Yahoo Tuning Groups Ultimate Backup tuning Fwd: Some 15-note scale/temperaments

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
These seem to be popular of late, so I'm giving two useful examples.

STEPHEN SZPAK WRITES:::::::::::::::::::::::

If 15 notes per octave is popular lately I assume full responsibility. I assume you read my
request for 15 note per octave variations considering what is below.
The Porcupine [15] in the 7-limit minimax tuning looks, at first glance, to have some
potential. When I see the harmonic 7th and harmonic 11th I know it has something
12 EDO can't have. You have obviously read about a 15 non-edo scale I came up with.
If you ever have any serious interest in it let me know. Thanks Gene.

The first consists of three circles of (56/11)^(1/4) fifth, completed
by a "wolf" of exactly 11/7. Notable is how two different sizes of
major third show up in a 5/4-5/4-11/7 176/175-magical augmented triad.

! fifaug.scl
Three circles of four (56/11)^(1/4) fifths with 11/7 as wolf
15
!
95.623008
113.130973
208.753982
304.376991
400.000000
495.623008
513.130973
608.753982
704.376991
800.000000
895.623008
913.130973
1008.753982
1104.376991
1200.000000

Here are the 0-4-9 pattern triads:

[400.000000, 304.376992, 704.376992]
[400.000000, 382.492035, 782.492035]
[400.000000, 304.376991, 704.376991]
[400.000000, 304.376991, 704.376991]
[400.000000, 304.376991, 704.376991]
[400.000000, 304.376992, 704.376992]
[400.000000, 382.492035, 782.492035]
[400.000000, 304.376991, 704.376991]
[400.000000, 304.376991, 704.376991]
[400.000000, 304.376991, 704.376991]
[400.000000, 304.376992, 704.376992]
[400.000000, 382.492035, 782.492035]
[400.000000, 304.376991, 704.376991]
[400.000000, 304.376991, 704.376991]
[400.000000, 304.376991, 704.376991]

Here is Porcupine[15] in the 7-limit minimax tuning (which I picked
since it gives us something close to 11-limit rms tuning.)

! porc15.scl
Pocupine[15] in 7-limit minimax tuning
12
!
60.839199
162.737257
223.576457
325.474514
386.313714
488.211772
549.050971
650.949029
711.788228
813.686286
874.525486
976.423543
1037.262743
1139.160801
1200.000000

Here are the 0-4-9 triads with this tuning. I apologize to Jon for the
entirely unnessessary and useless precision.

[427.3725722703284, 325.4745144540656, 752.8470867243940]
[386.3137138648360, 325.4745144540656, 711.7882283189016]
[427.3725722703280, 325.4745144540656, 752.8470867243936]
[386.3137138648360, 325.4745144540654, 711.7882283189014]
[427.3725722703280, 325.4745144540660, 752.8470867243940]
[386.3137138648360, 325.4745144540656, 711.7882283189016]
[427.3725722703280, 284.4156560485732, 711.7882283189012]
[386.3137138648358, 325.4745144540658, 711.7882283189016]
[427.3725722703284, 284.4156560485732, 711.7882283189016]
[386.3137138648360, 325.4745144540656, 711.7882283189016]
[386.3137138648356, 325.4745144540660, 711.7882283189016]
[386.3137138648360, 325.4745144540656, 711.7882283189016]
[386.3137138648362, 325.4745144540656, 711.7882283189018]
[386.3137138648356, 325.4745144540656, 711.7882283189012]
[386.3137138648360, 325.4745144540656, 711.7882283189016]

The wolf fifths are less than a cent away from being 17/11's, which
may or may not inspire you. The sharp major thirds are, in this
version of porky, exact 32/25's, but porcupine eats 225/224 and this
is supposed to count as a 9/7 therefore.
--- End forwarded message ---

_________________________________________________________________
Make your home warm and cozy this winter with tips from MSN House & Home. http://special.msn.com/home/warmhome.armx

🔗Stephen Szpak <stephen_szpak@hotmail.com>

--- In tuning@yahoogroups.com, "Stephen Szpak" <stephen_szpak@h...> wrote:
--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
These seem to be popular of late, so I'm giving two useful examples.

STEPHEN SZPAK WRITES:::::::::::::::::::::::

If 15 notes per octave is popular lately I assume full responsibility. I
assume you read my
request for 15 note per octave variations considering what is below.
The Porcupine [15] in the 7-limit minimax tuning looks, at first
glance, to have some
potential. When I see the harmonic 7th and harmonic 11th I know it has
something
12 EDO can't have. More comments towards bottom.

Thanks Gene.

Here are the 0-4-9 pattern triads:

Here is Porcupine[15] in the 7-limit minimax tuning (which I picked
since it gives us something close to 11-limit rms tuning.)

Here are the 0-4-9 triads with this tuning. I apologize to Jon for the
entirely unnessessary and useless precision.

STEPHEN SZPAK RESPONDS:::::::

The table immediately above would indicate to me that there are 5 tonics which are
unuseable. The perfect fifth is too big or the thirds are both way off. Correct? How
do people quickly analyze a scale like this for: harmonic 4ths, harmonic 7ths, major
3rds, perfect 5ths etc. if they only have the 15 tonic notes available? I write out the
scale in cents horizontally once, and then again, and do every thing by hand.

_________________________________________________________________
Expand your wine savvy � and get some great new recipes � at MSN Wine. http://wine.msn.com

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "Stephen Szpak" <stephen_szpak@h...> wrote:
> --- In tuning@yahoogroups.com, "Stephen Szpak" <stephen_szpak@h...>
wrote:
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> Here is Porcupine[15] in the 7-limit minimax tuning (which I picked
> since it gives us something close to 11-limit rms tuning.)
>
> ! porc15.scl
> Pocupine[15] in 7-limit minimax tuning
> 12
> !
> 60.839199
> 162.737257
> 223.576457
> 325.474514
> 386.313714
> 488.211772
> 549.050971
> 650.949029
> 711.788228
> 813.686286
> 874.525486
> 976.423543
> 1037.262743
> 1139.160801
> 1200.000000
>
> Here are the 0-4-9 triads with this tuning. I apologize to Jon for the
> entirely unnessessary and useless precision.
>
> [427.3725722703284, 325.4745144540656, 752.8470867243940]
> [386.3137138648360, 325.4745144540656, 711.7882283189016]
> [427.3725722703280, 325.4745144540656, 752.8470867243936]
> [386.3137138648360, 325.4745144540654, 711.7882283189014]
> [427.3725722703280, 325.4745144540660, 752.8470867243940]
> [386.3137138648360, 325.4745144540656, 711.7882283189016]
> [427.3725722703280, 284.4156560485732, 711.7882283189012]
> [386.3137138648358, 325.4745144540658, 711.7882283189016]
> [427.3725722703284, 284.4156560485732, 711.7882283189016]
> [386.3137138648360, 325.4745144540656, 711.7882283189016]
> [386.3137138648356, 325.4745144540660, 711.7882283189016]
> [386.3137138648360, 325.4745144540656, 711.7882283189016]
> [386.3137138648362, 325.4745144540656, 711.7882283189018]
> [386.3137138648356, 325.4745144540656, 711.7882283189012]
> [386.3137138648360, 325.4745144540656, 711.7882283189016]
>
> STEPHEN SZPAK RESPONDS:::::::
>
> The table immediately above would indicate to me that there are 5
tonics
> which are
> unuseable. The perfect fifth is too big or the thirds are both
way off.
> Correct?

That depends on what you use them for. The 427-325-753 chords might be
something you would want to use; 753 is quite close to 17/11, and
9/7-6/5-17/11 is "magic" with comma 595/594. The only way to really
know is to listen and see what you think. The other big third chords
are usable supermajor triads (approximate 1-9/7-3/2 triads.) The third
is actually a 32/25, which is flat from a true supermajor third, but
the payoff to that is that we have ten pure 5/4 major thirds to go
with these five flat supermajors. The sheer quantity of pure 5/4's in
this tuning of porky is a nice feature.

How
> do people quickly analyze a scale like this for: harmonic 4ths,
harmonic
> 7ths, major
> 3rds, perfect 5ths etc. if they only have the 15 tonic notes
available?

The fastest way is to load it into Scala and use "find locations".

🔗Stephen Szpak <stephen_szpak@hotmail.com>

wrote:
>--- In tuning@yahoogroups.com, "Stephen Szpak" <stephen_szpak@h...>
wrote:
>--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

>Here is Porcupine[15] in the 7-limit minimax tuning (which I picked
>since it gives us something close to 11-limit rms tuning.)
>
>! porc15.scl
>Pocupine[15] in 7-limit minimax tuning
>12
>!
>60.839199
>162.737257
>223.576457
>325.474514
>386.313714
>488.211772
>549.050971
>650.949029
>711.788228
>813.686286
>874.525486
>976.423543
>1037.262743
>1139.160801
>1200.000000
>
>Here are the 0-4-9 triads with this tuning. I apologize to Jon for the
>entirely unnessessary and useless precision.
>
>[427.3725722703284, 325.4745144540656, 752.8470867243940]
>[386.3137138648360, 325.4745144540656, 711.7882283189016]
>[427.3725722703280, 325.4745144540656, 752.8470867243936]
>[386.3137138648360, 325.4745144540654, 711.7882283189014]
>[427.3725722703280, 325.4745144540660, 752.8470867243940]
>[386.3137138648360, 325.4745144540656, 711.7882283189016]
>[427.3725722703280, 284.4156560485732, 711.7882283189012]
>[386.3137138648358, 325.4745144540658, 711.7882283189016]
>[427.3725722703284, 284.4156560485732, 711.7882283189016]
>[386.3137138648360, 325.4745144540656, 711.7882283189016]
>[386.3137138648356, 325.4745144540660, 711.7882283189016]
>[386.3137138648360, 325.4745144540656, 711.7882283189016]
>[386.3137138648362, 325.4745144540656, 711.7882283189018]
>[386.3137138648356, 325.4745144540656, 711.7882283189012]
>[386.3137138648360, 325.4745144540656, 711.7882283189016]
>
> STEPHEN SZPAK RESPONDS:::::::
>
> The table immediately above would indicate to me that there are 5
tonics
>which are
> unuseable. The perfect fifth is too big or the thirds are both
way off.
>Correct?

STEPHEN SZPAK WRITES:::::::::::::::

I wish I could listen.

The other big third chords
are usable supermajor triads (approximate 1-9/7-3/2 triads.) The third
is actually a 32/25, which is flat from a true supermajor third, but
the payoff to that is that we have ten pure 5/4 major thirds to go
with these five flat supermajors. The sheer quantity of pure 5/4's in
this tuning of porky is a nice feature.

How
> do people quickly analyze a scale like this for: harmonic 4ths,
harmonic
>7ths, major
> 3rds, perfect 5ths etc. if they only have the 15 tonic notes
available?

The fastest way is to load it into Scala and use "find locations".

STEPHEN SZPAK WRITES:

I downloaded Scala! (I guess I did it earlier in the year too.) I couldn't or didn't figure
out how to use it then. Maybe this time I will. This is Scala18 so apparently the "find
locations" feature isn't available. (My computer won't run a higher version of Scala.)
I really hope to get back to you on your technical comments above, assuming I can
figure them out. You are very helpful. Thanks.

--- End forwarded message ---
Stephen Szpak

_________________________________________________________________
Get reliable dial-up Internet access now with our limited-time introductory offer. http://join.msn.com/?page=dept/dialup

🔗Stephen Szpak <stephen_szpak@hotmail.com>

--- In tuning@yahoogroups.com, "Stephen Szpak" <stephen_szpak@h...> wrote:
wrote:
>--- In tuning@yahoogroups.com, "Stephen Szpak" <stephen_szpak@h...>
wrote:
>--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

>Here is Porcupine[15] in the 7-limit minimax tuning (which I picked
>since it gives us something close to 11-limit rms tuning.)
>
>! porc15.scl
>Pocupine[15] in 7-limit minimax tuning
>12
>!
>60.839199
>162.737257
>223.576457
>325.474514
>386.313714
>488.211772
>549.050971
>650.949029
>711.788228
>813.686286
>874.525486
>976.423543
>1037.262743
>1139.160801
>1200.000000
>
>Here are the 0-4-9 triads with this tuning. I apologize to Jon for the
>entirely unnessessary and useless precision.
>
>[427.3725722703284, 325.4745144540656, 752.8470867243940]
>[386.3137138648360, 325.4745144540656, 711.7882283189016]
>[427.3725722703280, 325.4745144540656, 752.8470867243936]
>[386.3137138648360, 325.4745144540654, 711.7882283189014]
>[427.3725722703280, 325.4745144540660, 752.8470867243940]
>[386.3137138648360, 325.4745144540656, 711.7882283189016]
>[427.3725722703280, 284.4156560485732, 711.7882283189012]
>[386.3137138648358, 325.4745144540658, 711.7882283189016]
>[427.3725722703284, 284.4156560485732, 711.7882283189016]
>[386.3137138648360, 325.4745144540656, 711.7882283189016]
>[386.3137138648356, 325.4745144540660, 711.7882283189016]
>[386.3137138648360, 325.4745144540656, 711.7882283189016]
>[386.3137138648362, 325.4745144540656, 711.7882283189018]
>[386.3137138648356, 325.4745144540656, 711.7882283189012]
>[386.3137138648360, 325.4745144540656, 711.7882283189016]
>
> STEPHEN SZPAK RESPONDS:::::::
>
> The table immediately above would indicate to me that there are 5
tonics
>which are
> unuseable. The perfect fifth is too big or the thirds are both
way off.
>Correct?

STEPHEN SZPAK WRITES:::::::::::::::

I wish I could listen.

How
> do people quickly analyze a scale like this for: harmonic 4ths,
harmonic
>7ths, major
> 3rds, perfect 5ths etc. if they only have the 15 tonic notes
available?

The fastest way is to load it into Scala and use "find locations".

STEPHEN SZPAK WRITES:

I downloaded Scala! (I guess I did it earlier in the year too.) I couldn't
or didn't figure
out how to use it then. Maybe this time I will. This is Scala18 so
apparently the "find
locations" feature isn't available. (My computer won't run a higher version
of Scala.)
I really hope to get back to you on your technical comments above, assuming
I can
figure them out. You are very helpful. Thanks.

STEPHEN SZPAK WRITES::::::::::::::

This is actually a reply to my own message! I can't understand how to use Scala to find
all the ratios of a scale. A 15 non-edo scale has 15 sets of 15 ratios as we know. The
first tonic might have a harmonic 7th but all 14 others might not. The same is true for
other stuff like major 3rds. How exactly do I use this program? I know I have to use
some command at the command line, but then what? The porcupine [15] in 7-limit
minimax tuning has to be entered somehow. Do I separate each cent grouping with
commas, dashed lines, periods, after I use the proper command?

--- End forwarded message ---
Stephen Szpak

_________________________________________________________________
Working moms: Find helpful tips here on managing kids, home, work � and yourself. http://special.msn.com/msnbc/workingmom.armx

🔗Manuel Op de Coul <manuel.op.de.coul@eon-benelux.com>

🔗Stephen Szpak <stephen_szpak@hotmail.com>

--- In tuning@yahoogroups.com, "Manuel Op de Coul" <manuel.op.de.coul@e...> wrote:

Stephen wrote:
>This is Scala18 so apparently the "find
>locations" feature isn't available. (My computer won't run a higher
version
>of Scala.)

The correct command is "show locations" and it's available in
your version: type "help show loc".
Best wishes to everyone,

Manuel
--- End forwarded message ---

STEPHEN SZPAK WRITES:::::::::

Thanks for the information. I'll try it when I can.

Stephen Szpak

_________________________________________________________________
Tired of slow downloads? Compare online deals from your local high-speed providers now. https://broadband.msn.com

🔗Stephen Szpak <stephen_szpak@hotmail.com>

--- In tuning@yahoogroups.com, "Stephen Szpak" <stephen_szpak@h...> wrote:
--- In tuning@yahoogroups.com, "Stephen Szpak" <stephen_szpak@h...> wrote:
>--- In tuning@yahoogroups.com, "Stephen Szpak" <stephen_szpak@h...>
wrote:

PLEASE SEE QUESTIONS AT FAR FAR BOTTOM. PERHAPS PAUL ERLICH
CAN RESPOND............

>Here is Porcupine[15] in the 7-limit minimax tuning (which I picked
>since it gives us something close to 11-limit rms tuning.)
>
>! porc15.scl
>Pocupine[15] in 7-limit minimax tuning
>12
>!
>60.839199
>162.737257
>223.576457
>325.474514
>386.313714
>488.211772
>549.050971
>650.949029
>711.788228
>813.686286
>874.525486
>976.423543
>1037.262743
>1139.160801
>1200.000000
>
>Here are the 0-4-9 triads with this tuning. I apologize to Jon for the
>entirely unnessessary and useless precision.
>
>[427.3725722703284, 325.4745144540656, 752.8470867243940]
>[386.3137138648360, 325.4745144540656, 711.7882283189016]
>[427.3725722703280, 325.4745144540656, 752.8470867243936]
>[386.3137138648360, 325.4745144540654, 711.7882283189014]
>[427.3725722703280, 325.4745144540660, 752.8470867243940]
>[386.3137138648360, 325.4745144540656, 711.7882283189016]
>[427.3725722703280, 284.4156560485732, 711.7882283189012]
>[386.3137138648358, 325.4745144540658, 711.7882283189016]
>[427.3725722703284, 284.4156560485732, 711.7882283189016]
>[386.3137138648360, 325.4745144540656, 711.7882283189016]
>[386.3137138648356, 325.4745144540660, 711.7882283189016]
>[386.3137138648360, 325.4745144540656, 711.7882283189016]
>[386.3137138648362, 325.4745144540656, 711.7882283189018]
>[386.3137138648356, 325.4745144540656, 711.7882283189012]
>[386.3137138648360, 325.4745144540656, 711.7882283189016]
>
> STEPHEN SZPAK RESPONDS:::::::
>
> The table immediately above would indicate to me that there are 5
tonics
>which are
> unuseable. The perfect fifth is too big or the thirds are both
way off.
>Correct?

STEPHEN SZPAK WRITES:::::::::::::::::::::

9/7 = 435
6/5 = 316
17/11 = 754

But I don't know what 595/594 equals. I also don't know what "magic"
means.

Thanks,

Stephen Szpak

_________________________________________________________________
Expand your wine savvy � and get some great new recipes � at MSN Wine. http://wine.msn.com

🔗Andrea Valle <marta_andrea@libero.it>

(Hi to all. Total newbie here.
Sorry for the obvious question: but what is porcupine?)

best

-a-

-----Messaggio originale-----
Da: Stephen Szpak [mailto:stephen_szpak@hotmail.com]
Inviato: lunedï¿½ 5 gennaio 2004 23.47
A: tuning@yahoogroups.com
Cc: stephen_szpak@hotmail.com
Oggetto: [tuning] Fwd: Some 15-note scale/temperaments

PLEASE SEE QUESTIONS AT FAR FAR BOTTOM. PERHAPS PAUL ERLICH
CAN RESPOND............

>Here is Porcupine[15] in the 7-limit minimax tuning (which I picked
>since it gives us something close to 11-limit rms tuning.)
>
>! porc15.scl
>Pocupine[15] in 7-limit minimax tuning
>12
>!
>60.839199
>162.737257
>223.576457
>325.474514
>386.313714
>488.211772
>549.050971
>650.949029
>711.788228
>813.686286
>874.525486
>976.423543
>1037.262743
>1139.160801
>1200.000000
>
>Here are the 0-4-9 triads with this tuning. I apologize to Jon for the
>entirely unnessessary and useless precision.
>
>[427.3725722703284, 325.4745144540656, 752.8470867243940]
>[386.3137138648360, 325.4745144540656, 711.7882283189016]
>[427.3725722703280, 325.4745144540656, 752.8470867243936]
>[386.3137138648360, 325.4745144540654, 711.7882283189014]
>[427.3725722703280, 325.4745144540660, 752.8470867243940]
>[386.3137138648360, 325.4745144540656, 711.7882283189016]
>[427.3725722703280, 284.4156560485732, 711.7882283189012]
>[386.3137138648358, 325.4745144540658, 711.7882283189016]
>[427.3725722703284, 284.4156560485732, 711.7882283189016]
>[386.3137138648360, 325.4745144540656, 711.7882283189016]
>[386.3137138648356, 325.4745144540660, 711.7882283189016]
>[386.3137138648360, 325.4745144540656, 711.7882283189016]
>[386.3137138648362, 325.4745144540656, 711.7882283189018]
>[386.3137138648356, 325.4745144540656, 711.7882283189012]
>[386.3137138648360, 325.4745144540656, 711.7882283189016]
>
> STEPHEN SZPAK RESPONDS:::::::
>
> The table immediately above would indicate to me that there are 5
tonics
>which are
> unuseable. The perfect fifth is too big or the thirds are both
way off.
>Correct?

STEPHEN SZPAK WRITES:::::::::::::::::::::

9/7 = 435
6/5 = 316
17/11 = 754

But I don't know what 595/594 equals. I also don't know what "magic"
means.

Thanks,

Stephen Szpak

_________________________________________________________________
Expand your wine savvy ï¿½ and get some great new recipes ï¿½ at MSN Wine.
http://wine.msn.com

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🔗Gene Ward Smith <gwsmith@svpal.org>

🔗wallyesterpaulrus <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "Stephen Szpak" <stephen_szpak@h...>
wrote:

> STEPHEN SZPAK WRITES:::::::::::::::::::::
>
> 9/7 = 435
> 6/5 = 316
> 17/11 = 754

In JI, yes.

> But I don't know what 595/594 equals.

As before, you'll want to factor these terms:

595 = 5*7*17
594 = 2*3*3*3*11

In JI, 595/594 is about 3 cents. In a temperament, the exact value
will depend on the values taken by the primes 17, 11, 7, 5, and 3
(and, if one allows tempered octaves, 2).

> I also don't know what "magic"
> means.

The idea here was that, if 595;594 vanishes, all the intervals in the
chord could be viewed as simple ratios, ratios which would not "fit
together" in JI.

🔗wallyesterpaulrus <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "Andrea Valle" <marta_andrea@l...>
wrote:
> (Hi to all. Total newbie here.
> Sorry for the obvious question: but what is porcupine?)
>
> best
>
> -a-

Hi Andrea.

Welcome to the land of musical mad scientists :)

"Porcupine" refers to a class of "experimental" scales and tuning
systems. A lot could be said about it, but roughly speaking, the idea
is to use an interval of about 163 cents to generate the notes,
repeating the interval as many times as one wishes (scales of 7, 8,
15, 22 . . . notes are the most logical stopping places though) and
wrapping around the octave. There are some nice harmonies to be found
in such scales, with decently-tuned renditions of both conventional
triads (though fitting together into progressions not possible in
conventional tunings) and "extended" harmonies deriving from higher
up in the harmonic series.

I've explored the 7-note porcupine scale in 22-tone equal temperament
in some of my performances. The scale can evoke a unique blend of
Thai, Arabic, and Western Renaissance flavors, or something
altogether otherworldly, depending on how you use it.

-Paul

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Andrea Valle" <marta_andrea@l...>
> wrote:

> > (Hi to all. Total newbie here.
> > Sorry for the obvious question: but what is porcupine?)

> "Porcupine" refers to a class of "experimental" scales and tuning
> systems. A lot could be said about it, but roughly speaking, the
idea
> is to use an interval of about 163 cents to generate the notes,
> repeating the interval as many times as one wishes (scales of 7, 8,
> 15, 22 . . . notes are the most logical stopping places though) and
> wrapping around the octave.

An example which stops at 13 is this:

http://66.98.148.43/~xenharmo/ogg/exotic/porcupinized/bald.ogg

The music may sound strangely familiar.