Yahoo Tuning Groups Ultimate Backup tuning Modes of porcupine[7]

I was explaining Porcupine[7] to some of my friends. I showed them
some comma pumps from it from my handy dandy iPhone app. Since they
seemed to think it was cool, the discussion turned eventually into how
we need to name the modes for it. I said that there are a infinite
amount of scales, and we have no way to reference the modes for any of
them. So I explained what a "generator" was, and conjectured a
universal system would have to be something like 1 generators going
up, two generators going up, etc. I proposed something like "1up,"
"2up," "3up," etc as shorthand for this.

My friend Steve had no idea why I was bombarding him with ridiculous
math and instead decided that Delorean mode was the way to go. He then
suggested Fallopian mode as well. I decided he was on the right track
and threw Presbyterian mode into the mix, and conjectured that perhaps
Barbarian mode might be a good option. Someone suggested Lesbian mode
in addition as being vaguely plausible.

Then tonight, after posting it on Facebook, my other friend Steve
suggested Aryan and Antidisestablishmentarian mode. This gives us 7
modes. For porcupine[8], it seemed natural that the last mode should
be Mixoantidisestablishmentarian mode, but after my ubiquitously drunk
friend Urie popped up on my Facebook wall, we're changing that to
Bacardian mode. So that makes 8 - Delorian, Fallopian, Presbyterian,
Lesbian, Barbarian, Aryan, Antidisestablishmentarian, and Bacardian
mode. Now we're set.

...

There is a huge divide between this community and real life musicians.
Real life musicians are interested in this stuff, but when they ask me
to explain it, I have no idea where to begin. My friend Steve, the
first Steve I mentioned, is one of the most musically talented people
on the planet, but he hates math. He doesn't want to hear me talk
about overtones and frequency ratios, he doesn't want to hear about
MOS scales, the word "temperament" makes his eyes glaze over, and when
I say "rank 2" he probably thinks I'm talking about the military.
We're dealing with people can barely handle that the whole thing is
called "the porcupine scale" to begin with. They cannot handle phrases
like "porcupine generator," nor can they handle the phrase "Hanson
pump" either. I have no idea how they'll react if I ever mention
Mothra or Wuerschmidt.

It's not even just this one issue. The divide manifests itself in
subtle little ways. For instance, at one point, I found myself
demonstrating the difference between 6/5 and 7/6, and then 9/7 vs 5/4.
Then, in the ensuing discussion, I dropped the "subminor" and
"supermajor" terminology. Now, we don't notice this when we're typing,
but "supermajor" is very unwieldy to say. It's four syllables. It's
not very hip. It sounds dumb. So I tried to just call it a "super
third," because that's much easier, and also saves calories.

My friend Tivon, who I was talking to at the time, finally had enough
of the uber-dorky phrase "super third" and decided we were going to
call them diminished and augmented thirds like normal people. I of
course told him subminor thirds were more like augmented seconds. Now,
another thing that we don't realize on this list is that this to call
7/6 an augmented second is absolutely ridiculous, because they're not
seconds, they're thirds, as anyone with a pair of ears can very easily
tell you. So I think we settled on "little minor third" and "big minor
third" at the end. (If you're going to respond to this paragraph with
a quote from Rothenberg, read between the lines.)

I have no idea how to solve this problem. All I know is how musicians
learn, which is that they like to take what they know and extend it.
This doesn't necessarily mean that everything has to fit into a
diatonic framework, but it does mean that I wish we had easy
pedagogical techniques to draw them into the new paradigm. As it
stands, I have no idea how to explain most of this stuff without
resorting to group theory. All I know is - try using the phrase "minor
whole tone" and see what kind of reaction you get. Or go try to
explain negri temperament to someone in 19-equal. Also may God have
mercy on your soul. Maybe Igs or Carl or someone else has some good
tips for all of this.

Ironically enough, while they couldn't handle generators, visualizing
JI lattices and talking about "prime intervals" seemed to pose no
trouble at all. So I don't get it.

-Mike

🔗cityoftheasleep <igliashon@...>

You should show your friends my Negri video and see what they think. I'm also uploading a 16-EDO video right now that you should show them, using the 5L+1s scale.

(Side note: Ron Sword calls 16-EDO's 5L+1s scale "Cynder". I don't think it's Cynder, though, because that's another name for Mothra and Mothra tempers out 1029/1024 and 81/80, whereas this scale tempers 135/128 instead of 81/80. I guess this makes it very much a gamelan temperament, since these two commas are respectively the gamelisma and the pelogic comma. Does it have a name somewhere?)

Anyway, these videos I've been making for YouTube reflect my best guess at the best way to present these scales. Whenever I show someone one of my guitars, I always start with the chords they're good and/or bad for, then maybe a couple scales, then I hand the instrument over and let them noodle around. (Interesting side-note: I recently showed someone my 19-EDO and 16-EDO guitars, and after playing both he thought 16-EDO sounded more "normal" and 19-EDO sounded out-of-tune. How do you like THEM apples??) I've found that it's usually a bad idea to try to explain anything too in-depth in a friendly conversation. Eventually I'll have a book to show people, but in the meantime I'm going to try to pump out a bunch of instructional videos.

What seems to be the most important thing is to go into as little background as possible. People don't know (and often don't want to know) anything about the psychoacoustic reasons we use 12-TET. They just know they like the sound of it and it's "normal". Absolutely the most important thing to do when showing off a new tuning is to show that it doesn't sound too weird to care about, but sounds weird enough to be different. Don't give them more information than they ask for, and under NO circumstances should you introduce any new terminology unless it's absolutely essential to answer a question they've asked. One question NO ONE has ever asked me is "why DOESN'T this sound bad to me?", and that is the ONLY question that would merit any discussion of psychoacoustics.

Visual aids can help as well--showing them how tunings and scales compare visually to a major or minor scale or 12-TET itself is great. This shows them how these new scales live "in the cracks" between familiar notes. You pretty much HAVE TO relate everything back to 12-TET, at least in the beginning. Some people might get really into this, and for those people you can start going into the bigger picture, but for most people it's an idle curiousity and they get bored quickly when you start barraging them with new information that they can't relate back to what they know.

Coming up with wacky mode names for Porcupine is great. Humor is immensely important here because it maintains interest. I used to hate the wacky hodge-podge of temperament names, but the more I try to explain this stuff to regular musicians, the more I appreciate names like "Godzilla" and "Orwell".

I wish Jacob and Andrew were still active here. They'd surely have excellent contributions to this topic.

-Igs

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> I was explaining Porcupine[7] to some of my friends. I showed them
> some comma pumps from it from my handy dandy iPhone app. Since they
> seemed to think it was cool, the discussion turned eventually into how
> we need to name the modes for it. I said that there are a infinite
> amount of scales, and we have no way to reference the modes for any of
> them. So I explained what a "generator" was, and conjectured a
> universal system would have to be something like 1 generators going
> up, two generators going up, etc. I proposed something like "1up,"
> "2up," "3up," etc as shorthand for this.
>
> My friend Steve had no idea why I was bombarding him with ridiculous
> math and instead decided that Delorean mode was the way to go. He then
> suggested Fallopian mode as well. I decided he was on the right track
> and threw Presbyterian mode into the mix, and conjectured that perhaps
> Barbarian mode might be a good option. Someone suggested Lesbian mode
> in addition as being vaguely plausible.
>
> Then tonight, after posting it on Facebook, my other friend Steve
> suggested Aryan and Antidisestablishmentarian mode. This gives us 7
> modes. For porcupine[8], it seemed natural that the last mode should
> be Mixoantidisestablishmentarian mode, but after my ubiquitously drunk
> friend Urie popped up on my Facebook wall, we're changing that to
> Bacardian mode. So that makes 8 - Delorian, Fallopian, Presbyterian,
> Lesbian, Barbarian, Aryan, Antidisestablishmentarian, and Bacardian
> mode. Now we're set.
>
> ...
>
> There is a huge divide between this community and real life musicians.
> Real life musicians are interested in this stuff, but when they ask me
> to explain it, I have no idea where to begin. My friend Steve, the
> first Steve I mentioned, is one of the most musically talented people
> on the planet, but he hates math. He doesn't want to hear me talk
> about overtones and frequency ratios, he doesn't want to hear about
> MOS scales, the word "temperament" makes his eyes glaze over, and when
> I say "rank 2" he probably thinks I'm talking about the military.
> We're dealing with people can barely handle that the whole thing is
> called "the porcupine scale" to begin with. They cannot handle phrases
> like "porcupine generator," nor can they handle the phrase "Hanson
> pump" either. I have no idea how they'll react if I ever mention
> Mothra or Wuerschmidt.
>
> It's not even just this one issue. The divide manifests itself in
> subtle little ways. For instance, at one point, I found myself
> demonstrating the difference between 6/5 and 7/6, and then 9/7 vs 5/4.
> Then, in the ensuing discussion, I dropped the "subminor" and
> "supermajor" terminology. Now, we don't notice this when we're typing,
> but "supermajor" is very unwieldy to say. It's four syllables. It's
> not very hip. It sounds dumb. So I tried to just call it a "super
> third," because that's much easier, and also saves calories.
>
> My friend Tivon, who I was talking to at the time, finally had enough
> of the uber-dorky phrase "super third" and decided we were going to
> call them diminished and augmented thirds like normal people. I of
> course told him subminor thirds were more like augmented seconds. Now,
> another thing that we don't realize on this list is that this to call
> 7/6 an augmented second is absolutely ridiculous, because they're not
> seconds, they're thirds, as anyone with a pair of ears can very easily
> tell you. So I think we settled on "little minor third" and "big minor
> third" at the end. (If you're going to respond to this paragraph with
> a quote from Rothenberg, read between the lines.)
>
> I have no idea how to solve this problem. All I know is how musicians
> learn, which is that they like to take what they know and extend it.
> This doesn't necessarily mean that everything has to fit into a
> diatonic framework, but it does mean that I wish we had easy
> pedagogical techniques to draw them into the new paradigm. As it
> stands, I have no idea how to explain most of this stuff without
> resorting to group theory. All I know is - try using the phrase "minor
> whole tone" and see what kind of reaction you get. Or go try to
> explain negri temperament to someone in 19-equal. Also may God have
> mercy on your soul. Maybe Igs or Carl or someone else has some good
> tips for all of this.
>
> Ironically enough, while they couldn't handle generators, visualizing
> JI lattices and talking about "prime intervals" seemed to pose no
> trouble at all. So I don't get it.
>
> -Mike
>

🔗genewardsmith <genewardsmith@...>

🔗cityoftheasleep <igliashon@...>

🔗Herman Miller <hmiller@...>

🔗cityoftheasleep <igliashon@...>

🔗Mike Battaglia <battaglia01@...>

On Sun, May 8, 2011 at 12:57 PM, cityoftheasleep
<igliashon@...> wrote:
>
> You should show your friends my Negri video and see what they think. I'm also uploading a 16-EDO video right now that you should show them, using the 5L+1s scale.

I dug the Negri video, but I think it would be too out there for them.
In general, I think what would work really well are more free improvs
like you have up with your 16 and 17-EDO improvs, where you just play
stuff that sounds good and play things like comma pumps just as they
come up.

> Anyway, these videos I've been making for YouTube reflect my best guess at the best way to present these scales. Whenever I show someone one of my guitars, I always start with the chords they're good and/or bad for, then maybe a couple scales, then I hand the instrument over and let them noodle around. (Interesting side-note: I recently showed someone my 19-EDO and 16-EDO guitars, and after playing both he thought 16-EDO sounded more "normal" and 19-EDO sounded out-of-tune. How do you like THEM apples??)

In what sense did they hear 19-EDO as being out of tune?

> What seems to be the most important thing is to go into as little background as possible. People don't know (and often don't want to know) anything about the psychoacoustic reasons we use 12-TET. They just know they like the sound of it and it's "normal". Absolutely the most important thing to do when showing off a new tuning is to show that it doesn't sound too weird to care about, but sounds weird enough to be different. Don't give them more information than they ask for, and under NO circumstances should you introduce any new terminology unless it's absolutely essential to answer a question they've asked. One question NO ONE has ever asked me is "why DOESN'T this sound bad to me?", and that is the ONLY question that would merit any discussion of psychoacoustics.

I've heard that plenty of times. "Why does this work? It violates
{insert simplified xyz principle that bastardizes Rothenberg we all
learned in music school}". Then the answer puts them to sleep.

-Mike

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> I dug the Negri video, but I think it would be too out there for them.

Stylistically or informationally?

> In general, I think what would work really well are more free improvs
> like you have up with your 16 and 17-EDO improvs, where you just play
> stuff that sounds good and play things like comma pumps just as they
> come up.

As opposed to what? Sticking to a particular scale, or including information about the scale I'm using?

> In what sense did they hear 19-EDO as being out of tune?

It was mostly the non-diatonic intervals they didn't like--subminors and supermajors. When I played some 5-limit chords they thought they sounded "normal" and didn't notice anything especially "more in-tune". On the other hand, the warbly fifth of 16-EDO proved to be a source of great fascination, as did the neutral 2nd. One of my friends spent a good five minutes playing what was basically Mavila in the open position and thought it sounded totally normal.

> I've heard that plenty of times. "Why does this work? It violates
> {insert simplified xyz principle that bastardizes Rothenberg we all
> learned in music school}". Then the answer puts them to sleep.

That's because you're answering them in the wrong way. Say you went to cooking school and studied French cuisine in great depth. Say you were taught all sorts of rules about how different flavors and ingredients should be combined and so on. Then say you go out to a Thai restaurant where all the rules you were taught are broken, but you love the food. You ask your friend Bill (who is a food scientist and also a pretty good cook in his own right) why this food--which breaks all the rules of French cuisine--tastes so good. He launches into a long diatribe about the chemistry of flavor and the anatomy of the tongue and the neurophysiology of taste perception. Sure, his answer might be technically correct and very informative, but it probably won't succeed in answering your question because you won't understand most of it and will probably get bored and tune it out.

Now imagine you ask your friend Zombo (a worldly chap who spends all his free time and money traveling the world and sampling the cuisines of various cultures) the same question. His response is short and simple: "the rules of French cuisine are not universal. Lots of things can taste good if you have an open mind and an adventurous spirit. There are very few absolutes and most "rules" are culture-specific, not universal. To make good food, all one needs is a sensitive tongue, a desire to experiment, and a bit of common sense (and maybe a bit of basic knowledge about how to properly and safely use various cooking implements found in a kitchen)."

Granted, if you were already interested in food science a little bit, you might appreciate Bill's answer a bit more than Zombo's. But if you're just interested in cooking and eating, Bill's answer will turn you off and maybe even make you regret you asked the question. Zombo's answer, OTOH, will probably open your mind a bit and maybe inspire you to experiment a bit with breaking some of your usual rules. This is a much better outcome, and the outcome we should strive for when talking with regular musicians. It's better to foster an attitude of curiousity and experimentalism than to try to inculcate a rigorous factual understanding. The deeper math/science stuff should only ever be introduced after someone is already making their own microtonal music and is looking to answer questions/solve problems that can't really be solved any other way, or unless they're already versed in math and/or physics and/or psychoacoustics.

-Igs

🔗Mike Battaglia <battaglia01@...>

On Mon, May 9, 2011 at 10:07 PM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > I dug the Negri video, but I think it would be too out there for them.
>
> Stylistically or informationally?
//snip
> As opposed to what? Sticking to a particular scale, or including information about the scale I'm using?

Stylistically, I think. Musically, maybe. I don't know. They generally
hear lots of stuff as being "out of tune." I'm trying to find more
examples that magically end up sounding in tune, in ways they can't
explain. I think if I showed them Negri they'd end up hearing chords
that are moving by strange root movements, such that the whole thing
sounds disconnected. They could probably get used to it eventually,
but I don't think they'd hear the logic in it at first. I'm not sure I
myself can wrap my head around it.

> > In what sense did they hear 19-EDO as being out of tune?
>
> It was mostly the non-diatonic intervals they didn't like--subminors and supermajors. When I played some 5-limit chords they thought they sounded "normal" and didn't notice anything especially "more in-tune". On the other hand, the warbly fifth of 16-EDO proved to be a source of great fascination, as did the neutral 2nd. One of my friends spent a good five minutes playing what was basically Mavila in the open position and thought it sounded totally normal.

Did they get to play with 15-equal at all?

-Mike

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> Stylistically, I think. Musically, maybe. I don't know. They generally
> hear lots of stuff as being "out of tune." I'm trying to find more
> examples that magically end up sounding in tune, in ways they can't
> explain. I think if I showed them Negri they'd end up hearing chords
> that are moving by strange root movements, such that the whole thing
> sounds disconnected. They could probably get used to it eventually,
> but I don't think they'd hear the logic in it at first. I'm not sure I
> myself can wrap my head around it.

Interesting. I don't think Negri sounds weird at all. It sounds generically "arabic" to me, reminiscent of the harmonic minor scale but with a few xentonal movements thrown in. If you put it in 19-EDO meantone notation with the LLLLLsLLLL mode starting on E, you get E F Gb G# A Bb B C Db D# E, which becomes a 7-note scale if you drop the flats, E F G# A B C D# E, which permuted to use A as the tonic gives you A B C D# E F G# A. This sounds similar to A harmonic minor but with a #4, but it still lets you do the usual V-i cadence. Going back to E as the tonic, you can do the whole flamenco I-bII-I thing, or (expanding back to 10 notes and going back to A as the tonic) you can do a really neat variation on the usual i-VII-VI-V-i (a la "Walk Don't Run") progression that replaces the VII with a #vii. The weirdest-sounding thing in the 5-limit you can do is (back to E as the tonic) a I-#II movement, or else the I-bv movement. Otherwise it all sounds pretty vanilla to me.

> Did they get to play with 15-equal at all?

No, but I think that would have gone over really well. Maybe even the best. I think I might try to convert my nylon-string to 15-EDO myself eventually. After f***ing around with 20 for a while now, I think I do actually prefer 15. It's easier on the fingers, and after playing around with Negri a bunch I think I could navigate Porcupine better than I used to be able to. Also it's just so damn easy to play in and it's really fun. I could use a guitar that's really fun and easy to play but isn't 12.

-Igs

🔗Graham Breed <gbreed@...>

Mike Battaglia <battaglia01@...> wrote:

> It's not even just this one issue. The divide manifests
> itself in subtle little ways. For instance, at one point,
> I found myself demonstrating the difference between 6/5
> and 7/6, and then 9/7 vs 5/4. Then, in the ensuing
> discussion, I dropped the "subminor" and "supermajor"
> terminology. Now, we don't notice this when we're typing,
> but "supermajor" is very unwieldy to say. It's four
> syllables. It's not very hip. It sounds dumb. So I tried
> to just call it a "super third," because that's much
> easier, and also saves calories.

That's normally fine because if there are submajor and
superminor thirds, they'll be classed as "neutral
thirds".

Note that the original (and, possibly, linguistically
correct) term was "supramajor thirds". I go for "super"
because it's more familiar to most of us. They're also
called "car horn thirds" because car horns really were
tuned to them.

> My friend Tivon, who I was talking to at the time,
> finally had enough of the uber-dorky phrase "super third"
> and decided we were going to call them diminished and
> augmented thirds like normal people. I of course told him
> subminor thirds were more like augmented seconds. Now,
> another thing that we don't realize on this list is that
> this to call 7/6 an augmented second is absolutely
> ridiculous, because they're not seconds, they're thirds,
> as anyone with a pair of ears can very easily tell you.
> So I think we settled on "little minor third" and "big
> minor third" at the end. (If you're going to respond to
> this paragraph with a quote from Rothenberg, read between
> the lines.)

I much prefer "subminor" to "diminished". If you want to
think of them this way, one interpretation is that the
difference between 6/5 and 7/6 is the same as that between
5/4 and 6/5. That amounts to 25:24 being the same interval
as 36:35. That, in turn, leads to 875:864 being tempered
out.

http://x31eq.com/cgi-bin/uv.cgi?uvs=875/864

The general case as apparently called "Supermagic" so
875:864 must be the supermagic comma. Magic is, of course,
part of the family. Other notable members are Keemun,
Flattone, Porcupine, Doublewide, Superkleismic, Sycamore,
and Dicot. (This is all from following the link.)

> I have no idea how to solve this problem. All I know is
> how musicians learn, which is that they like to take what
> they know and extend it. This doesn't necessarily mean
> that everything has to fit into a diatonic framework, but
> it does mean that I wish we had easy pedagogical
> techniques to draw them into the new paradigm. As it
> stands, I have no idea how to explain most of this stuff
> without resorting to group theory. All I know is - try
> using the phrase "minor whole tone" and see what kind of
> reaction you get. Or go try to explain negri temperament
> to someone in 19-equal. Also may God have mercy on your
> soul. Maybe Igs or Carl or someone else has some good
> tips for all of this.

This is why I identified it as a paradigm. You have to
assume a paradigm to explain things within it. Alternative
regular temperaments can be explained withing the diatonic
paradigm, but it becomes unwieldy. You can
make everything relative to a porcupine diatonic but at
some point you need to identify the equivalent of the
spiral of fifths, and then you need the generator.

> Ironically enough, while they couldn't handle generators,
> visualizing JI lattices and talking about "prime
> intervals" seemed to pose no trouble at all. So I don't
> get it.

How about 5-limit lattices with added 9-limit sub and super
thirds? There are others:

http://x31eq.com/lattice.htm#alt7limit

I find lattices to be useful, especially in two dimensions,
which amounts to a planar temperament. They were, in the
past, considered a sign of over-mathematicizing. That was
a shame because they're a simple way of presenting harmonic
relationships and they make use of spatial thinking.

Graham

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

On Tue, May 10, 2011 at 3:35 AM, Graham Breed <gbreed@...> wrote:
>
> Note that the original (and, possibly, linguistically
> correct) term was "supramajor thirds". I go for "super"
> because it's more familiar to most of us. They're also
> called "car horn thirds" because car horns really were
> tuned to them.

Were they tuned like that on purpose?

> The general case as apparently called "Supermagic" so
> 875:864 must be the supermagic comma. Magic is, of course,
> part of the family. Other notable members are Keemun,
> Flattone, Porcupine, Doublewide, Superkleismic, Sycamore,
> and Dicot. (This is all from following the link.)

The specific reason I didn't want to have him think of it this way is
that I didn't want him to have to get used to flattone. It's more like
a semi-diminished third than a diminished third. But maybe that's a
good way to draw people into the new paradigm - teach them å cognitive
structure in which 875/864 vanishes just for simplicity's sake, so
they can catch on, then draw them away from it later once they get the
concept and realize it's not always the best way to temper.

> This is why I identified it as a paradigm. You have to
> assume a paradigm to explain things within it. Alternative
> regular temperaments can be explained withing the diatonic
> paradigm, but it becomes unwieldy. You can
> make everything relative to a porcupine diatonic but at
> some point you need to identify the equivalent of the
> spiral of fifths, and then you need the generator.

What do you mean the equivalent of the spiral of fifths? Is the
equivalent of the spiral of fifths in porcupine the spiral of 10/9's?
Or are you saying that 3/2 is relevant?

> > Ironically enough, while they couldn't handle generators,
> > visualizing JI lattices and talking about "prime
> > intervals" seemed to pose no trouble at all. So I don't
> > get it.
>
> How about 5-limit lattices with added 9-limit sub and super
> thirds? There are others:
>
> http://x31eq.com/lattice.htm#alt7limit

Like having them think in terms of the marvel-tempered lattice? Sure,
why not? It might also be useful for them to think in terms of the
supermagic-tempered lattice, just because it's intuitive, and then
have them break away from it later on.

For them to break away from meantone, it might also be useful for them
to think in terms of there being just two new intervals - something
called a "comma," and something called a "diesis" (or we can pick
better names). 64/63, and 81/80, and the pythagorean comma, and really
as many commas as possible, should all become tempered to the same
"comma" entity, meaning that the schisma has to vanish along with some
other things. The same should apply to the diesis - the addition of a
diesis should transform 7/6 into 6/5, and 4/3 into 11/8, and 75/64
into 6/5, which I suppose means that 225/224 is tempered in addition
to some other things. The above setup also would mean that one diesis
is two commas, that would be even better. I'm not sure what resulting
temperament this would be, probably some 11-limit extension of
schismatic or something.

-Mike

🔗Graham Breed <gbreed@...>

On 10 May 2011 16:32, Mike Battaglia <battaglia01@...> wrote:
> On Tue, May 10, 2011 at 3:35 AM, Graham Breed <gbreed@...> wrote:
>>
>> Note that the original (and, possibly, linguistically
>> correct) term was "supramajor thirds". I go for "super"
>> because it's more familiar to most of us. They're also
>> called "car horn thirds" because car horns really were
>> tuned to them.
>
> Were they tuned like that on purpose?

Apparently, yes. The resulting sound is most penetrating against
background traffic noise.

>> The general case as apparently called "Supermagic" so
>> 875:864 must be the supermagic comma. Magic is, of course,
>> part of the family. Other notable members are Keemun,
>> Flattone, Porcupine, Doublewide, Superkleismic, Sycamore,
>> and Dicot. (This is all from following the link.)
>
> The specific reason I didn't want to have him think of it this way is
> that I didn't want him to have to get used to flattone. It's more like
> a semi-diminished third than a diminished third. But maybe that's a
> good way to draw people into the new paradigm - teach them å cognitive
> structure in which 875/864 vanishes just for simplicity's sake, so
> they can catch on, then draw them away from it later once they get the
> concept and realize it's not always the best way to temper.

They'll have to learn more than one cognitive structure, and
eventually assimilate them in terms of different commas being tempered
out, or different combinations of equal temperaments, or whatever
concept they find useful to hang it on.

> What do you mean the equivalent of the spiral of fifths? Is the
> equivalent of the spiral of fifths in porcupine the spiral of 10/9's?
> Or are you saying that 3/2 is relevant?

The generator is generally the equivalent of the fifth in the spiral
of fifths. The simplest modulation between two scales is the same as
transposition by a generator. You can get simple chords or scales by
stacking generators. I'm saying one way that 3/2 is relevant in
traditional music is that it's the generator of meantone.

>> > Ironically enough, while they couldn't handle generators,
>> > visualizing JI lattices and talking about "prime
>> > intervals" seemed to pose no trouble at all. So I don't
>> > get it.
>>
>> How about 5-limit lattices with added 9-limit sub and super
>> thirds? There are others:
>>
>> http://x31eq.com/lattice.htm#alt7limit
>
> Like having them think in terms of the marvel-tempered lattice? Sure,
> why not? It might also be useful for them to think in terms of the
> supermagic-tempered lattice, just because it's intuitive, and then
> have them break away from it later on.

If they're starting with porcupine, it's better to learn the
supermagic lattice. If they're learning more temperament classes,
they'll have to learn that different approximations apply, and so
different lattices. The marvel lattice is a useful because it's
consistent with a lot of important temperaments.

> For them to break away from meantone, it might also be useful for them
> to think in terms of there being just two new intervals - something
> called a "comma," and something called a "diesis" (or we can pick
> better names). 64/63, and 81/80, and the pythagorean comma, and really
> as many commas as possible, should all become tempered to the same
> "comma" entity, meaning that the schisma has to vanish along with some
> other things. The same should apply to the diesis - the addition of a
> diesis should transform 7/6 into 6/5, and 4/3 into 11/8, and 75/64
> into 6/5, which I suppose means that 225/224 is tempered in addition
> to some other things. The above setup also would mean that one diesis
> is two commas, that would be even better. I'm not sure what resulting
> temperament this would be, probably some 11-limit extension of
> schismatic or something.

If you choose a small set of small intervals, you can define any equal
temperament in terms of the number of steps for each small interval.
16:15, 25:24, and 81:80 are a good set to start with. There's no need
to worry about dieses directly: you can always find them by
subtracting the number of steps for 16:15 and 25:24.

Anything that tempers out the schisma will be some kind of extension
of schismatic. Garibaldi tempers out 225:224.

Between 7/6 and 6/5 is 36:35. Between 4/3 and 11/8 is 33:32.
Equating 36:35 and 33:32 means tempering out 33/32*35/36 = 11/32*35/12
= 385:384. 11-limit Garibaldi does this.

Graham

🔗Mike Battaglia <battaglia01@...>

Igs, sorry I missed this.

On Mon, May 9, 2011 at 11:11 PM, cityoftheasleep
<igliashon@...> wrote:
>
>
> Interesting. I don't think Negri sounds weird at all. It sounds generically "arabic" to me, reminiscent of the harmonic minor scale but with a few xentonal movements thrown in. If you put it in 19-EDO meantone notation with the LLLLLsLLLL mode starting on E, you get E F Gb G# A Bb B C Db D# E, which becomes a 7-note scale if you drop the flats, E F G# A B C D# E, which permuted to use A as the tonic gives you A B C D# E F G# A. This sounds similar to A harmonic minor but with a #4, but it still lets you do the usual V-i cadence. Going back to E as the tonic, you can do the whole flamenco I-bII-I thing, or (expanding back to 10 notes and going back to A as the tonic) you can do a really neat variation on the usual i-VII-VI-V-i (a la "Walk Don't Run") progression that replaces the VII with a #vii. The weirdest-sounding thing in the 5-limit you can do is (back to E as the tonic) a I-#II movement, or else the I-bv movement. Otherwise it all sounds pretty vanilla to me.

That's an interesting way to put it. The arabic-ish sounding stuff
sounded pretty normal, but certain aspects of the rest of it sounded a
bit out. But I like out, as you know, so I didn't mind. After
listening to it again, I think for them they'd hear something that
sounds pretty normal most of the time (the phrygian dominant/phrygian
dominant #7 stuff) with a few "out of tune" notes thrown in. That's
how I think it'd go down with this group specifically.

> > Did they get to play with 15-equal at all?
>
> No, but I think that would have gone over really well. Maybe even the best. I think I might try to convert my nylon-string to 15-EDO myself eventually. After f***ing around with 20 for a while now, I think I do actually prefer 15. It's easier on the fingers, and after playing around with Negri a bunch I think I could navigate Porcupine better than I used to be able to. Also it's just so damn easy to play in and it's really fun. I could use a guitar that's really fun and easy to play but isn't 12.

I like them both. I think 15 is a better ET than 20 on the whole - 15
has porcupine and Blackwood, making it possibly the most xenharmonic
system in existence. Throw in stuff like triforce as well and you've
got yourself a clear winner. 20 has tetracot and Blackwood, which is
cool, but tetracot isn't anywhere near as cool as porcupine, not by a
long shot. Maybe the MODMOS's of tetracot are where it's at. But being
as I'm in this transitional period away from scales and more towards
harmony, I'm not sure how much I even care. The only reason I like
Blackwood is because of the 256/243 comma pump anyway.

Anyway, 20-equal is definitely more colorful than 15-equal blackwood,
that's for sure.

-Mike