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Hello all. I'm Jacob. Aspiring composer, instrument inventor/builder, omniscient
being. Currently residing in Hooston, Texas where I am also undergraduating. Still
weighing the Great Microtonal Question: Is It Worth the Trouble? but currently
bearing the microtonal torch for the betterment of my peers.

I guess I have a few questions. For those of you who check this thing five times a
day, this seems more of a hobby than a formal pursuit for you. I venture this because
making a living as a composer let alone a microtonal one is a staggering challenge.
The exception is JP it seems. Is this right? What does everybody do for a living?

I know there are more microtonal composers out there, of course. Is it true that
many have been on here for some time but left in dissatisfaction? That would be a
shame (especially because I'm just getting on the scene).

Regarding Wally...er..Paul...rus' recent mention of 12 nice scales to write in, I would
be more than happy to try something. But I simply don't understand your
explanations or "horagrams." Looks more like families of scales, and I recognize the
red numbers as associated with such properties (e.g. the multiples of 3 belonging to
the "augmented" family). But the step sizes are unequal? Or are they? Scl files would
be nice.

(How to end? I like Szanto's "Cheers" and Reinhard's "Best"...I'll go with) Godspeed!

Jacob

Welcome to the list, Jacob!

--- In tuning@yahoogroups.com, "piccolosandcheese" <jbarton@r...>
wrote:

> I guess I have a few questions. For those of you who check this
>thing five times a
> day, this seems more of a hobby than a formal pursuit for you. I
>venture this because
> making a living as a composer let alone a microtonal one is a
>staggering challenge.
> The exception is JP it seems. Is this right?

Joseph Pehrson? A fine and prolific composer to be sure, but I don't
think he makes all or even most of his income that way . . . Joe?

>What does everybody >do for a living?

I don't make a living as a microtonal composer, and though I foresee
decades in which I'll be more heavily involved with microtonal
composition, I doubt it'll ever pay the bills. I play guitar
(including microtonal ones) and a bit of keyboard in various styles,
and generate even more income from a non-musical day job. I suspect
this sort of thing is true for the vast majority of composers anyway
(remember Charles Ives?) . . . Anyway, the description of this list
in no way suggests that you need to be a professional composer to
participate -- and most of the important tuning theorists in history
were not professional composers, so I'm not exactly sure what you're
getting at with "formal pursuit" . . .

> I know there are more microtonal composers out there, of course.
>Is it true that
> many have been on here for some time but left in dissatisfaction?

I beg of you -- let's not reopen old wounds. There were some
misunderstandings on this list in which both sides felt badly
wronged. During some of the worst times here, some splinter groups
were formed. Most of the mathematical material is now posted on the
tuning-math list instead of here, and there's also a list,
MakeMicroMusic, where practical, technical, and creative concerns are
on-topic, but theory isn't. I think those are the two most active of
the splinter groups by far. Fortunately, we are now seeing very good
vibes here even between parties who didn't get along for years, so I
hope we can keep it positive and avoid a replay (or rehashing) of old
conflicts as more new members arrive on this list.

> Regarding Wally...er..Paul...rus' recent mention of 12 nice scales
>to write in,

As you correctly discern below, they are not scales at all. Which is
why I referred to them as tuning systems, not as scales. ;)

> I would
> be more than happy to try something. But I simply don't understand
your
> explanations or "horagrams."

I'd be happy to spend time clarifying. Let me know where you got hung
up on my explanations. Horagrams, an invention of Erv Wilson, are
explained briefly below, but I'd be happy to elaborate and/or clarify
if you wish.

> Looks more like families of scales,

Yes -- precisely.

> and I recognize the
> red numbers as associated with such properties (e.g. the multiples
>of 3 belonging to
> the "augmented" family). But the step sizes are unequal?

Yes. Each ring represents a scale belonging to the family, and the
black numbers in the ring tell you the step sizes, rounded to the
nearest cent. On the outside of the horagram, you can see all the
pitches of the family, rounded to the nearest hundredth of a cent.
Hopefully that wasn't too concise an explanation -- let me know.

Peace,
Paul

--- In tuning@yahoogroups.com, "piccolosandcheese" <jbarton@r...>

/tuning/topicId_52708.html#52708

wrote:
> Hello all. I'm Jacob. Aspiring composer, instrument
inventor/builder, omniscient
> being. Currently residing in Hooston, Texas where I am also
undergraduating. Still
> weighing the Great Microtonal Question: Is It Worth the Trouble?
but currently
> bearing the microtonal torch for the betterment of my peers.
>
> I guess I have a few questions. For those of you who check this
thing five times a
> day, this seems more of a hobby than a formal pursuit for you. I
venture this because
> making a living as a composer let alone a microtonal one is a
staggering challenge.
> The exception is JP it seems. Is this right? What does everybody
do for a living?
>

***Hello Jacob,

While it's true that my works are published and I also get ASCAP
royalties and occasional commissions here and there, I most certainly
don't make a living composing. One would have to either be a pop or
film composer to do that. I don't even make a living fundraising for
our non-profit music group, but I *do* make a living doing non-profit
fundraising for another, larger, social services charity...(i.e., I
also have a "day job...")

[However I also have to say I made a living *exclusively* as a
pianist in New York for over 13 years, a poverty-stricken experience
I would not soon like to repeat...]

But I can vouch that several people on this list are dedicated
musicians (Jon Szanto and Johnny Reinhard come immediately to mind)
and I think most of the people here are more dedicated than
just "hobbyists..."

I like your Big Question: "Is it worth the trouble..." :)

As a composer, you will most probably know when you *need* something
more than 12-equal... it has to be something *internal* you want to
*hear* and not because other people are doing it or it's some kind of
fad... etc...

> I know there are more microtonal composers out there, of course.

***Many. And there are more and more every day, some reaching
extraordinary international stature. I just wrote up a review of the
(now deceased) Italian composer Giacinto Scelsi who is, predominantly
above everything else, a microtonalist. He is reaching that stature
of late...

Is it true that
> many have been on here for some time but left in dissatisfaction?
That would be a
> shame (especially because I'm just getting on the scene).
>

***The Internet is a "funky" medium and people sometimes aren't
sensitive to the way others might interpret the written word. If we
were all together in a group, physically, some of these things would
not happen... So, I think it's more problems involving *that* than
anything specific about this forum. My impression is that these
problems occur in *many* forums... So, no, this place is just as
great as the people who "inhabit" it...

> Regarding Wally...er..Paul...rus' recent mention of 12 nice scales
to write in, I would
> be more than happy to try something. But I simply don't understand
your
> explanations or "horagrams." Looks more like families of scales,
and I recognize the
> red numbers as associated with such properties (e.g. the multiples
of 3 belonging to
> the "augmented" family). But the step sizes are unequal? Or are
they? Scl files would
> be nice.
>
> (How to end? I like Szanto's "Cheers" and Reinhard's "Best"...I'll
go with) Godspeed!

***Hmmm. Sounds like a musical. You're going to make a living as a
composer after all... :)

JP

So Paul writes:

> I don't make a living as a microtonal composer,

So what do you end up doing? Just curious...

>
> I'd be happy to spend time clarifying. Let me know where you got hung
> up on my explanations. Horagrams, an invention of Erv Wilson, are
> explained briefly below, but I'd be happy to elaborate and/or clarify
> if you wish.

Upon Googling, I find Finnnamore's page helpful (although it would be nice =
to to have
it in the Tonalsoft Enc—ahhh it's probably already been suggested). Explain=
s a little
more. But why do your horagrams not quite have octave equivalence? Always =

something like 1195 cents - what's up with that?

--- In tuning@yahoogroups.com, "piccolosandcheese" <jbarton@r...>
wrote:
> So Paul writes:
>
> > I don't make a living as a microtonal composer,
>
> So what do you end up doing? Just curious...

Part time, playing music (as a member of Stretch and It and
accompanying Kevin So, Katrin Roush, Deep C, Hugh McGowan, The Well,
etc. etc.), mostly guitar (a bit of keys and djembe too), both live
and studio. Part time, doing quantitative research in a financial
company, which mostly means posting to these lists (shhh . . .).

> But why do your horagrams not quite have octave equivalence?

In TOP ("Tempered Octaves, Please") the octave, like all the other
consonances, usually gets tempered (though it's tempered by the
smallest amount in cents). Octave-repetition is still assumed, though
it's repetition at this (usually) tempered octave.

> Always =
>
> something like 1195 cents - what's up with that?

Some of these temperaments widen the octave slightly, some of them
narrow it slightly. The overall effect is to improve the tuning of
the worst-tuned consonances, making for a smoother sound in general.
Try it!

If that's unacceptable for you for whatever reason, each of these
tuning systems comes in varieties with pure octaves, which is how
they've appeared on these lists until very recently. The tuning-math
list is full of details on this stuff and is probably the best place
to ask if you want to get into the nitty-gritty of how various sets
of assumptions on 'optimal temperament' lead to various
specifications for these and other tuning systems.

--- In tuning@yahoogroups.com, "piccolosandcheese" <jbarton@r...>
wrote:

> Regarding Wally...er..Paul...rus' recent mention of 12 nice scales
to write in, I would
> be more than happy to try something. But I simply don't understand
your
> explanations or "horagrams."

Here's a longer explanation of the horagrams, which I'm excising from
my paper as I work to replace them with more original "floragrams":

. . . one can say that the meantone system is generated by its
approximations of the 2:1 and 3:1 ratios. And, as tuning systems are
usually constructed so as to repeat themselves at intervals of
approximately 2:1 (the octave), the ~2:1 generator functions as the
period of the system. Musical cultures whose scales repeat at the
~2:1 treat pitches separated by ~2:1 as "equivalent", typically
giving them the same name. Then ~3:1, or equivalently 3:2 (the fifth)
or 3:4 (the fourth) can be regarded simply as the generator. In this
guise, meantone temperament, though 2-dimensional, has been referred
to as a "linear temperament" by Erv Wilson and others.

It's not always the case, though, that a 2-dimensional temperament
can be generated by a pair of intervals such that one of them is
~2:1. [[[[[[[[[[[[[[[examples, with technical explanations,
deleted]]]]]]]]]]]]]]] Such fractions-of-octave periods, though, are
clearly not psychoacoustic or cultural intervals of equivalence. So
the applicability of the term "linear temperament" to all 2-
dimensional temperaments is debatable.

Once the period and generator of a 2-dimensional temperament are
identified, scales can be created in a straightforward way. Starting
with one note per period, the generator is used to add more and more
pitches to the scale. At certain points in this process, the scale
has only two different step sizes. At these points, traversing any
given number of consecutive steps in the scale can result in at most
two specific sizes of interval, regardless of where one begins in the
scale. The number of sizes will be exactly two except where the
interval is the period or a multiple thereof (in which case there's
only one size). In cases where the period is an octave, these points
have been referred to as Moments-Of-Symmetry, or MOS scales, by Erv
Wilson and others. They've also been called Myhill scales. A more
general term that includes the cases where the octave is a multiple
number of periods is Distributionally Even scale (DES).

Pitches in scales that repeat every (tempered) octave can be grouped
together into "equivalence classes". We'll use the term "pitch class"
to indicate a pitch along with all its (tempered) octave-
transpositions. Using this idea, we can concisely display DESs by
employing a type of diagram called a "horagram" by Erv Wilson. He
uses them to depict MOS scales but I will take the liberty of
applying the term to this more general case. Take a look now at the
horagrams which comprise the bulk of this paper. Let's use the TOP
meantone horagram as an example. The horagram depicts pitch classes
as rays, and intervals as angles, with a (tempered) octave
represented, like an hour on a clock, as a full circle. The diagram
begins with one pitch class per period shown as rays emanating from
the center of the diagram. In the TOP meantone case, this is a single
vertical ray, representing 0 cents, the tempered octave of 1201.7
cents (explicitly indicated), and all integer multiples thereof. Then
the process of repeatedly applying the generator to add more pitch
classes occurs. By convention, the smallest possible interval is
chosen to represent the generator – in this case, the tempered fourth
of 504.13 cents. So the second pitch obtained within the frame of an
octave is shown as 504.13 cents. Unlike Wilson, in whose horagrams
the generator is always applied in the same direction, I apply the
generator alternately upward from one end of the chain(s) and
downward from the other. So the third pitch obtained within the
octave is obtained by applying the generator downward from the first
pitch class: 1201.7 - 504.13 = 697.57 cents. The fourth pitch class
is obtained by applying the generator upward from the second pitch
class: 504.13 + 504.13 = 1008.26 cents. And the fifth pitch class is
obtained by applying the generator downward from the third pitch
class: 697.57 - 504.13 = 193.44 cents. Each time a DES is formed, a
concentric ring is drawn, the number of notes per octave in the DES
is written in the ring near the top, and each step is labeled with
its size in cents. The process continues with the rays emanating from
the outside of the ring. Successive rings get drawn further and
further from the center.

TOP meantone shows 5- and 7-note rings, corresponding to the familiar
pentatonic and diatonic scales. If the 0/1201.7-cent pitch class is
assigned to the note D, the rest of the 7-note ring will correspond
to the notes E, F, G, A, B, and C. A chain of 7 generators produces
the small interval of 76.19 cents, which first shows itself in the 12-
note ("chromatic") ring. This interval is also the difference between
the two step sizes in the 7-note ring. Raising a note by this
interval appends a "sharp" (#) to its name, while a like lowering
appends a "flat" (b-). With these symbols, any meantone pitch class
can be assigned a unique name. A similar notation scheme can be
devised for any 2-dimensional temperament. The reader may find it
useful or enjoyable to concoct such schemes using the horagrams here
provided.

wallyesterpaulrus wrote:

> In cases where the period is an octave, these points
> have been referred to as Moments-Of-Symmetry, or MOS scales, by Erv
> Wilson and others.

I might be reading this wrong and the context may have caused you to
explain it in this way by Erv 's is Horagrams are not tied to the octives
at all.

> They've also been called Myhill scales. A more
> general term that includes the cases where the octave is a multiple
> number of periods is Distributionally Even scale (DES).
>
> Unlike Wilson, in whose horagrams
> the generator is always applied in the same direction, I apply the
> generator alternately upward from one end of the chain(s) and
> downward from the other. So the third pitch obtained within the
> octave is obtained by applying the generator downward from the first
> pitch class: 1201.7 - 504.13 = 697.57 cents. The fourth pitch class
> is obtained by applying the generator upward from the second pitch
> class: 504.13 + 504.13 = 1008.26 cents. And the fifth pitch class is
> obtained by applying the generator downward from the third pitch
> class: 697.57 - 504.13 = 193.44 cents.

I do not see what is gained by such a process compared to the original
method of superimposing the same interval. you end up with the same scales
except in a different mode. Isn't this like changing the Major scale to a
dorian?

>

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

--- In tuning@yahoogroups.com, kraig grady <kraiggrady@a...> wrote:
>
>
> wallyesterpaulrus wrote:
>
> > In cases where the period is an octave, these points
> > have been referred to as Moments-Of-Symmetry, or MOS scales, by
Erv
> > Wilson and others.
>
> I might be reading this wrong and the context may have caused you to
> explain it in this way by Erv 's is Horagrams are not tied to the
octives
> at all.

Last time we went over this, you told me L s s s s L s s s s
repeating at the octave would not be considered an MOS. Several years
before that, you said it would, so I made extra sure you were sure
the last time . . . or so I thought . . .

> I do not see what is gained by such a process compared to the
original
> method of superimposing the same interval. you end up with the same
scales
> except in a different mode. Isn't this like changing the Major
scale to a
> dorian?

It would be like changing Lydian or Locrian to Dorian, yes. The
original method gives Lydian or Locrian; my method above gives
Dorian. In general, if you're looking for the tempered approximation
of a particular consonant interval, there's almost a 50% chance that
you'll never encounter it in relation to the root if you use the
original method. Lydian has no perfect fourth or minor third above
the root, Locrian no perfect fifth or major sixth above the root, and
this would remain the case no matter how far out one went in the
horagram. If one generates alternately up and down from the root, one
eventually encounters every interval in relation to the root.

That's how the horagrams that Jacob was looking at, and that I sent
you (since you were not here at the time), were produced. But now I'm
making 'floragrams', in which the generators do proceed in only one
direction from the root (and its period-transpositions, if any). I'm
currently banging my head against the wall as to how to best
alleviate the issues I mentioned above, in connection with the
original method, which will plague me here.

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

> Here's a longer explanation of the horagrams, which I'm excising from
> my paper as I work to replace them with more original "floragrams":

Looking good. Are you going to let the tuning-math gang review it
before sending it off?

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> > Here's a longer explanation of the horagrams, which I'm excising
from
> > my paper as I work to replace them with more
original "floragrams":
>
> Looking good. Are you going to let the tuning-math gang review it
> before sending it off?

Yes.

>That's how the horagrams that Jacob was looking at, and that I sent
>you (since you were not here at the time), were produced. But now I'm
>making 'floragrams', in which the generators do proceed in only one
>direction from the root (and its period-transpositions, if any). I'm
>currently banging my head against the wall as to how to best
>alleviate the issues I mentioned above, in connection with the
>original method, which will plague me here.

I don't get it; why not stick with your bi-directional method?

-Carl

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, kraig grady <kraiggrady@a...> wrote:
> >
> >
> > wallyesterpaulrus wrote:
> >
> > > In cases where the period is an octave, these points
> > > have been referred to as Moments-Of-Symmetry, or MOS scales, by
> Erv
> > > Wilson and others.
> >
> > I might be reading this wrong and the context may have caused you to
> > explain it in this way by Erv 's is Horagrams are not tied to the
> octives
> > at all.
>
> Last time we went over this, you told me L s s s s L s s s s
> repeating at the octave would not be considered an MOS. Several years
> before that, you said it would, so I made extra sure you were sure
> the last time . . . or so I thought . . .
>
> > I do not see what is gained by such a process compared to the
> original
> > method of superimposing the same interval. you end up with the same
> scales
> > except in a different mode. Isn't this like changing the Major
> scale to a
> > dorian?
>
> It would be like changing Lydian or Locrian to Dorian, yes. The
> original method gives Lydian or Locrian; my method above gives
> Dorian. In general, if you're looking for the tempered approximation
> of a particular consonant interval, there's almost a 50% chance that
> you'll never encounter it in relation to the root if you use the
> original method. Lydian has no perfect fourth or minor third above
> the root, Locrian no perfect fifth or major sixth above the root, and
> this would remain the case no matter how far out one went in the
> horagram. If one generates alternately up and down from the root, one
> eventually encounters every interval in relation to the root.
>
> That's how the horagrams that Jacob was looking at, and that I sent
> you (since you were not here at the time), were produced. But now I'm
> making 'floragrams', in which the generators do proceed in only one
> direction from the root (and its period-transpositions, if any). I'm
> currently banging my head against the wall as to how to best
> alleviate the issues I mentioned above, in connection with the
> original method, which will plague me here.

Thanks for the further explanation. The mode issue is indeed confusing. However, it
is much easier for me to see what's going on in the generation of the scale if the
symmetry is centered around 12 o'clock, which happens some of the time when you
go in both directions.

Meanwhile I'm having issues generating MOSes in (command-line) Scala...I want to be
able to just put in a generating interval and see which ones are possible, and then
choose one. It doesn't seem this easy...

Jacob

Jacob Barton wrote:
>Meanwhile I'm having issues generating MOSes in (command-line) Scala...
>I want to be able to just put in a generating interval and see which
>ones are possible, and then choose one. It doesn't seem this easy...

You can use the CONVERGENTS/SEMI command for that. A MOS will be
distributionally even for the convergents and semi-convergents
of log(generator)/log(period). So the numerator is the generator
degree and the denominator the number of tones.

Manuel

>That's how the horagrams that Jacob was looking at, and that I sent
>you (since you were not here at the time), were produced. But now
>I'm making 'floragrams', in which the generators do proceed in only
>one direction from the root (and its period-transpositions, if any).
>I'm currently banging my head against the wall as to how to best
>alleviate the issues I mentioned above, in connection with the
>original method, which will plague me here.

I don't get it; why not stick with your bi-directional method?

-Carl