New (Improved!) Temperament (Extra)ordinare

Gene Ward Smith: Welcome back!

Dr. Oz: Take note!

After >35 years of tweaking & tinkering with 12-tone circulating temperaments, I thought that my 5/23-comma temperament (extra)ordinaire, version of November 2008, would be the very best I could do. Lo & behold: when I looked at the numbers the other day (2 April), I found a way to lower the error of the flat-wise chords to make them balanced with the sharp-wise ones (by changing 2 pitches, Eb & Bb), without sacrificing the overall proportionality of the beat rates. (This results in a smoother and more symmetrical progression of interval sizes as you go around the circle of 5ths.) Formerly there were 5, but there are now 6 major triads with <8.22 cents error in the major 3rd, a significant improvement over 12-equal that you can readily hear.

Here's the Scala listing:

! Secor5_23TX.scl
!
George Secor's synchronous 5/23-comma temperament extraordinaire
12
!
62/59
66/59
70/59
591/472
315/236
331/236
353/236
745/472
395/236
1051/590
221/118
2/1

The major triads on the far side of the circle will not be very suitable as tonic chords, but they're all usable for temporary modulations, and their high 3rds make wonderful leading tones in minor keys (esp. in E minor & B minor).

--George

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

> The major triads on the far side of the circle will not be very suitable as tonic chords, but they're all usable for temporary modulations, and their high 3rds make wonderful leading tones in minor keys (esp. in E minor & B minor).

They've definately got some juice, but the numbers look good to me. With a little more oomph, they'd be 14/11s, if you like those.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "gdsecor" <gdsecor@> wrote:
>
> > The major triads on the far side of the circle will not be very suitable as tonic chords, but they're all usable for temporary modulations, and their high 3rds make wonderful leading tones in minor keys (esp. in E minor & B minor).
>
> They've definately got some juice, but the numbers look good to me. With a little more oomph, they'd be 14/11s, if you like those.

I experimented with a 1/4-comma temperament (extra)ordinaire about 4 years ago, in which the widest major 3rd was tempered about 30 cents wide. Oz thought that it was too much (and I agree). I found that I could get away with up to 27.7 cents if the 5ths in the triads are tempered a few cents, inasmuch as their beating tends to mask the harshness of the wide 3rds somewhat.

--George

Dear George, sorry for replying so late! Yes, I am trying this new
tuning now that I have completed my responsibilities here this month.

Let's see... Goodness! It sounds awesome. Here, for your pleasure, I
made a rather long improvisation based on your 5/23 synchronous
beating rational Xtra Modified Meantone:

http://www.ozanyarman.com/files/music/FHimpro_Secor5_23RTX.mp3

This improvisation uses French Horns from the Logic Pro 8 library,translated to SF2 by Chicken Systems Translator and whose pitches are
bent using Aaron Andrew Hunt's H-Pi Scordatura. I used my P-200
Electronic Piano hooked to Axiom-25. Audio capture into Logic was
accomplished by Jack Pilot. Messy huh?

This attempt also shows my skills on the *sticky keys* of P-200 and my
knowledge of common-practice harmony.

Forgive the slurs during the recording.

I hope you like it!

More on my new book in response to congratulations.

Cordially,
Oz.

✩ ✩ ✩
www.ozanyarman.com

On Apr 7, 2010, at 12:46 AM, gdsecor wrote:

>
> Gene Ward Smith: Welcome back!
>
> Dr. Oz: Take note!
>
> After >35 years of tweaking & tinkering with 12-tone circulating
> temperaments, I thought that my 5/23-comma temperament
> (extra)ordinaire, version of November 2008, would be the very best I
> could do. Lo & behold: when I looked at the numbers the other day
> (2 April), I found a way to lower the error of the flat-wise chords
> to make them balanced with the sharp-wise ones (by changing 2
> pitches, Eb & Bb), without sacrificing the overall proportionality
> of the beat rates. (This results in a smoother and more symmetrical> progression of interval sizes as you go around the circle of 5ths.)
> Formerly there were 5, but there are now 6 major triads with <8.22
> cents error in the major 3rd, a significant improvement over 12-
> equal that you can readily hear.
>
> Here's the Scala listing:
>
> ! Secor5_23TX.scl
> !
> George Secor's synchronous 5/23-comma temperament extraordinaire
> 12
> !
> 62/59
> 66/59
> 70/59
> 591/472
> 315/236
> 331/236
> 353/236
> 745/472
> 395/236
> 1051/590
> 221/118
> 2/1
>
> The major triads on the far side of the circle will not be very
> suitable as tonic chords, but they're all usable for temporary
> modulations, and their high 3rds make wonderful leading tones in
> minor keys (esp. in E minor & B minor).
>
> --George
>
>
>
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
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> Yahoo! Groups Links
>
>
>

The improvisation is great but doesn't sound very different from 12 tet.

Not that that is a bad thing - I think what it means is that this well
balanced tuning to my ears.

Chris

On Thu, Apr 29, 2010 at 7:34 PM, Ozan Yarman <ozanyarman@...> wrote:
>
>
>
> Dear George, sorry for replying so late! Yes, I am trying this new tuning now >
> After >35 years of tweaking & tinkering with 12-tone circulating temperaments, I thought that my 5/23-comma temperament (extra)ordinaire, version of November 2008, would be the very best I could do.  Lo & behold: when I looked at the numbers the other day (2 April), I found a way to lower the error of the flat-wise chords to make them balanced with the sharp-wise ones (by changing 2 pitches, Eb & Bb), without sacrificing the overall proportionality of the beat rates.  (This results in a smoother and more symmetrical progression of interval sizes as you go around the circle of 5ths.)  Formerly there were 5, but there are now 6 major triads with <8.22 cents error in the major 3rd, a significant improvement over 12-equal that you can readily hear.
>
> Here's the Scala listing:
>
> ! Secor5_23TX.scl
> !
> George Secor's synchronous 5/23-comma temperament extraordinaire
> 12
> !
> 62/59
> 66/59
> 70/59
> 591/472
> 315/236
> 331/236
> 353/236
> 745/472
> 395/236
> 1051/590
> 221/118
> 2/1
>
> The major triads on the far side of the circle will not be very suitable as tonic chords, but they're all usable for temporary modulations, and their high 3rds make wonderful leading tones in minor keys (esp. in E minor & B minor).
>
> --George
>
>
>
>
> ------------------------------------
>
> 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
>
>
>
>
>

Actually, I find it a breath of fresh air compared to the unpalatable
tones of 12-equal.

Here are two more amateurish executions in this tuning:

http://www.ozanyarman.com/files/music/2partinventionBach.mp3

http://www.ozanyarman.com/files/music/G#Prelude_Bach.mp3

Excuse the mistakes! I was too tired and worn out playing.

Oz.

✩ ✩ ✩
www.ozanyarman.com

On Apr 30, 2010, at 4:21 AM, Chris Vaisvil wrote:

> The improvisation is great but doesn't sound very different from 12
> tet.
>
> Not that that is a bad thing - I think what it means is that this well
> balanced tuning to my ears.
>
>
> Chris
>
> On Thu, Apr 29, 2010 at 7:34 PM, Ozan Yarman <ozanyarman@...
> > wrote:
>>
>>
>>
>> Dear George, sorry for replying so late! Yes, I am trying this new
>> tuning now >
>> After >35 years of tweaking & tinkering with 12-tone circulating
>> temperaments, I thought that my 5/23-comma temperament
>> (extra)ordinaire, version of November 2008, would be the very best
>> I could do. Lo & behold: when I looked at the numbers the other
>> day (2 April), I found a way to lower the error of the flat-wise
>> chords to make them balanced with the sharp-wise ones (by changing
>> 2 pitches, Eb & Bb), without sacrificing the overall
>> proportionality of the beat rates. (This results in a smoother and
>> more symmetrical progression of interval sizes as you go around the
>> circle of 5ths.) Formerly there were 5, but there are now 6 major
>> triads with <8.22 cents error in the major 3rd, a significant
>> improvement over 12-equal that you can readily hear.
>>
>> Here's the Scala listing:
>>
>> ! Secor5_23TX.scl
>> !
>> George Secor's synchronous 5/23-comma temperament extraordinaire
>> 12
>> !
>> 62/59
>> 66/59
>> 70/59
>> 591/472
>> 315/236
>> 331/236
>> 353/236
>> 745/472
>> 395/236
>> 1051/590
>> 221/118
>> 2/1
>>
>> The major triads on the far side of the circle will not be very
>> suitable as tonic chords, but they're all usable for temporary
>> modulations, and their high 3rds make wonderful leading tones in>> minor keys (esp. in E minor & B minor).
>>
>> --George
>>
>>
>>
>>
>> ------------------------------------
>>
>> 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
>>
>>
>>
>>
>>
>
>
> ------------------------------------
>
> 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
>
>
>

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> The improvisation is great but doesn't sound very different from 12 tet.
s
Oh, golly! I'm pleasantly shocked to hear this, because virtually all of the improv. stayed on the far side of the circle of 5ths, on the least tolerable triads, with only a few seconds spent on the really good ones (around 3:00, where C major goes to F major)! If you think it didn't sound too different from 12-ET, then I guess it's a success.

Dr. Oz, why don't you give us something that uses the 6 best major triads, from Bb to A?

--George

> Not that that is a bad thing - I think what it means is that this well
> balanced tuning to my ears.
>
>
> Chris
>
> On Thu, Apr 29, 2010 at 7:34 PM, Ozan Yarman <ozanyarman@...> wrote:
> >
> >
> >
> > Dear George, sorry for replying so late! Yes, I am trying this new tuning now >
> > After >35 years of tweaking & tinkering with 12-tone circulating temperaments, I thought that my 5/23-comma temperament (extra)ordinaire, version of November 2008, would be the very best I could do.  Lo & behold: when I looked at the numbers the other day (2 April), I found a way to lower the error of the flat-wise chords to make them balanced with the sharp-wise ones (by changing 2 pitches, Eb & Bb), without sacrificing the overall proportionality of the beat rates.  (This results in a smoother and more symmetrical progression of interval sizes as you go around the circle of 5ths.)  Formerly there were 5, but there are now 6 major triads with <8.22 cents error in the major 3rd, a significant improvement over 12-equal that you can readily hear.
> >
> > Here's the Scala listing:
> >
> > ! Secor5_23TX.scl
> > !
> > George Secor's synchronous 5/23-comma temperament extraordinaire
> > 12
> > !
> > 62/59
> > 66/59
> > 70/59
> > 591/472
> > 315/236
> > 331/236
> > 353/236
> > 745/472
> > 395/236
> > 1051/590
> > 221/118
> > 2/1
> >
> > The major triads on the far side of the circle will not be very suitable as tonic chords, but they're all usable for temporary modulations, and their high 3rds make wonderful leading tones in minor keys (esp. in E minor & B minor).
> >
> > --George
> >
> >
> >
> >
> > ------------------------------------
> >
> > 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
> >
> >
> >
> >
> >
>

George, 5-limit approx. are boring triads for me. I like the sparkle
and dazzle of Modified Meantone Temperaments. Heck, my piano is tuned
to a Temperament Ordinaire. Strange as it may seem, the JI consonances
do not appeal to my tastes. The flowing music seems to demand wider
major thirds and narrower minor thirds. That is why I constantly veer
off to the remote keys. That Chris cannot distinguish these from 12-
equal is another sign why 12-equal happens to be a good compromise.
Its triads are nearer what the audience wants to hear compared to 5-
limit JI.

Oz.

✩ ✩ ✩
www.ozanyarman.com

On Apr 30, 2010, at 7:27 AM, gdsecor wrote:

>
>
> --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>>
>> The improvisation is great but doesn't sound very different from 12
>> tet.
> s
> Oh, golly! I'm pleasantly shocked to hear this, because virtually
> all of the improv. stayed on the far side of the circle of 5ths, on
> the least tolerable triads, with only a few seconds spent on the
> really good ones (around 3:00, where C major goes to F major)! If> you think it didn't sound too different from 12-ET, then I guess
> it's a success.
>
> Dr. Oz, why don't you give us something that uses the 6 best major
> triads, from Bb to A?
>
> --George
>
>> Not that that is a bad thing - I think what it means is that this
>> well
>> balanced tuning to my ears.
>>
>>
>> Chris
>>
>> On Thu, Apr 29, 2010 at 7:34 PM, Ozan Yarman <ozanyarman@...> wrote:
>>>
>>>
>>>
>>> Dear George, sorry for replying so late! Yes, I am trying this new
>>> tuning now >
>>> After >35 years of tweaking & tinkering with 12-tone circulating
>>> temperaments, I thought that my 5/23-comma temperament
>>> (extra)ordinaire, version of November 2008, would be the very best
>>> I could do. Lo & behold: when I looked at the numbers the other
>>> day (2 April), I found a way to lower the error of the flat-wise
>>> chords to make them balanced with the sharp-wise ones (by changing
>>> 2 pitches, Eb & Bb), without sacrificing the overall
>>> proportionality of the beat rates. (This results in a smoother>>> and more symmetrical progression of interval sizes as you go
>>> around the circle of 5ths.) Formerly there were 5, but there are
>>> now 6 major triads with <8.22 cents error in the major 3rd, a
>>> significant improvement over 12-equal that you can readily hear.
>>>
>>> Here's the Scala listing:
>>>
>>> ! Secor5_23TX.scl
>>> !
>>> George Secor's synchronous 5/23-comma temperament extraordinaire
>>> 12
>>> !
>>> 62/59
>>> 66/59
>>> 70/59
>>> 591/472
>>> 315/236
>>> 331/236
>>> 353/236
>>> 745/472
>>> 395/236
>>> 1051/590
>>> 221/118
>>> 2/1
>>>
>>> The major triads on the far side of the circle will not be very
>>> suitable as tonic chords, but they're all usable for temporary
>>> modulations, and their high 3rds make wonderful leading tones in
>>> minor keys (esp. in E minor & B minor).
>>>
>>> --George
>>>
>>>
>>>
>>>
>>> ------------------------------------
>>>
>>> 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
>>>
>>>
>>>
>>>
>>>
>>
>
>
>
>
> ------------------------------------
>
> 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.
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> 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
>
>
>

--- In tuning@yahoogroups.com, "gdsecor" <gdsecor@...> wrote:
> ! Secor5_23TX.scl
> !
> George Secor's synchronous 5/23-comma temperament extraordinaire
> 12
> !
> 62/59 ! C#
> 66/59 ! D
> 70/59 ! Eb
> 591/472 ! E
> 315/236 ! F
> 331/236 ! F#
> 353/236 ! G
> 745/472 ! G#
> 395/236 ! A
> 1051/590! Bb
> 221/118 ! B
> 2/1
>
Hi George,
Here comes my analysis in a cycle of 5ths
in terms of an 3n+1 Collatz-sequence:

C: 59
G: (D/3:=11 22 44 88 176 352 <) 353 (< 354 177 := 3*C)
D: 33 66
A: (3*D=99 198 396 >) 395 (> 394 197=:E/3)
E: (B/3=221/3 442/3 884/3 < 885/3=295 590 <) 591
B: 221 442 884 (< 885 := 295*3)
F#: 331 662 (< 663 := B*3)
C#: 31 62 124 248 496 992 (< 993 := F#*3)
G#: (3*C#=93 186 372 744 <) 745 = 5*149 = 5*(447/3)
Eb: 35 70 140 280 560 1120 2240 = 5*448 (> 447*5 = 149*5*3)
Bb: (3*Eb=105 <) 105.1
F: 315 := Eb*9
C: 59 118 236 472 944 (< 945 := F*3)

Or consider all that dozen pitches in chromatic ascending order:

c' 236 middle_C4
#' 248
d' 264
#' 280
e' 295.5
f' 315
#' 331
g' 353
#' 372.5
a' 395
#' 420.4 Hz
b' 442
c" 472 tenor_C5

Here the usage of 59 remebers me about my own investigation,
of superparticular decompositions of the schisma in:
/tuning-math/message/17405
"
2; 59,7-limit
(945/944)*(14337/14336) := (7*5*3^3/59/2^4)*(59*3^5/7/2^11)
~1.8329637...Cents + ~0.120757092...Cents

Here my similar alternative
which uses that 59-limit decomposition of the schisma
@ 5ths: E-B & D#-Bb

Bb: 7
F: 21
C: 63
G: (D/3=47 94 188 <) 188.5 (<189 := C*3)
D: (E/9= 35 70 140 < A/3 140.5 <) 141 := 47*3
A: (E/3=105 210 420 <) 421.5 843
E: 315
B: 59 118 236 472 944 (< 945 := E*3)
F# 177 := 59*3
C# 531
G# 1593
D# 4779
Bb 7 14 28 56 112 224 448 896 1792 3584 7168 14336 (< 14337 := 59*3^5)

c' 252 middle_C4
#' 265.5
d' 282
#' 298.6875
e' 315
f' 336
#' 354
g' 377
#' 398.25
a' 421.5
#' 448
b' 472

! Sp59limSchismatic.scl
Sparschuh's 59-limit Schisma-decomposition into (945/944)(14337/14336)
12
!
531/448 ! C# (135/128)*(944/945) = (256/243)*(14337/14336)
141/126 ! D (9/8)*(188/189)
4479/3584 ! Eb (32/27)*(14337/14336 +~0.120757092...Cents)
5/4 ! E
4/3 ! F
177/112 ! F# (1024/729)*(14337/14336) = (45/32)*(944/945)
377/224 ! G (3/2)*(377/378)
1539/896 ! G# (128/81)*(14337/14336) = (135/128)*(944/945)
843/448 ! A (5/3)*(281/280)
16/9 ! Bb
15/8 ! B
2/1
!
![eof]