmony myself. But then
again, I guess I can see why you don't like it; I'm not a fan of
straight I-IV-V 5-limit stuff, which unfortunately comprises most pop
music.

-Mike

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

🔗Chris Vaisvil <chrisvaisvil@...>

Thanks Gene,

then in that case Igs maybe interested in the mp3's here
http://micro.soonlabel.com/hobbit_scales/

Specifically
http://micro.soonlabel.com/hobbit_scales/daily20101231-archytas12-winds.mp3
http://micro.soonlabel.com/hobbit_scales/daily201031--hobbit-archytas12.mp3

Chris

On Tue, Jan 25, 2011 at 2:10 PM, genewardsmith
<genewardsmith@...>wrote:

>
>
>
>
> --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>, Chris Vaisvil
> <chrisvaisvil@...> wrote:
> >
> > A question
> >
> > Is the 7 note version more or less included in the 12 or 17 note versions
> of
> > Archytas?
>
> The 5-limit transversal for Archytas[7] goes 9/8, 5/4, 4/3, 3/2, 8/5, 16/9,
> 2. The transversal for Archytas[12] goes 16/15, 9/8, 6/5, 5/4, 4/3, 45/32,
> 3/2, 8/5, 27/16, 16/9, 15/8, 2. So yes, it's included. This sort of thing is
> not guaranteed to happen with hobbits, but it's very common.
>
>
>

🔗Petr Parízek <petrparizek2000@...>

🔗akjmicro <aaron@...>

Cool idea.

AKJ

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
>
> > I hear some pretty sweet functional 7-limit harmony myself. But then
> > again, I guess I can see why you don't like it; I'm not a fan of
> > straight I-IV-V 5-limit stuff, which unfortunately comprises most pop
> > music.
>
> Make 'em write music in Kleismic[11]. That would cure them. All the lovely 5-limit triads you could want, and no I-IV-V.
>
> Who's willing to give us some bubblegum or boy band music in Kleismic[11]? This could be the breakthrough Michael has been asking for. Just refret your guitar, and you are in business.
>

🔗Michael <djtrancendance@...>

MikeB> "I hear some pretty sweet functional 7-limit harmony myself. But then
again, I guess I can see why you don't like it; I'm not a fan of
> > straight I-IV-V 5-limit stuff, which unfortunately comprises most pop music.
> > Make 'em write music in Kleismic[11]. That would cure them. All the lovely
>5-limit triads you could want, and no I-IV-V.

So where can I find a scala file for Kleismic...or what MOS-type mapping (IE
sLLsL...) of what TET yields it?

I find 5-limit triads a bit plain but, putting ego aside, if I (and perhaps
other members) could actually put together a piece of music that's notoriously
easy to listen to (think the typical "hip hop-ish" boy band breakbeats), find
some pretty-boy type to sing and dance for it, shove something on You Tube, and
promote it to death (IE send it to Yahoo news, journalists for local TV
stations)...I think we just might have a chance for a cheap-but-effective
breakthrough...
The fact we have loads of people on here who are capable of some killer
symphonic backup (think punchy brass and string sections) and others with a
knack for beats and glitch effects (think the kind of stuff BT uses on NSync's
"pop") can only make it cooler.

More importantly, it would likely put us a step closer to doing the type of
stuff we really want. Once we have an established "cheap boy band that doesn't
play in 12TET"...we can move onto things like a rock band in 7 or 9-limit or
even eventually something like a soul/funk band in some strong 11-limit (think
Mohajira or similar). I just say rock and funk because those are the two
styles, beside hip-hop, that seem to hold a fairly large fan base...bands like
Daft Punk, Red Hot Chili Peppers, and a lot of popular house music has strong
funk influences and yet, at many times, a knack for odd chords.

Another scary thing...let's face it: The Beatles were a boy band. :-D

🔗akjmicro <aaron@...>

Who can sing in Kleismic[11] a-capella? That would be something to behold.

AKJ

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> MikeB> "I hear some pretty sweet functional 7-limit harmony myself. But then
> again, I guess I can see why you don't like it; I'm not a fan of
> > > straight I-IV-V 5-limit stuff, which unfortunately comprises most pop music.
> > > Make 'em write music in Kleismic[11]. That would cure them. All the lovely
> >5-limit triads you could want, and no I-IV-V.
>
>
> So where can I find a scala file for Kleismic...or what MOS-type mapping (IE
> sLLsL...) of what TET yields it?
>
> I find 5-limit triads a bit plain but, putting ego aside, if I (and perhaps
> other members) could actually put together a piece of music that's notoriously
> easy to listen to (think the typical "hip hop-ish" boy band breakbeats), find
> some pretty-boy type to sing and dance for it, shove something on You Tube, and
> promote it to death (IE send it to Yahoo news, journalists for local TV
> stations)...I think we just might have a chance for a cheap-but-effective
> breakthrough...
> The fact we have loads of people on here who are capable of some killer
> symphonic backup (think punchy brass and string sections) and others with a
> knack for beats and glitch effects (think the kind of stuff BT uses on NSync's
> "pop") can only make it cooler.
>
> More importantly, it would likely put us a step closer to doing the type of
> stuff we really want. Once we have an established "cheap boy band that doesn't
> play in 12TET"...we can move onto things like a rock band in 7 or 9-limit or
> even eventually something like a soul/funk band in some strong 11-limit (think
> Mohajira or similar). I just say rock and funk because those are the two
> styles, beside hip-hop, that seem to hold a fairly large fan base...bands like
> Daft Punk, Red Hot Chili Peppers, and a lot of popular house music has strong
> funk influences and yet, at many times, a knack for odd chords.
>
>
>
> Another scary thing...let's face it: The Beatles were a boy band. :-D
>

🔗genewardsmith <genewardsmith@...>

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

> So where can I find a scala file for Kleismic...or what MOS-type mapping (IE
> sLLsL...) of what TET yields it?

I suggested already 38338338338 in 53et. Five each of 53's superlative major and minor triads. If that's too tame, these can be extended to tetrads using seriously flat 7/4, 7/5 and 7/6's. If you can stand what passes for septimal harmony in 12et these should do fine. Anyway, whatever you call them they are chords which are not triads, so you aren't limited to just triads; plus there are eight of this scale's version of diminished seventh chords. That should be plenty for a boy band, or even the Beatles.

Here's the scale:

! hanson11.scl
!
Hanson[11] (Kleismic[11]) in 53-et
11
!
67.92453
249.05660
316.98113
384.90566
566.03774
633.96226
701.88679
883.01887
950.94340
1018.86792
2/1

🔗Chris Vaisvil <chrisvaisvil@...>

probably not what you wanted....

Dimension Pro 1.5 and modified Pianoteq in Hanson11

http://micro.soonlabel.com/Hanson/daily20110127-in-hanson11.mp3

On Wed, Jan 26, 2011 at 3:59 PM, genewardsmith
<genewardsmith@sbcglobal.net>wrote:

>
>
>
>
> --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>, Michael
> <djtrancendance@...> wrote:
>
> > So where can I find a scala file for Kleismic...or what MOS-type mapping
> (IE
> > sLLsL...) of what TET yields it?
>
> I suggested already 38338338338 in 53et. Five each of 53's superlative
> major and minor triads. If that's too tame, these can be extended to tetrads
> using seriously flat 7/4, 7/5 and 7/6's. If you can stand what passes for
> septimal harmony in 12et these should do fine. Anyway, whatever you call
> them they are chords which are not triads, so you aren't limited to just
> triads; plus there are eight of this scale's version of diminished seventh
> chords. That should be plenty for a boy band, or even the Beatles.
>
> Here's the scale:
>
> ! hanson11.scl
> !
> Hanson[11] (Kleismic[11]) in 53-et
> 11
> !
> 67.92453
> 249.05660
> 316.98113
> 384.90566
> 566.03774
> 633.96226
> 701.88679
> 883.01887
> 950.94340
> 1018.86792
> 2/1
>
>
>