Yahoo Tuning Groups Ultimate Backup tuning Eikosany... what's going on here?

I hear of this idea... it's called Eikosany. Apparently, you can create music without a tonal center, yet still be consonant. I'm interested in this idea, but so far haven't found any resource which explains how to use it musically.

I'm not interested in the mathematics, I would just love to know a few things. :-) They are...

Is the eikosany.scl scala file a useful starting point for a composition? It has 20 notes - how can I use them effectively? Progressions, melodic resources, what can it do?

What does eikosany music sound like? How is it described? Can it be ambiguous, can it be jazzy, does it have a good range of moods?

Importantly, who's working with this kind of tuning today? Is it a worthwhile area for new musical compositions?

Thanks all,

microtonally,

Sean A

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, "sevishmusic" <sevish@...> wrote:
>
> I hear of this idea... it's called Eikosany. Apparently, you
> can create music without a tonal center, yet still be consonant.
> I'm interested in this idea, but so far haven't found any
> resource which explains how to use it musically.

There are many eikosanies, but the one called the
"1.3.5.7.9.11 eikosany" is usually meant if it isn't
specified.

The 1.3.5.7.9.11 means the basic chord is the otonal hexad.
An otonal hexad is a 4:5:6:7:9:11 chord, voiced inside two
octaves. Still with me?

Except you don't get the whole hexad, only four notes of it.
You have 4:5:6:7 and 4:5:6:11 and 6:7:9:11 and so on. In
fact you get all such chords, and their subharmonic inverses,
all in those 20 notes.

The rule with the eikosany is that one modulates by common
dyad. In the diatonic scale one does too, though the dyad
is usually a 5th (or sometimes a 3rd). In the eikosany, all
the dyads are used for such modulations.

Now the best way to understand all this, especially as one
is sitting over an instrument starting out with it, is to
look at Erv Wilson's diagram:

http://lumma.org/temp/Figure13.png

Given the clues above, does this figure make sense to you?

> Is the eikosany.scl scala file a useful starting point for a
> composition? It has 20 notes - how can I use them effectively?
> Progressions, melodic resources, what can it do?

Putting all the notes in pitch-height order hides the structure
somewhat. You might try coming up with sticky labels for your
MIDI keyboard to expose the structure. Alternatively, if you're
handy with something like Max/MSP or one of the newfangled
iPad things, you can design an onscreen controller based on
Erv's diagram.

> What does eikosany music sound like?

Here is a tour around part of the 1.3.5.7.9.11 eikosany:

http://lumma.org/music/theory/demo/progs/EikosanyProgression2.mp3

>How is it described? Can it be ambiguous, can it be jazzy,
>does it have a good range of moods?

Tunings don't admit to such descriptions -- only music.

> Is it a worthwhile area for new musical compositions?

You bet!

-Carl

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:

> > Is it a worthwhile area for new musical compositions?
>
> You bet!

There are three basic operations on sets (or multisets, which are sets with repeated elements) of note classes ("scales") which lead to bigger ones. They are usually defined in terms of just intonation only, but needn't be, and the three are related. They are the genus, the cps, and the diamond. The genus of a multiset is all products of all elements of the multiset, where the product is a product of note classes, ie, take the product of notes, reduce to the octave, and those are your classes. In a special case this gives the Euler genus. The cps, or combination product (multi)set, is like the genus except you take not all products but products taken some number k at a time. The eikosanies are a special case. The diamond takes all ratios of two elements. All of these can start from multisets or sets and produce bigger multisets or sets, and so can be iterated or combined. Any scale in the Scala directory, or any chord in any tuning, can have any one of these applied to it, with results which are pretty much unexplored territory. Don't bother applying them to edos, however.

🔗Domina Catrina Lee <ahulijing@...>

Carl
your example sounds gorgeous.
Wish I could get my head around the numbers and terms :(

Catrina

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "sevishmusic" <sevish@> wrote:
> >
> > I hear of this idea... it's called Eikosany. Apparently, you
> > can create music without a tonal center, yet still be consonant.
> > I'm interested in this idea, but so far haven't found any
> > resource which explains how to use it musically.
>
> There are many eikosanies, but the one called the
> "1.3.5.7.9.11 eikosany" is usually meant if it isn't
> specified.
>
> The 1.3.5.7.9.11 means the basic chord is the otonal hexad.
> An otonal hexad is a 4:5:6:7:9:11 chord, voiced inside two
> octaves. Still with me?
>
> Except you don't get the whole hexad, only four notes of it.
> You have 4:5:6:7 and 4:5:6:11 and 6:7:9:11 and so on. In
> fact you get all such chords, and their subharmonic inverses,
> all in those 20 notes.
>
> The rule with the eikosany is that one modulates by common
> dyad. In the diatonic scale one does too, though the dyad
> is usually a 5th (or sometimes a 3rd). In the eikosany, all
> the dyads are used for such modulations.
>
> Now the best way to understand all this, especially as one
> is sitting over an instrument starting out with it, is to
> look at Erv Wilson's diagram:
>
> http://lumma.org/temp/Figure13.png
>
> Given the clues above, does this figure make sense to you?
>
> > Is the eikosany.scl scala file a useful starting point for a
> > composition? It has 20 notes - how can I use them effectively?
> > Progressions, melodic resources, what can it do?
>
> Putting all the notes in pitch-height order hides the structure
> somewhat. You might try coming up with sticky labels for your
> MIDI keyboard to expose the structure. Alternatively, if you're
> handy with something like Max/MSP or one of the newfangled
> iPad things, you can design an onscreen controller based on
> Erv's diagram.
>
> > What does eikosany music sound like?
>
> Here is a tour around part of the 1.3.5.7.9.11 eikosany:
>
> http://lumma.org/music/theory/demo/progs/EikosanyProgression2.mp3
>
> >How is it described? Can it be ambiguous, can it be jazzy,
> >does it have a good range of moods?
>
> Tunings don't admit to such descriptions -- only music.
>
> > Is it a worthwhile area for new musical compositions?
>
> You bet!
>
> -Carl
>

🔗Carl Lumma <carl@...>

🔗Chris Vaisvil <chrisvaisvil@...>

I have a question

Is the lack of tonal center supposed to be a function of the tuning
("1.3.5.7.9.11 eikosany")

or a function of the procedures used when using the tuning as, for
instance described by Gene in the reply to the post I quote here?

And let me comment

1. modulation with a common dyad (or chord or whatever) implies tonality.
2. I see no reason one couldn't proceduralize diatonic chords in such
a manner to retain consonant and weaken (or break) tonality.

Chris

On Tue, Jul 13, 2010 at 11:35 PM, Carl Lumma <carl@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "sevishmusic" <sevish@...> wrote:
> >
> > I hear of this idea... it's called Eikosany. Apparently, you
> > can create music without a tonal center, yet still be consonant.
> > I'm interested in this idea, but so far haven't found any
> > resource which explains how to use it musically.
>
> There are many eikosanies, but the one called the
> "1.3.5.7.9.11 eikosany" is usually meant if it isn't
> specified.
>

🔗Graham Breed <gbreed@...>

On 14 July 2010 13:57, Chris Vaisvil <chrisvaisvil@...> wrote:
> I have a question
>
> Is the lack of tonal center supposed to be a function of the tuning
> ("1.3.5.7.9.11 eikosany")
>
> or a function of the procedures used when using the tuning as, for
> instance described by Gene in the reply to the post I quote here?

It's a function of that set of notes. I don't think it matters much
how you tune them but as they work in JI it's normal to stay in JI.

The idea is that a tonality diamond has a strong tonal center, because
every note's related to the 1/1. With CPS scales, like this, you take
the 1/1 away but leave plenty of consonant chords connected by common
notes.

> And let me comment
>
> 1. modulation with a common dyad (or chord or whatever) implies tonality.

It may, but it doesn't imply a tonal center. You can keep moving from
one chord to another without one of them being established as the
tonic.

> 2. I see no reason one couldn't proceduralize diatonic chords in such
> a manner to retain consonant and weaken (or break) tonality.

I don't know what you mean. Use the normal 7 notes but somehow avoid
a key being established? You can try, but there'll be a strong
tendency to here it as a traditional mode.

The rationale of the eikosany is that you can use a kind of consonant
atonality, with higher-limit chords. But it's surely possible to use
it in a more tonal way if you want. A tonal center doesn't have to be
a fundamental. But with a tonality diamond, everything can end up
sounding like a subset of the two basic chords, or a single timbre,
and that can be a problem. The main thing with the eikosany is that
you get consonant chords in a way that isn't supposed to work in just
intonation with true harmonic movement.

Graham

🔗Chris Vaisvil <chrisvaisvil@...>

Hi Graham,

That answered all of my questions.

Thanks!!

Re: diatonic - I was going to write common practice chords. - I agree one
can randomize consonant chords in 12 and obfuscate or eliminate the tonal
center.

On Wed, Jul 14, 2010 at 9:12 AM, Graham Breed <gbreed@...> wrote:

>
>
> On 14 July 2010 13:57, Chris Vaisvil <chrisvaisvil@...<chrisvaisvil%40gmail.com>>
> wrote:
> > I have a question
> >
> > Is the lack of tonal center supposed to be a function of the tuning
> > ("1.3.5.7.9.11 eikosany")
> >
> > or a function of the procedures used when using the tuning as, for
> > instance described by Gene in the reply to the post I quote here?
>
> It's a function of that set of notes. I don't think it matters much
> how you tune them but as they work in JI it's normal to stay in JI.
>
> The idea is that a tonality diamond has a strong tonal center, because
> every note's related to the 1/1. With CPS scales, like this, you take
> the 1/1 away but leave plenty of consonant chords connected by common
> notes.
>
>
>

🔗sevishmusic <sevish@...>

I can tell this will take a lot of work for me to fully understand - so I'm looking forward to some fun. :)

Carl your info was very helpful... especially the diagram, I can use that to help me move from chord to chord, at least at first.

Talking with some other people, I think it would be beneficial for me to start with a simpler structure, like the hexany or dekany thing. Perhaps this way I can better understand eikosany through analogy?

Sitting at the keyboard, with Scala and Erv's diagram on screen, the biggest issue I'm having is finding the right notes. I can't tell whether I'm on the right root note to be playing 5:9:11 for example. Looks like I need to study up a lot more.

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, "sevishmusic" <sevish@...> wrote:
>
> I can tell this will take a lot of work for me to fully
> understand - so I'm looking forward to some fun. :)
>
> Carl your info was very helpful... especially the diagram,
> I can use that to help me move from chord to chord, at least
> at first.

Glad to hear it.

> Talking with some other people, I think it would be beneficial
> for me to start with a simpler structure, like the hexany or
> dekany thing. Perhaps this way I can better understand eikosany
> through analogy?

One isn't much easier to understand than the other, but the
hexany certainly is easier to deal with since it has 6 notes
instead of 20. Here is a similar progression to the one I
posted before, but based on a 1.3.5.7 hexany:
http://lumma.org/music/theory/demo/progs/HexanyProgression.mp3

Actually it's based on the stellated hexany, which has 14
notes (each of the hexany's 8 triads is completed to a full
tetrad, so 6 notes of the hexany plus 8 for the completions
gives 14).

To be clear, this and the eikosany example each use only
12 notes out of the larger structures, for ease of use with
my score editor. Here's the score to this one:
http://lumma.org/music/theory/demo/progs/HexanyProgression.png

and the scala file in case you're interested:
http://lumma.org/music/theory/demo/progs/HexanyProgression.scl

> Sitting at the keyboard, with Scala and Erv's diagram on
> screen, the biggest issue I'm having is finding the right
> notes. I can't tell whether I'm on the right root note to
> be playing 5:9:11 for example. Looks like I need to study
> up a lot more.

One thing you might try is an out-of-order mapping to your
midi keyboard. There are lots of clever ways to do this
that you can fiddle with, if your synth allows any midi note
to be mapped to any pitch. Perhaps there's one that gives
each chord roughly the same fingering. That would rock.
You might try to write Kraig Grady directly as he may have
already worked something like this out.

-Carl