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

stephen_szpak@hotmail.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-
Welcome!
Boy are you asking the wrong person! This link is supposed to be one of the best
examples:

ftp://ftp.io.com/pub/usr/hmiller/music

click on Porcupine Overture mp3

(STEPHEN SZPAK)

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

--- 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?

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.

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

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

PLEASE SEE QUESTIONS AT FAR FAR BOTTOM:::::::::::::::::::::::::::::::::::::::::::::

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.

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.

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

Thanks Wally

Gene Ward Smith wrote a while back that Procupine eats 225/224. I'll
probably factor this out later, but, the term "eats" relates to "magic"
and "vanish" I assume???????????

Thanks,

Stephen Szpak

_________________________________________________________________
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FW: Fwd: Some 15-note scale/temperaments

🔗Stephen Szpak <stephen_szpak@hotmail.com>

🔗Stephen Szpak <stephen_szpak@hotmail.com>

🔗wallyesterpaulrus <paul@stretch-music.com>