22 tet interval names

Hi Paul

At your suggestion I'm posting to this list regarding your offer to
carry out the consonance/dissonance ranking of 22 tet dyads. I'll
forward my own suggestions for descriptive terms to the main list and
perhaps get your comments there. Many thanks.

Kind regards
a.m.

--- In harmonic_entropy@y..., Alison Monteith <alison.monteith3@w...>
wrote:
> Hi Paul
>
> At your suggestion I'm posting to this list regarding your offer to
> carry out the consonance/dissonance ranking of 22 tet dyads. I'll
> forward my own suggestions for descriptive terms to the main list
and
> perhaps get your comments there. Many thanks.
>
> Kind regards
> a.m.

hi alison. you may not have seen my suggestions on the tuning list
yet. it may be that those are right up your alley so that there will
be no need to be "scientific" about it . . . however, i'll take a
crack at some 12-equal rankings when i get a chance . . .

(we decided on the tuning list to go with inversional equivalence, at
least for now)

here we go, using octave-equivalent harmonic entropy with s=0.75%:

22-equal_degrees entropy
0 4.1198
9 5.5323
13 5.5323
(perfect consonances)

7 5.6824
15 5.6824
16 5.7135
6 5.7135
(soft consonances)

17 5.7409
5 5.7409
11 5.7494
18 5.7529
4 5.7529
(mild mesonances)

8 5.7535
14 5.7535
19 5.7705
3 5.7705
(semisharp mesonances)

12 5.7777
10 5.7777
(restless/unstable -- you might also say "weak dissonances")

2 5.8007
20 5.8007
(sharp dissonances)

21 5.8986
1 5.8986
(supersharp dissonances)

to my amazement, the ranking i presented on the tuning list is
comfirmed *perfectly*!! of course, this gives finer gradations of
consonance/dissonance, should you care to use them . . .

--- In harmonic_entropy@y..., "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:

> (perfect consonances)

whoops . . . meant to say *open* consonances . . .

alison, please take a look at

/harmonic_entropy/files/Erlich/alison.gif

this shows the entire harmonic entropy function used below, and the
points where it intersects the 22-equal degrees. it's easy to see
from this graph how the intervals would tend to be shifted if
adaptive tuning / adaptive JI were used, and one were to keep the
inversional/octave-equivalence assumption.

--- In harmonic_entropy@y..., "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:
> (we decided on the tuning list to go with inversional equivalence,
at
> least for now)
>
> here we go, using octave-equivalent harmonic entropy with s=0.75%:
>
>
> 22-equal_degrees entropy
> 0 4.1198
> 9 5.5323
> 13 5.5323
> (perfect consonances)
>
>
> 7 5.6824
> 15 5.6824
> 16 5.7135
> 6 5.7135
> (soft consonances)
>
>
> 17 5.7409
> 5 5.7409
> 11 5.7494
> 18 5.7529
> 4 5.7529
> (mild mesonances)
>
>
> 8 5.7535
> 14 5.7535
> 19 5.7705
> 3 5.7705
> (semisharp mesonances)
>
>
> 12 5.7777
> 10 5.7777
> (restless/unstable -- you might also say "weak dissonances")
>
>
> 2 5.8007
> 20 5.8007
> (sharp dissonances)
>
>
> 21 5.8986
> 1 5.8986
> (supersharp dissonances)
>
> to my amazement, the ranking i presented on the tuning list is
> comfirmed *perfectly*!! of course, this gives finer gradations of
> consonance/dissonance, should you care to use them . . .

wallyesterpaulrus wrote:

> alison, please take a look at
>
> /harmonic_entropy/files/Erlich/alison.gif
>
> this shows the entire harmonic entropy function used below, and the
> points where it intersects the 22-equal degrees. it's easy to see
> from this graph how the intervals would tend to be shifted if
> adaptive tuning / adaptive JI were used, and one were to keep the
> inversional/octave-equivalence assumption.

Excellent. Looks like somebody's dental records. Seriously though I wish
I had time to learn more about these processes. I don't even know what
"s" means.

>
> --- In harmonic_entropy@y..., "wallyesterpaulrus"
> <wallyesterpaulrus@y...> wrote:
> > (we decided on the tuning list to go with inversional equivalence,
> at
> > least for now)
> >
> > here we go, using octave-equivalent harmonic entropy with s=0.75%:
> >
> >
> > 22-equal_degrees entropy
> > 0 4.1198
> > 9 5.5323
> > 13 5.5323
> > (open consonances)

(I changed perfect to open)

>
> >
> >
> > 7 5.6824
> > 15 5.6824
> > 16 5.7135
> > 6 5.7135
> > (soft consonances)
> >
> >
> > 17 5.7409
> > 5 5.7409
> > 11 5.7494
> > 18 5.7529
> > 4 5.7529
> > (mild mesonances)
> >
> >
> > 8 5.7535
> > 14 5.7535
> > 19 5.7705
> > 3 5.7705
> > (semisharp mesonances)
> >
> >
> > 12 5.7777
> > 10 5.7777
> > (restless/unstable -- you might also say "weak dissonances")

Weak dissonances is better for me.

>
> >
> >
> > 2 5.8007
> > 20 5.8007
> > (sharp dissonances)
> >
> >
> > 21 5.8986
> > 1 5.8986
> > (supersharp dissonances)
> >
> > to my amazement, the ranking i presented on the tuning list is
> > comfirmed *perfectly*!! of course, this gives finer gradations of
> > consonance/dissonance, should you care to use them . . .

Clever boy. And a job well done. Mesonance is particularly inspired. I
assume the etymology is meso = half way or some such thing. Perhaps the
French would call it a mi-sonance. I assume you won't mind if I use this
on future web pages (due credit given of course)?

Next step is to work out the key signatures in 5 line staff notation for
all the decatonics in all the keys. That makes 80 key signatures.

Then learn to sight read using staff notation. That should be bags of
fun :(

I've also to get used to some notational problems, one being the simple
question of the C major triad and the notation I'm using for guitar.
Taking C as the root I should notate that as c^ if I want a 5/4 with 'e'
on the fourth string fourth fret. Then my 3/2 wth c^ is notated 'a'
flat. I seem to remember transposing the guitar fretboard notation to
accommodate the open strings. Better change back.

> Many thanks Paul

Kind Regards
a.m.

--- In harmonic_entropy@y..., "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:
> alison, please take a look at
>
>
/harmonic_entropy/files/Erlich/alison.gif
>
> this shows the entire harmonic entropy function used below, and the
> points where it intersects the 22-equal degrees. it's easy to see
> from this graph how the intervals would tend to be shifted if
> adaptive tuning / adaptive JI were used, and one were to keep the
> inversional/octave-equivalence assumption.

I'm not Alison, but perhaps you'll remember me as the picky diner
from a while back.

What you have there looks really super, now that you've added the
vertical lines! Do you think you could redo this one:

/harmonic_entropy/files/dyadic/secorts3.g
if

with reference lines every 50 cents (i.e., 24-ET)? And is it asking
too much to get each pixel on the x axis to correspond to a cent?

Please? Please? (Pretty please?)

--Picky Diner

--- In harmonic_entropy@y..., Alison Monteith <alison.monteith3@w...>
wrote:
>
>
> wallyesterpaulrus wrote:
>
> > alison, please take a look at
> >
> >
/harmonic_entropy/files/Erlich/alison.gif
> >
> > this shows the entire harmonic entropy function used below, and
the
> > points where it intersects the 22-equal degrees. it's easy to see
> > from this graph how the intervals would tend to be shifted if
> > adaptive tuning / adaptive JI were used, and one were to keep the
> > inversional/octave-equivalence assumption.
>
> Excellent. Looks like somebody's dental records. Seriously though I
wish
> I had time to learn more about these processes. I don't even know
what
> "s" means.

do you at least understand what the graph is showing, about for
example where the local minima of dissonance are, and how 22-equal
comes close to, but doesn't always nail, a lot of them?

> > --- In harmonic_entropy@y..., "wallyesterpaulrus"
> > <wallyesterpaulrus@y...> wrote:
> > > (we decided on the tuning list to go with inversional
equivalence,
> > at
> > > least for now)
> > >
> > > here we go, using octave-equivalent harmonic entropy with
s=0.75%:
> > >
> > >
> > > 22-equal_degrees entropy
> > > 0 4.1198
> > > 9 5.5323
> > > 13 5.5323
> > > (open consonances)
>
> (I changed perfect to open)
>
> >
> > >
> > >
> > > 7 5.6824
> > > 15 5.6824
> > > 16 5.7135
> > > 6 5.7135
> > > (soft consonances)
> > >
> > >
> > > 17 5.7409
> > > 5 5.7409
> > > 11 5.7494
> > > 18 5.7529
> > > 4 5.7529
> > > (mild mesonances)
> > >
> > >
> > > 8 5.7535
> > > 14 5.7535
> > > 19 5.7705
> > > 3 5.7705
> > > (semisharp mesonances)
> > >
> > >
> > > 12 5.7777
> > > 10 5.7777
> > > (restless/unstable -- you might also say "weak dissonances")
>
> Weak dissonances is better for me.
>
> >
> > >
> > >
> > > 2 5.8007
> > > 20 5.8007
> > > (sharp dissonances)
> > >
> > >
> > > 21 5.8986
> > > 1 5.8986
> > > (supersharp dissonances)
> > >
> > > to my amazement, the ranking i presented on the tuning list is
> > > comfirmed *perfectly*!! of course, this gives finer gradations
of
> > > consonance/dissonance, should you care to use them . . .
>
> Clever boy. And a job well done. Mesonance is particularly
inspired. I
> assume the etymology is meso = half way or some such thing.

right.

> Perhaps the
> French would call it a mi-sonance. I assume you won't mind if I use
this
> on future web pages (due credit given of course)?

go for it!

> Next step is to work out the key signatures in 5 line staff
notation for
> all the decatonics in all the keys.

this doesn't make sense. how can you indicate what happens each of
the 10 pitches when you have only 7 locations per octave?

> That makes 80 key signatures.

wha?? how are you getting that number??

> I've also to get used to some notational problems, one being the
simple
> question of the C major triad and the notation I'm using for guitar.
> Taking C as the root I should notate that as c^ if I want a 5/4
with 'e'
> on the fourth string fourth fret. Then my 3/2 wth c^ is notated 'a'
> flat. I seem to remember transposing the guitar fretboard notation
to
> accommodate the open strings. Better change back.

i'm not following. are you saying there's something wrong with having
the open strings notated E A d g b' e'; that is, as the "naturals"?

--- In harmonic_entropy@y..., "gdsecor" <gdsecor@y...> wrote:

> Do you think you could redo this one:
>
>
/harmonic_entropy/files/dyadic/secorts3.g
> if
>
> with reference lines every 50 cents (i.e., 24-ET)?

here ya go:

/harmonic_entropy/files/dyadic/secor4.gif

> And is it asking
> too much to get each pixel on the x axis to correspond to a cent?
>
> Please? Please? (Pretty please?)

i can't see how to do that. but i could give you the raw data, if you
had some way of doing it yourself.

--- In harmonic_entropy@y..., Alison Monteith <alison.monteith3@w...>
wrote:

> I've also to get used to some notational problems, one being the
simple
> question of the C major triad and the notation I'm using for guitar.
> Taking C as the root I should notate that as c^ if I want a 5/4
with 'e'
> on the fourth string fourth fret.

yes.

> Then my 3/2 wth c^ is notated 'a'
> flat.

it's also notated g^. remember, in a pythagorean-based notation such
as this, traditional interval names have meaning. ^ or v is the
diatonic semitone in 22-equal. a flat or sharp is the chromatic
semitone, as always. the diatonic semitone plus the chromatic
semitone always equals the whole tone. here, this means 1 + 3 = 4.
keep this in mind as you ponder the notation.

wallyesterpaulrus wrote:

> --- In harmonic_entropy@y..., Alison Monteith <alison.monteith3@w...>
>
> wrote:
> >
> >
> > wallyesterpaulrus wrote:
> >
> > > alison, please take a look at
> > >
> > >
> /harmonic_entropy/files/Erlich/alison.gif
>
> > >
> > > this shows the entire harmonic entropy function used below, and
> the
> > > points where it intersects the 22-equal degrees. it's easy to see
> > > from this graph how the intervals would tend to be shifted if
> > > adaptive tuning / adaptive JI were used, and one were to keep the
> > > inversional/octave-equivalence assumption.
> >
> > Excellent. Looks like somebody's dental records. Seriously though I
> wish
> > I had time to learn more about these processes. I don't even know
> what
> > "s" means.
>
> do you at least understand what the graph is showing, about for
> example where the local minima of dissonance are, and how 22-equal
> comes close to, but doesn't always nail, a lot of them?

Yes, me being facetious. I can interpret the data, I just don't know how
one arrives at it. I tend to ignore maths until I need it.

>
>
> > > --- In harmonic_entropy@y..., "wallyesterpaulrus"
> > > <wallyesterpaulrus@y...> wrote:
> > > > (we decided on the tuning list to go with inversional
> equivalence,
> > > at
> > > > least for now)
> > > >
> > > > here we go, using octave-equivalent harmonic entropy with
> s=0.75%:
> > > >
> > > >
> > > > 22-equal_degrees entropy
> > > > 0 4.1198
> > > > 9 5.5323
> > > > 13 5.5323
> > > > (open consonances)
> >
> > (I changed perfect to open)
> >
> > >
> > > >
> > > >
> > > > 7 5.6824
> > > > 15 5.6824
> > > > 16 5.7135
> > > > 6 5.7135
> > > > (soft consonances)
> > > >
> > > >
> > > > 17 5.7409
> > > > 5 5.7409
> > > > 11 5.7494
> > > > 18 5.7529
> > > > 4 5.7529
> > > > (mild mesonances)
> > > >
> > > >
> > > > 8 5.7535
> > > > 14 5.7535
> > > > 19 5.7705
> > > > 3 5.7705
> > > > (semisharp mesonances)
> > > >
> > > >
> > > > 12 5.7777
> > > > 10 5.7777
> > > > (restless/unstable -- you might also say "weak dissonances")
> >
> > Weak dissonances is better for me.
> >
> > >
> > > >
> > > >
> > > > 2 5.8007
> > > > 20 5.8007
> > > > (sharp dissonances)
> > > >
> > > >
> > > > 21 5.8986
> > > > 1 5.8986
> > > > (supersharp dissonances)
> > > >
> > > > to my amazement, the ranking i presented on the tuning list is
> > > > comfirmed *perfectly*!! of course, this gives finer gradations
> of
> > > > consonance/dissonance, should you care to use them . . .
> >
> > Clever boy. And a job well done. Mesonance is particularly
> inspired. I
> > assume the etymology is meso = half way or some such thing.
>
> right.
>
> > Perhaps the
> > French would call it a mi-sonance. I assume you won't mind if I use
> this
> > on future web pages (due credit given of course)?
>
> go for it!
>
> > Next step is to work out the key signatures in 5 line staff
> notation for
> > all the decatonics in all the keys.
>
> this doesn't make sense. how can you indicate what happens each of
> the 10 pitches when you have only 7 locations per octave?
>
> > That makes 80 key signatures.
>
> wha?? how are you getting that number??

Actually 80 is wrong. But by analogy with 12tet - 2 modes (major and
minor) starting on each of 12 tones = 24 keys, given that relative maj
and min have the same signature. So in 22 tet 2 modes x 22 tones = 44
keys. Could be I'm on a wild goose chase but the Standard pentachordal
major for example in 'c' has three accidentals (I'm using Fokker's
notation BTW), f sharp, b and d flat. That's all I've done so far. If
you or anybody else has already done all this, ie worked out the
conventional sharp and flat key signatures on a 5 line staff, please
fire away and save me some time.

> I've also to get used to some notational problems, one being the

> simple
> > question of the C major triad and the notation I'm using for guitar.
>
> > Taking C as the root I should notate that as c^ if I want a 5/4
> with 'e'
> > on the fourth string fourth fret. Then my 3/2 wth c^ is notated 'a'
> > flat. I seem to remember transposing the guitar fretboard notation
> to
> > accommodate the open strings. Better change back.
>
> i'm not following. are you saying there's something wrong with having
> the open strings notated E A d g b' e'; that is, as the "naturals"?

Well there's nothing wrong but if I want the open strings strings
natural then 'c' will be c^. As I'm serious about writing for other
conventional instruments, with or without guitar I'm prepared to
sacrifice an initial convenience on the guitar, ie 'natural' open
strings, so that I can have a straight 'c'. I don't know what your
thoughts are on that. I'm going right back for a fresh start with 22
tet and as a result am trying to build a firm foundation.

One other point. I've read your paper again in depth and a lot is
clearer. It is quite "dense" in information, there's little redundancy
and very few examples in the 'narrative' of the text (for example in the
section on micro-chromaticism) but I understand that that is the nature
of the scholarly paper. This is good in the long run from the point of
view of a thicko like me who has to work everything out slowly and
surely. Please understand that these are merely observations and not
criticisms.

Finally, I've made a start at connecting chords concentrating on good
voice leading on the guitar from various degrees of the decatonics,
starting with triads, just to get a feel for the fingerings. Some
successful root movements are obviously the same as in 12 tet, eg by 5/4
and 4/3. Have you done much with this and if so, have you found any
particularly successful connections?

Kind Regards
a.m.

>

wallyesterpaulrus wrote:

> --- In harmonic_entropy@y..., Alison Monteith <alison.monteith3@w...>
>
> wrote:
>
> > I've also to get used to some notational problems, one being the
> simple
> > question of the C major triad and the notation I'm using for guitar.
>
> > Taking C as the root I should notate that as c^ if I want a 5/4
> with 'e'
> > on the fourth string fourth fret.
>
> yes.
>
> > Then my 3/2 wth c^ is notated 'a'
> > flat.
>
> it's also notated g^. remember, in a pythagorean-based notation such
> as this, traditional interval names have meaning. ^ or v is the
> diatonic semitone in 22-equal. a flat or sharp is the chromatic
> semitone, as always. the diatonic semitone plus the chromatic
> semitone always equals the whole tone. here, this means 1 + 3 = 4.
> keep this in mind as you ponder the notation.
>

OK. Thanks for the reminder.

Regards
a.m.

i replied but i'm not sure if the reply made it through. either way,
could you post this (or your reply to my reply) to the tuning list?

--- In harmonic_entropy@y..., Alison Monteith <alison.monteith3@w...>
wrote:
>
>
> wallyesterpaulrus wrote:
>
> > --- In harmonic_entropy@y..., Alison Monteith
<alison.monteith3@w...>
> >
> > wrote:
> > >
> > >
> > > wallyesterpaulrus wrote:
> > >
> > > > alison, please take a look at
> > > >
> > > >
> >
/harmonic_entropy/files/Erlich/alison.gif
> >
> > > >
> > > > this shows the entire harmonic entropy function used below,
and
> > the
> > > > points where it intersects the 22-equal degrees. it's easy to
see
> > > > from this graph how the intervals would tend to be shifted if
> > > > adaptive tuning / adaptive JI were used, and one were to keep
the
> > > > inversional/octave-equivalence assumption.
> > >
> > > Excellent. Looks like somebody's dental records. Seriously
though I
> > wish
> > > I had time to learn more about these processes. I don't even
know
> > what
> > > "s" means.
> >
> > do you at least understand what the graph is showing, about for
> > example where the local minima of dissonance are, and how 22-equal
> > comes close to, but doesn't always nail, a lot of them?
>
> Yes, me being facetious. I can interpret the data, I just don't
know how
> one arrives at it. I tend to ignore maths until I need it.
>
> >
> >
> > > > --- In harmonic_entropy@y..., "wallyesterpaulrus"
> > > > <wallyesterpaulrus@y...> wrote:
> > > > > (we decided on the tuning list to go with inversional
> > equivalence,
> > > > at
> > > > > least for now)
> > > > >
> > > > > here we go, using octave-equivalent harmonic entropy with
> > s=0.75%:
> > > > >
> > > > >
> > > > > 22-equal_degrees entropy
> > > > > 0 4.1198
> > > > > 9 5.5323
> > > > > 13 5.5323
> > > > > (open consonances)
> > >
> > > (I changed perfect to open)
> > >
> > > >
> > > > >
> > > > >
> > > > > 7 5.6824
> > > > > 15 5.6824
> > > > > 16 5.7135
> > > > > 6 5.7135
> > > > > (soft consonances)
> > > > >
> > > > >
> > > > > 17 5.7409
> > > > > 5 5.7409
> > > > > 11 5.7494
> > > > > 18 5.7529
> > > > > 4 5.7529
> > > > > (mild mesonances)
> > > > >
> > > > >
> > > > > 8 5.7535
> > > > > 14 5.7535
> > > > > 19 5.7705
> > > > > 3 5.7705
> > > > > (semisharp mesonances)
> > > > >
> > > > >
> > > > > 12 5.7777
> > > > > 10 5.7777
> > > > > (restless/unstable -- you might also say "weak dissonances")
> > >
> > > Weak dissonances is better for me.
> > >
> > > >
> > > > >
> > > > >
> > > > > 2 5.8007
> > > > > 20 5.8007
> > > > > (sharp dissonances)
> > > > >
> > > > >
> > > > > 21 5.8986
> > > > > 1 5.8986
> > > > > (supersharp dissonances)
> > > > >
> > > > > to my amazement, the ranking i presented on the tuning list
is
> > > > > comfirmed *perfectly*!! of course, this gives finer
gradations
> > of
> > > > > consonance/dissonance, should you care to use them . . .
> > >
> > > Clever boy. And a job well done. Mesonance is particularly
> > inspired. I
> > > assume the etymology is meso = half way or some such thing.
> >
> > right.
> >
> > > Perhaps the
> > > French would call it a mi-sonance. I assume you won't mind if I
use
> > this
> > > on future web pages (due credit given of course)?
> >
> > go for it!
> >
> > > Next step is to work out the key signatures in 5 line staff
> > notation for
> > > all the decatonics in all the keys.
> >
> > this doesn't make sense. how can you indicate what happens each of
> > the 10 pitches when you have only 7 locations per octave?
> >
> > > That makes 80 key signatures.
> >
> > wha?? how are you getting that number??
>
> Actually 80 is wrong. But by analogy with 12tet - 2 modes (major and
> minor) starting on each of 12 tones = 24 keys, given that relative
maj
> and min have the same signature. So in 22 tet 2 modes x 22 tones =
44
> keys. Could be I'm on a wild goose chase but the Standard
pentachordal
> major for example in 'c' has three accidentals (I'm using Fokker's
> notation BTW), f sharp, b and d flat. That's all I've done so far.
If
> you or anybody else has already done all this, ie worked out the
> conventional sharp and flat key signatures on a 5 line staff, please
> fire away and save me some time.
>
> > I've also to get used to some notational problems, one being the
>
> > simple
> > > question of the C major triad and the notation I'm using for
guitar.
> >
> > > Taking C as the root I should notate that as c^ if I want a 5/4
> > with 'e'
> > > on the fourth string fourth fret. Then my 3/2 wth c^ is
notated 'a'
> > > flat. I seem to remember transposing the guitar fretboard
notation
> > to
> > > accommodate the open strings. Better change back.
> >
> > i'm not following. are you saying there's something wrong with
having
> > the open strings notated E A d g b' e'; that is, as
the "naturals"?
>
> Well there's nothing wrong but if I want the open strings strings
> natural then 'c' will be c^. As I'm serious about writing for other
> conventional instruments, with or without guitar I'm prepared to
> sacrifice an initial convenience on the guitar, ie 'natural' open
> strings, so that I can have a straight 'c'. I don't know what your
> thoughts are on that. I'm going right back for a fresh start with
22
> tet and as a result am trying to build a firm foundation.
>
> One other point. I've read your paper again in depth and a lot is
> clearer. It is quite "dense" in information, there's little
redundancy
> and very few examples in the 'narrative' of the text (for example
in the
> section on micro-chromaticism) but I understand that that is the
nature
> of the scholarly paper. This is good in the long run from the point
of
> view of a thicko like me who has to work everything out slowly and
> surely. Please understand that these are merely observations and not
> criticisms.
>
> Finally, I've made a start at connecting chords concentrating on
good
> voice leading on the guitar from various degrees of the decatonics,
> starting with triads, just to get a feel for the fingerings. Some
> successful root movements are obviously the same as in 12 tet, eg
by 5/4
> and 4/3. Have you done much with this and if so, have you found any
> particularly successful connections?
>
> Kind Regards
> a.m.
>
> >

--- In harmonic_entropy@y..., "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:
> --- In harmonic_entropy@y..., "gdsecor" <gdsecor@y...> wrote:
>
> > Do you think you could redo this one:
>
/harmonic_entropy/files/dyadic/secorts3.g
if
> >
> > with reference lines every 50 cents (i.e., 24-ET)?
>
> here ya go:
>
/harmonic_entropy/files/dyadic/secor4.gif

That looks great!

> > And is it asking
> > too much to get each pixel on the x axis to correspond to a cent?
> >
> > Please? Please? (Pretty please?)
>
> i can't see how to do that. but i could give you the raw data, if
you
> had some way of doing it yourself.

Yes, I'd appreciate that. (You could send it off list.)

--George

wallyesterpaulrus wrote:

> i replied but i'm not sure if the reply made it through. either way,
> could you post this (or your reply to my reply) to the tuning list?

--- In harmonic_entropy@y..., "gdsecor" <gdsecor@y...> wrote:

> > i can't see how to do that. but i could give you the raw data, if
> you
> > had some way of doing it yourself.
>
> Yes, I'd appreciate that. (You could send it off list.)

here it is, from 0 cents to 1200 cents in 1-cent increments:

/harmonic_entropy/files/Erlich/george.txt

--- In harmonic_entropy@y..., "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:
> here it is, from 0 cents to 1200 cents in 1-cent increments:
>
/harmonic_entropy/files/Erlich/george.txt

Got it. Thank you!

--George

--- In harmonic_entropy@y..., "gdsecor" <gdsecor@y...> wrote:
> --- In harmonic_entropy@y..., "wallyesterpaulrus"
> <wallyesterpaulrus@y...> wrote:
> > here it is, from 0 cents to 1200 cents in 1-cent increments:
> >
>
/harmonic_entropy/files/Erlich/george.txt
>
> Got it. Thank you!
>
> --George

i got a request for a 96-equal grid instead. here it is:

/harmonic_entropy/files/dyadic/vincent.gi
f

note that this is only meant to apply to intervals less than or equal
to an octave in width, and that there are many other ways of defining
the curve (as the history of this list evidences), depending on your
particular instrument, ears, and musical style. ymmv.

note also that the local minima of this curve would be captured far
better than 72-equal than by 96-equal. thus 72-equal would have more
opportunity for contrast between concordance and discordance.