Re: a 24 tone non-edo scale

--- In tuning@yahoogroups.com, "Stephen Szpak" <stephen_szpak@h...> wrote:
--- In tuning@yahoogroups.com, kraig grady <kraiggrady@a...> wrote:
>
HI KRAIG

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

Thanks for this insight. I did not know that. I originally thought the
neural 3rd of 360.88
cents was within 10 cents of perfect though. I was told by Max Zanetti
that it was not. I'm
sure he knows more than me so I'm assuming he's right. I do think, as
you do that it's close
enough. He thinks it's close enough as well.

If you didn't see it before, the Szpak Scale actually has 2 types of
neutral 3rds.

using 12 EDO tonics neutral 3rds = 360.88 cents
using the other 12 tonics neutral 3rd = 339.12 cents
===========================================================
Hello Stephen!

The neutral third which historicly was and is used primarily by the arabic
and persian informed cultures never relied on limits in generating there
tunings. The variation of this interval throught this area of the world is a
matter of personal
taste and from what i am told cultural/regonal identity. The idea that there
is one and only one neural third is contrary to practice. It is not
subjected to the same scutiny that the a harmonic would have. There is
plenty of room for all types
of neutral thirds.

>
> From: "Stephen Szpak" <stephen_szpak@h...>
>
>
> Stephen Szpak writes:
>
> (Please note this is, I believe your first reply to my original message >a
>few days ago.)
>
> I think we're thinking on 2 separate plains here. You are >analyzing
>the Szpak Scale
> with "odd-limit" "prime-limit" and other terms, and I am looking at the
>scale regarding
> the harmonics it contains.
>
> If one uses the tonics of the 12 EDO system (ignoring the richness of >the
>other half of
> the Szpak Scale) you have the ability to reach, access, use all of the
>first 12 harmonics.
> The 12 EDO scale does NOT have the 7th and 11th harmonics.
>
> 12 EDO 7th harmonic not available
> 12 EDO 11th harmonic not available
>
> 24 EDO 7th harmonic not available
> 24 EDO 11 harmonic available in 24 tonics
>
> Szpak Scale 7th harmonic available in 12 tonics (the 12 western
>tonic notes)
> Szpak Scale 11th harmonic available in 12 tonics (the 12 western
>tonic notes)
>
> The reason that the neutral 3rd may be slightly off (I guess it is off
>by more than 10 cents)
> if because of this. The 24 EDO scale, which is what the Szpak Scale is
>based on, is really
> 2 12 EDO scales that have been interlaced. If the first scale is
>untouched the 12 familiar
> notes of western music are intact. The second scale has to be shifted
>however, if the
> harmonic 7th is to be included.
> But here's the important point. If the second scale is shifted too
>much the 11 th harmonic
> is lost. The Szpak Scale includes the 7th and 11 harmonics BOTH at >less
>than 10 cents off
> their ideal locations at the expense of losing other ratios. In fact >the
>shift of the second
> scale can only exist (you can check the math if you really want to )
>within a 2.49 cent
> window. Otherwise the 7th harmonic is off by 10 cents or more OR >the
>11 th harmonic
> is off by 10 cents or more. I realize that the "10 cent" business is
>arbitrary on my part, but
> the line has to be drawn somewhere.
>
> 0 58.827 100 158.827 200 258.827 etc. until 1200
>
> 0 61.317 100 161.317 200 261.317 etc until 1200
>
> 0 60.88 100 160.88 200 260.88 etc until 1200
>(Szpak Scale)
>
> I suppose you might have realized all this already. Feel free to get
>back to me either way.
>
> Stephen Szpak
>
>

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST
--- End forwarded message ---

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