Yahoo Tuning Groups Ultimate Backup tuning-math Re: [tuning-math] Digest Number 1338

why 112?
according to my computations, 112 hits all the pure
tones and is the lowest number to do so. perhaps i was
off by one.

--- tuning-math@yahoogroups.com wrote:

> There are 4 messages in this issue.
>
> Topics in this digest:
>
> 1. Re: electronic synth keyboards-infinite
> tunings.....help?...
> From: "elfdreambaby"
> <elfdreambaby@yahoo.com>
> 2. Re: electronic synth keyboards-infinite
> tunings.....help?...
> From: "Gene Ward Smith"
> <gwsmith@svpal.org>
> 3. Tone group relative epimorphic scales
> From: "Gene Ward Smith"
> <gwsmith@svpal.org>
> 4. A 19-note breed tempered diamond scale
> From: "Gene Ward Smith"
> <gwsmith@svpal.org>
>
>
>
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>
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>
> Message: 1
> Date: Thu, 14 Jul 2005 09:25:00 -0000
> From: "elfdreambaby" <elfdreambaby@yahoo.com>
> Subject: Re: electronic synth keyboards-infinite
> tunings.....help?...
>
> thanks for the response, graham.
> well, to start, i totally reject 12-semitone equql
> temperament, and i
> have heard that most keyboards are fixed in that
> system. i would like
> an instrument designed for infinite experimentation
> with tunings and
> scales and that might include a a preset for Just
> Intonation. I would
> like to try a 112 part equal temperament, for
> example. What keyboards
> are designed with this kind of use in mind? Is
> manipulating the
> keyboard thru external computer software the only
> way? If so, ok. I
> just like the idea of an alternative keyboard
> instrument designed with
> creators like me in mind. btw, what is a soft synth.
> oz.
>
> --- In tuning-math@yahoogroups.com, Graham Breed
> <gbreed@g...> wrote:
> > On 6/17/05, elfdreambaby <elfdreambaby@y...>
> wrote:
> > > I want to by a keyboard that will allow me to
> experiment with my
> own
> > > tunings and that will allow me to split the
> octave into large
> numbers
> > > as well as just tuning....I am lost trying to
> find which
> > > manufacturers
> > > offer such instruments. Can anyone offer me any
> guidance? What
> brands
> > > cater to the radical composer if any?
> > > any tips much appreciated.
> >
> > Any MIDI keyboard will work if you plug it into
> your computer and
> use
> > a soft synth. If that doesn't suit you, you'd
> better tell us why to
> > save us guessing about your exact circumstances ;)
> >
> >
> > Graham
>
>
>
>
>
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>
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>
> Message: 2
> Date: Thu, 14 Jul 2005 21:50:18 -0000
> From: "Gene Ward Smith" <gwsmith@svpal.org>
> Subject: Re: electronic synth keyboards-infinite
> tunings.....help?...
>
> --- In tuning-math@yahoogroups.com, "elfdreambaby"
> <elfdreambaby@y...>
> wrote:
>
> > I would
> > like to try a 112 part equal temperament, for
> example.
>
> What's the attraction of 112? I would think both 111
> (which is a
> strong high-limit system) and 113 (which supports
> miracle) would make
> more sense.
>
>
>
>
>
>
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>
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>
> Message: 3
> Date: Thu, 14 Jul 2005 22:19:25 -0000
> From: "Gene Ward Smith" <gwsmith@svpal.org>
> Subject: Tone group relative epimorphic scales
>
> By "tone group" I mean a regular temperament
> equipped with a
> particular tuning, see
>
> http://66.98.148.43/~xenharmo/regular.html
>
> I've mentioned a few times that the definition of
> epimorphic scales
> generalizes to tone groups; p-limit JI, after all,
> is a tone group. A
> tone group can be defined as a finitely generated
> subgroup of the
> additive reals, or equivalently of the
> multiplicative positive reals.
>
> Epimorphic scales for r2 temperaments include
> MOS/DE, and are very
> close to the "modmos" scales I've discussed before.
> For an r3
> temperament, they sometimes are pretty close to
> being 5-limit scales.
> For instance, the 7-limit can be expressed in terms
> of [2,3,5,7], but
> equally well in terms of [2,3,5,225/224]; if we
> invert the matrix of
> monzos we get a matrix with columns
> [<1 0 0 -5|, <0 1 0 2|, <0 0 1 2|, <0 0 0 -1|]. The
> first three define
> the mapping of the 7-limit to the generators of
> tempered 2,3,5 for
> marvel tempering. If we choose the tuning where
> 2,3,5 are pure, we get
> the 5-limit (and not very terrific, but certainly
> usable, 7s.) In
> practical situations, if we have an epimorphic scale
> in this tuning,
> it will stay epimorphic if we retune to 1/4
> kleismic, 72-edo, etc.
>
> This approach won't always work. For 2401/2400, we
> need something like
> [2,49/40,10/7,2401/2400] to represent the 7-limit,
> and the group
> generated by {2,49/40,10/7}, is not a p-limit group,
> but is {2,5,7}.
> We could, therefore, look at epimorphic scales in
> terms of just the
> primes 2, 5 and 7, and those for practical purposes
> could be taken as
> epimorphic breed temperament scales. Inverting the
> monzo matrix of
> [2,5,7,2401/2400] gives us
> [<1 -5 0 0|, <0 -2 1 0|, <0 4 0 1|, <0 -1 0 0|],
> which allows us to
> translate the 7-limit to breed-tempered 2,5, and 7.
> 5-limit scales
> which temper well via marvel tend to be spread along
> the secor axis,
> and similarly here we would look along the 49/40,
> neutral third, axis.
> Perhaps a look at {2,5,7} diamonds tempered by breed
> would be interesting.
>
>
>
>
>
>
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>
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>
> Message: 4
> Date: Fri, 15 Jul 2005 03:50:15 -0000
> From: "Gene Ward Smith" <gwsmith@svpal.org>
> Subject: A 19-note breed tempered diamond scale
>
> I find four {2,5,7} diamond-type scales with no more
> than 19 notes to
> the octave and at least six breed-tempered otonal
> tetrads. Only one of
> these is convex, the scale resulting from taking all
> ratios of
> [25, 12,5 175, 245, 1715, 2401] and reducing to the
> octave. If we TM
> reduce this by 2401/2400, we get
>
>
=== message truncated ===

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Re: [tuning-math] Digest Number 1338

🔗elfdream baby <elfdreambaby@yahoo.com>

🔗Gene Ward Smith <gwsmith@svpal.org>