Yahoo Tuning Groups Ultimate Backup tuning Cents/Sense

This is pretty disingenuous!
Cents didn't merely coincide with 12ET.
I find in practice that cent 'deviation' from ET pins musicians into a
way of working that goes against understanding and is often crippling.

Steve P.

On 26 Jun 2011, at 13:32, Afmmjr@... wrote:

>
> "The choice of the cent as the base of a system of musical
> logarithms has been highly approved by all musicians interested in
> the scientific side of their art. It has been adopted by all modern
> acousticians who consider intervals as musicians do.
>
>
>
> "Thus it has come about that, while the selection of some method of
> logarithmic representation of musical intervals was necessitated by
> a peculiarity of audition, the various values proposed for the base
> of the system have coincided with intervals of a particular musical
> scale."
>
>
>
> J. Murray Barbour, "Musical Logarithms"
>
>
> Lobawad, hopefully this will help flesh out some common ground on
> cents.
>
>
> Johnny Reinhard
>
>
>
>
>

🔗Mike Battaglia <battaglia01@...>

🔗Michael <djtrancendance@...>

Steve>"I find in practice that cent 'deviation' from ET pins musicians into a
way of working that goes against understanding and is often crippling."

Agreed! And this gets even more confusing when you get, say, a note 18 cents under a 12TET minor seventh (near 16/9) that is used as a sixth in a microtonal tuning!

The 12TET musician thinking in cents is bound to say "but it's closer to a 12TET minor seventh, so it must BE a type of seventh".

Not to mention other weird intervals in 12TET beside 16/9 such as sqrt(2), the 12TET minor third, and the 12TET minor 6th...which are far off the Just versions of those interval classes and lie near the edge vs. other interval classes.

So why are so many people so keen on holding on to a system that, while logarithmic (which alone is a good quality that corresponds to how the human ear works)...fails miserably to summarize interval classes?

BTW, as a solution, I'm again leaning toward 31TET...which has intervals that fall smack in the middle of Just interval classes, thus lessening the chance of confusion and intervals that fall "on the-edge-of/virtually-between classes" like often they do in 12TET.

🔗Mike Battaglia <battaglia01@...>

🔗Steve Parker <steve@...>

72-tet is great - especially to play on the piano!
But suggesting that the genesis of 1200 cents an octave was
coincidental (in either sense) in relation to 12ET is disingenuous.

> But then, to keep it simple, rather than saying
> there are 7200 cents per octave, we can divide 7200 by something to
> keep it simpler. Like, say, maybe 6.

Stylishly done ;-) yet still crippling to musicians who never get the
chance to learn that they can hear and play these intervals as they
stand.
I'm (mostly) of the opinion that if you can't get a player to hear and
perform an interval it is probably not going to have much distinct
meaning for an audience member either.
Surely the idea that a 5/4 is a 'flat' major third is crazy and cent
deviancy leads to exactly that kind of thinking.

Steve P.

On 26 Jun 2011, at 14:45, Mike Battaglia wrote:

>
> I doubt it's as disingenuous as you think - 72-tet is a zeta
> integral tuning after all.
>
> -Mike
>
> On Jun 26, 2011, at 9:00 AM, Steve Parker <steve@...> wrote:
>
>>
>> This is pretty disingenuous!
>>
>> Cents didn't merely coincide with 12ET.
>> I find in practice that cent 'deviation' from ET pins musicians
>> into a way of working that goes against understanding and is often
>> crippling.
>>
>> Steve P.
>
>
>> __,_._,__
>
>

🔗genewardsmith <genewardsmith@...>

🔗Steve Parker <steve@...>

On 26 Jun 2011, at 22:37, genewardsmith wrote:

> > Surely the idea that a 5/4 is a 'flat' major third is crazy and cent
> > deviancy leads to exactly that kind of thinking.
>
> I missed when the tag labeling 400 cents as "this is a major third" > was affixed. Obviously, you need to think that in the first place to > see 386.314 cents as flat, so it doesn't lead to such thinking at > all. You are confusing cause and effect.

I really am not! The average professional player (even string players!) *know* that a major 3rd is 400 cents.. and notating my music with cent deviation from 12ET reinforces this.
I've not worked with a player yet who can't hear and produce any interval I need, but I've worked with quite a few who make life difficult for themselves by insisting for a while on 'cents from ET'.
This gets particularly crazy with something like a string quartet who are not used to tuning in ET yet still think that their Major 3rd is 400 cents! Cent deviation from that gets nowhere..

An awful lot of players were present when that tag was affixed even if they never play such a thing.

Steve P.

🔗Mike Battaglia <battaglia01@...>

On Sun, Jun 26, 2011 at 5:16 PM, Steve Parker <steve@...> wrote:
>
> 72-tet is great - especially to play on the piano!
>
> But suggesting that the genesis of 1200 cents an octave was coincidental (in either sense) in relation to 12ET is disingenuous.

I'm not saying that it was coincidental. I'm saying that there are
reasons to keep it around besides the fact that 12ET is in common use.

> > But then, to keep it simple, rather than saying
> > there are 7200 cents per octave, we can divide 7200 by something to
> > keep it simpler. Like, say, maybe 6.
>
> Stylishly done ;-) yet still crippling to musicians who never get the chance to learn that they can hear and play these intervals as they stand.
> I'm (mostly) of the opinion that if you can't get a player to hear and perform an interval it is probably not going to have much distinct meaning for an audience member either.
> Surely the idea that a 5/4 is a 'flat' major third is crazy and cent deviancy leads to exactly that kind of thinking.

72TET is great, and in terms of learning where just intervals lay out
I recommend all beginners start with it. Saying that a just 5/4 is 386
cents, or about one sixth of a semitone flat of 12-tet 400 cents,
isn't that difficult to understand. It certainly doesn't equate to
some kind of voodoo mind meld that 400 cents is more consonant than
386 cents just because it's a nice big round number with a lot of
zeroes in it.

-Mike

🔗Steve Parker <steve@...>

> > But suggesting that the genesis of 1200 cents an octave was > coincidental (in either sense) in relation to 12ET is disingenuous.
>
> I'm not saying that it was coincidental. I'm saying that there are
> reasons to keep it around besides the fact that 12ET is in common use.
>
I was replying to this:

> "Thus it has come about that, while the selection of some method of > logarithmic representation of musical intervals was necessitated by > a peculiarity of audition, the various values proposed for the base > of the system have coincided with intervals of a particular musical > scale."
>
I think there is no chance of abandoning it due to it's use in MIDI applications. A cent is also about the right size too.

> Saying that a just 5/4 is 386
> cents, or about one sixth of a semitone flat of 12-tet 400 cents,
> isn't that difficult to understand. It certainly doesn't equate to
> some kind of voodoo mind meld that 400 cents is more consonant than
> 386 cents just because it's a nice big round number with a lot of
> zeroes in it.
>
I do see that exact voodoo mind meld. I've been dealing with JI intervals in cents for a long time and still wish
that I could think of 612 cents without 'knowing' instantly that it is a sharp 12ET augmented 4th.
Players that are not used to dealing with it have more trouble if they relate everything to 12ET than if they take the intervals for what they are
- especially when they do things like playing a 5/4 naturally whilst thinking that it is 400 cents.
I've hit this a lot.

Steve P.

(I'm not much into any ET but am having serious fun after your (Mike B.'s) suggestion to try 13ET - it is really pretty nice to play on the piano!)

🔗Steve Parker <steve@...>

🔗genewardsmith <genewardsmith@...>

🔗Steve Parker <steve@...>

🔗Afmmjr@...

Steve, where are you working and with whom? I have NEVER had a problem in
NYC working with professional players. Every year I bring in new
musicians so that the pool of players that are deft with cents increases. When the
player sees 386 cents (no decimals please), they HEAR the correct interval
rather instantaneously. There is NO confusion with a movement from 400
cents because the 5/4 is so distinctive. 386 cents, like any cents value,
puts the player in the ball park, but the ear and mind must be engaged.
Using new number approaches makes little sense.

The Barbour quote certainly did stir up the dust around here.

Johnny

On 27 Jun 2011, at 00:15, genewardsmith wrote:

So where's the problem? The average string player doesn't play a 400 cent
major third, and you experience no difficulty getting them to play what
you'd like them to play, and yet you are upset over what they "know", which is
apparently merely definitional.

This is getting further and further from what I meant.. and from where the
thread started.. which was about needing to notate cents from 12ET for
musicians.
The only thing I'm saying is that IME it is often a hindrance.

Steve P.

🔗Jake Freivald <jdfreivald@...>

I think the flavor of cents is just about right: 386 cents is a pure
5/4, but 12-tET sharpens that to 400 cents for the sake of a variety
of conveniences. To get back to pure tones -- whether it's (say) a 6/5
m3 (12-tET is 16 cents too flat) or a 13/11 m3 (12-tET is 11 cents too
sharp) -- you have to deviate from the 100-cent boundaries. Why is
that hard?

Perhaps more important than identifying what's similar to 12-tET,
cents show you what's dissimilar: The farther away your
notes/dyads/etc. are from 100-cent boundaries, the less you'll sound
like 12-tET.

Any system will have arbitrary aspects. Cents seems like a pretty good
map to what you need.

Regards,
Jake

On 6/26/11, Afmmjr@... <Afmmjr@...> wrote:
>
> Steve, where are you working and with whom? I have NEVER had a problem in
> NYC working with professional players. Every year I bring in new
> musicians so that the pool of players that are deft with cents increases.
> When the
> player sees 386 cents (no decimals please), they HEAR the correct interval
> rather instantaneously. There is NO confusion with a movement from 400
> cents because the 5/4 is so distinctive. 386 cents, like any cents value,
> puts the player in the ball park, but the ear and mind must be engaged.
> Using new number approaches makes little sense.
>
> The Barbour quote certainly did stir up the dust around here.
>
> Johnny
>
>
>
>
> On 27 Jun 2011, at 00:15, genewardsmith wrote:
>
>
> So where's the problem? The average string player doesn't play a 400 cent
> major third, and you experience no difficulty getting them to play what
> you'd like them to play, and yet you are upset over what they "know", which
> is
> apparently merely definitional.
>
>
> This is getting further and further from what I meant.. and from where the
> thread started.. which was about needing to notate cents from 12ET for
> musicians.
> The only thing I'm saying is that IME it is often a hindrance.
>
>
> Steve P.
>
>
>
>

🔗Michael <djtrancendance@...>

Jake>"The farther away your notes/dyads/etc. are from 100-cent boundaries, the less you'll sound like 12-tET."

I wouldn't say that necessary holds as a rule...
You could have a scale of 50,150, 250,350,450,550...1150...or 25,125,225....1125 cents...and the only thing different would be the chords containing 0 cents and octave equivalents.

I think the very bane of the "cent" system is that is weighs things so far as closeness to 12EDO, rather than closeness to Just intervals.

19EDO cents, even...would, in general, be a large step up from 12EDO cents far as accurately approximating Just intervals for most steps in the tuning...even if you don't like my idea of using 31EDO to get "virtually every 11-or-less odd-limit" Just interval possible.

>"Any system will have arbitrary aspects."
Granted. But what's more important: closeness to 12EDO or closeness to Just intervals?

Personally I'd say it's closeness to Just Intervals...and 12 EDO does quite a poor-man's approximation of Just Intervals. And if you take the number of intervals in 12TET quite close to Just intervals, you only get about 4 intervals (and that's optimistically assuming you want the 16/9 instead of a 7/4 or 9/5!) With 19EDO, your get more like 10 low-odd-limit (9-limit or less) intervals within 8 cents or less error: 58% more notes, but over 100% more near-Just notes. And with 31EDO...over 20 notes are near 9-odd-limit Just intervals. So the chance of your hitting a note with a precise Just-interval musical meaning is much higher.

🔗Steve Parker <steve@...>

Oh he player's can handle it either way. I'm definitely not talking about lesser players. I use Ben Johnston's notation and some player's annotate with cent deviation or at least discuss it. They are the ones who don't learn the intervals for their own sound and take a lot longer to understand what is going on. I use consistent sounding accidentals to move from a standard just grid.
I give up because I'm failing to make a point that is my daily experience:
Using cents implicitly compares everything to 12ET and this slows understanding of what is on the page.
It is of course possible to get players to just play at a tuner... Most players will eventually come to a deeper understanding, but it sure slows it up.

Steve P.

On 27 Jun 2011, at 00:43, Afmmjr@... wrote:

> I have NEVER had a problem in NYC working with professional > players. Every year I bring in new musicians so that the pool of > players that are deft with cents increases. When the player sees > 386 cents (no decimals please), they HEAR the correct interval > rather instantaneously. There is NO confusion with a movement from > 400 cents because the 5/4 is so distinctive. 386 cents, like any > cents value, puts the player in the ball park, but the ear and mind > must be engaged. Using new number approaches makes little sense.

🔗Steve Parker <steve@...>

I'm not arguing for losing cents in any way - just for not using them as a performance aid in non 12ET music.
I'm perfectly happy to use cents for Kontakt etc.

On 27 Jun 2011, at 04:20, Jake Freivald wrote:

> I think the flavor of cents is just about right: 386 cents is a pure
> 5/4, but 12-tET sharpens that to 400 cents for the sake of a variety
> of conveniences. To get back to pure tones -- whether it's (say) a 6/5
> m3 (12-tET is 16 cents too flat) or a 13/11 m3 (12-tET is 11 cents too
> sharp) -- you have to deviate from the 100-cent boundaries. Why is
> that hard?
>
> Perhaps more important than identifying what's similar to 12-tET,
> cents show you what's dissimilar:

This is exactly my point - cents as performance aid set up 12ET as a standard which is deviated from.
They set it up not because players are incompetent but because every microtone illiterate musician in the world 'knows' that a semitone is 100 cents.
You can give me plenty of other ways of looking at it, but the comparison with 12ET is inescapable.

Steve P.

🔗Wolf Peuker <wolfpeuker@...>

🔗wolfpeuker <wolfpeuker@...>

🔗clumma <carl@...>

🔗Wolf Peuker <wolfpeuker@...>

🔗Jake Freivald <jdfreivald@...>

Me:
>> The farther away your notes/dyads/etc. are from 100-cent
>> boundaries, the less you'll sound like 12-tET.

Michael:
> I wouldn't say that necessary holds as a rule...
> You could have a scale of 50,150,250,350,450,550...1150...or
> 25,125,225....1125 cents...and the only thing different would be
> the chords containing 0 cents and octave equivalents.

...Which is why I explicitly said, "notes/dyads/etc." Notes are
measured in relation to the choice of unison. Dyads are measured in
relation to each other. "Etc" (meaning chords, scales, overtones, etc)
are related to multiple things in sometimes complex ways. For any one
of those things, if you see values close to 100-cent boundaries,
you're close to 12-tET.

Better still, you're proving my point. Let's say you used millioctaves
or 31-EDO pseudo-cents instead of "50,150,250,350,450,550...1150".
Quickly, now -- what values would you have chosen? I know that I'd
need a calculator. Worse, I'd need to recalculate for every pitch
class. It would have taken you several minutes longer to write that
sentence, and me longer still to interpret it. (Since I'm writing this
on a BlackBerry, I probably wouldn't have bothered, in fact.)

So perhaps if you stop thinking of cents as "the hegemony of 12-tET"
and instead think of it as a measure of the ordinariness of your
notes/dyads/etc., you would realize why I think it's so useful.

> I think the very bane of the "cent" system is that is weighs
> things so far as closeness to 12EDO, rather than closeness to
> Just intervals.
And:
> ....But what's more important: closeness to 12EDO or
> closeness to Just intervals?

2 answers:

1. I'm not sure. Being newish to microtonality, I'm still leaving open
a lot of possibilities. One possibility is that EDOs are valuable as
structures in their own right. On your recommendation, I bought Easley
Blackwood's microtonal etudes. It comes with a very successful guitar
suite in 15-EDO. Looking at the scale, I see good approximations only
to 6/5, 13/9, and 5/3. How shall I explain the success of this suite
if I assume that good music is made with just intervals? And if good
music doesn't require just intervals, why should I throw out a
well-known system of measurement to support them? Aren't I just
replacing one tyrant with another?

2. Which just intervals? You just said, "with 31EDO...over 20 notes
are near 9-odd-limit Just intervals." Should we privilege these 20
notes over all others? Do we *have* to include the 3/2? (That seems
so... So... Well, so 3-limit, you know? People should learn to break
the hegemony of the fifth.) Where's my 13/11 minor third? And what
about the 33% of the notes that are *not* near just intervals? Should
we privilege these inharmonicities above all others? The bottom line
is, I think you want to *break* people from the habit of looking to
the measurement system for guidance about what "sounds good", and you
can't do that when you're specifically designing your unit of measure
to guide them to tones you think are particularly harmonic.

Regards,
Jake

On 6/26/11, Michael <djtrancendance@...> wrote:
> Jake>"The farther away your notes/dyads/etc. are from 100-cent boundaries,
> the less you'll sound like 12-tET."
>
>    I wouldn't say that necessary holds as a rule...
>    You could have a scale of 50,150, 250,350,450,550...1150...or
> 25,125,225....1125 cents...and the only thing different would be the chords
> containing 0 cents and octave equivalents.
>
> I think the very bane of the "cent" system is that is weighs things so far
> as closeness to 12EDO, rather than closeness to Just intervals.
>
> 19EDO cents, even...would, in general, be a large step up from 12EDO cents
> far as accurately approximating Just intervals for most steps in the
> tuning...even if you don't like my idea of using 31EDO to get "virtually
> every 11-or-less odd-limit" Just interval possible.
>
>>"Any system will have arbitrary aspects."
>     Granted. But what's more important: closeness to 12EDO or closeness to
> Just intervals?
>
> Personally I'd say it's closeness to Just Intervals...and 12 EDO does
> quite a poor-man's approximation of Just Intervals. And if you take the
> number of intervals in 12TET quite close to Just intervals, you only get
> about 4 intervals (and that's optimistically assuming you want the 16/9
> instead of a 7/4 or 9/5!)   With 19EDO, your get more like 10 low-odd-limit
> (9-limit or less) intervals within 8 cents or less error: 58% more notes,
> but over 100% more near-Just notes. And with 31EDO...over 20 notes are near
> 9-odd-limit Just intervals. So the chance of your hitting a note with a
> precise Just-interval musical meaning is much higher.
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>

🔗lobawad <lobawad@...>

--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
>
> "The choice of the cent as the base of a system of musical >logarithms has
> been highly approved by all musicians interested in the scientific side of
> their art. It has been adopted by all modern acousticians who consider
> intervals as musicians do.
> "Thus it has come about that, while the selection of some method of
> logarithmic representation of musical intervals was necessitated by a peculiarity
> of audition, the various values proposed for the base of the system have
> coincided with intervals of a particular musical scale."
> J. Murray Barbour, "Musical Logarithms"
> Lobawad, hopefully this will help flesh out some common ground on cents.
> Johnny Reinhard
>

As I said before, I have nothing against cents and use them all the time- in fact I also have something of a 1200-edo grid internalized, too, and could probably, with practice, perform from AFMM notation.
I was talking about how notation relates to internal structure. And, I was specifically thinking about how conception of notation interacts with compositional thinking.

I'm a firm believer in whatever-works-for-you, as far as performance.
At the same time, I'm a big fan of individual intonational expression, as long as structural meaning is retained. So, my own notation is something between the Turkish Koma system and Helmholtz-Ellis, but the way I look at things, it would be the correct thing to do for any group using the AFMM system to rewrite the score using the exact cent values that float their personal collective boat but it would be simply silly for me to compose and write the original score using the AFMM system. It would be superfluous to add cent modifications to the pure Pythagorean grid I use, and it would just plain go against core beliefs about music to specify EVERY interval to the cent (being a stickler about the specific intonations of my own interpretations is not the same as expecting anyone else to use the same exact intonations, nor even to terribley exact if they don't want to).

Hm, I'll post an example and apologia as soon as possible, maybe we can agree to disagree but you'll see that I'm speaking thoughtfully and not just talking crap. :-)

🔗genewardsmith <genewardsmith@...>

🔗lobawad <lobawad@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
>
> > As I said before, I have nothing against cents and use them all the time- in fact I also have something of a 1200-edo grid internalized, too, and could probably, with practice, perform from AFMM notation.
>
> Who's going to be the first to internalize 3600 edo, I wonder? It does more than merely divide cents into thirds and the Dröbisch Angle into tenths. It also supports ennealimmal temperament, and in fact does a damned good job of it. The 3/2 is your old friend, 702 cents. 5/4 is your new friend, 386.333 cents. And 7/4 does OK as 968.667 cents. 2401/2400 and 4375/4374 are tempered out.
>

Won't be I that's for sure- reading off cents and knowing what Just intervals they might, and being able to perform roughly about there (with greater accuracy on blending tones obviously) is one thing, performing anything and everything accurately to one cent is far far more precise than what I can do.

🔗Michael <djtrancendance@...>

Jake>"...Which is why I explicitly said, "notes/dyads/etc." Notes are measured in relation to the choice of unison. Dyads are measured in relation to each other. "Etc" (meaning chords, scales, overtones, etc) are related to multiple things in sometimes complex ways. For any one of those things, if you see values close to 100-cent boundaries, you're close to 12-tET."

Sorry I missed that...if you mean individual dyad gaps being different than 100 cents IE 100 vs. 250 cents or if you have information on a full chord at once IE 100 250 325 cents...then yes, that's true.
The problem can come again though when you add such dyads IE with a 100 250 dyad and the same dyad starting at 250 = a 100 250 400 triad where the new 100-400 dyad is "just 12TET", even though the other two aren't. So still, I observe a pattern that trying to reduce a scale's 12TET-edness to how close it is to 12TET intervals at a glance is a method that can be easily flawed...unless you literally stick with very close and consistent values IE 102 197 305....cents or 50 154 248 cents.

>"Better still, you're proving my point. Let's say you used millioctaves or 31-EDO pseudo-cents instead of "50,150,250,350,450,550...1150". Quickly, now -- what values would you have chosen?"

True, you'd need to calculate. But the only information you'd lose, is how far away you are from 12EDO (and again, my point is I agree you lose the ability to quickly find dyads in 12EDO...but gain the ability to quickly find a whole lot of Just dyads...Just meaning "9-odd-limit-or-less...drawing from the 16/9 is about the highest limit dyad in 12EDO").
And since about 22 or so of the 31 notes in 31EDO are very close to 9-odd-limit or less JI, you can be fairly certain the notes you've chosen form something Just. The caveat is you'd need to memorize the position of certain intervals IE the minor/major 2nd, 3rd, perfect 5th...but the good news is all those intervals could be memorized as just whole numbers (1-31) * 100...no need to memorize longer numbers with inconsistent values after the hundreds place...like 386 cents and 204 cents as you have to with 12EDO.

>"It comes with a very successful guitar suite in 15-EDO. Looking at the scale, I see good approximations only to 6/5, 13/9, and 5/3. How shall I explain the success of this suite

if I assume that good music is made with just intervals?"

From experience, I've found anything up to about 11-odd-limit works well so far as dyads (including 15TET's 11/6 and 7/4) and 15TET's sharp fifth and 13/9 aren't bad either: the area around the 5th seems to allow a good deal of slack for sharpness. The number of Just dyads in here actually seems competitive with or slightly better than in 12EDO, the only disadvantage if you're using more notes to get a similar range of good dyads.
In short, I think you're picking a wrong scale to be surprised with so far as "how does this sound so good?!" Try something like 13TET, which has maybe 3 "Just-ish" dyads...if that.

>"2. Which just intervals? You just said, "with 31EDO...over 20 notes are near 9-odd-limit Just intervals." Should we privilege these 20 notes over all others? Do we *have* to include the 3/2?"

I'd say yes. Virtually every scale I've made that's easy to compose with almost completely avoids dyads other than those 20 (minus some "extended JI" 11-limit intervals). The idea is being Just holds higher precedence than being "12TET-like" or "Common Practice/Meantone-like". For the record, I don't think 3/2 ever HAS to be included (or even a 'bad version' of 3/2 such as the 50/33 in 15EDO )...though when you come across a tuning that has it...I'd say "of course use it...there's no harm". I even swap the diminished fifth at 22/15 in place of 3/2 myself...though I don't expect others to go that far.

🔗Jake Freivald <jdfreivald@...>

> The problem can come again though when you add such dyads
> IE with a 100 250 dyad and the same dyad starting at 250
> = a 100 250 400 triad where the new 100-400 dyad is "just
> 12TET", even though the other two aren't.

I think you're reaching too hard.

I've recently been noodling with a 17-note scale that uses prime 11 a lot.
It includes a 0-352-703 chord (in cents, of course). Even if I didn't know
the 5/4 and 6/5 cents values, I would know this is similar to a 12-tET major
or minor chord, but with a third that's smack between major and minor.
That's a good thing: I expect the stability and familiarity of the fifth,
and the different sound of the neutral third.

Would it be so much better if I called it a 0-909-1817 chord? (That's (log
base 2 of Ratio)*3100, which is, I'm presuming, what you're talking about
with 31-EDO-based pseudo-cents.) I really don't see how. Forget what
information I have or haven't lost: What information have I gained?

> And since about 22 or so of the 31 notes in 31EDO are very close
> to 9-odd-limit or less JI, you can be fairly certain the notes
> you've chosen form something Just.

If I'm trying to get aleatoric on people, then that might be important.
Realistically, though, I'm not choosing any old notes and hoping they're
just.

> The caveat is you'd need to memorize the position of certain
> intervals IE the minor/major 2nd, 3rd, perfect 5th...

I'm fine with memorizing stuff if there's a benefit. I have to do that now
with cents: Who knew a year ago that I'd be interested in four types of
minor thirds and three different major thirds?

> but the good news is all those intervals could be memorized
> as just whole numbers (1-31) * 100...no need to memorize longer
> numbers with inconsistent values after the hundreds place...like
> 386 cents and 204 cents as you have to with 12EDO.

Unless I'm missing something, no, not really.

Here are the pitches of some common intervals in 31-EDO pseudo-cents ((log
base 2 of ratio) * 3100):

16/15 289
13/11 747
6/5 815
5/4 998
9/7 1124
4/3 1287
7/5 1505
3/2 1813
5/3 2285
7/4 2503

I see that 5/4, 7/5, and 7/4 are close to 31-Epc boundaries: 1000, 1500, and
2500, respectively. Eight cents is 21 31-Epcs, so I could consider 16/15,
6/5, 4/3, 3/2, and 5/3 to be "close enough" to a 100-31-Epc boundary, but I
still have to memorize their values if I want better than 8-cent precision.
Saying a 6/5 is 800 Epcs gets me close, but among people who frequently post
cents values to five digits, I don't think I'm going to be satisfied with
that approximation. Ultimately, my memorization has been complicated, not
simplified, by going to this measure.

Here are some notes that I picked, literally at random, from the 31-Epc
list:

1300 89/42
1700 8/3
3000 379/67
200 55/49
2300 185/49

What new information have I gained by choosing 31-Epc instead of cents?

Remember, I'm giving up a widely used and well-understood system to adopt
this one. What is the benefit I receive from doing so?

The only benefit I see from moving to this system is that it trains people
to think in 31-EDO. If 31-EDO were everything, I'd be on board.

> Virtually every scale I've made that's easy to compose with almost
> completely avoids dyads other than those 20 (minus some "extended JI"
> 11-limit intervals).

That's interesting, but I wonder how many people share your experience. It
sounds like you're recommending we move from the hegemony of 12-tET to the
hegemony of 31-tET simply because it contains intervals you like. That
doesn't sound like a good reason to adopt a completely new set of
measurements.

Regards,
Jake