Yahoo Tuning Groups Ultimate Backup tuning Hyper-MOS question

Welcome to the Alternate Tunings Mailing List.Hi Chris,

Dan Stearns and I had a long discussion a while back about the generation of hyper-mos scales which should be trivalent, three interval sizes for each possible number of scale degrees, by analogy with a MOS which has two interval sizes for each possible number of scale degrees. It was partly motivated by the observation that many scales in the SCALA archive are trivalent, and many are also quadrivalent, or more.

I had the idea of a generator involving two intervals such as 5/4 6/5 alternating,
1/1 5/4 3/2,
which you then repeat as:
1/1 5/4 3/2 15//8 9/8 45/32 27/16
which is where the scale you found on the tunesmithy site comes from.
That is trivalent, as you can check in Scala.

If you continue a bit further you get another trivalent "moment of symmetry" at seventeen notes.

So the method produces a few trivalent scales, but is only moderately successful.

You can read more about my alternating generators method here:
http://www.tunesmithy.netfirms.com/fts_help/More_scales.htm#mos

Dan followed another line of investigation which was far more successful and he could produce many trivalent scales to order. However I got busy with programming and he took a long break not long after so the discussion got rather broken off, and I can't say I understand his method quite yet. Also since then I have been so pre-occupied with programming FTS and particularly the upcoming FTS 3.0 release that I have done little by way of further scales explorations.

I added that programming to FTS as part of the process of investigation. I see that II didn't explain the situation properly in the help. I just explained how the option in FTS works. To give the context properly, I should have explainedhat what I was describing is just one of two current candidates for a notion of Hyper MOS, and give the reader some pointer to Dan's more successful method

Anyway, he is the one to ask, as I think his version is probably a better candidate for the label "Hyper MOS" as it is more successful at generating trivalent scales.

This is Dan Stearn's Eureka post about his Hyper MOS method:

/tuning/topicId_16061.html#16585
/tuning/topicId_19322.html#19361

Then it got taken up again on the tuning-math list in a discussion of "Tribonacci scales". But I hadn't got the time to follow the discussion there either.

I hope I get a chance to get back to this some time. It would be great to program Dan's method as well as mine.

He also had an interesting conjecture that every trivalent scale with an even number of notes has to contain an irrational interval, and later I think he concluded that it has to be a subset of an n-et as well, so if that is so, the rational hyper-mos's have to have an odd number of notes.

Unfortunately I haven't go tthe time to join in discussing it at present either. But if anyone feels they could summarize the conclusions and describe it to me - the construction algorithm for his scales - sufficiently so that I can program it, then I'm interested to program it in FTS, and should do to complement my own less successful method. Or later once I have the time to read it all up and get up to date with it. Also I wonder if it might be in Scala by now?

Meanwhile anyway I'll add a note to the help and to the window in FTS to make it clear that Dan Stearns method exists and is probably a better candidate for the term "hyper MOS"

Robert

----- Original Message -----
From: tuning@yahoogroups.com
To: tuning@yahoogroups.com
Sent: Wednesday, October 25, 2006 11:50 AM
Subject: [tuning] Digest Number 4177

Welcome to the Alternate Tunings Mailing List.
Messages In This Digest (6 Messages)
1a. Re: Score PDF for barbershop (was: re: One more barbershop JI track) From: Aaron Wolf
1b. Re: Score PDF for barbershop (was: re: One more barbershop JI track) From: Carl Lumma
1c. Re: Score PDF for barbershop (was: re: One more barbershop JI track) From: Carl Lumma
1d. Re: Score PDF for barbershop (was: re: One more barbershop JI track) From: Carl Lumma
2. Re: Kirkwood gaps scale From: George D. Secor
3. Re: History again - first mention of 55-division? From: threesixesinarow
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1a. Re: Score PDF for barbershop (was: re: One more barbershop JI track)
Posted by: "Aaron Wolf" backfromthesilo@yahoo.com backfromthesilo
Tue Oct 24, 2006 8:32 am (PST)
--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > Thanks for the enthusiastic encouragement. I wasn't going to
> > bother, but fine... here it is:
> >
> > http://ozmusic.com/aaron/mp3/WMeetAgain/WMA.pdf
> >
> > I wrote in pencil and I scanned it quickly, it isn't perfect.
>
> Thanks! I'll try to set aside time this weekend to crunch on
> this.
>
> > I've been trying to figure out what notation will be easiest
> > for me to read musically, easiest to use when editing on the
> > computer, and easiest to explain to others...
>
> From my point of view, you aren't there yet. :)
>
> What did you think of my suggestion (did it make any sense
> to you)?
>

I understand a little, but I feel neither of us is really there.
I do want to start having commas more apparent.

My idea for something to be taught to actual singers is something like
this:

How about this? a notation that indicates the fundamental of each
chord in such a way that is simple and clear, and if it is a
pythagorean note, then indicate what power of 3 that it is (in other
words, like the old time barbershopper's "clock" system that says how
many fifths away on the circle of fifths we are). Then use different
note heads to simply indicate a 3, 5, 7 etc identity in relation to
the fundamental. If that could be combined with a very simple
indication of melodic comma shifts (no need to specify different
commas), that should cover everything. What do you think?

-Aaron

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Messages in this topic (10)
1b. Re: Score PDF for barbershop (was: re: One more barbershop JI track)
Posted by: "Carl Lumma" clumma@yahoo.com clumma
Tue Oct 24, 2006 8:59 pm (PST)
> My idea for something to be taught to actual singers is something
> like this:
>
> How about this? a notation that indicates the fundamental of
> each chord in such a way that is simple and clear, and if it is
> a pythagorean note, then indicate what power of 3 that it is
> (in other words, like the old time barbershopper's "clock"
> system that says how many fifths away on the circle of fifths
> we are). Then use different note heads to simply indicate a
> 3, 5, 7 etc identity in relation to the fundamental. If that
> could be combined with a very simple indication of melodic
> comma shifts (no need to specify different commas), that should
> cover everything. What do you think?

Sounds good, except I don't like the part about the fundamental's
absolute pitch. First off, what happens if it isn't a power
of 3? Secondly, I don't think performers (or composers) need
to know this. There's no way a bass is going to be able to say,
"Oh, 3129/8080, I was a bit flat there, wasn't I?"

Performers are more likely to be interested in which note
remain unchanged or nearly unchanged between chords. They
can then tune pure to it/them. For nearly unchanged notes,
yes I agree plenty of mileage could be gotten out of only one
type of "nearly". I like drawing lines to make the common
tones obvious. Then one doesn't even have to read music (or
both clefs) to know that he's got to match the bari's previous
pitch. Dotted lines make a good nearly, with perhaps a plus
or minus sign above them to indicate direction.

That takes care of shifts. Drift I think is best shown as a
cumulative cents offset from concert pitch. Every time the
offset changes direction -- say it's been going flat and
starts going sharp -- the current offset should be printed
above the barline. Say we start out at A=440, go 20 cents
flat every other bar for 5 bars, then go 20 cents sharp every
other bar for 5 bars and end on A=440. The notation would
show "-100" above the 6th barline and "+-0" above the last
barline. The point is that this is something that should
happen naturally if one tunes pure and respects the shifts
notation (above). It's just there as a check so you can
troubleshoot whether you're going flat 'cause you're tired
or because the composer/arranger intended it.

-Carl

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Messages in this topic (10)
1c. Re: Score PDF for barbershop (was: re: One more barbershop JI track)
Posted by: "Carl Lumma" clumma@yahoo.com clumma
Tue Oct 24, 2006 10:06 pm (PST)
[I wrote...]
> Just take this example:
>
> http://lumma.org/music/score/Retrofit_JI.pdf
> (this is 4MB, might take a while to load)
>
> It's a formative showing of the notation I suggested in my
> previous message, but I haven't gone through and made sure
> the commas don't accumulate. I really should get around to
> doing that one day.

There are 24 root changes in the piece:

9/8
3/2
7/4
9/8
6/5
9/8
16/9
8/7
28/15
60/49
10/7
3/2
4/3
9/8
27/16
3/2
64/35
7/4
9/8
21/16
4/3
9/8
8/5
9/8

This adds up to 3^18 * 5^-2 * 7^-1, or 387420489/367001600,
or about 94 cents. I don't know if that's up or down, but
I don't think it'll be a problem in a 3-minute piece with
24 root changes.

-Carl

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Messages in this topic (10)
1d. Re: Score PDF for barbershop (was: re: One more barbershop JI track)
Posted by: "Carl Lumma" clumma@yahoo.com clumma
Tue Oct 24, 2006 11:40 pm (PST)
> This adds up to 3^18 * 5^-2 * 7^-1, or 387420489/367001600,
> or about 94 cents. I don't know if that's up or down, but
> I don't think it'll be a problem in a 3-minute piece with
> 24 root changes.

One *can* write a neoclassical piece in 12-tET, fancifully
assign it an 11-limit adaptive JI tuning, and come out OK.

-Carl

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Messages in this topic (10)
2. Re: Kirkwood gaps scale
Posted by: "George D. Secor" gdsecor@yahoo.com gdsecor
Tue Oct 24, 2006 2:13 pm (PST)
--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Robert walker" <robertwalker@>
wrote:
>
> > I had a go at retuning it to 17-et - a similarly sized semitone
> though not otherwise very close, anyway, this is the mode I used,
> closest to your scale:
> > 0 3 4 6 7 10 13 14 17
> > and here is the result:
>
> Here are retunings to 31, 34 (the sharp 7 version), 46, 68, and 99,
> as well as the JI original. I'm fond of the extra shimmer 99 adds
on,
> though it generally sounds a lot like the JI version. Anyway, people
> can compare to 31 and see if sharp fifths are really melodically
> better as George claims.
>
> http://bahamas.eshockhost.com/~xenharmo/midi/examples/kirkwood/

Hi Gene & Robert,

I got a chance to listen to the Kirkwood gaps (original & all of the
retunings) last night (several times) to decide if I had any
preferences. I observed that 34 is the only tuning that has both a
good 5/4 and 5/3 and also has the Archytas comma tempered out in the
upward jump of the fifth between 7/4 and 4/3 (at 0:27-0:28). But I
can't say that it's clearly my favorite for that reason, because I
also liked 46 and 68 better than the others.

In the paper, I didn't mean to give the impression that wide fifths
are necessarily better melodically under all circumstances -- I was
writing specifically about a diatonic scale, where wide fifths result
in significantly narrower-than-12ET diatonic semitones. Several
times in the paper (pp. 59, 74, 75), I made statements to the effect
that chromatic semitones in 31-ET could be used to enhance the
melodic effect of that (narrow-fifth) tuning, so the size of the
fifths is, under more general circumstances, beside the point.

If your tuning has dozens of tones/octave, you then have
opportunities to alter the mood on the fly by making subtle
substitutions in your scale subset, so it's not wise to draw
conclusions too quickly about one of these tunings vs. another.

--George

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Messages in this topic (9)
3. Re: History again - first mention of 55-division?
Posted by: "threesixesinarow" CACCOLA@NET1PLUS.COM threesixesinarow
Tue Oct 24, 2006 4:33 pm (PST)
--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
> ...
> What Sauveur said in 1701 would be good to know too, though I'm
> waiting for that article on order.

http://gallica.bnf.fr/ark:/12148/bpt6k3503q/f6.item
"Système générale des Intervalles des Sons" 1701, page 299
http://gallica.bnf.fr/ark:/12148/bpt6k3489j/f420.table
"Table générale des Systemes temperés de Musique." 1707, article page
203, commentary page 117
http://gallica.bnf.fr/ark:/12148/bpt6k35149
"Table generale des Systemes temperés de Musique " 1711, article page
307, commentary page 80
http://gallica.bnf.fr/ark:/12148/bpt6k3516x/f449.table
"Rapport des Sons des Cordes d'Instruments de Musique aux Fléches des
Cordes; Et nouvelle détermination des Sons fixes." 1713, page 324

all in _Histoire de l'Académie royale des sciences avec les mémoires
de mathématique et de physique tirés des registres de cette Académie_

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Hi Robert

May be a relation between your n-valent scales and my intervallic pattern model . Please go to :

/tuning/topicId_67764.html#67764

although they are tetrachordal examples.

1- As I saw in mails( may be wrong) , the concept of valency in this model is related to number of divisions in a scale or system , and you prefer to use only three divisions of L,S and M size and their combination.( is L for large , S for small ,…?)

2- As you wrote : <<<…….9/8 32/27 101.95500086538762 32/27 9/8 101.95500086538762

following the

S L M L S M

scale pattern….>>>

I am confused,if L is for larger interval then we must have M L S L M S.

Any way what about other patterns related to this pattern such as :

S L M M L S or M L S S L M or L M S M L S ?

waiting for your reply.

Shaahin Mohaajeri

Tombak Player & Researcher , Microtonal Composer

My web site <http://240edo.tripod.com/>

My farsi page in Harmonytalk <http://www.harmonytalk.com/id/908>

My tombak musics in Rhythmweb <http://www.rhythmweb.com/gdg>

My article in DrumDojo <http://www.drumdojo.com/world/persia/tonbak_acoustics.htm>

________________________________

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of Robert walker
Sent: Friday, October 27, 2006 4:10 PM
To: tuning@yahoogroups.com
Subject: [tuning] Hyper-MOS question

Hi Gene,

I've just realised why it is that every even numbered trivalent scale must contain its midpoint, and so be irrational. It is a very simple, one-liner type proof.

If the scale has 2n degrees, the inversion of every interval of n degrees also consists of n degrees. Since there is more than one interval in each interval class, you have one interval of n degrees which isn't its inversion. That leaves only one more interval in the interval class to find if the scale is trivalent, so that remaining interval must be its own inversion, so must be the midpoint. QED.

The same applies to 5-valency, 7-valency etc.

Also, I answered the question about whether all even numbered trivalent scales are subsets of n-ets by making a counter example:

9/8 4/3 600.0 894.1349974038377 1098.0449991346127 2/1

steps:

9/8 32/27 101.95500086538762 32/27 9/8 101.95500086538762

following the

S L M L S M

scale pattern

- which has an even number of steps and is trivalent

Robert

Hyper-MOS question

🔗c.m.bryan <chrismbryan@gmail.com>

🔗Robert walker <robertwalker@robertinventor.com>

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

🔗Robert walker <robertwalker@robertinventor.com>

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

🔗Mohajeri Shahin <shahinm@kayson-ir.com>