Yahoo Tuning Groups Ultimate Backup tuning Re: [tuning] classic quarter-tone piano music

Thanks Dan, this is interesting, and it's great to see important pioneering
work in microtones up on YouTube.

Checking out a couple of these links got me realizing once again...I have to
say, my personal interest in going beyond 12-tet is both the increase of
consonance, and also what I call "meta-dissonance" where something is very
unstable in a traditional (sometimes Western sense) sense, but it doesn't
necessarily read as "harsh or violent" in affect....Asian music, some Middle
Eastern/Eastern European music, Cameron Bobro's "shadow tunings" and how he
uses them, and Igliashon Jones' xentonal work spring to mind as what I mean
here by "meta-dissonance".

Thus, I enjoyed the Haba MUCH more than the Wyschnegradsky as a result...the
Haba was like micro-tinged Martinu to me, and the Wyschnegradsky was like
2nd Viennese school angst on steroids. Not my cup-o-tea. The Ives was pretty
cool, though---not my favorite composer overall (sorry, I know that the
height of coolness and hipness to many many composers is to worship at the
Ives alter) but certainly contains some juicy stuff, and I think, very
neo-Romantic in gesture more than modernists like to think...I hear much in
common with late Scriabin and a lot of Ives piano music. Although the Ives
has a little bit more of that quintessential American flavor and devilish
humor. Like in the 2nd movement, at around 1'50"--those American marching
band type moments that are so Ives.

The picture put up to go with the Wyschnegradsky music says it all--a stark
B&W woodcut of a man clearly pushed to psychic limits of sanity. Very, very,
post 2nd Viennese school, and not at all what interests me or turns me on as
a composer OR listener....although I respect the likes of Schoenberg, and
much of the music inspired in their wake, I never find myself rushing to buy
or swim in their sounds. Not a fan of Babbitt or Boulez. Or Carter. I have
enough neurosis and anxiety in my own inner life, thank you very much---I
like much that can settle me, calm me, or give me a catharsis in a much
tamer way. Plus, it's 2009, not 1961. I know, I know, to each his own!

It could also be the _gestures_ of these composers that I react to even more
than the tunings or even sonorities---I have ZERO problem with the gentle,
Zen-like beauty of Morton Feldman, which actually soothes me for hours.
Maybe I like my ultra-dissonance pianissimo? In any event, for me, if I feel
like I'm getting paper cuts in my ears listening any more, I turn it off and
look elsewhere.

Let me say this, though---Ives as a rhythmic innovator is unparalled,
however, and I do enjoy the amazing, and amazingly *humorous* piano studies.
With Schoenberg, I tend to like the neo-tonal stuff best, both early and
late periods---e.g. Verklarte Nacht, and say the 2nd chamber symphony. And
if I'm in the right mood, the 5 orchestral pieces hit the spot.

AKJ

On Tue, Oct 13, 2009 at 7:55 AM, daniel_anthony_stearns <
daniel_anthony_stearns@...> wrote:

> quarter-tones have taken a lot of slag over the years, but I never really
> bought it, and man.... God bless YouTube!
>
> Alois Haba:
> http://www.youtube.com/watch?v=s7vZURdhucM
> http://www.youtube.com/watch?v=F83DtE2JPwg
> http://www.youtube.com/watch?v=gMeqU7XC0o0
>
> Ivan Wyschnegradsky:
> http://www.youtube.com/watch?v=HxWRu2PY_c8
> http://www.youtube.com/watch?v=d2biiLLoF4Y
> (and)
> http://www.youtube.com/watch?v=3EGriPbFmKE
> http://www.youtube.com/watch?v=YXyNPKKjz7w
>
> Charles Ives:
> http://www.youtube.com/watch?v=EXJPnUZhETg
> http://www.youtube.com/watch?v=EU85bUyDPWs
> http://www.youtube.com/watch?v=0JESZY4VK68
>
> the Ives has been up for a while, but the Wyschnegradsky and Haba have not
> what can I say.....lots of great stuff and food for thought here ImO
>
>
>
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
> Yahoo! Groups Links
>
>
>
>

Aaron Krister Johnson
http://www.akjmusic.com
http://www.untwelve.org

🔗Chris Vaisvil <chrisvaisvil@...>

🔗Raintree Goldbach <thefractalgourmet@...>

The following scale is both a well temperament and "just intonation epimorphic",
according to Scala.

The scale in ratios

1/1

200/189

28/25

25/21

63/50

75/56

567/400

112/75

100/63

42/25

25/14

189/100

2/1

The scale in cents

0.0

97.937

196.198

301.847

400.108

505.757

604.018

694.243

799.892

898.153

1003.802

1102.063

1200.0

Method for tuning by ear:

All sharps and flats are to be considered as enharmonic, Gb = F#, etc.

In each step only one string is to be adjusted,

which is indicated at the beginning of the step, i.e., "Tune A", "Tune B", etc.

Steps 1-3 are used to establish a value for D of 28/25.

1) Tune Bb, such that C-Bb forms a pure 7/4 minor seventh.

Bb will be retuned, step 7.

2) Tune Gb, such that Gb-Bb forms a pure 5/4 major third.

Gb will be retuned, step 16.

3) Tune D, such that D-Gb forms a pure 5/4 major third.

Therefore D = (7/4)*(4/5)*(4/5) = 28/25.

Steps 4-6 are used to establish a value for Bb of 25/14.

4) Tune E, such that C-E forms a pure 5/4 major third.

E will be retuned, step 14.

5) Tune G#, such that E-G# forms a pure 5/4 major third.

G# will be retuned, step 10.

6) Tune Bb, below C, such that Bb-G# forms a pure 7/4 minor seventh.

Therefore Bb = (5/4)*(5/4)*(4/7) = 25/28 = 25/14.

7) Tune Bb, above C, to form an octave with Bb below C.

Emanating from Bb and D,

the scale is completed by a series of 9 perfect fourths/fifths.

8) Tune F, such that F-Bb forms a perfect 4/3 fourth.

9) Tune Eb, such that Eb-Bb forms a perfect 3/2 fifth.

10) Tune Ab, such that Eb-Ab forms a perfect 4/3 fourth.

11) Tune Db, such that Db-Ab forms a perfect 3/2 fifth.

12)   Tune G,    such that D-G     forms a perfect 4/3 fourth.

13) Tune A, such that D-A forms a perfect 3/2 fifth.

14) Tune E, such that E-A forms a perfect 4/3 fourth.

15) Tune B, such that E-B forms a perfect 3/2 fifth.

16) Tune F#, such that F#-B forms a perfect 4/3 fourth.

17) The reference octave is now complete.

Any opinions and/or analysis would be greatly appreciated.

Thanks,

Raintree

🔗Carl Lumma <carl@...>

🔗Raintree Goldbach <thefractalgourmet@...>

Carl,

I apologize for the delay in responding.

The temperament was created in 2003, using The Fractal Tune Smithy and Scala.

However, I have not introduced it until quite recently, since, theoretically speaking, there are numerous objections that one could make, without ever listening to any music played using the scale.

There are in fact 3 major thirds of 81/64, G-B, D-F#, and C#-E#, for instance.

My definition of a "Celestial Tuning System" is "a just intonation well temperament".

To that end, according to Scala, it is a "Celestial Tuning System".

Also, I originally thought of celestial tuning systems as being 5-limit only, which is another reason that I overlooked this tuning system.

At the very least it might be said that it is the first known celestial tuning system, even if it is not "The" celestial tuning system.

there should now follow a plethora of celestial tuning systems, one of which should be able to replace 12 eq, and would thereby be worthy of the title "The Celestial Tuning System".

Nonetheless, there is one technique that i believe is very valuable in creating well temperaments, and scales of all sorts in general, and that is to invert every interval.

If G = 112/75 and F = 75/56, then the two notes will vibrate sympathetically, much more so than if they were unrelated ( i offer this as a theory only at this time ).

Also, theoretically speaking, If A resonates with B, then A should also resonate with 1/B.

In conclusion, it would appear as if 7-limit just intonation is minimal for obtaining a well temperament.

Thanks for the feedback,

Raintree

--- On Thu, 10/15/09, Carl Lumma <carl@...> wrote:

From: Carl Lumma <carl@...>
Subject: [tuning] Re: The Celestial Tuning System
To: tuning@yahoogroups.com
Date: Thursday, October 15, 2009, 4:04 AM

--- In tuning@yahoogroups. com, Raintree Goldbach <thefractalgourmet@ ...> wrote:

> The following scale is both a well temperament and

> "just intonation epimorphic", according to Scala.

Hi Raintree,

It doesn't match any of the WTs in my collection. Why do

you call it "celestial"?

I like the fact that you've posted a bearing plan. Tuning

by ear is still more fun and better exercise than using an

electronic tuner.

You might try a different permutation of the 5ths, since

as soon as four pure fifths are consecutive on the chain

we get harsh 81/64 thirds. You have three flat fifths,

which is just enough to make sure no 81/64 thirds appear.

Here's something closer to scala-parsable format for those

following along at home:

Raintree Goldbach's "Celestial Tuning System"

200/189

28/25

25/21

63/50

75/56

567/400

112/75

100/63

42/25

25/14

189/100

2/1

By the way, your contributions to wikipedia on intonation are

very much appreciated.

-Carl

🔗Raintree Goldbach <thefractalgourmet@...>

Carl,

in regards to wikipedia, i have not directly contributed to any articles.

could you provide a url?

Thanks,

Raintree

--- On Thu, 10/15/09, Carl Lumma <carl@...> wrote:

From: Carl Lumma <carl@...>
Subject: [tuning] Re: The Celestial Tuning System
To: tuning@yahoogroups.com
Date: Thursday, October 15, 2009, 4:04 AM

--- In tuning@yahoogroups. com, Raintree Goldbach <thefractalgourmet@ ...> wrote:

> The following scale is both a well temperament and

> "just intonation epimorphic", according to Scala.

Hi Raintree,

It doesn't match any of the WTs in my collection. Why do

you call it "celestial"?

I like the fact that you've posted a bearing plan. Tuning

by ear is still more fun and better exercise than using an

electronic tuner.

You might try a different permutation of the 5ths, since

as soon as four pure fifths are consecutive on the chain

we get harsh 81/64 thirds. You have three flat fifths,

which is just enough to make sure no 81/64 thirds appear.

Here's something closer to scala-parsable format for those

following along at home:

Raintree Goldbach's "Celestial Tuning System"

200/189

28/25

25/21

63/50

75/56

567/400

112/75

100/63

42/25

25/14

189/100

2/1

By the way, your contributions to wikipedia on intonation are

very much appreciated.

-Carl

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, Raintree Goldbach <thefractalgourmet@...> wrote:
>
> My definition of a "Celestial Tuning System" is "a just intonation
> well temperament".

'round these parts they're known as "rational well temperaments",
or RWTs for short.

> Also, I originally thought of celestial tuning systems as being
> 5-limit only, which is another reason that I overlooked this
> tuning system.

Several RWTs published here have made use of things like the
17/12 tritone and 19/16 minor third, and even the 24/19
major third.

> Nonetheless, there is one technique that i believe is very
> valuable in creating well temperaments, and scales of all sorts
> in general, and that is to invert every interval.

That is a useful technique.

Last year, I used a brute force computer search to find RWTs
with the maximum number of 19-limit intervals. I currently
have my Yamaha upright tuned in one of them (though it could
stand to be touched up at the moment).

Back in 2003, Bob Wendell demonstrated an approach to well
temperaments, which is to try and get the ratio between the
beat rates of the major and minor 3rds to be simple, in as
many of the triads as possible. For instance, if C-E beats
3 times/second and E-G beats 6 times/second, the beat ratio of
the C major triad is said to be 2 (or 1/2, depending how you
define it), which is a simple ratio. Bob claimed such triads
sound better than triads with a similar amount of temperament
but more complicated beat ratios.

Gene Ward Smith called beat ratios "brats" for short, and
posted some equations to help generate WTs with simple brats.
And it turns out that RWTs tend to have simple brats. In
fact, Gene was able to find a more exact version of Bob's
"Natural Synchronus Well" temperament using rational
arithmetic.

-Carl

🔗Carl Lumma <carl@...>

🔗Raintree Goldbach <thefractalgourmet@...>

Carl,

fascinating, could you give the ratio and/or cents for the 19-limit RWT?

i still prefer the term "celestial", and believe that it is more descriptive, when applied to a system that is sufficiently close to just, whereas a rational interval, by definition, could be just, close to just, or almost infinitely distant from just, depending on the number of steps required to obtain the note using a series of just intervals.

just intervals are more connected to the physical, the biology of the ear, brain, and body, as well as that which we describe as spiritual ( celestial ).

therefore, in my opinion, and in the opinion of the old-timers, a just solution is the only solution.

perhaps if the temperament can be described in a certain number of steps, each of them just, then a temperament would be both a RWT and a CT?

also, does Scala define every RWT as just intonation epimorphic?

are any of the well temperaments as flexible as 12 eq?

is there any well temperament that the majority of the tuning list believes is optimal?

is there at least one well temperament that could reasonably well replace 12 eq?

every midi file that i retune using the CTS sounds exquisite, yet, clearly, there may be issues related to the 81/64 thirds, and the 3 attenuated fifths.

i have a rational explanation for the fifths, yet such explanation could not possibly counter act the auditory sensation produced, if they are not correct.

also, is it possible for a temperament to sound correct when retuning midi files, yet incorrect when applied to an instrument "in the real world", so to speak?

Thanks,

Raintree

--- On Sat, 10/17/09, Carl Lumma <carl@...> wrote:

From: Carl Lumma <carl@...>
Subject: [tuning] Re: The Celestial Tuning System
To: tuning@yahoogroups.com
Date: Saturday, October 17, 2009, 2:08 AM

--- In tuning@yahoogroups. com, Raintree Goldbach <thefractalgourmet@ ...> wrote:

> My definition of a "Celestial Tuning System" is "a just intonation

> well temperament" .

'round these parts they're known as "rational well temperaments" ,

or RWTs for short.

> Also, I originally thought of celestial tuning systems as being

> 5-limit only, which is another reason that I overlooked this

> tuning system.

Several RWTs published here have made use of things like the

17/12 tritone and 19/16 minor third, and even the 24/19

major third.

> Nonetheless, there is one technique that i believe is very

> valuable in creating well temperaments, and scales of all sorts

> in general, and that is to invert every interval.

That is a useful technique.

Last year, I used a brute force computer search to find RWTs

with the maximum number of 19-limit intervals. I currently

have my Yamaha upright tuned in one of them (though it could

stand to be touched up at the moment).

Back in 2003, Bob Wendell demonstrated an approach to well

temperaments, which is to try and get the ratio between the

beat rates of the major and minor 3rds to be simple, in as

many of the triads as possible. For instance, if C-E beats

3 times/second and E-G beats 6 times/second, the beat ratio of

the C major triad is said to be 2 (or 1/2, depending how you

define it), which is a simple ratio. Bob claimed such triads

sound better than triads with a similar amount of temperament

but more complicated beat ratios.

Gene Ward Smith called beat ratios "brats" for short, and

posted some equations to help generate WTs with simple brats.

And it turns out that RWTs tend to have simple brats. In

fact, Gene was able to find a more exact version of Bob's

"Natural Synchronus Well" temperament using rational

arithmetic.

-Carl

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, Raintree Goldbach <thefractalgourmet@...> wrote:

> fascinating, could you give the ratio and/or cents for the
> 19-limit RWT?

It's a VRWT, where the V stands for "Victorian", which means
the key contrast is mild compared to WTs of the baroque.

!
[2 3 17 19] well temperament.
12
!
19/18
323/288
19/16
64/51
4/3
24/17
3/2
19/12
57/34
16/9
32/17
2/1
!
! 68 19-limit intervals = maximum for a VRWT.
! (P P P b P P a P P b c a) a=(-3 1 1) b=(-2 0 -1) c=(3 -2 0)

> i still prefer the term "celestial", and believe that it is more
> descriptive, when applied to a system that is sufficiently close
> to just,

Well temperaments contain chords that sound like 5-limit triads,
but are not 5-limit triads. They're tempered. If we use
rational numbers to describe such triads, that doesn't make
them just. They still have beats and still cannot be tuned
directly by ear.

> also, does Scala define every RWT as just intonation epimorphic?

Scala doesn't have a definition of RWT built in. It depends
on your definition of WT, but most WTs should be epimorphic.

> are any of the well temperaments as flexible as 12 eq?

I'm finding that even with my mild VRWT, the keys like C# on
my piano are harsher than I'd like.

> is there any well temperament that the majority of the tuning
> list believes is optimal?

Heh. No. :)

> is there at least one well temperament that could reasonably
> well replace 12 eq?

There are several that are so close to 12-ET that they are
practically indistinguishable...

> every midi file that i retune using the CTS sounds exquisite,
> yet, clearly, there may be issues related to the 81/64 thirds,
> and the 3 attenuated fifths.

You have to test all keys.

> also, is it possible for a temperament to sound correct when
> retuning midi files, yet incorrect when applied to an
> instrument "in the real world", so to speak?

I'm not sure of the explanation, but I find the distant keys
of WTs (like C#) to be much more objectionable on my piano than
in MIDI retunings that I've done.

-Carl

🔗Kraig Grady <kraiggrady@...>

🔗Raintree Goldbach <thefractalgourmet@...>

Carl,

wonderful!

it is therefore quite evident that WT's, of various sorts, could thoroughly enliven the classical/baroque/romantic repertoire, enliven and invigorate.

"Well temperaments contain chords that sound like 5-limit triads,

but are not 5-limit triads. They're tempered. If we use

rational numbers to describe such triads, that doesn't make

them just. They still have beats and still cannot be tuned

directly by ear."

which is exactly what i was saying in an earlier post, that not all RWTs are CWTs.

The Celestial Tuning System, with all of it's soon to be corrected flaws, if possible, is tunable by ear, and is also a verifiable WT, to the extent that one can trust Scala, which should be in the 99+ percentile.

Also, I am now of the opinion that 7-limit, which is inclusive of 5-limit, is the method of choice, both from a practical standpoint, in creating well temperaments that are tunable by ear, and in the ambience thereby produced.

"Scala doesn't have a definition of RWT built in. It depends

on your definition of WT, but most WTs should be epimorphic."

if epimorphic then tunable by ear? or there could be 2 classes, epimorphic and not tunable by ear, and, of course, epimorphic and tunable by ear.

"You have to test all keys."

I have played through both books of the WTC numerous times, various piano concertos from all eras, etc, everything sounds good, as far as I can tell.

"I'm not sure of the explanation, but I find the distant keys

of WTs (like C#) to be much more objectionable on my piano than

in MIDI retunings that I've done."

this is my greatest concern when testing any system, perhaps the only real answer is to have a piano/harpsichord tuner on standby.

the C# major prelude and fugue Bk I sounds very good, in my opinion, using your 19-limit WT.

Thanks,

Raintree

--- On Sat, 10/17/09, Carl Lumma <carl@lumma.org> wrote:

From: Carl Lumma <carl@...>
Subject: [tuning] Re: The Celestial Tuning System
To: tuning@yahoogroups.com
Date: Saturday, October 17, 2009, 10:56 AM

--- In tuning@yahoogroups. com, Raintree Goldbach <thefractalgourmet@ ...> wrote:

> fascinating, could you give the ratio and/or cents for the

> 19-limit RWT?

It's a VRWT, where the V stands for "Victorian", which means

the key contrast is mild compared to WTs of the baroque.

[2 3 17 19] well temperament.

19/18

323/288

19/16

64/51

4/3

24/17

3/2

19/12

57/34

16/9

32/17

2/1

! 68 19-limit intervals = maximum for a VRWT.

! (P P P b P P a P P b c a) a=(-3 1 1) b=(-2 0 -1) c=(3 -2 0)

> i still prefer the term "celestial", and believe that it is more

> descriptive, when applied to a system that is sufficiently close

> to just,

Well temperaments contain chords that sound like 5-limit triads,

but are not 5-limit triads. They're tempered. If we use

rational numbers to describe such triads, that doesn't make

them just. They still have beats and still cannot be tuned

directly by ear.

> also, does Scala define every RWT as just intonation epimorphic?

Scala doesn't have a definition of RWT built in. It depends

on your definition of WT, but most WTs should be epimorphic.

> are any of the well temperaments as flexible as 12 eq?

I'm finding that even with my mild VRWT, the keys like C# on

my piano are harsher than I'd like.

> is there any well temperament that the majority of the tuning

> list believes is optimal?

Heh. No. :)

> is there at least one well temperament that could reasonably

> well replace 12 eq?

There are several that are so close to 12-ET that they are

practically indistinguishable. ..

> every midi file that i retune using the CTS sounds exquisite,

> yet, clearly, there may be issues related to the 81/64 thirds,

> and the 3 attenuated fifths.

You have to test all keys.

> also, is it possible for a temperament to sound correct when

> retuning midi files, yet incorrect when applied to an

> instrument "in the real world", so to speak?

I'm not sure of the explanation, but I find the distant keys

of WTs (like C#) to be much more objectionable on my piano than

in MIDI retunings that I've done.

-Carl

🔗Carl Lumma <carl@...>

Raintree wrote:

> if epimorphic then tunable by ear?

Epimorphic has to do with how the scale degrees map just
intonation. It answers questions like "Is the best 3:2
always a fifth?" Doesn't have much to do with tuning by
ear at all.

What's tunable by ear is, by definition, what you can
tune by ear. Give it a try and see! Note, when we say
an interval or chord is tunable by ear, we mean directly,
without moving through a bearing plan.

>> You have to test all keys.
>
> I have played through both books of the WTC numerous times,
> various piano concertos from all eras, etc, everything sounds
> good, as far as I can tell.

The problem, as far as making comparative statements about
scales, is that real music:

* has its own emotional content that colors your perception
of the harmony

* takes time to hear, e.g. your memory of Amin will fade
before you get to Bmin.

* does not treat all intervals equally. even in a large
work like the WTC, if you were to plot a histogram of the
intervals by duration (i.e. C-E would be distinct from E-G#),
I bet the plot would have significant peaks and valleys.

Therefore, you should compare all the major and minor triads
as bare chords when evaluating WTs. Music is always a good
test too, but it must be supplemented with something more
controlled if WTs are going to be objectively compared.

>> I'm not sure of the explanation, but I find the distant
>> keys of WTs (like C#) to be much more objectionable on my
>> piano than in MIDI retunings that I've done.
>
> this is my greatest concern when testing any system, perhaps
> the only real answer is to have a piano/harpsichord tuner on
> standby.

Harpsichord is a lot easier for this sort of thing. Tuning
pianos is fairly exhausting, and they don't like to have their
tuning moved around too much.

> the C# major prelude and fugue Bk I sounds very good, in my
> opinion, using your 19-limit WT.

Well thanks. The question is, does the 19-limit part have
anything to do with that? I'm not entirely sure, but it's a
comforting idea at least.

-Carl

🔗Raintree Goldbach <thefractalgourmet@...>

Kraig,

please forgive me for taking so long to respond, my physical condition is such that i have to take several days off from time to time.

whatever George is doing is working, the notes have a unique sparkle to them, and there is also an overall sense of unity, simultaneously.

there were times when i felt as if the melodies were slightly detuned, yet, nonetheless, the overall unity and harmony proceeded forth in the same manner as before.

it is such a promising method that it could certainly replace 12 eq, with enough research.

the sound is magical to say the least.

thanks,

Raintree

--- On Sun, 10/18/09, Kraig Grady <kraiggrady@...> wrote:

From: Kraig Grady <kraiggrady@...>
Subject: [tuning] Re: The Celestial Tuning System
To: tuning@yahoogroups.com
Date: Sunday, October 18, 2009, 1:38 AM

Hello Raintree~

a fascinating area to look at. George Secor came up with one where he

uses Just ratios to have equal beating triads. He did a few but myself

and a few others really liked this one.

! Secor5_23STX. scl

George Secor's synchronous 5/23-comma temperament extraordinaire

62/59

66/59

559/472

591/472

315/236

331/236

353/236

745/472

395/236

210/118

221/118

2/1

i have some info on my blog on the piece i did for it.

http://anaphoriasou th.blogspot. com/search/ label/George% 20Secor

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_

Mesotonal Music from:

_'''''''_ ^North/Western Hemisphere:

North American Embassy of Anaphoria Island <http://anaphoria. com/>

_'''''''_ ^South/Eastern Hemisphere:

Austronesian Outpost of Anaphoria <http://anaphoriasou th.blogspot. com/>

',',',',',', ',',',',' ,',',',', ',',',',' ,',',',', ',',',',' ,

a momentary antenna as i turn to water

this evaporates - an island once again

🔗Kraig Grady <kraiggrady@...>

🔗gdsecor <gdsecor@...>

Raintree,

I regard any circulating temperament with such a high key contrast as my "extrordinaire" as an *alternative* to 12-equal, rather than a replacement. I find the key of B minor interesting, because its highly dissonant dominant triad (with a very high leading tone) resolves very effectively to a highly consonant tonic triad, which is very effective both melodically and harmonically. However, you probably wouldn't want to play anything (except for medieval music, which sounds fantastic) in the keys of B, F#, C#, of G# major because the thirds of the tonic triads are extremely wide -- perhaps acceptable in passing, but not for the home key.

If you're seeking a replacement, then IMO a Victorian rational well (low-contrast) temperament (such as Carl Lumma and Aaron Johnson advocate) would be in order. (As Carl noted, there's no consensus regarding which one is "best".) One of my leading candidates is:

! SecorVRWT-24e.scl
!
George Secor's 24-triad proportional-beating Victorian rational well-temperament (24e), based on Ellis #2
12
!
581/550
28/25
653/550
345/275
367/275
31/22
412/275
871/550
461/275
89/50
47/25
2/1

--George

--- In tuning@yahoogroups.com, Raintree Goldbach <thefractalgourmet@...> wrote:
>
> Kraig,
>
> please forgive me for taking so long to respond, my physical condition is such that i have to take several days off from time to time.
>
> whatever George is doing is working, the notes have a unique sparkle to them, and there is also an overall sense of unity, simultaneously.
>
> there were times when i felt as if the melodies were slightly detuned, yet, nonetheless, the overall unity and harmony proceeded forth in the same manner as before.
>
> it is such a promising method that it could certainly replace 12 eq, with enough research.
>
> the sound is magical to say the least.
>
> thanks,
>
> Raintree
>
> --- On Sun, 10/18/09, Kraig Grady <kraiggrady@...> wrote:
>
> From: Kraig Grady <kraiggrady@...>
> Subject: [tuning] Re: The Celestial Tuning System
> To: tuning@yahoogroups.com
> Date: Sunday, October 18, 2009, 1:38 AM
>
> Hello Raintree~
> a fascinating area to look at. George Secor came up with one where he
> uses Just ratios to have equal beating triads. He did a few but myself
> and a few others really liked this one.
>
> ! Secor5_23STX. scl
> !
> George Secor's synchronous 5/23-comma temperament extraordinaire
> 12
> !
> 62/59
> 66/59
> 559/472
> 591/472
> 315/236
> 331/236
> 353/236
> 745/472
> 395/236
> 210/118
> 221/118
> 2/1
>
> i have some info on my blog on the piece i did for it.
>
> http://anaphoriasou th.blogspot. com/search/ label/George% 20Secor
>
> --
>
> /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> Mesotonal Music from:
> _'''''''_ ^North/Western Hemisphere:
> North American Embassy of Anaphoria Island <http://anaphoria. com/>
>
> _'''''''_ ^South/Eastern Hemisphere:
> Austronesian Outpost of Anaphoria <http://anaphoriasou th.blogspot. com/>
> ',',',',',', ',',',',' ,',',',', ',',',',' ,',',',', ',',',',' ,
>
> a momentary antenna as i turn to water
> this evaporates - an island once again
>

🔗Raintree Goldbach <thefractalgourmet@...>

George,

thanks once again.

i am now in the process of playing through all of the WTC Bk II in both temperaments, comparing them at each step.

could you tell me how the process works?

are you always using primes?

how do you calculate the beats, and is the proportionality absolute, or within a certain parameter?

which intervals are equal beating?

and, finally, are you hoping, at some point, to produce a WT, as robustly so as 12 eq, with the spice of your "alternative" temperaments, and/or do you consider it to be possible?

as it stands, i believe that your method produces the most vibrant harmonies, and the notes seem to be free, unrestrained, and, simultaneously, very well organized, in the sense that they are all produced from the same fabric, so to speak.

when i play your temperament compared to my own it is almost as if, in your temperament, another instrument has been added, it is a truly amazing phenomenon that i wish to understand to the utmost.

my temperament, of which i am still quite fond, does not seam amenable to alteration, any change causes it to lose some ineffable quality which is more important to me than "theoretical correctness".

however, if i can learn your system, maybe in the future the methods could be combined.

i especially would want to hear the WTC performed by a notable artist using one of your temperaments!

Thanks,

Raintree

--- On Tue, 10/27/09, gdsecor <gdsecor@...> wrote:

From: gdsecor <gdsecor@...>
Subject: [tuning] Re: The Celestial Tuning System
To: tuning@yahoogroups.com
Date: Tuesday, October 27, 2009, 11:00 AM

Raintree,

! SecorVRWT-24e. scl

George Secor's 24-triad proportional- beating Victorian rational well-temperament (24e), based on Ellis #2

581/550

28/25

653/550

345/275

367/275

31/22

412/275

871/550

461/275

89/50

47/25

2/1

--George

--- In tuning@yahoogroups. com, Raintree Goldbach <thefractalgourmet@ ...> wrote:

> Kraig,

> please forgive me for taking so long to respond, my physical condition is such that i have to take several days off from time to time.

> whatever George is doing is working, the notes have a unique sparkle to them, and there is also an overall sense of unity, simultaneously.

> there were times when i felt as if the melodies were slightly detuned, yet, nonetheless, the overall unity and harmony proceeded forth in the same manner as before.

> it is such a promising method that it could certainly replace 12 eq, with enough research.

> the sound is magical to say the least.

> thanks,

> Raintree

> --- On Sun, 10/18/09, Kraig Grady <kraiggrady@ ...> wrote:

> From: Kraig Grady <kraiggrady@ ...>

> Subject: [tuning] Re: The Celestial Tuning System

> To: tuning@yahoogroups. com

> Date: Sunday, October 18, 2009, 1:38 AM

> Hello Raintree~

> a fascinating area to look at. George Secor came up with one where he

> uses Just ratios to have equal beating triads. He did a few but myself

> and a few others really liked this one.

> ! Secor5_23STX. scl

> !

> George Secor's synchronous 5/23-comma temperament extraordinaire

> 12

> !

> 62/59

> 66/59

> 559/472

> 591/472

> 315/236

> 331/236

> 353/236

> 745/472

> 395/236

> 210/118

> 221/118

> 2/1

> i have some info on my blog on the piece i did for it.

> http://anaphoriasou th.blogspot. com/search/ label/George% 20Secor

> --

> /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_

> Mesotonal Music from:

> _'''''''_ ^North/Western Hemisphere:

> North American Embassy of Anaphoria Island <http://anaphoria. com/>

> _'''''''_ ^South/Eastern Hemisphere:

> Austronesian Outpost of Anaphoria <http://anaphoriasou th.blogspot. com/>

> ',',',',',', ',',',',' ,',',',', ',',',',' ,',',',', ',',',',' ,

> a momentary antenna as i turn to water

> this evaporates - an island once again

__________________________________________________
Do You Yahoo!?
Tired of spam? Yahoo! Mail has the best spam protection around
http://mail.yahoo.com

🔗Raintree Goldbach <thefractalgourmet@...>

🔗gdsecor <gdsecor@...>

--- In tuning@yahoogroups.com, Raintree Goldbach <thefractalgourmet@...> wrote:
>
> George,
>
> thanks once again.
>
> i am now in the process of playing through all of the WTC Bk II in both temperaments, comparing them at each step.
>
> could you tell me how the process works?

It has taken many, many years of experimentation (both number-crunching and listening), trial and error, and subsequent refinement (and repetition of the foregoing steps) to arrive at the latest versions of the rational temperaments I'm advocating. That's the best I can do to describe the process, short of writing a thesis on the subject.

> are you always using primes?

Prime number content of the ratios is irrelevant.

> how do you calculate the beats, and is the proportionality absolute, or within a certain parameter?

I constructed a spreadsheet to calculate the beats:
http://xenharmony.wikispaces.com/space/showimage/RT-wksht.xls
You'll have to input the numbers in the colored cells. The cents in the ratios are immediately to the right. The beat ratios (or "brats") are farther to the right (in bold), then the total tempering error in each triad, then the error of each interval in the triad. The actual beat rates are farther to the right (cols. S-U), and the frequencies of each note in the root-position triad are at the extreme right (cols. W-Y). Examine the formulas in the cells to see how frequencies, beat rates, and brats are calculated.

In the two temperaments I gave you, all 24 major & minor triads have exact proportional beating. In general, the triads having the smallest amount of tempering have the simplest brats.

> which intervals are equal beating?
>
> and, finally, are you hoping, at some point, to produce a WT, as robustly so as 12 eq, with the spice of your "alternative" temperaments, and/or do you consider it to be possible?

I don't know what you mean by 12-equal being "robust" -- do you mean acceptable in all keys? It took a very long time for 12-equal to become generally acceptable in the West, and now it appears that it will be a very long time before anything else might displace it.

> as it stands, i believe that your method produces the most vibrant harmonies, and the notes seem to be free, unrestrained, and, simultaneously, very well organized, in the sense that they are all produced from the same fabric, so to speak.

The proportional beating of the triads makes the beating seem more unified and possibly less discordant.

> when i play your temperament compared to my own it is almost as if, in your temperament, another instrument has been added, it is a truly amazing phenomenon that i wish to understand to the utmost.
>
> my temperament, of which i am still quite fond, does not seam amenable to alteration, any change causes it to lose some ineffable quality which is more important to me than "theoretical correctness".
>
> however, if i can learn your system, maybe in the future the methods could be combined.

If you enter your ratios into my spreadsheet, you'll see that there are already 9 just fifths; any triad with a just fifth will automatically have proportional beating between the thirds. Of the remaining triads, only C major has reasonably simple proportional beating (M3:5th is 3:1).

It's possible that ratios giving simpler proportions could be found, but I think that you would have to settle for fewer just fifths.

> i especially would want to hear the WTC performed by a notable artist using one of your temperaments!
>
> Thanks,
>
> Raintree

Best,

--George

> > --- On Tue, 10/27/09, gdsecor <gdsecor@...> wrote:
> >
> > Raintree,
> >
> > I regard any circulating temperament with such a high key contrast as my "extrordinaire" as an *alternative* to 12-equal, rather than a replacement. ...

Re: [tuning] classic quarter-tone piano music

🔗Aaron Johnson <aaron@...>

🔗Chris Vaisvil <chrisvaisvil@...>

🔗Raintree Goldbach <thefractalgourmet@...>

🔗Carl Lumma <carl@...>

🔗Raintree Goldbach <thefractalgourmet@...>

🔗Raintree Goldbach <thefractalgourmet@...>

🔗Carl Lumma <carl@...>

🔗Carl Lumma <carl@...>

🔗Raintree Goldbach <thefractalgourmet@...>

🔗Carl Lumma <carl@...>

🔗Kraig Grady <kraiggrady@...>

🔗Raintree Goldbach <thefractalgourmet@...>

🔗Carl Lumma <carl@...>

🔗Raintree Goldbach <thefractalgourmet@...>

🔗Kraig Grady <kraiggrady@...>

🔗gdsecor <gdsecor@...>

🔗Raintree Goldbach <thefractalgourmet@...>

🔗Raintree Goldbach <thefractalgourmet@...>

🔗Raintree Goldbach <thefractalgourmet@...>

🔗gdsecor <gdsecor@...>