Blackwood 7ths

So I wrote a stupid little tune in 15-EDO Blackwood[10] exploring the sound of the "seventh" chords, including the septimal otonal tetrad, utonal tetrad, and the 5-limit major and minor 7ths. It sounds pretty cheezy to me and I'm not at all proud of it, but I think it's important just to have a ready-to-hand example of what larger vertical harmony in 15-EDO sounds like (not very good).

/tuning/files/IgliashonJones/Blackwood7ths.mp3

This example was meant to help me see if 15-EDO really sounds like something I want to explore further (since I kept suspecting I would be into it) or if 22-EDO would be worth going back to. I have concluded that the answer to all of these is "no". My feeling with 15-EDO is that even its 7-limit properties don't give it any audible advantage over 12-TET/Dominant temperament. So if you're trying to pimp it as Blacksmith (the "uber-simple 7-limit temperament with 5 otonal and 5 utonal tetrads as well as 5 major and 5 minor 7th chords!) that's a bad idea because it doesn't sound anything like 7-limit JI and you're not fooling anybody. The point comes across, sure, but it's really rough and would probably bother the hell out of most people, so in 15-EDO your best bet is to do as I do and keep the harmony simple. It's just not very good as a full 7-limit temperament.

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:

> This example was meant to help me see if 15-EDO really sounds like something I want to explore further (since I kept suspecting I would be into it) or if 22-EDO would be worth going back to.

No and yes. Considering the dubious things you use, it's strange you turn up your nose at 22, which does a bang-up job on porcupine.

>It's just not very good as a full 7-limit temperament.

Agreed. Forget 15. Do not forget 22, especially for porcupine.

--- "cityoftheasleep" <igliashon@...> wrote:

> This example was meant to help me see if 15-EDO really sounds
> like something I want to explore further (since I kept suspecting
> I would be into it) or if 22-EDO would be worth going back to.
> I have concluded that the answer to all of these is "no". My
> feeling with 15-EDO is that even its 7-limit properties don't
> give it any audible advantage over 12-TET/Dominant temperament.
> So if you're trying to pimp it as Blacksmith (the "uber-simple
> 7-limit temperament with 5 otonal and 5 utonal tetrads as well
> as 5 major and 5 minor 7th chords!) that's a bad idea because
> it doesn't sound anything like 7-limit JI and you're not
> fooling anybody. The point comes across, sure, but it's really
> rough and would probably bother the hell out of most people,
> so in 15-EDO your best bet is to do as I do and keep the
> harmony simple. It's just not very good as a full 7-limit
> temperament.

I agree about blacksmith, but not the part about it meaning
22 is no good. And, I like 15 for 5-limit harmony when it's
done carefully. It's not as accurate as 12 but I really like
the blackwood comma pump and the melodic nature of the
blackwood decatonic.

-Carl

Sorry, there was meant to be a 2nd part to that post that I cutoff because my girlfriend got home.

I *also* wrote a little stupid ditty in 22-EDO Pajara:

/tuning/files/IgliashonJones/Pajara7ths.mp3

I spent a while on Graham's temperament finder comparing 7-limit temperaments, and concluded that Pajara is basically the top 7-limit temperament that is not near-optimal in 12-TET. I meant to edit out all the references to 22 in that other post, but I guess I missed one in my hurry.

What I was going to say is that after diddling around with Pajara again, I came to the conclusion that I still don't like it. And if I don't like Pajara, there's not much hope for me and 7-limit harmony, because the next-best temperaments to Pajara that aren't near-optimal in 12-TET all pretty much fail to match the harmonic efficiency of either Pajara or Blacksmith, meaning there are significant proportions of notes in the scales that aren't roots of some otonal or utonal tetrad or some major or minor 7th chord. I looked at Negri and Lemba, but both seem rather limited compared to Pajara. I think one would need to go up to 12-note scales to get close to Pajara, and that's not a jump I'm willing to make (I'd rather just abandon the idea of a scale altogether at that point).

Why don't I like Pajara? For one, it doesn't sound significantly different from 12-TET to me (I'm pretty sure all those tetrads wouldn't lose much in retuning to 12-TET), but more importantly, I got bored real quick with the sound of everything.

I'm pretty sure I actually just don't care much for music that emphasizes harmony so heavily. I think it's not so much Pajara or 7-limit harmony as it is that I'm actually somewhat of a minimalist, I'd prefer a melody or a soundscape or maybe a simple 3-part line over a large, intricate chord progression. I am a simple man, and I guess I just finally realized that the reason I like the tunings I like is because they are simple and they sound good when I do simple things with them.

And also, 12-TET is a damn good 7-limit temperament, apparently.

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> So I wrote a stupid little tune in 15-EDO Blackwood[10] exploring the sound of the "seventh" chords, including the septimal otonal tetrad, utonal tetrad, and the 5-limit major and minor 7ths. It sounds pretty cheezy to me and I'm not at all proud of it, but I think it's important just to have a ready-to-hand example of what larger vertical harmony in 15-EDO sounds like (not very good).
>
> /tuning/files/IgliashonJones/Blackwood7ths.mp3
>
> This example was meant to help me see if 15-EDO really sounds like something I want to explore further (since I kept suspecting I would be into it) or if 22-EDO would be worth going back to. I have concluded that the answer to all of these is "no". My feeling with 15-EDO is that even its 7-limit properties don't give it any audible advantage over 12-TET/Dominant temperament. So if you're trying to pimp it as Blacksmith (the "uber-simple 7-limit temperament with 5 otonal and 5 utonal tetrads as well as 5 major and 5 minor 7th chords!) that's a bad idea because it doesn't sound anything like 7-limit JI and you're not fooling anybody. The point comes across, sure, but it's really rough and would probably bother the hell out of most people, so in 15-EDO your best bet is to do as I do and keep the harmony simple. It's just not very good as a full 7-limit temperament.
>

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> Sorry, there was meant to be a 2nd part to that post that I cutoff because my girlfriend got home.
>
> I *also* wrote a little stupid ditty in 22-EDO Pajara:
>
> /tuning/files/IgliashonJones/Pajara7ths.mp3

Which sounds just fine, unlike your 15-EDO ditty.

> I spent a while on Graham's temperament finder comparing 7-limit temperaments, and concluded that Pajara is basically the top 7-limit temperament that is not near-optimal in 12-TET.

You obviously didn't spend nearly enough time, since if you put in 2, 3, 4, 5, 6, 7, 8, 9 or 10 cent target errors into Graham's machine, the answer which comes out is meantone. When you get to 11, dominant is optimal, but if we eliminate that on the grouds that 12 does such a good job with it, we are finally left with pajara.

I meant to edit out all the references to 22 in that other post, but I guess I missed one in my hurry.

> What I was going to say is that after diddling around with Pajara again, I came to the conclusion that I still don't like it. And if I don't like Pajara, there's not much hope for me and 7-limit harmony, because the next-best temperaments to Pajara that aren't near-optimal in 12-TET all pretty much fail to match the harmonic efficiency of either Pajara or Blacksmith, meaning there are significant proportions of notes in the scales that aren't roots of some otonal or utonal tetrad or some major or minor 7th chord.

Pajara is nifty, but I was pounding away on the thought of porcupine as a 22 temperament because unlike pajara, it gets us completely outside of the orbit of the familiar; it is not supported by 12.

> Why don't I like Pajara? For one, it doesn't sound significantly different from 12-TET to me (I'm pretty sure all those tetrads wouldn't lose much in retuning to 12-TET), but more importantly, I got bored real quick with the sound of everything.

Bah. It's significantly sweeter than 12.

> I'm pretty sure I actually just don't care much for music that emphasizes harmony so heavily.

It's about all I'm interested in, that and counterpoint. I don't much like minimalism or soundscapes.

> And also, 12-TET is a damn good 7-limit temperament, apparently.

In the age of electronics we can produce any tuning we wish, which reduces the attractiveness of low-complexity temperaments.

On Sat, May 28, 2011 at 12:47 PM, cityoftheasleep
<igliashon@...> wrote:
>
>
> What I was going to say is that after diddling around with Pajara again, I came to the conclusion that I still don't like it.

You might like the 5-limit version a lot more - chord progressions in
diaschismatic[10] have a certain "sound" that I think is simply
beautiful (check Petr's comma pump for an example). You end up with
two tonal centers that are a tritone apart - diaschismatic[10] relates
these and combines them into a single scale, so that they become two
sides of one coin. I usually don't support the notion that there's
anything special about scales but diaschismatic[10] really nails it in
this regard.

The 2.3.5.11 subgroup version of Pajara can also be used to (subtle)
musical effect, because it can be used to create tetrachordal scales
that contain 16:17:18:20 starting on 1/1, 4/3, and 3/2. It takes some
finessing to get to "work" though, I plan to come up with an example
soon.

Both of these techniques certainly don't sound that "xenharmonic"
compared to something like porcupine or miracle, but they're certainly
new musical techniques encoded in 12-equal that have gone unnoticed
for centuries. And being as I enjoy 12-tet music too, I think they're
worth a shot. Pajara's main flaw is that it doesn't live up to its
stated goal
of being an immediately "xenharmonic" and novel system unlike anything
anyone has heard before - the combination of 7-limit harmony and
whatever scalar features are supposed to lead to tonality clearly
wasn't a grand slam right out of the bat, but it does lead to some
interesting musical resources in 12-tet.

-Mike

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:

> > I'm pretty sure I actually just don't care much for music that emphasizes harmony so heavily.
>
> It's about all I'm interested in, that and counterpoint.

Not really true, now that I think of it. I'm perfectly happy listening to the pentatonic simplicity of Old Man River. But that's not the sort of thing I try to create myself these days.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:

> Which sounds just fine, unlike your 15-EDO ditty.

And is about as exciting as watching paint dry.

> You obviously didn't spend nearly enough time, since if you put in > 2, 3, 4, 5, 6, 7, 8, 9 or 10 cent target errors into Graham's
> machine, the answer which comes out is meantone.

I started with a 12-cent target error hoping for a good mix of reasonable accuracy and reasonable simplicity.

> Pajara is nifty, but I was pounding away on the thought of
> porcupine as a 22 temperament because unlike pajara, it gets us
> completely outside of the orbit of the familiar; it is not
> supported by 12.

I'll give Porcupine another shake.

> Bah. It's significantly sweeter than 12.

Sure, and glycyrrhizin is 30-50 times sweeter than table sugar. Sweetness on its own is no big deal.

> > And also, 12-TET is a damn good 7-limit temperament, apparently.
>
> In the age of electronics we can produce any tuning we wish, which > reduces the attractiveness of low-complexity temperaments.

Producing a tuning is one thing, figuring out how to work with it is quite another. Low complexity for me is less about physical manageability and more about mental manageability.

-Igs

On Sat, May 28, 2011 at 1:15 PM, genewardsmith
<genewardsmith@...> wrote:
>
> > What I was going to say is that after diddling around with Pajara again, I came to the conclusion that I still don't like it. And if I don't like Pajara, there's not much hope for me and 7-limit harmony, because the next-best temperaments to Pajara that aren't near-optimal in 12-TET all pretty much fail to match the harmonic efficiency of either Pajara or Blacksmith, meaning there are significant proportions of notes in the scales that aren't roots of some otonal or utonal tetrad or some major or minor 7th chord.
>
> Pajara is nifty, but I was pounding away on the thought of porcupine as a 22 temperament because unlike pajara, it gets us completely outside of the orbit of the familiar; it is not supported by 12.

YES. Thank you. I'm glad that all of my MODMOS work didn't go
completely in vain. Porcupine is one of the best and simplest
xenharmonic tonal systems we have. ANY of the following will work

1) Create scales tetrachordally. The tetrachords are JI versions of
the diatonic ones we're used to, BUT ALSO you get the ultra-trippy and
xenharmonic 3-ED4/3 tetrachord as well
2) Create a system with parallel tonal scales, akin to the natural,
melodic, and harmonic minor scales, except serving a "major" function
3) In general, take the porcupine[7] MOS and alter any note and still
end up with a proper scale.

For #2, some attractive choices are

- Lssssss b4, which turns the 11/8 into a 4/3, which means the lower
tetrachord is a JI 1/1 9/8 5/4 4/3, and the upper is a porcupine
tempered 3-ED4/3
- Lssssss #7, which turns the 11/6 into a 15/8 for leading tone
purposes, which means the upper tetrachord is 1/1 9/8 5/4 4/3 and the
lower pentachord is 8:9:10:11:12
- The combination of both, which is a JI major scale and is the
long-lost xenharmonic bridge between porcupine and the more usual
fifth-based harmony
- Lssssss b7, which turns the 11/6 into a 7/4, giving you an almost otonality
- sssLsss #2, which is a symmetric "Dorian" scale - with the 10/9 over
the root transformed into 9/8 in order to otonally strengthen it. USE
THIS A LOT

etc. And I will scream this from the top of the highest mountain until
people catch on! More realistically, I will write a piece of music to
demo its capabilities, eventually, but as you remember, I'm not hear,
so I can't. Either way, thanks for keeping the dream alive. I think
this is important enough to warrant a xenwiki page about it, or maybe
an addition to the porcupine family page.

We also need to delve into the MODMOS's of miracle and orwell, which
will probably melt faces off all across the globe, but I just have no
time now... will have to put it on my backlog of stuff I've said I'm
going to do.

> In the age of electronics we can produce any tuning we wish, which reduces the attractiveness of low-complexity temperaments.

Except where comma pumps are concerned, which you seemed to agree
before were of pretty important and fundamental concern. Consider that
in 12-tet, the root fits otonally on top of the IV chord, but then the
IV sits as a very rough 7-limit ratio on top of the V chord, which
sits on top of the I chord. And then, on top of that, you have the
81/80 comma pump that lets you run in circles endlessly while flirting
with all of this. Humans seem to like such endless running in circles.

More importantly, if we could find low-complexity temperaments that
have similar setups, where going utonally from the root can land you
otonally above another note that's otonal from the root, that might
lead to some magical possibilities. (hint)

-Mike

Also, now that I can actually listen to the songs -

I didn't think the Blackwood[10] option sounded that bad, but in terms
of concordant 7-limit harmony I agree it's pretty flat. Funny how
after the cognitive revolution last month we're right back at
concordance again.

I think that 15-EDO is best thought of containing two subgroups
2.3.5(.11)
2.7.11

The latter is very concordant, although it doesn't often go well with
the former for perhaps the sole reason that the 7/6 is unbearably
flat. But you can do some nice things by playing 4:7:11 triads and
moving planar-ly by fifth. Don't forget that the 2.7.11 interpretation
of Blackwood is also there (except the "otonal" mode is the 5-limit
Blackwood minor mode and vice versa).

The 22-tet Pajara one sounded "fine," so if your goal is to write
"fine" music then I say go with Pajara. I thought it started to sound
beyond "just fine" when you left cliche 7-limit Pajara cheeseville and
started playing with 5-limit stuff, augmented major 7 chords and so
on. If people would draw from -ALL- of the tonal resources that Pajara
has to offer, I think they'd like it more. It supports some pretty out
there sounds, like 8:10:12:14:15 and 8:10:12:14:15:16:17:18:19:20,
both of which sound strange and conflicted at first but sound amazing
in the hands of a suitable composer (I think Debussy hinted at using
it this way).

-Mike

On Sat, May 28, 2011 at 2:12 AM, cityoftheasleep
<igliashon@...> wrote:
>
> So I wrote a stupid little tune in 15-EDO Blackwood[10] exploring the sound of the "seventh" chords, including the septimal otonal tetrad, utonal tetrad, and the 5-limit major and minor 7ths. It sounds pretty cheezy to me and I'm not at all proud of it, but I think it's important just to have a ready-to-hand example of what larger vertical harmony in 15-EDO sounds like (not very good).
>
> /tuning/files/IgliashonJones/Blackwood7ths.mp3