Yahoo Tuning Groups Ultimate Backup tuning Trippy Trojans

Thank you Graham. I saw Trojan notation come up on facebook a few days ago
and didn't know what it was - now I do!

I think, also, someone has sagittal notation working in Sibelius, something
I really should investigate.

Chris

On Sat, Jul 2, 2011 at 6:50 AM, Graham Breed <gbreed@...> wrote:

> **
>
>
> After years in the making, my PDF on Trojan output from
> Tripod input is now finished:
>
> http://x31eq.com/magic/trip-trojan.pdf
>
> It outlines how you can write music using one pitch system,
> and produce scores in a different system.
>
> Graham
>
>

🔗Mike Battaglia <battaglia01@...>

"The pitches are specified using the short *yan tan tethera* names from
Tripod Notation. This is what makes the system *trippy*."

Haha! Yes it is.

By the way, the tripod scale is what I was calling "locally subperiodic" at
one point, which is a generalization of omnitetrachordality. The period is
2/1, the subperiod is 5/4, and the generator is a marvel-tempered 15/14. I
wrote about them on tuning-math some time ago but had to cut work on them
short due to time constraints.

The basic idea I had worked out, which might be useful to work out a tripod
"chromatic" scale, is to work out some "primary MOS" where the generator is
a major third (in your case 1L2s), and then shift the entire thing x amount
of times by the second generator of your choice (15/14), so that the first
thing I called a generator now becomes a sub-period.

If doing so causes you to encroach on another "foot," then you replicate the
pattern of steps in the foot in the other feet, and repeat the process until
you end up at a stable scale, and if you do this long enough you'll find
that you have now mysteriously ended up at a different primary MOS than you
started with (perhaps let's say 3L4s), and that thing has mysteriously been
shifted by your original generator. I still haven't worked out some kind of
precise formula for it but that's the gist of it. It's also one of the neat
techniques that rank-3 scales make available to us, which I think might be
more useful to explore than 3GMP scales.

-Mike

On Sat, Jul 2, 2011 at 6:50 AM, Graham Breed <gbreed@...> wrote:
>
> After years in the making, my PDF on Trojan output from
> Tripod input is now finished:
>
> http://x31eq.com/magic/trip-trojan.pdf
>
> It outlines how you can write music using one pitch system,
> and produce scores in a different system.
>
> Graham

🔗Tim Reeves <reevest360@...>

hi Graham

wow, I think I can relate to your system...it seems like I could easily adapt it to a natural whole tone and half tone system, ie, where there are 8 whole tone notes, then the octave, with the half tones being easily designated with sharps or flats. Thanks for opening my eyes beyond the standard clef notations!
Tim

--- On Sat, 7/2/11, Graham Breed <gbreed@...> wrote:

From: Graham Breed <gbreed@...>
Subject: [tuning] Trippy Trojans
To: tuning@yahoogroups.com
Date: Saturday, July 2, 2011, 10:50 AM

After years in the making, my PDF on Trojan output from
Tripod input is now finished:

http://x31eq.com/magic/trip-trojan.pdf

It outlines how you can write music using one pitch system,
and produce scores in a different system.

Graham

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🔗Graham Breed <gbreed@...>

Mike Battaglia <battaglia01@...> wrote:

> By the way, the tripod scale is what I was calling
> "locally subperiodic" at one point, which is a
> generalization of omnitetrachordality. The period is 2/1,
> the subperiod is 5/4, and the generator is a
> marvel-tempered 15/14. I wrote about them on tuning-math
> some time ago but had to cut work on them short due to
> time constraints.

16/15 and 15/14 are marvel-tempered to be the same, and the
"secor" of Miracle temperament. Decimal notation is the
one-footed equivalent of tripod notation.

With two feet of five toes each, you have Paul Erlich's
decatonic notation. That makes Pajara the most human
version of tripod notation.

The 9 note MOS of Orwell has five 16:15/15:14 steps and four
smaller steps. That gives it three feet of one toe each
and one foot with two toes. You can write the MOS in
tripod notation by lowering the first degree (yan to yab)
and raising the last degree (dov to doj). If you can
imagine a mutant horse with its two-hooved foot standing in
a river, this might help you to write Orwell music in
tripod notation.

Chromatic notation for Meantone has 5 feet.

Graham

🔗Graham Breed <gbreed@...>

Tim Reeves <reevest360@...> wrote:

> wow, I think I can relate to your system...it seems like
> I could easily adapt it to a natural whole tone and half
> tone system, ie, where there are 8 whole tone notes, then
> the octave, with the half tones being easily designated
> with sharps or flats. Thanks for opening my eyes beyond
> the standard clef notations! Tim

I'm glad you're inspired, although I don't know what you're
describing. These people are interested in alternative
notations:

http://musicnotation.org/musicnotations/

The seem to not like accidentals. That seems to follow
from them only thinking there are 12 pitches to the octave
that they need to worry about.

The good thing about computer typesetting, anyway, is that
you can experiment with strange notations and still convert
the score to something more normal.

Graham

🔗Tim Reeves <reevest360@...>

Hi Graham,

I have been describing a method of microtuning that deals directly with the natural harmonic series. I call it "next tone theory" because the interval relationships are based on the very next harmonic in the series from a tonic.

The initial sequence creates a natural whole tone scale
A * 9/8=B B+ (B-A) = C C+ (B-A)=D etc

. It produces an added factor scale that continues throughout the octave , but you must double that factor in each succeeding octave. Comparing the results of this method with those of other approaches shows that it is indeed viable...just look at my post that compares my natural quarter tone scale with the dwarf 19 edo scale that (is available on scala but) was posted on the tuning group earlier this week.

You would be correct in thinking that this is a different method than what most microtuners use.

This is only the basis, it is expandable to include other natural numeric systems and certainly more treatments. The result is a very organized approach to deriving scale values. You will see that all intervals are eventually revealed with this system, no matter how bizarre or well conceived that someone's "new" or "historically ancient" interval value may be.

Here's a good question for the group:

Is there any concensus on how to notate beyond sharps and flats??? I can easily write values of quarter tone, eighth tone etc but haven't really seen a system that everyone who microtunes will adhere to. I haven't read your link yet, maybe it has the answer to my question.
Thanks
Tim

--- On Mon, 7/4/11, Graham Breed <gbreed@...> wrote:

From: Graham Breed <gbreed@...>
Subject: Re: [tuning] Trippy Trojans
To: tuning@yahoogroups.com
Date: Monday, July 4, 2011, 12:48 PM

Tim Reeves <reevest360@...> wrote:

I'm glad you're inspired, although I don't know what you're
describing. These people are interested in alternative
notations:

http://musicnotation.org/musicnotations/

The seem to not like accidentals. That seems to follow
from them only thinking there are 12 pitches to the octave
that they need to worry about.

The good thing about computer typesetting, anyway, is that
you can experiment with strange notations and still convert
the score to something more normal.

Graham

------------------------------------

🔗Graham Breed <gbreed@...>

Tim Reeves <reevest360@...> wrote:

> I have been describing a method of microtuning that deals
> directly with the natural harmonic series. I call it
> "next tone theory" because the interval relationships are
> based on the very next harmonic in the series from a
> tonic.

> The initial sequence creates a natural whole tone
> scale A * 9/8=B B+ (B-A) = C C+ (B-A)=D etc . It
> produces an added factor scale that continues throughout
> the octave , but you must double that factor in each
> succeeding octave. Comparing the results of this method
> with those of other approaches shows that it is indeed
> viable...just look at my post that compares my natural
> quarter tone scale with the dwarf 19 edo scale that (is
> available on scala but) was posted on the tuning group
> earlier this week.

That much should work. But LilyPond won't be happy if
accidentals are supposed to work as "added factors" as well.

> Here's a
> good question for the group: Is there any concensus on
> how to notate beyond sharps and flats??? I can easily
> write values of quarter tone, eighth tone etc but haven't
> really seen a system that everyone who microtunes will
> adhere to. I haven't read your link yet, maybe it has the
> answer to my question.

This link has some answers:

http://lumma.org/music/theory/microtools/

The only comprehensive standard is Sagittal. As it's the
best standard we have, I don't think anybody of note is
using it. I am.

There is general agreement on Tartini-Couper for
quartertones among "contemporary music" performers. Arabic
music uses a different half-flat. Maneri-Sims has some
weight behind it.

Extended Helmholtz-Ellis JI Pitch Notation is the second
most comprehensive system. Try this:

http://gfax.ch/literature/TheExtendedHelmholtz-Ellis-J-I-PitchNotation.pdf

Graham

🔗Tim Reeves <reevest360@...>

Thanks so much Graham, been gone all day and still need to look it all over. Thanks again
Tim

--- On Mon, 7/4/11, Graham Breed <gbreed@...> wrote:

From: Graham Breed <gbreed@...>
Subject: Re: [tuning] Trippy Trojans
To: tuning@yahoogroups.com
Date: Monday, July 4, 2011, 3:49 PM

Tim Reeves <reevest360@...> wrote:

That much should work. But LilyPond won't be happy if
accidentals are supposed to work as "added factors" as well.

This link has some answers:

http://lumma.org/music/theory/microtools/

The only comprehensive standard is Sagittal. As it's the
best standard we have, I don't think anybody of note is
using it. I am.

There is general agreement on Tartini-Couper for
quartertones among "contemporary music" performers. Arabic
music uses a different half-flat. Maneri-Sims has some
weight behind it.

Extended Helmholtz-Ellis JI Pitch Notation is the second
most comprehensive system. Try this:

http://gfax.ch/literature/TheExtendedHelmholtz-Ellis-J-I-PitchNotation.pdf

Graham

------------------------------------

🔗gdsecor <gdsecor@...>

--- In tuning@yahoogroups.com, Tim Reeves <reevest360@...> wrote:
> ...
> Here's a good question for the group:
>
> Is there any concensus on how to notate beyond sharps and flats??? I can easily write values of quarter tone, eighth tone etc but haven't really seen a system that everyone who microtunes will adhere to. I haven't read your link yet, maybe it has the answer to my question.
> Thanks
> Tim

Hi Tim,

A web search will show that there are many different ways to notate microtones, and there is no consensus as to how this should be done.

Dave Keenan & I addressed this problem about 10 years ago and, after several years of work, came up with a system of microtonal accidentals, which is by far the most comprehensive one:
http://sagittal.org/sagittal.pdf
If that link doesn't work, then try:
http://dkeenan.com/sagittal/sagittal.pdf

In the Sagittal paper (actually a reprint of a Xenharmonikon 18 article), you will find not only specifics of the notation, but also a brief discussion (beginning on p. 19) of several issues involving new microtonal notations and their suitability for various kinds of tunings. For example, a notation for just intonation is usually designed to indicate the prime factors of ratios, but the symbols tend to get cumbersome with complex ratios and may not be very suitable for notating complex temperaments. With Sagittal, the symbols are relatively simple, and they may be used for both complex JI and all sorts of temperaments. Although there are many symbols in the system, the simpler tunings require only a small subset. The symbols are logically constructed from only a few symbol elements (called "flags").

You may also notice that the Sagittal paper is the source of the term "trojan", as it appears in the subject line of this thread.

--George

Trippy Trojans

🔗Graham Breed <gbreed@...>

🔗Chris Vaisvil <chrisvaisvil@...>

🔗Mike Battaglia <battaglia01@...>

🔗Tim Reeves <reevest360@...>

🔗Graham Breed <gbreed@...>

🔗Graham Breed <gbreed@...>

🔗Tim Reeves <reevest360@...>

🔗Graham Breed <gbreed@...>

🔗Tim Reeves <reevest360@...>

🔗gdsecor <gdsecor@...>