Re: JI progression with 21:16 fourth -- welcome to Gordon Rumson

Hello, there, Gordon Rumson, and welcome to the Tuning List. Thank you
for sharing with us some of your background and perspective which has
already enriched our dialogue.

While your advocacy of the "Just" could apply on various levels, one
musical interpretation would be encouragement for just intonation (JI)
systems.

Accordingly, to welcome you to our group, here's a link to an example
of a progression in JI with some notable connections to our forum's
history:

http://value.net/~mschulter/sesen002.mid

The opening sonority is one made famous by Keenan Pepper a young
musician and theorist who described here last summer. It has a ratio
of 16:21:24:28 (a rounded 0-471-702-969 cents). Using a notation where
C4 represents middle C, and "v" shows a note a septimal comma (64:63,
~27.26 cents) lower than the usual Pythagorean step, here's the
progression:

Fv4 E4
D4 E4
Cv4 A3
G3 A3

In this kind of style, called "neo-Gothic" because of its derivation
from the music of Gothic Europe during the 13th-14th centuries, a
minor seventh often contracts to a stable fifth, and this happens here
between the outer voices.

As Keenan Pepper pointed out, the opening unstable sonority includes
a narrow fourth at 21:16 (G3-Cv4), a septimal comma narrower than 4:3;
he described this interval as "crunchy."

At least in some timbres, I tend to find the overall effect of this
sonority on the concordant side: the usual fifths and fourths, pure in
this tuning, seem to provide a space which the narrow fourth can fill
with energy or "illumine." It seems almost like a music of
interstellar space.

These were my impressions when I tried this progression in what I call
the Sesquisexta tuning; _sesquisexta_ is a medieval Latin name for the
ratio of 7:6, and in this tuning defines the interval of a 7:6 minor
third between two 12-note manuals in a standard Pythagorean tuning
(Eb-G#).

Curiously, the visual layout of the progression in Sesquisexta is as
follows, using a curly brace "}" to show a note on the upper keyboard,
a 7:6 (~266.87 cents) higher than its usual Pythagorean counterpart:

D}4 E4
D4 E4
A}3 A3
G3 A3

The descending semitone Fv4-E4 -- or D}4-E4 as played on the keyboard
-- lends the progression some of its flavor, and has a size of 28:27
(~62.96 cents), a very nice cadential semitone (or, some would say,
"thirdtone").

Here's the same Keenan Pepper sonority with a different resolution,
this time involving ascending rather than descending melodic
semitone, again by a 28:27 "thirdtone":

http://value.net/~mschulter/sesen003.mid

Using the above notations, we have:

Fv4 Ebv4 D}4 C}4
D4 Ebv4 D4 C}4
Cv4 Abv3 A}3 F}3
G3 Abv3 or G3 F}3

The lowest voice ascends G3-Abv3, and the next-to-highest ascends
D4-Ebv4, while the other two voices proceed in contrary motion.

At least in the synthesizer timbre I used, the preset "Puff Pipes"
(voice A56) on a Yamaha TX-802, this type of progression has a kind of
energetic and engaging concord which I really like.

Please let me add, Gordon, that while your mention of the "Just" led
me to post examples in JI, I also warmly support your suggestion that
dialogue can partake of the equitable and the friendly on a basic
human level also.

Again, welcome to our forum.

Most appreciatively,

Margo Schulter
mschulter@value.net

--- In tuning@y..., mschulter <MSCHULTER@V...> wrote:

> As Keenan Pepper pointed out, the opening unstable sonority includes
> a narrow fourth at 21:16 (G3-Cv4), a septimal comma narrower than
4:3;
> he described this interval as "crunchy."

A small correction . . . he didn't describe this interval as crunchy,
he described the whole tetrad as crunchy. His definition of a crunchy
chord was one in which one interval is much more dissonant than all
the others. His first example of a crunchy chord was a major seventh
chord, 8:10:12:15, in which the 8:15 interval is much more dissonant
than all five of the other intervals in the chord.

--- In tuning@y..., mschulter <MSCHULTER@V...> wrote:
> The opening sonority is one made famous by Keenan Pepper a young
> musician and theorist who described here last summer. It has a ratio
> of 16:21:24:28 (a rounded 0-471-702-969 cents). Using a notation
where
> C4 represents middle C, and "v" shows a note a septimal comma
(64:63,
> ~27.26 cents) lower than the usual Pythagorean step, here's the
> progression:
>
> Fv4 E4
> D4 E4
> Cv4 A3
> G3 A3

Thanks Margo.

Can I suggest that you might wish to adopt Monz's ASCII accidentals
for septimal comma (and nearby) shifts, namely ">" for septimal comma
high and "<" for septimal comma low. There seems to be wide agreement
on these particular microtonal ASCII accidentals, even if there is on
no others. They can be seen as approximations of the numeral "7",
upright for high and inverted for low. They also resemble Sims' half
arrows which correspond to 1/6-tone shifts.

> As Keenan Pepper pointed out, the opening unstable sonority includes
> a narrow fourth at 21:16 (G3-Cv4), a septimal comma narrower than
4:3;
> he described this interval as "crunchy."

I beg to differ. I believe he described the interval (a subfourth)
simply as dissonant. He described the _chord_ as crunchy, as he did
all chords containing a single dissonant interval. I suggest that the
most familiar example of a crunchy chord is the major seventh chord. I
also wonder if a chord with a root, a perfect fifth and both a major
and minor third, is in some sense the simplest crunchy tetrad, and the
_most_ crunchy by Keenan Pepper's definition?

Regards,
-- Dave Keenan

Greetings,

Thanks VERY much for your message and greeting.

So well written, so informative. You are a marvel of erudition. I've read
your posts (recent and in the past off the mills list I think) with
amazement. Brilliant.

I'm interested in the neo Gothic tuning in part because I have a medieval
project I'd like to provide a striking sound for. I will investigate
further, but please forgive me as I am slow of mind by nature and short of
time by circumstance. But if I come to understand it and it fits the
project, then I might come sit at your feet and learn what I can. That is
NOT meant in a derogatory fashion. I'm on this list to learn what I can and
you know a HUGE amount and are strikingly willing to share.

My reference to Just had more to do with justice than a tuning scheme per
se. In all honesty I am not and for personal reasons can never be an
adherent of any one tuning scheme (sorry to all who might be offended by
that, though I expect no one will be really).

But I am also aware that tuning is something we need to live with in order
to come to terms with its characteristics and there will be a limited number
of schemes we can really absorb. At least this is what I think. I wonder
what others think on this point...

Further, it seems to me that there are physiological reason for some sounds
appealing to some people and not others. Some of the warped canons made my
teeth itch and that cannot be a comment upon the validity of the scheme,
just my physiology.

Again, thank you for sharing your knowledge and for the welcome!

All best wishes,
Gordon Rumson
Pianist and composer

"Has it ever occurred to anyone that the reason government funded schools do
not function well is that it is in the government¹s interest not to have an
intelligent electorate?" A question by Gordon Rumson...

Web page: http://www.cadvision.com/Home_Pages/accounts/liszt/rumson.html

Hi Dave K. and everybody,

5/4
/ \
/ \
/ \
1/1-----3/2
\ /
\ /
\ /
6/5

This chord has been tagged the bimodal chord by Cuban composer Enrique
Ubieta -- "The essence of the harmonic discipline of Bimodalism lies
in the simultaneous blending of major and minor modes in triads with
the same fundamental root."

Keep in mind that chords that fit the "crunchy" criteria don't
necessarily sound anything alike. Like most chords that mix minor and
major sonorities, I think piquant seems an apt description for this
chord; Ubieta actually refers to it as a triad -- "Although the
bimodal chord does in fact consist of four sounds (such as C-Eb-E-G),
I will refer to it as a triad, in keeping with the lexicon of
harmony."

Ubieta wrote that "by joining major and minor triads (and only these
triads) of the same root on each degree of the chromatic scale, we
obtain 12 bimodal chords".

I tried my hand at taking this basic premise down a generalized
diatonic line of reasoning and pretty much concluded that 9 equal is
to the "bimodal triad" what 7 equal is to the "major triad". (I latter
started using a 9 out of 20 bimodal scale as one possible microtonal
extension of Ubieta's ideas.)

Ubieta is an accomplished composer with a beautiful feel for guitar
compositions. He recently sent me "three solo works in bimodal
harmony" -- two for guitar, and one for harpsichord. I tried to turn
him towards the charm and potential of his ideas in non 12 tunings,
but he seemed quite content where he is, and seemed to think that was
an avenue best pursued by others.

--Dan Stearns

Hello, there, Paul Erlich and Dave Keenan, and thank you both very much
for your important correction to my article about Keenan Pepper's
"crunchy" 16:21:24:28 sonority. As you'll see, I warmly embrace the
substance of this correction, with a small friendly emendation.

In addition to very rightly focusing our attention on what Keenan
Pepper himself did and did not say about the concept of "crunchiness,"
your remarks have given me the opportunity to consider and clarify
some evident differences between Pepper's perception of this sonority
and mine.

First, please let me accept the correction you both offer than Keenan
Pepper indeed refers to 16:21:24:28 as a "crunchy" sonority, but does
not use this term _specifically_ for the narrow fourth at 21:16.

While as you note, Paul, this may be a "small correction," it's a
significant one: someone reading my article might get the idea that
Pepper's concept of "crunchiness" focuses especially on 21:16 or its
qualities as a simple interval.

In fact, as you both very aptly sum up, Pepper's crunchiness is
primarily a property of sonorities such as 16:21:24:28 where a single
interval is deemed, ideally, to contribute more dissonance than all of
the others combined.

To show how well-taken this general point of emphasis and focus is,
Paul and Dave, I'm including a link to Keenan Pepper's original post
of 27 August 2000:

/tuning/topicId_11922.html#11922

Now we come to my friendly emendation. While Pepper does not
_specifically_ refer to 21:16 as a "crunchy interval," he does more
generally sanction this usage by using the term "crunchy" for either a
sonority as a whole, or its most tense or dissonant interval:

> My goal is to find a cruchy chord in which the harmonic entropy of
> the crunchy interval is more than the sum of all the other entropies
> combined. Such a chord would be as crunchy as ice cold raw green
> pepper, proven to be the most crunchy food.

Thus we might indeed refer to 16:21:24:28 as a "crunchy chord" or
sonority, and also the 21:16 narrow fourth as a "crunchy interval,"
while following the original Pepperian usage.

However, I enthusiastically embrace the substance of your correction:
especially for readers who may not already be familiar with Pepper's
elegant presentation, to illustrate the concept of "crunchiness" by
giving as a first example a simple interval such as 21:16 is to
confuse rather than clarify this concept.

Now we come to the more subjective side of this discussion:
considering your remarks has led me to the conclusion that my emphasis
on the 21:16 narrow fourth itself may reflect my own musical viewpoint
rather than Pepper's.

To me, while this type of fourth is indeed intensely dissonant in many
timbres -- the term "Wolf" is not too much of an exaggeration of the
effect of those "howling" beats -- it can be more or less concordant
in others. For example, I've attempted in a vibraphone-like timbre to
use 9/23 octave (~469.57 cents) as a stable fourth, and succeded at
least in part as judged by my own ear.

This kind of experiment might be taken to support a "semi-Setharean"
interpretation of a familiar proverb: "You _can_ make a silk purse
from a sow's ear -- if the ear happens to belong to the listener."

Anyway, I warmly agree that in Pepper's presentation, the most
relevant thing about 21:16 is that it is "quite dissonant," to quote
his words, in contrast to my interest in "Sethareanizing" it.

Also, in discussing the overall effect of 16:21:24:28, Pepper remarks
that the 21:16 is "quite dissonant, giving this chord the melancholy
sound common to all crunchy chords."

In contrast, I find this sonority spacious, energetic, radiant, like
an expanse of interstellar space filled with illumination.

Could these different impressions reflect the variable of timbre, or
other factors?

Anyway, having accepted a very helpful correction and considered these
different responses to a beautiful sonority, I would like to conclude
by agreeing with Dave Keenan that a sonority such as 20:24:25:30
(e.g. C4-Eb4-E4-G4 in 5-limit just intonation, with C4 as middle C)
might be an ideal example of "crunchiness."

Here we have a pure 3:2 fifth (C4-G4), two pure 5:4 major thirds
(C4-E4, Eb4-G4), and two pure 6:5 minor thirds (C4-Eb4, E4-G4) -- plus
an outstandingly dissonant 25:24 chromatic semitone (Eb4-E4).

While the use of such sonorities in "Blues-like" styles has sometimes
been interpreted as an effort to approximate a neutral third by
sounding both major and minor forms of this interval at the same time,
"crunchiness" is an attractive alternative explanation, and would fit
Pepper's suggested "melancholy" quality for crunchy sonorities.

Most appreciatively,

Margo Schulter
mschulter@value.net

--- In tuning@y..., Gordon Rumson <RUMSONG@C...> wrote:
>
> "Has it ever occurred to anyone that the reason government funded
schools do
> not function well is that it is in the government¹s interest not to
have an
> intelligent electorate?" A question by Gordon Rumson...

Sorry for posting a non-tuning reply here, but I just *can't* let
this howler go by without expressing my strong disapproval. In the
first place, you present no evidence to support the claim that
government-funded schools do not function well. I happen to be a
product of public schools and I take great offense at the implication
that my education or my teachers are or were in *any* way inferior to
anyone else's! How do you define whether a school functions well or
not? Which specific government-funded schools do you claim do not
function well?

And to claim that it is in the government's interest not to have an
intelligent electorate? That doesn't insult just me -- it insults
*millions* of hard-working people! I'd like very much to be able to
get back to tuning, but please ... if you're going to post political
propaganda, take it to a list where it will be appreciated. If you
posted garbage like this to one of *my* lists, I'd ban your sorry
tush in a heartbeat!
--
M. Edward (Ed) Borasky, Chief Scientist, Borasky Research
http://www.borasky-research.net http://www.aracnet.com/~znmeb
mailto:znmeb@borasky-research.com mailto:znmeb@aracnet.com

If there's nothing to astrology, how come so many famous men were
born on holidays?

Greetings,

A recent letter has drawn negative attention to one of my signature lines
and caused the writer to call for my unsubbing.

I am very sorry that my signature line offended him so much. I suggested to
him that he simply in future delete my messages, but this is not a fair
suggestion to him. He is entitled to operate in a place where he feels
comfortable.

Therefore, I think it is in the best interests of all if I simply unsub. I
do not wish for a 'variation' of recent list troubles to be caused by _my_
emails. The subject should remain tuning and I will do what I can to
facilitate that.

Goodbye and happy tuning!

Please note: I will not reply to any messages from tuning list members.
This is designed to keep the peace by allowing the situation to fade out. I
would prefer to not receive any further flames.

Please accept my apology.

All best wishes,
Gordon Rumson
Pianist and composer

"Has it ever occurred to anyone that the reason government funded schools do
not function well is that it is in the government¹s interest not to have an
intelligent electorate?" A question by Gordon Rumson...

Web page: http://www.cadvision.com/Home_Pages/accounts/liszt/rumson.html

Ed!
First get some humor!

Guess what,*millions* of hard-working people need to get insulted. Look what they watch on TV.
Look at what they listen to. Look at what they value and look at who they elect! and allow to
seize power. Watch how they execute. I could go on. Look at how the constitution has been taken as
a document invalid if it validates trade laws. Gordon question only suffers in that it implies
that there are still countries (well they are like states now).
Gordon stay on the list

Ed Borasky wrote:..

> Sorry for posting a non-tuning reply here, but I just *can't* let
> this howler go by without expressing my strong disapproval. In the
> first place, you present no evidence to support the claim that
> government-funded schools do not function well. I happen to be a
> product of public schools and I take great offense at the implication
> that my education or my teachers are or were in *any* way inferior to
> anyone else's! How do you define whether a school functions well or
> not? Which specific government-funded schools do you claim do not
> function well?
>
> And to claim that it is in the government's interest not to have an
> intelligent electorate? That doesn't insult just me -- it insults
> *millions* of hard-working people! I'd like very much to be able to
> get back to tuning, but please ... if you're going to post political
> propaganda, take it to a list where it will be appreciated. If you
> posted garbage like this to one of *my* lists, I'd ban your sorry
> tush in a heartbeat!
>

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

[Ed Borasky wrote:]
>if you're going to post political propaganda, take it to a list where
>it will be appreciated. If you posted garbage like this to one of *my*
>lists, I'd ban your sorry tush in a heartbeat!

Nice going, Ed: your gratuitous rant has caused a new member, someone
who very obviously loves music and alternate tunings, to apologize and
leave the list. I think YOU are the one who should be apologizing!

First off: you want to debate government schools? I'll take you on,
with pleasure!! We can do it on metatuning, tuning_gossip,
tuning-challenges, or any place else where we won't clutter the big
tuning list.

Second point: this is a _signature tag_, a throw-away line after the
substance of a post is through. You yourself have such tags, howbeit
that they're fluff (your choice). Wouldn't it be more appropriate to
focus your eyes on the substance of anyone's posts?

Third point: saying that government schools stink is NOT the same as
insulting their teachers or graduates. My own wife teaches in
government schools, and _I_ insult them without insulting her. She is
capable understanding the difference; why aren't you?

JdL

"Has it ever occurred to anyone that the reason government funded
schools do not function well is that it is in the government's interest
not to have an intelligent electorate?" A question by Gordon Rumson...