Yahoo Tuning Groups Ultimate Backup tuning EDI/UDI/etc.

> What was Drew's suggestion, EDI for equally divided interval tuning? I like
> that. So EDIs contain EDOs (which contains equal temperaments and equal
> tunings) and CETs, while UDIs (unequal division of the interval) contain
> UDOs (which contain just intonation, pelog, slendro, etc.) and pretty much
> all other tuning schemes. Well, it makes sense. This is sort of cool. We
> have in effect an international tuning congress, and some of the things we
> agree on here may well become the defacto standards of the future, due to
> the power of the internet. I hope we can agree on some sensible definitions
> and terminology, and use them consistently.

Hey John, flattered that you find it interesting.

It was actually "ESI", for equally spaced intervals.

However, "EDI" and "UDI" seem more useful & informative by giving a handle
on the larger interval, for example an octave, that the tuning covers.

And "UDO" for Unequally Divided Octave, directly complimenting Dan's "EDO".

Could be extended a little more with :
"EDNO" for an Equally Divided Non_Octave and "UDNO"

You can look at them as simply logical extensions of "EDO" which has been
quite well received.

That's : EDO, EDNO, UDO and EDI, UDI (these two being the more generic)

Ciao,
Drew

__________________________________________________
Do You Yahoo!?
Talk to your friends online with Yahoo! Messenger.
http://messenger.yahoo.com

🔗Joe Monzo <monz@xxxx.xxxx>

>> [John Starrett, TD 461.5]
>> What was Drew's suggestion, EDI for equally divided
>> interval tuning? I like that. So EDIs contain EDOs (which
>> contains equal temperaments and equal tunings) and CETs,
>> while UDIs (unequal division of the interval) contain
>> UDOs (which contain just intonation, pelog, slendro,
>> etc.) and pretty much all other tuning schemes. Well,
>> it makes sense. This is sort of cool. We have in effect
>> an international tuning congress, and some of the things
>> we agree on here may well become the defacto standards of
>> the future, due to the power of the internet. I hope we
>> can agree on some sensible definitions and terminology,
>> and use them consistently.

> [Drew Skyfyre, TD 462.4]
> Hey John, flattered that you find it interesting.
>
> It was actually "ESI", for equally spaced intervals.
>
> However, "EDI" and "UDI" seem more useful & informative
> by giving a handle on the larger interval, for example an
> octave, that the tuning covers.
>
> And "UDO" for Unequally Divided Octave, directly
> complimenting Dan's "EDO".
>
> Could be extended a little more with :
> "EDNO" for an Equally Divided Non_Octave and "UDNO"
>
> You can look at them as simply logical extensions of "EDO"
> which has been quite well received.
>
> That's : EDO, EDNO, UDO and EDI, UDI (these two being the
> more generic)

Yes, I like this too!

So some familiar tunings can be classified under this
system as:

UDO
----
JI
pelog/slendro
meantones
well-temperaments

EDO
---
ET (= equal-temperament and equal tuning)

EDNO
----
CET
Bohlen-Pierce
Lucytuning

UDNO
----
typical 'stretch' piano tuning
several tunings used by Brian McLaren

Then my previous suggestion for using the mathematical
notation could also include these, so we could have
for example:

2^(12/12) EDO [= 12-tET]
2^(31/31) EDO [= 31-tET]
(3/2)^(19/19) EDNO
11-limit JI UDO
Werckmeister III UDO

etc.

I also usually like to try to indicate in a concise numeric
form what type of JI I'm using also, delimited the boundaries
of a system or periodicity block, such as:

3^(-6...5) UDO is a typical Pythagorean 12-tone scale

3^(-1...2) * 5^(-1...1) UDO is a typical 5-limit JI 12-tone scale

This is good!

At the same time, I think it's important to retain the idea
of 'temperament'. As Daniel Wolf, Dan Stearns, and others
have pointed out, there is a crucial difference in whether
or not a composer/theorist *intended* for his EDI to be a
temperament, and this distinction should be retained in
any discussion of that person's work.

-monz

Joseph L. Monzo Philadelphia monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
--------------------------------------------------

🔗Paul H. Erlich <PErlich@xxxxxxxxxxxxx.xxxx>

🔗Herman Miller <hmiller@io.com>

On Wed, 29 Dec 1999 09:02:48 -0500, Joe Monzo <monz@juno.com> wrote:

>So some familiar tunings can be classified under this
>system as:
>
>
>UDO
>----
>JI
>pelog/slendro
>meantones
>well-temperaments

Some meantones are EDO's, though. Should pelog and slendro be considered as
UDO? (must "octave" always be a perfect 2/1?) or as UDNO? I think that, for
instance, my "starling scale" with tempered octaves has more in common with
my original "starling scale" than it does with most non-octave scales.

>EDO
>---
>ET (= equal-temperament and equal tuning)

Since I've been playing recently with scales that have slightly tempered
octaves (but not enough that I would consider them as "non-octave" scales),
I think it makes sense to allow for some flexibility in the definition of
"octave". In that case, my 38.8-CET / 30.9-TET scale might be more usefully
considered a 31-EDO with a 3-cent-sharp octave! The 1203-cent interval
certainly acts like an octave, and I think it makes sense to call it one.
What do you think?

>EDNO
>----
>CET
>Bohlen-Pierce
>Lucytuning

Isn't Lucytuning a meantone scale?

>UDNO
>----
>typical 'stretch' piano tuning
>several tunings used by Brian McLaren

and Ben Johnston's "Sonata for Microtonal Piano" (which is a JI scale).
I've also played around with scales like this (one that I remember is a JI
scale that repeats at the fifth instead of the octave), but I never really
got the hang of them. Octaves are so fundamental that it's a real challenge
to do without them. I ought to try again now that I've had more experience
with things like fifthless scales.

--
see my music page ---> +--<http://www.io.com/~hmiller/music/music.html>--
Thryomanes /"If all Printers were determin'd not to print any
(Herman Miller) / thing till they were sure it would offend no body,
moc.oi @ rellimh <-/ there would be very little printed." -Ben Franklin

🔗Joe Monzo <monz@xxxx.xxxx>

> [Paul Erlich, TD 463.16]
>
> Joe Monzo wrote,
>
>> UDO
>> ----
>> JI
>> pelog/slendro
>> meantones
>> well-temperaments
>>
>>
>> EDO
>> ---
>> ET (= equal-temperament and equal tuning)
>>
>>
>> EDNO
>> ----
>> CET
>> Bohlen-Pierce
>> Lucytuning
>>
> Joe, that doesn't make sense. Lucytuning is just another
> meantone. Because of octave reduction, meantones (including
> Lucytuning) are not simply equal divisions of any interval.

Right, Paul - I caught that myself when I received the TD and
read it again. Lucytuning should have been classified as
UDO, same as the other meantones. I was in a rush this
morning when I wrote that, and made a slip.

>>UDNO
>>----
>>typical 'stretch' piano tuning
>
> Why is that not an EDNO?

Because the intervals are not equally stretched all the way
across the range of the piano. They typically have deviations
from strict 12-EDO of from 0 cents around middle-C to +/-
3 or 4 cents a couple of 'octaves' above and below middle-C,
respectively.

Then in the higher and lower 'octaves', near the extremes of
the keyboard, the tuning diverges more, and more rapidly (so
to speak, going from one note to the next in the series), until
it reaches about 30 cents deviation at either end, the high
pitches being stretched sharp more than the low pitches are
stretched flat.

So there are many note-to-note intervals that are equal,
particularly in the 'octaves' surrounding middle-C, but
several that are not, and they become more and more unequal
as you progress toward the extremes of the keyboard.

I still have a stretch tuning chart that came with the manual
of my ancient Fender Rhodes, and I ran across it the other
day. I'll put it up on my website as soon as I can, but that
may not be until mid-January, when I return from California.

Perhaps Ed Foote can elaborate on this...?

-monz

🔗Clark <caccola@xxxxxxxx.xxxx>

> Perhaps Ed Foote can elaborate on this...?
>
I will try in the meanwhile. Joe Monzo wrote

> >>UDNO
> >>----
> >>typical 'stretch' piano tuning
>
and Paul Erlich wrote

> Why is that not an EDNO?
>
Common practice has most plain string octave speaking lengths roughly in a
1:1.89 relationship, changing by half a wire guage every half octave or so.
A proper bridge adjusts string lengths according with the guages so that the
inharmonicity doubles every octave going up the scale; very often this is
not applied in the low tenor bridge where the constraints of case geometry
suggest foreshortening of string lengths for better bridge placement,
usually strung with plain wire at much lower tension and inharmonicity than
the rest of the plain strings. Bridges may be notched evenly - rather simply
follow the exponential curve (some bridges are beveled so that the unisons
unevenly follow this curve) - so even without incongruous plain string
grouping, the relationships of partials may not be consistent due
inharmonicity. The result is that their tuning is neither strictly equal or
octave-based.

Further variables are introduced by wound bass strings. Guidelines for their
design have been introduced only recently and the trend is rather to raise
their inharmonicity going down the scale (observe that most bass bridges
either are straight or curved 'the wrong way'). Then, even, the (re)builder
is at the mercy of the string winder, many of whom refuse redesigned scales
in favor of traditional stock scales, usually quite inconsistent when they
are wound correctly.

So not all pianos are created equal. ;)

I kind of like this new terminology.

Clark

🔗Joe Monzo <monz@xxxx.xxxx>

> [Herman Miller, TD 464.1]
>
>> [me, monz, in a tentative effort at new tuning classification]
>> UDO
>> ----
>> JI
>> pelog/slendro
>> meantones
>> well-temperaments
>
> [Herman]
> Some meantones are EDO's, though.

Well... this brings up the distinction between EDO and
temperament with which I concluded that posting. Meantones
are generally thought of as temperaments, wherein JI intervals
are approximated while other desirable properties (which do
not exist in JI), such as closure and vanishing commas,
are acquired. EDOs, on the other hand, are thought of
as being simply equal divisions of the 'octave', and properties
other than their closeness to JI are explored.

> Should pelog and slendro be considered as UDO? (must "octave"
> always be a perfect 2/1?) or as UDNO? I think that, for
> instance, my "starling scale" with tempered octaves has more
> in common with my original "starling scale" than it does with
> most non-octave scales.

First off, I'm hardly the person to answer any questions
concerning Indonesian tunings - I've never made a good
study of that. Perhaps Daniel Wolf, Kriag Grady, or Bill
Alves could offer more here.

Concerning the 'perfect octave', I think, again, we're dealing
with distinctions between temperament and non-temperament
here. I certainly would not hesitate to call an interval
of 1203 cents a *tempered* 'octave', or even one quite a
bit larger than that. I read among Brian McLaren's voluminous
writings, referring to acoustical studies he'd read, that
*all* intervals are considered by listeners to be at their
most consonant when tuned slightly larger than small-integer
ratios, and he specifically cited the 1215-cent 'octave' as
being the 'octave' that listeners considered the most consonant.
That's one reason why Brian is so interested in UDNO tunings.

But I think that for purposes of terminological exactness,
we should stick to a precise 1:2 'octave' for EDO/UDO,
and use EDNO/UDNO for all tempered 'octaves'.

>
>> EDO
>> ---
>> ET (= equal-temperament and equal tuning)
>
> Since I've been playing recently with scales that have
> slightly tempered octaves (but not enough that I would
> consider them as "non-octave" scales), I think it makes
> sense to allow for some flexibility in the definition of
> "octave". In that case, my 38.8-CET / 30.9-TET scale might
> be more usefully considered a 31-EDO with a 3-cent-sharp
> octave! The 1203-cent interval certainly acts like an octave,
> and I think it makes sense to call it one.
> What do you think?
>

Well, what you say here does make a lot of sense. See what
I said above for my opinion, but I'm not entirely convinced
either.

>> EDNO
>> ----
>> CET
>> Bohlen-Pierce
>> Lucytuning
>
> Isn't Lucytuning a meantone scale?

Yes, I made a mistake here. Paul Erlich and I both pointed
it out by the time I read your posting here.

>
>> UDNO
>> ----
>> typical 'stretch' piano tuning
>> several tunings used by Brian McLaren
>
> and Ben Johnston's "Sonata for Microtonal Piano" (which is
> a JI scale).

Hmmm... as strong a supporter as I am of Ben's music, I'm
much more familiar with several of his string quartets than
with any of his other pieces. I've seen references to the
tuning of this piece before, but don't have them handy and
don't have time to look now. Gives us more info!

> I've also played around with scales like this (one that
> I remember is a JI scale that repeats at the fifth instead
> of the octave), but I never really got the hang of them.
> Octaves are so fundamental that it's a real challenge
> to do without them. I ought to try again now that I've
> had more experience with things like fifthless scales.

I, too, have never explored scales without 'octaves', except
for the 'stretched' piano tuning I wrote about here, which
really is more a 'tempered octave' than a 'non-octave' tuning.
Now that I'm using JI in a really extended sense, I'll be
looking more into this aspect in my future compositions.

Carl Lumma's observations in TD 646.4 are also illuminating.
I'm sorry I won't have enough access to my emails for the
next week to really follow this discussion, but I'm most
interested in where it will lead!

For the record, I agree totally with John Starrett that
*we* should hash this out now, and set the standard ourselves
for the rest of the world, because if we *do* set it, they
*will* follow.

> [Carl Lumma, TD 464.3]
> True, I forgot that some chords are temperament-only. But
> a composer demanding the sort of accuracy we're talking about
> wouldn't want them.

Such a sweeping statement! Carl, composers who demand
accuracy in tuning exhibit as much variety in their
harmonic/melodic wants and needs as with any other aspects
of their music!

Some 'accurately-tuned' composers *will* want 12-tET
'diminished 7th' chords, or meantone 'major 6/9' chords, etc.
What's nice is to be able to finally *state* the tuning you
want and have performers (and listeners?...) who are capable
of understanding and producing it.

-monz

🔗Drew Skyfyre <skyfyre2@xxxxx.xxxx>

>>EDNO
>>----
>>CET
>>Bohlen-Pierce
>>Lucytuning
>
> Isn't Lucytuning a meantone scale?

Herman, a tuning can be many different things.
So, tuning X may be a meantone, and an EDNO. Daniel recently pointed out how
a given EDO and ET may be physically identical, but conceptually different.
The intent in a given application is what defines the tuning in that
particular situation.

--------

Is there a name for tunings that do not repeat, i.e. are *endless* ?
88CET is an example of such a tuning (I think). Perhap keeping with the
"ED_" family, they may be called "EDS" for Equal Divisions of (or, in) the
(audio) Spectrum, which is infinite.

--------
Just a note regarding my butting in with all this stuff :
I am but a proverbial babe in the woods with regard to Xenharmonics, however
even as I study & read the theory & ideas both here and elsewhere, I keep
needing someway of classifying & labelling things so I may better understand
them. Kind of scientific like.

Salut,
Drew

__________________________________________________
Do You Yahoo!?
Talk to your friends online with Yahoo! Messenger.
http://messenger.yahoo.com

🔗Herman Miller <hmiller@xx.xxxx>

On Thu, 30 Dec 1999 13:01:03 -0500, Joe Monzo <monz@juno.com> wrote:

>Hmmm... as strong a supporter as I am of Ben's music, I'm
>much more familiar with several of his string quartets than
>with any of his other pieces. I've seen references to the
>tuning of this piece before, but don't have them handy and
>don't have time to look now. Gives us more info!

This is all I have specifically on the tuning, from the liner notes of the
CD from KOCH International Classics (3-7369-2-H1):

"My _Sonata for Microtonal Piano_ deploys chains of just-tuned (untempered)
triadic intervals over the whole piano range in interlocked consonant
patterns. Only seven of the eighty-eight white and black keys of the piano
have octave equivalents, one pair encompassing the distance of a double
octave and the remaining six pairs separated by almost the entire length of
the keyboard. Thus there are eighty-one different pitches, providing a
piano with almost no consonant octaves."

🔗Herman Miller <hmiller@xx.xxxx>

🔗Joe Monzo <monz@xxxx.xxxx>

> [Drew Skyfyre, TD 466.15]
> a tuning can be many different things. So, tuning X may be
> a meantone, and an EDNO. Daniel recently pointed out how a
> given EDO and ET may be physically identical, but conceptually
> different.
> The intent in a given application is what defines the tuning
> in that particular situation.

I think the most admirably crafted expositions illustrating
this are Margo Schulter's articles posted here.
They're work printing and saving: go visit the Archives.

> [Drew]
> Is there a name for tunings that do not repeat, i.e. are
> *endless* ? 88CET is an example of such a tuning (I think).
> Perhap keeping with the "ED_" family, they may be called "EDS"
> for Equal Divisions of (or, in) the (audio) Spectrum, which is
> infinite.

I like the poetry of 'EDS', but 88-cet can already be classified
as EDNO. The 'octave' in a EDO or UDO is what creates the
repetition to which you refer. The non-repetition in 88-cet
is due to it lack of 'octaves', thus EDNO.

-monz

EDI/UDI/etc.

🔗Drew Skyfyre <skyfyre2@yahoo.com>

🔗Joe Monzo <monz@xxxx.xxxx>

🔗Paul H. Erlich <PErlich@xxxxxxxxxxxxx.xxxx>

🔗Herman Miller <hmiller@io.com>

🔗Joe Monzo <monz@xxxx.xxxx>

🔗Clark <caccola@xxxxxxxx.xxxx>

🔗Joe Monzo <monz@xxxx.xxxx>

🔗Drew Skyfyre <skyfyre2@xxxxx.xxxx>

🔗Herman Miller <hmiller@xx.xxxx>

🔗Herman Miller <hmiller@xx.xxxx>

🔗Joe Monzo <monz@xxxx.xxxx>