Yahoo Tuning Groups Ultimate Backup tuning I want to name the modes of porcupine[7]

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> But I don't want to do it without Herman Miller's blessing for what
> theme he'd like the names to take.
>
> Also, I'm not sure what exactly to name them after. It would be
> fantastic to get away from regions of ancient Greece for a change (we
> just named the mavila[9] modes here:
> http://xenharmonic.wikispaces.com/Mavila+Temperament+Modal+Harmony).
> But, it would also be nice to give the modes somewhat serious names,
> as opposed to "Fallopian" and "Delorean" and "Presbyterian" like my
> friends suggested a while back.
>
> Hence, I'd like to inquire as to what Herman and everyone else thinks
> would be a good naming system for porcupine. Any thoughts?

Capital idea. I actually started a page http://xenharmonic.wikispaces.com/Porcupine+modes to keep track of some stuff, but that should be merged into your one.

I think it makes sense for mavila to share a bunch of mode names with meantone, because they both have 4/3 generators so the structures are similar. But porcupine needs all new names.

Keenan

🔗Mike Battaglia <battaglia01@...>

On Nov 1, 2011, at 12:28 PM, "Keenan Pepper" <keenanpepper@...> wrote:

Capital idea. I actually started a page
http://xenharmonic.wikispaces.com/Porcupine+modes to keep track of some
stuff, but that should be merged into your one.

As an aside, I saw you mentioned the #.#####.# MODMOS as having 3 step
sizes of L, m, s. I suggest the sequence A/L/s/d, short for
aug/large/small/dim, to denote the relative size ordering of seconds for
any MODMOS. A is just L+c, d is s-c. So harmonic minor is LsLLsAs, and
porcupine 6|0 #7 is LssssLd.

I think it makes sense for mavila to share a bunch of mode names with
meantone, because they both have 4/3 generators so the structures are
similar. But porcupine needs all new names.

Somewhere lurking around here is that beautiful solution which is deep
enough to yield an unlimited amount of resources for naming all of the
regular temperaments, is simple enough for people to remember, which the
existing mode names are sort of related to, and are sensible enough for
working musicians to take seriously. But until we figure out what that is,
my best suggestion is Lssssss be "Kardashian" mode, and maybe sLsssss can
be Dr. Kevorkian mode.

I guess the obvious choice is species of porcupine, or something like that,
although I'm not sure how to turn that concept into something catchy or if
it's necessary. But I'll let Herman weigh in on that too.

-Mike

🔗Herman Miller <hmiller@...>

On 11/1/2011 10:08 AM, Mike Battaglia wrote:
> But I don't want to do it without Herman Miller's blessing for what
> theme he'd like the names to take.
>
> Also, I'm not sure what exactly to name them after. It would be
> fantastic to get away from regions of ancient Greece for a change (we
> just named the mavila[9] modes here:
> http://xenharmonic.wikispaces.com/Mavila+Temperament+Modal+Harmony).
> But, it would also be nice to give the modes somewhat serious names,
> as opposed to "Fallopian" and "Delorean" and "Presbyterian" like my
> friends suggested a while back.
>
> Hence, I'd like to inquire as to what Herman and everyone else thinks
> would be a good naming system for porcupine. Any thoughts?

If you want a suggestion, how about "names of stars in the constellation Ursa Major" (as "porcupine" the temperament is named after "Mizarian Porcupine Overture", which is named after the star Mizar). Otherwise, I'm okay with whatever you come up with.

I like the name "Delorean" mode, so I think I'll steal the idea for another temperament (preferably one in which "The Power of Love" can be played).

Herman

🔗Jason Conklin <jason.conklin@...>

On Tue, Nov 1, 2011 at 18:08, Herman Miller <hmiller@...> wrote:
>
> If you want a suggestion, how about "names of stars in the constellation
> Ursa Major" (as "porcupine" the temperament is named after "Mizarian
> Porcupine Overture", which is named after the star Mizar). Otherwise,
> I'm okay with whatever you come up with.
>

Named stars in the Big Dipper:

Alkaid
Alcor / Mizar (actually a bunch of binary stars)
Alioth
Megrez (near the Hubble Deep Field)
Phecda
Dubhe
Merak

Named stars in the rest of Ursa Major:

Muscida
Talitha Borealis/Australis (two stars)
Tania Borealis/Australis (two stars)
Alula Borealis/Australis (two stars)

Some pretty sweet mode names in there, if you ask me. Alcorian, Aliothan,
Megrezian, Phecdan, Dubhean, Merakian...

> I like the name "Delorean" mode, so I think I'll steal the idea for
> another temperament (preferably one in which "The Power of Love" can be
> played).
>

I'd rock out to that number!

Jason

🔗dkeenanuqnetau <d.keenan@...>

I note that any MOS has exactly one symmetrical mode, although it may be neccessary to force its generator to be an irrational fraction of its period to avoid being fooled by "non-essential" symmetries.

Therefore modes can be referred to unabiguously as "symmetric", "symmetric plus one", "symmetric minus one" etc.

e.g. for the "white note" diatonic scale the symmetric mode is the mode on D. The mode on C is symmetric minus one. The mode on E is "symmetric plus one" etc.

Alternatively the symmetric mode could be referred to as "mode 0" and others as "mode -1", "mode 1" etc. This has the property that mode -n is always the inverse of mode n.

Or if it is preferred to avoid negative numbers then just use integers modulo the number of notes N in the scale. So the diatonic mode on C would be mode 6. Mode N-n will be the inverse of mode n.

-- Dave Keenan

🔗Keenan Pepper <keenanpepper@...>

--- In tuning@yahoogroups.com, "dkeenanuqnetau" <d.keenan@...> wrote:
>
> I note that any MOS has exactly one symmetrical mode, although it may be neccessary to force its generator to be an irrational fraction of its period to avoid being fooled by "non-essential" symmetries.

This is incorrect - only MOSes with an odd number of notes per period have a symmetrical mode.

For example, meantone[12] has no symmetrical mode. You have to include either the augmented fourth or the diminished fifth, either of which makes the scale asymmetrical.

> Therefore modes can be referred to unabiguously as "symmetric", "symmetric plus one", "symmetric minus one" etc.
>
> e.g. for the "white note" diatonic scale the symmetric mode is the mode on D. The mode on C is symmetric minus one. The mode on E is "symmetric plus one" etc.
>
> Alternatively the symmetric mode could be referred to as "mode 0" and others as "mode -1", "mode 1" etc. This has the property that mode -n is always the inverse of mode n.
>
> Or if it is preferred to avoid negative numbers then just use integers modulo the number of notes N in the scale. So the diatonic mode on C would be mode 6. Mode N-n will be the inverse of mode n.

I much prefer Mike Battaglia's system of naming modes, based on generators rather than steps: http://xenharmonic.wikispaces.com/Modal+UDP+Notation

In this system the white keys starting on D is "3|3", which makes it obvious it's symmetric. The white keys starting on C is "5|1" and the white keys starting on E is "1|5", which makes it obvious they're inverses.

Keenan

🔗genewardsmith <genewardsmith@...>

🔗Keenan Pepper <keenanpepper@...>

🔗dkeenanuqnetau <d.keenan@...>

Hi Keenan,

Thanks for correcting me. I was foolishly only thinking in terms of the chain of generators, and thinking, as Gene hinted, that MOS does stand for "moment of symmetry".

I _could_ say I was wrong because a MOS with an even number of notes has _two_ symmetric "modes". But for that you'd have to allow that a "mode" can begin and end at the middle of an interval instead of on a note.

e.g. This meantone[12] as a chain of fifths is centered on the D:A fifth.
Eb Bb F C G D A E B F# C# G#

It has these two symmetric "modes"

F# G G# A Bb B C C# D Eb E F
C C# D Eb E F F# G G# A Bb B

But that's stretching things a bit.

I thought there might be some sense in which one of the above was centered on D:A but the other was centered on the wolf G#:Eb. But I can't see it.

Mike's generator-based U|D(P) notation is beautiful -- well thought out. I was not aware of it.

I note that it contains redundant information, which is not a bad thing when dealing with humans. But one _could_ define a more compact version as well, being a single integer mode number M of the kind I was trying to come up with in my previous post.

I believe it would be simply M = (U-D)/P. Knowing the name of the temperament gives you P, and knowing the number of notes in the MOS gives you N = U+D+P. Therefore the single mode number M = (U-D)/P lets you recover U and D as

U = ((U+D)+(U-D))/2
= ((N-P)+(M*P))/2

D = ((U+D)-(U-D))/2
= ((N-P)-(M*P))/2

where
M is the mode number
N is the number of notes per period, and
P is the number of periods per equivalence interval.

For example the symmetric meantone[7] mode (white notes from D) would be mode 0. Plug M = 0, N = 7, P = 1 into the above formulas and get U = 3, D = 3 so 3|3(1).

The two diminished[8] modes would be mode 1 and mode -1. Which unpack to 4|0(4) and 0|4(4).

-- Dave

🔗Mike Battaglia <battaglia01@...>

On Fri, Nov 11, 2011 at 9:07 AM, dkeenanuqnetau <d.keenan@...> wrote:
>
> I note that it contains redundant information, which is not a bad thing when dealing with humans. But one _could_ define a more compact version as well, being a single integer mode number M of the kind I was trying to come up with in my previous post.
>
> I believe it would be simply M = (U-D)/P. Knowing the name of the temperament gives you P, and knowing the number of notes in the MOS gives you N = U+D+P. Therefore the single mode number M = (U-D)/P lets you recover U and D as

Sure, or M = U would work as well, if I understand what you mean. That
could be an ultra-ultrashorthand version of the notation. Right now
U|D(P) is the long version, U|D is the short version if P = 1, and I
suppose you could just use U if you really wanted to be ultra-ultra
shorthand about it.

-Mike

🔗dkeenanuqnetau <d.keenan@...>

🔗Mike Battaglia <battaglia01@...>

On Fri, Nov 11, 2011 at 7:37 PM, dkeenanuqnetau <d.keenan@...> wrote:
>
> I was aiming for a single mode number M that preserved as many of the useful properties of the full notation as possible, including making inverses and symmetrical modes obvious (i.e. inverse of mode n is mode -n and mode 0 is symmetrical). I was also hoping adjacent modes would have mode numbers differing by 1. That requires M = (U-D)/2P and would result in modes of scales where N/P is even having mode numbers all ending in a half. i.e. ... -1.5 -0.5 0.5 1.5 ... If integers are desired, these could be rounded away from zero, -2 -1 1 2.

Hmmmm! Not a bad idea! So if I've understood, then intuitively
speaking, this just tells you the number of generators up or down from
the symmetrical mode then? And if there is no symmetrical mode, then
there's no mode 0, just +1 and -1?

-Mike

🔗dkeenanuqnetau <d.keenan@...>

🔗Mike Battaglia <battaglia01@...>

On Sun, Nov 13, 2011 at 2:40 AM, dkeenanuqnetau <d.keenan@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> > Hmmmm! Not a bad idea! So if I've understood, then intuitively
> > speaking, this just tells you the number of generators up or down from
> > the symmetrical mode then? And if there is no symmetrical mode, then
> > there's no mode 0, just +1 and -1?
>
> That's it. With your excellent rule for choosing the generator, ensuring that the most negative numbered mode has "the most flats".

So it's just (U-D)/P then. That's great! What should we call it? I'll
put it on the wiki.

UDP fingerprint perhaps? Maybe something that doesn't have to do with
UDP at all?

Also, what do you think about the notation meantone[7](...), where ...
is the mode? So it's like, meantone[7] is the function, and then it
takes one parameter which returns the scale you want. You can say
meantone[7](3|3), meantone[7](3|3(1)), meantone[7](0), all of which
specify Dorian mode.

-Mike

🔗dkeenanuqnetau <d.keenan@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> So it's just (U-D)/P then.

No, I was wrong the first time. As an Excel formula it's
M = ROUND((U-D)/(2*P),0)

>That's great! What should we call it? I'll
> put it on the wiki.
>
> UDP fingerprint perhaps? Maybe something that doesn't have to do with
> UDP at all?

Hmm. Majorness? Majoritude? Majitude? Majoricity? Majicity? Majorivity? Majivity? Majility? Majity? Majorance? But not "Majority"?

> Also, what do you think about the notation meantone[7](...), where ...
> is the mode? So it's like, meantone[7] is the function, and then it
> takes one parameter which returns the scale you want. You can say
> meantone[7](3|3), meantone[7](3|3(1)), meantone[7](0), all of which
> specify Dorian mode.

Works for me. Although I'd probably throw the word "mode" in there unless it was clear from the context, like meantone[7] mode(3|3) or meantone[7] mode 0.

🔗genewardsmith <genewardsmith@...>

🔗dkeenanuqnetau <d.keenan@...>

🔗Mike Battaglia <battaglia01@...>

On Sun, Nov 13, 2011 at 9:34 AM, dkeenanuqnetau <d.keenan@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> > So it's just (U-D)/P then.
>
> No, I was wrong the first time. As an Excel formula it's
> M = ROUND((U-D)/(2*P),0)

Oh, right. That makes sense.

> >That's great! What should we call it? I'll
> > put it on the wiki.
> >
> > UDP fingerprint perhaps? Maybe something that doesn't have to do with
> > UDP at all?
>
> Hmm. Majorness? Majoritude? Majitude? Majoricity? Majicity? Majorivity? Majivity? Majility? Majity? Majorance?

These all sound good, but they're a bit awkward. How about "majority?"

> But not "Majority"?

Well, I'm all out of ideas.

> > Also, what do you think about the notation meantone[7](...), where ...
> > is the mode? So it's like, meantone[7] is the function, and then it
> > takes one parameter which returns the scale you want. You can say
> > meantone[7](3|3), meantone[7](3|3(1)), meantone[7](0), all of which
> > specify Dorian mode.
>
> Works for me. Although I'd probably throw the word "mode" in there unless it was clear from the context, like meantone[7] mode(3|3) or meantone[7] mode 0.

OK, fair enough. Very nice.

Also, what should we name the modes of porcupine? Whatever it is, I
think it should be something that normal musicians can take seriously.
Something charming and poetic, that people would be enticed to
remember for some reason. So nothing after brands of dental floss or
whatever. It doesn't necessarily have to be Greek-sounding words that
end in "ian". (The stars in ursa major I think are a bit too arcane to
really be easily memorized, but if everyone really likes that idea we
can use that.)

If we can't come up with anything, then my friend has recommended that
we just find the most annoying mode and name it "Kardashian" mode.

BTW, we named the modes of mavila[9] a little while ago, which worked
out nicely - you can see here for the list:
http://xenharmonic.wikispaces.com/Mavila+Temperament+Modal+Harmony

This took place on the "Xenharmonic Alliance" group on Facebook, which
I'm not sure you're a part of, but Paul Erlich is really active on
there, which is a plus. It's been more active than the tuning list for
a while now, so maybe you'd enjoy checking it out.

-Mike

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

On Mon, Nov 14, 2011 at 11:50 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "dkeenanuqnetau" <d.keenan@...> wrote:
> >
> > --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> > > Great. What are U, D and P, and what is ROUND(x, y)?
>
> None of that provides the requested definitions so far as I can see, and the Xenwiki article really should.

What on the wiki article do you find ambiguous? I gave explicit
definitions and examples for everything as far as I know. Here's the
definition for UDP:

"Definition
The UDP notation for any mode is U|D|(P), where "u" specifies the
number of chroma-aligned generators "up," d specifies the number of
chroma-aligned generators "down," and p specifies the number of
periods per equivalence interval. The chroma-aligned generator is the
one such that more generators "up" also means more "major" scale
degrees, or more generally, more "large" intervals that contain the
root of the scale."

What of that do you find ambiguous?

-Mike

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> What on the wiki article do you find ambiguous? I gave explicit
> definitions and examples for everything as far as I know. Here's the
> definition for UDP:
>
> "Definition
> The UDP notation for any mode is U|D|(P), where "u" specifies the
> number of chroma-aligned generators "up," d specifies the number of
> chroma-aligned generators "down," and p specifies the number of
> periods per equivalence interval. The chroma-aligned generator is the
> one such that more generators "up" also means more "major" scale
> degrees, or more generally, more "large" intervals that contain the
> root of the scale."
>
> What of that do you find ambiguous?

You don't actually say what these terms mean, except for the definition of p. "Number of chroma-aligned generators up"--up from where? How does this define a scale? What does "more large intervals which contain the root of the scale" mean? Can'tr you try to make it a bit more like a math paper, with actual precise definitions?

🔗dkeenanuqnetau <d.keenan@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> Well, I'm all out of ideas.

How about "brightness"?

I found this article by Paul Schmeling on modes:
http://www.berkleeshares.com/music_education/major_minor_music_modes
which contains the sentence:
"Notice that Dorian sounds brighter than Aeolian, but Phrygian and especially Locrian have a much darker sound quality."

I don't know about you, but I have never memorised all those mode names and so I had to look them up to satisfy myself that the author's assessment of bright and dark did indeed correspond to the relative number of sharps or flats when the modes are on the same tonic.

In fact you use "bright" and "dark" with the same meaning here:
http://xenharmonic.wikispaces.com/Modal+UDP+Notation

So instead of meaningless names that have to be memorised, or looked up every time, like

Lydian
Ionian
Mixolydian
Dorian
Aeolian
Phrygian
Locrian

why not call them

ultra-dark
very-dark
dark
medium
bright
very-bright
ultra-bright

There are 3 more standard prefixes available -- super, extremely, tremendously -- which is more than enough -- getting us as far as 13 note scales -- way beyond the Miller limit. They were standardised for the naming of radio frequency bands.
http://en.wikipedia.org/wiki/ITU_Radio_Bands#By_frequency

> Also, what should we name the modes of porcupine? Whatever it is, I
> think it should be something that normal musicians can take seriously.
> Something charming and poetic, that people would be enticed to
> remember for some reason.

I'm afraid I consider the desire for yet more meaningless names that waste precious human memory resources or waste precious human lifetimes looking them up, to be a form of collective insanity that has overtaken this list (and apparently others). :-)

It's lots of fun for the people doing the naming. But not much fun for those who come in late and want to join the conversation, but don't have a clue what you're talking about. "Ultra-dark" is poetic enough for me.

If you must have meaningless names then why not reuse the existing Greek terms, in generator order, and add a few more at each end for scales with more than 7 notes. See
http://en.wikipedia.org/wiki/File:Anatolia_Ancient_Regions_base.svg
(Locri is in Italy and Mixolydia doesn't exist. It just mixes the properties of Lydian with those of another mode, apparently Dorian).

-- Dave

🔗Mike Battaglia <battaglia01@...>

On Tue, Nov 15, 2011 at 1:03 AM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > What on the wiki article do you find ambiguous? I gave explicit
> > definitions and examples for everything as far as I know. Here's the
> > definition for UDP:
> >
> > "Definition
> > The UDP notation for any mode is U|D|(P), where "u" specifies the
> > number of chroma-aligned generators "up," d specifies the number of
> > chroma-aligned generators "down," and p specifies the number of
> > periods per equivalence interval. The chroma-aligned generator is the
> > one such that more generators "up" also means more "major" scale
> > degrees, or more generally, more "large" intervals that contain the
> > root of the scale."
> >
> > What of that do you find ambiguous?
>
> You don't actually say what these terms mean, except for the definition of p. "Number of chroma-aligned generators up"--up from where? How does this define a scale? What does "more large intervals which contain the root of the scale" mean? Can'tr you try to make it a bit more like a math paper, with actual precise definitions?

I would very much like to make it more like a math paper, with actual
precise definitions. It would help me to do so if you could precisely
detail what level of precision mathematicians consider to be
necessary. This is an interdisciplinary field, so obviously that's not
something I would know.

But I have to ask, do you really find the page to be that unclear, or
are you just saying that you don't like the stylistic tone of the
article or something?

-Mike

🔗Mike Battaglia <battaglia01@...>

On Tue, Nov 15, 2011 at 1:16 AM, dkeenanuqnetau <d.keenan@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> > Well, I'm all out of ideas.
>
> How about "brightness"?
>
> I found this article by Paul Schmeling on modes:
> http://www.berkleeshares.com/music_education/major_minor_music_modes
> which contains the sentence:
> "Notice that Dorian sounds brighter than Aeolian, but Phrygian and especially Locrian have a much darker sound quality."
>
> I don't know about you, but I have never memorised all those mode names and so I had to look them up to satisfy myself that the author's assessment of bright and dark did indeed correspond to the relative number of sharps or flats when the modes are on the same tonic.

Yeah, that's a great idea. That's what they called it at UM. Maybe we
can call it the "brightness coefficient" or something?

> There are 3 more standard prefixes available -- super, extremely, tremendously -- which is more than enough -- getting us as far as 13 note scales -- way beyond the Miller limit. They were standardised for the naming of radio frequency bands.
> http://en.wikipedia.org/wiki/ITU_Radio_Bands#By_frequency

Eh, Miller limit schmiller limit. I have 12 notes in my head just
fine, and it's taken me several years now to learn to think in 9-EDO
or 10-EDO. Plus, there's this

http://en.wikipedia.org/wiki/The_Magical_Number_Seven,_Plus_or_Minus_Two

But anyway, I like the idea you've laid out here - names based on
brightness, what a concept! Although I think the radio spectrum names
are a bit counterintuitive, but as far as 7-note scales are concerned,
this scheme works fine

Ultrabright
Superbright
Bright
Symmetric
Dark
Superdark
Ultradark

Whether this is better than the radio version is up for debate, but
man, what a concept! Maybe there's some cool sounding name for shades
of brightness...

> > Also, what should we name the modes of porcupine? Whatever it is, I
> > think it should be something that normal musicians can take seriously.
> > Something charming and poetic, that people would be enticed to
> > remember for some reason.
>
> I'm afraid I consider the desire for yet more meaningless names that waste precious human memory resources or waste precious human lifetimes looking them up, to be a form of collective insanity that has overtaken this list (and apparently others). :-)
>
> It's lots of fun for the people doing the naming. But not much fun for those who come in late and want to join the conversation, but don't have a clue what you're talking about. "Ultra-dark" is poetic enough for me.

I agree in general, but I think this is actually important. Porcupine
is one of the best temperaments there is, and I actually want to use
these scales. And it's rather annoying to talk constantly about
porcupine[7] 4|2, or even porcupine[7]+1, or something like that.
Especially if you're saying it out loud.

I like your brightness-oriented names though, that's the obvious and
very creative solution.

> If you must have meaningless names then why not reuse the existing Greek terms, in generator order, and add a few more at each end for scales with more than 7 notes. See
> http://en.wikipedia.org/wiki/File:Anatolia_Ancient_Regions_base.svg
> (Locri is in Italy and Mixolydia doesn't exist. It just mixes the properties of Lydian with those of another mode, apparently Dorian).

I think that'd be more confusing than coming up with new names. We did
that though with the modes of mavila[9], where it actually ended up
making some kind of sense:
http://xenharmonic.wikispaces.com/Mavila+Temperament+Modal+Harmony

-Mike

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

On Tue, Nov 15, 2011 at 2:12 AM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > But I have to ask, do you really find the page to be that unclear, or
> > are you just saying that you don't like the stylistic tone of the
> > article or something?
>
> But I don't like dealing with definitions which aren't built up in logical order. First define, precisely, what "up" and "down" mean, then define, precisely, what your base point is. Then define how, using the base point and "up" and "down", you can define a mode of a MOS. The basic stuff. Avoid dragging in terms like "chroma" unless the definition really needs them. I'm also wondering about the formula which was tossed out but never really explained.

If we're to be really rigorous, then you need to define a base point
before you can even define anything called a "mode." Without some
concept of a "root" for some scale, there is no such thing as a mode
at all, and otherwise there's no difference between LLsLLLs and
sLLLsLL either. Both of them imply some kind of arbitrary starting and
stopping point, and without that you just have
...LLsLLLsLLsLLLsLLsLLLs... as a infinite set.

The base point is completely subjective, and in some cases arbitrary.
So we can say that a mode is defined with respect to a periodic scale
s[n], an equivalence interval, and a note in the scale called the
"root."

UDP notation is only defined for periodic scales which are also MOS.
Periodic scales which are MOS can also be written out as 1D Fokker
blocks in period-equivalent space. However, it isn't clear which way
to orient the axes on this line; there are two possible ways to do it.
UDP notation orients the axes such that the translation of the set in
the positive direction causes a new periodic scale s'[n] to be formed,
and where s'[n] >= s[n] for all n. This also means that the point
corresponding to L is on the positive side of the axis, and the point
corresponding to L-s is also on the positive side of the axis. This
also orients the axes such that the point (0,1) corresponds to the
generator of the MOS which is the larger specific interval in its
generic interval class.

Example: the axes should be oriented for meantone[7] such that 3/2
corresponds to the point 1 on the line. For mavila[7], they should be
oriented such that 4/3 corresponds to point 1.

For a periodic MOS s[n], call its convex representation in period
equivalent space S[g]. Every entry in S[g] will be in the form [* g>,
where this specifies a period-equivalent monzo within the tempered
lattice. Let [* r> correspond to the note chosen as root. Then, the
number of generators "up" consists of the number of points that are in
S[g] and in which g>r, multiplied by the number of periods per octave.
The number of generators "down" consists of the number of points that
are in S[g] and in which g<r, multiplied by the number of periods per
octave.

UDP is then up|down(period), or up|down for short. For example,
porcupine's sssLsss mode is 3|3(1), or 3|3 for short. There are 18
other examples on the wiki page as well.

Dave's "brightness" measure is then round((up-down)/(2*period)), where
the round(n) function returns the integer with the next-largest
absolute value if abs(frac(n)) >= 0.5, and with the next-smallest
absolute value if abs(frac(n)) < 0.5.

-Mike

🔗Mike Battaglia <battaglia01@...>

Also, you wrote this:

On Tue, Nov 15, 2011 at 2:12 AM, genewardsmith
<genewardsmith@...> wrote:
> I'm also wondering about the formula which was tossed out but never really explained.

That was one of Keenan's contributions. Here's a sketch of his proof:

For some MOS xLys, if we're looking at the period-equivalent generator
chain, then x*L + y*s = 0, where L and s denote points on the chain.
Since we're using a contiguous chain of generators of length x+y, then
the only two solutions actually present in the MOS are that L = y and
s = -x, or L = -y and s = x. However, we already know that we want L-s
to be positive, which means we want L to be positive and s to be
negative. Since x and y are both positive, the sole remaining solution
is that L = y and s = -x. So for 5L2s, L will be 2 chroma-aligned
generators and s will be -5 chroma-aligned generators.

The expression 1/y mod (x+y) can hence be turned into 1/L mod (L-s);
this expression hence tells you how many segments of generators
representing "L" it takes you to get to a generator, mod the acquired
chromas. But segments of generators representing "L" translate to
steps in the scale, since L is one step in the scale. So this also
tells you the number of "L" steps it takes to get to a generator, mod
all the acquired chromas. Hence, it also tells you how many steps it
takes you to get to the generator, and hence it tells you what scale
degree the generator is on.

I added one on the wiki article, so that it's (1/y mod (x+y)) + 1, so
that it hence gives you this number in a form that matches up with the
common terminology for scale degrees: a value of 5 means it's "a
fifth," a value of 4 means it's "a fourth," a value of 3 means it's "a
third," etc. Otherwise it's that a value of 4 means it's a fifth and
so on.

I think Keenan knows some more general theorem that led him to suspect
this, though, because he conjectured it almost immediately after
hearing the problem and said it "seemed obvious" to him. So maybe
there's a simpler proof than the one outlined above.

-Mike

🔗dkeenanuqnetau <d.keenan@...>

Mike,

All you need to do to improve your UDP page is add [up or down] "from the tonic". You have used the word "root" in some places, but that's not strictly correct. A chord has a root. A scale has a tonic, which is simply its first note.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> But anyway, I like the idea you've laid out here - names based on
> brightness, what a concept! Although I think the radio spectrum names
> are a bit counterintuitive, but as far as 7-note scales are concerned,
> this scheme works fine
>
> Ultrabright
> Superbright
> Bright
> Symmetric
> Dark
> Superdark
> Ultradark
>
> Whether this is better than the radio version is up for debate, but
> man, what a concept! Maybe there's some cool sounding name for shades
> of brightness...

I assume you understand that I intend these names to apply to _any_ MOS, not only Porcupine[7]. So, given that article on Miller's magic number (thanks), we would want to have _at_least_ 13 such names up our sleeve, which means at least 5 intensifiers or booster prefixes.

Unfortunately there seems to be no agreement on the ordering of: Very, Extra, Super-, Hyper-, Mega-, Ultra- and Extremely. Not to mention the more rare or frivolous Giga, Turbo, Uber and Tremendously.

About the only thing that everyone _except_ the radio guys agrees on is that Ultra comes after (is greater than) Super.

Based on some Google research and hit-count measurements I just did, what seems to happen is something like this: If you think you only need 2 you use Super and Ultra (although the radio guys used Very and Ultra). If you think you need 3 you use Super, Hyper and Ultra in that order. If you think you need 4 you use Super, Hyper, Mega and Ultra in that order. Everyone wants "Ultra" to be the last one because it sounds so much like "ultimate". But people find out later that they need more than they thought they would. They have already used "Ultra" so they have no choice but to use whatever's left and make it come _after_ Ultra. So we end up with a complete mess. No consistency whatsoever. I'm pretty sure that's what happened with the radio spectrum.

So maybe it would be better to use the intensifiers that are commonly used for cream and chocolate.

triple dark
double dark
dark
symmetric
bright
double bright
triple bright

There's no need to make your page read like a math textbook. Some diagrams wouldn't hurt though. e.g. [display as monospaced source]

BbF C G D A E D dark (D minor)
4 | 2

F C G D A E B D symmetric
3 | 3

C G D A E B F# D bright
2 | 4

G D A E B F#C# D double bright (D major)
1 | 5

-- Dave

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

On Tue, Nov 15, 2011 at 7:47 AM, dkeenanuqnetau <d.keenan@...> wrote:
>
> Mike,
>
> All you need to do to improve your UDP page is add [up or down] "from the tonic". You have used the word "root" in some places, but that's not strictly correct. A chord has a root. A scale has a tonic, which is simply its first note.

There are a few problems with that.

First is that if Gene wasn't happy with me just dropping the word
"root" without further explanation, I doubt he'd be happy with the
word "tonic" either. And the problem is finding a rigorous
mathematical way to make reference to the "first note" of a scale,
which is harder to pin down than you think; the concept has its origin
in a subjective perceptual distinction that doesn't even need to
include 1/1.

Secondly, the root doesn't have to be the tonic of the piece. I used
the word "root" deliberately here. For example, if I were going to do
Dm7 -> G7#11 -> Cmaj, I'd do D dorian over the first chord, G lydian
dominant over the second one, and C ionian over the last one. That'd
be a case in which the mode is defined with regard to the root, not
just the tonic. There's a mode defined over the tonic in this case
too, which is C major or ionian. Another example would be if I were
playing Dm7b5 -> G7#11b13 -> Cm, I might play D locrian #2 over the
first chord, G altered over the second, and C melodic minor over the
last one.

It's not uncommon in lead sheets for jazz to see things notated like
Cphry | Flyd | etc. It's common to see "modal" pieces written that
way. A few examples of compositions in this style:

http://www.youtube.com/watch?v=MigYYKlttV8
http://www.youtube.com/watch?v=P1jOIAos3nk

etc.

> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> > But anyway, I like the idea you've laid out here - names based on
> > brightness, what a concept! Although I think the radio spectrum names
> > are a bit counterintuitive, but as far as 7-note scales are concerned,
> > this scheme works fine
> >
> > Ultrabright
> > Superbright
> > Bright
> > Symmetric
> > Dark
> > Superdark
> > Ultradark
> >
> > Whether this is better than the radio version is up for debate, but
> > man, what a concept! Maybe there's some cool sounding name for shades
> > of brightness...
>
> I assume you understand that I intend these names to apply to _any_ MOS, not only Porcupine[7]. So, given that article on Miller's magic number (thanks), we would want to have _at_least_ 13 such names up our sleeve, which means at least 5 intensifiers or booster prefixes.

Yeah, I think it's an awesome idea. It's exactly what I had in mind:
something poetic, which has some sort of basic synesthetic correlate
which isn't too demanding, something which doesn't sound cheesy,
something which works for every MOS. And it's something musicians can
remember because they already know the "bright"/"dark" dichotomy. It's
definitely the best solution possible for this problem.

Damn, I spent weeks on this!

> triple dark
> double dark
> dark
> symmetric
> bright
> double bright
> triple bright
>
> There's no need to make your page read like a math textbook. Some diagrams wouldn't hurt though. e.g. [display as monospaced source]

That's great. Yeah, I like that a lot. I'll also ask some of my
musician friends what they think as well, just to see if they have any
ideas too. We have names like "augmented fifth" in music, but then
that got compressed to #5.

It's becoming some kind of weird hobby of mine to take ideas that seem
extremely mathematical and arcane in nature and figure out how they're
related to ordinary things that all musicians know. I'm not sure why
it's so difficult to see these correspondences sometimes. Even better
is when it works in reverse, when you realize something that's already
intuitive and obvious has some correlate in an arcane mathematical
concept, like with MODMOS's.

-Mike

🔗Mike Battaglia <battaglia01@...>

On Tue, Nov 15, 2011 at 1:48 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> Thanks Mike. This is much more comprehensible, particularly because of the definition of "up".
>
> > So we can say that a mode is defined with respect to a periodic scale
> > s[n], an equivalence interval, and a note in the scale called the
> > "root."
>
> Good start, but why call the base point the "root"? What about "tonic" or something of that sort?

Because the tonic usually refers to the tonal center of a piece, and
modes are often refined with respect to individual chords. For
example, over in 12-equal, dominant 7 chords, you can play mixolydian
(4|2), lydian dominant (4|2 #4), octatonic (0|4), or if you omit the
5th, you can use the altered scale, which has its origin in schismatic
temperament (0|6 b4).

So for Dm7 G7 Cmaj it might make sense to just say that the whole
thing is part of C major, but for Dm7 G7#11 Cmaj it wouldn't, because
the #11 in G will be C#. So you'd tell someone to "play D dorian over
the first one," "play G lydian dominant or octatonic over the second
one," "play C ionian over the last one." That'd be a case in which
modes are defined with respect to each passing chord, not just the
overarching mode of the piece. See my response to Dave Keenan for
more.

> Also, are you planning to edit the UDP article? If you don't I'm afraid I will.

I'll edit it, but perhaps you should get it started so I can see what you want.

This is the same problem that we ran into when I was editing the
articles for "val" and such, just in reverse - this time it's a
general theory article being made more mathematical. I can see that
the way I mathematically described the notation above made immediate
and obvious sense to you, but I think the way it's written will make
more conceptual sense for musicians without a mathematical background.
So there are 2 solutions -

1) Make an all-in-one math+general version and link to it on both pages
2) Spin this version off into a mathematical version and link to that
on the "Mathematical Theory" pages

What do you think?

-Mike

🔗dkeenanuqnetau <d.keenan@...>

A key or scale is conventionally named by giving the name of one note and the name for the pattern of step sizes up from that note. The note is called the tonic and the pattern of step sizes is called the mode. <key> = <tonic> <mode> e.g. C major, F phrygian.

It doesn't matter whether the music is atonal or the key changes with every chord. If a key name appears, the note the key is named after is called the tonic. The note a chord is named after is called the root.

There's no need to worry about any other definition of tonic, or what it means to be the "first note".

Of course when we go microtonal we add the name of the MOS as well (which was conventionally assumed to be meantone[7]). So now we have
<key> = <MOS> <tonic> <mode>
<MOS> = <temperament> "[" <cardinality> "]"

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> Secondly, the root doesn't have to be the tonic of the piece.

I would say "The tonic doesn't have to be the tonal center of the piece".

> I used
> the word "root" deliberately here. For example, if I were going to do
> Dm7 -> G7#11 -> Cmaj, I'd do D dorian over the first chord, G lydian
> dominant over the second one, and C ionian over the last one. That'd
> be a case in which the mode is defined with regard to the root, not
> just the tonic.

I would say that in this case the tonic changes to match the root of each chord, not just the tonal center of the piece.

> There's a mode defined over the tonic in this case
> too, which is C major or ionian.

"There's a mode defined over the tonal centre in this case too ..."

----------------------
UDP notation is defined in such a way that it simultaneously describes the following properties of the mode in question:

How many scale degrees (or intervals up from the tonic) are of the "larger" or "major" variant, vs the "smaller" or "minor" variant.
How many generators up vs down (from the tonic) it requires to generate the mode.
----------------------

-- Dave

🔗Mike Battaglia <battaglia01@...>

On Tue, Nov 15, 2011 at 5:48 PM, dkeenanuqnetau <d.keenan@...> wrote:
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> > Secondly, the root doesn't have to be the tonic of the piece.
>
> I would say "The tonic doesn't have to be the tonal center of the piece".
>
> > I used
> > the word "root" deliberately here. For example, if I were going to do
> > Dm7 -> G7#11 -> Cmaj, I'd do D dorian over the first chord, G lydian
> > dominant over the second one, and C ionian over the last one. That'd
> > be a case in which the mode is defined with regard to the root, not
> > just the tonic.
>
> I would say that in this case the tonic changes to match the root of each chord, not just the tonal center of the piece.

So what would you say for Cmaj -> Am -> Dm -> Gmaj -> Cmaj? That the
tonic keeps changing from C -> A -> D -> G -> C? That's a different
terminology than I'm used to. I would say that the tonic is still C
throughout (unless I modulate to some other key). I'd say that the
chord keeps changing, that the root is the "main note" for the chord,
and that the mode at any moment is the scale you'd play to flesh out
each of those chords, which means it's defined with respect to the
same root as the chord.

> > There's a mode defined over the tonic in this case
> > too, which is C major or ionian.
>
> "There's a mode defined over the tonal centre in this case too ..."

I've been using the term "tonic" synonymously with "tonal center." How
are you using it and how is it different from a root?

> ----------------------
> UDP notation is defined in such a way that it simultaneously describes the following properties of the mode in question:
>
> How many scale degrees (or intervals up from the tonic) are of the "larger" or "major" variant, vs the "smaller" or "minor" variant.
> How many generators up vs down (from the tonic) it requires to generate the mode.
> ----------------------

Other than the use of the word "tonic" I'm happy with that, but what
does Gene think?

-Mike

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

On Tue, Nov 15, 2011 at 6:41 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > First is that if Gene wasn't happy with me just dropping the word
> > "root" without further explanation, I doubt he'd be happy with the
> > word "tonic" either. And the problem is finding a rigorous
> > mathematical way to make reference to the "first note" of a scale,
> > which is harder to pin down than you think; the concept has its origin
> > in a subjective perceptual distinction that doesn't even need to
> > include 1/1.
>
> If S is a periodic scale, then S[0]=0 is the "first note".

I thought you wanted S[0] = 0 to be the "1/1" for the whole piece.

Consider the chord progression Cmaj | Am | Dm | Gmaj | Cmaj. Let's say
I'm soloing and I just play C major over the whole thing. Does S
remain the same throughout the progression?

What if instead I said that I play C ionian, A aeolian, D dorian, G
mixolydian, and C ionian, in order? That's the same as C major, but I
just phrased it differently. Does S change then?

Consider the chord progression Cmaj | F#7 | Fmaj7 | G7b9#11 | Cmaj.
I'd play C ionian over the first chord, F# octatonic over the second,
F lydian over the third one, G octatonic over the fourth one, and C
ionian over the last one. Does S change in that case?

-Mike

🔗genewardsmith <genewardsmith@...>

🔗dkeenanuqnetau <d.keenan@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> So what would you say for Cmaj -> Am -> Dm -> Gmaj -> Cmaj? That the
> tonic keeps changing from C -> A -> D -> G -> C?

Not at all. (Assuming that's intended as a sequence of chords, not a sequence of keys or scales). A tonic is part of a key or scale and not a part of a chord. A root is a part of a chord and not a part of a key or scale.

> I would say that the tonic is still C
> throughout (unless I modulate to some other key).

That may be the case, but how can we tell that from the list of chord names. If we saw it on the staff, or with additional annotations of the kind you mentioned previously "F phryg" etc) it might show otherwise. Excuse me while I replace the LYD of my ION MIXture, and shut the DOR of AEOL PHRYG and LOC it. :-)

> I'd say that the
> chord keeps changing, that the root is the "main note" for the chord,

No argument with that.

> and that the mode at any moment is the scale you'd play to flesh out
> each of those chords, which means it's defined with respect to the
> same root as the chord.

The chord sequence alone doesn't tell us that. But if you tell me that this specific genre requires that the scale change to one whose name begins with the same note name that the chord name begins with, then yes I would say that the tonic changes from C -> A -> D -> G -> C, because I'm taking "tonic" to mean nothing more than "the note the scale is named after", just as the "root" need be nothing more than "the note the chord is named after". However the tonal centre of the piece as a whole may be considered to remain as C throughout, or it may have no tonal centre.

> I've been using the term "tonic" synonymously with "tonal center."
> How are you using it and how is it different from a root?

I don't know how to explain that better than in my previous message. Maybe reread it now that you understand that I _am_ using the two terms differently. And maybe try substituting the word "scale" for the word "key". And hopefully the above will help.

I'm not saying this is common usage. I just think it will cause less confusion relative to common usage than will adopting the term "root" for a property of a scale, since it has previously only been the property of a chord.

The correspondence that you point to, between the roots of chords and the notes which the scales are named after, seems to me to belong only to one specific musical genre.

-- Dave

🔗genewardsmith <genewardsmith@...>

🔗dkeenanuqnetau <d.keenan@...>

🔗Mike Battaglia <battaglia01@...>

On Tue, Nov 15, 2011 at 7:24 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> >
> >
> >
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > > What do you think?
> >
> > Why don't I do an edit and then you decide how it needs to be fixed?
>
> I stuck in a mathematical definition section. I still think the article is a bit of a mess.

I'm not entirely sure that I understand your definition; it doesn't
seem to be the same thing I'm describing. I guess I really did a bad
job of explaining it after all. I could rigorously debug your
definition, but I think I've failed to explain the core idea to you.
(Now you know how I felt when I was trying to understand tablets!) I
think the best way to explain what I mean is by drawing a diagram. If
you think that this is what you said, then I'll debug your definition
on the wiki instead.

The entire thing requires a paradigm shift to stop looking at MOS's as
second-based patterns of scale steps, e.g. LLsLLLs, and instead look
at them as octave-reduced generator chains, e.g. rank-2 periodicity
blocks. There are some simple theorems which can translate statements
from one viewpoint into the other. But without further ado, here is a
nicely readable table with the UDP-notated 7 diatonic modes:

/tuning/files/MikeBattaglia/UDPTable.gif

The Fundamental Theorem of MOS Modal Harmony is basically that
shifting the periodicity block by a single generator in either
direction will give you a periodic scale that has every note in common
with the original except one. This note will be either sharpened or
flattened from the original by exactly the interval of size L-s.
Furthermore, translation of an n-sized block by m units results in a
new periodic scale which has (n-m) tones in common with the original,
unless n-m is negative in which case it has 0 tones in common with the
original.

The thing that you described has to do with cyclically rotating the
pattern of step sizes in the mode, so that a "modal shift" of 1
changes LLsLLLs into LsLLLsL - from Ionian to Dorian. If you replace
the cyclic shift in your definition by a translation of the set on the
octave-equivalent lattice, then your definition holds true.

-Mike

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Tue, Nov 15, 2011 at 7:24 PM, genewardsmith

> I'm not entirely sure that I understand your definition; it doesn't
> seem to be the same thing I'm describing.

Your diagram makes it clear it is just backwards. The Lydian mode is the highest one up, so I thought it would be notated 0|6 since there are no modes up and six down, but you have it as 6|0.

I guess I really did a bad
> job of explaining it after all. I could rigorously debug your
> definition, but I think I've failed to explain the core idea to you.

Since it's just backwards, I don't think so.

> The entire thing requires a paradigm shift to stop looking at MOS's as
> second-based patterns of scale steps, e.g. LLsLLLs, and instead look
> at them as octave-reduced generator chains, e.g. rank-2 periodicity
> blocks.

Octave-reduced generator chains is the standard way to look at a MOS. I prefer not to use either of your "paradigms" and work with periodic scales.

> The thing that you described has to do with cyclically rotating the
> pattern of step sizes in the mode, so that a "modal shift" of 1
> changes LLsLLLs into LsLLLsL - from Ionian to Dorian.

Nothing I said has anything to do with changing Ionian to Dorian in one step. Note I did not say shift up or down by U or D, but by mU or mD, where m what you need to get to the generator.

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

On Tue, Nov 15, 2011 at 9:52 PM, genewardsmith
<genewardsmith@...> wrote:
>
> > The entire thing requires a paradigm shift to stop looking at MOS's as
> > second-based patterns of scale steps, e.g. LLsLLLs, and instead look
> > at them as octave-reduced generator chains, e.g. rank-2 periodicity
> > blocks.
>
> Octave-reduced generator chains is the standard way to look at a MOS. I prefer not to use either of your "paradigms" and work with periodic scales.

I don't understand. Octave-reduced generator chains are the second way
I said. You just said that the second way I said is the standard way
to look at an MOS, but that you prefer to not look at them in either
of the ways I've said, and instead prefer to work with them in the
first way I said.

> > The thing that you described has to do with cyclically rotating the
> > pattern of step sizes in the mode, so that a "modal shift" of 1
> > changes LLsLLLs into LsLLLsL - from Ionian to Dorian.
>
> Nothing I said has anything to do with changing Ionian to Dorian in one step. Note I did not say shift up or down by U or D, but by mU or mD, where m what you need to get to the generator.

That's not what you originally said, but I see that you've changed it.
But you still have this:

"Given a periodic scale S, a modal shift by n may be defined as S'[i]
= S[i+n]-S[n]. A modal shift is a shift up if S'[i] >= S[i] for all i.
This definition applies to the case which especially concerns us,
where S is a monotonically strictly increasing periodic scale defined
by a MOS. In this case, depending on the choice of generator g, shifts
up will occur either when n is positive (if m such that S[m]=g shifts
up) or negative (if it shifts down.)"

It looks like modal shifts by successive values of "n" will result in
successive cyclic rotations of the scale. Then you say that depending
on the choice of g, all of the shifts of positive n will either be
"up" or "down," depending on whether the generator is sharpened or
not. However, this isn't true; if you're in ionian mode then modal
shifting by n=1 is dorian, which is down, and modal shifting by n=-1
is locrian, which is also down. Another example is starting on
phrygian, where both n=1 and n=-1 shift up. And if you start on
dorian, then S[m] = g doesn't change for either n=1 or n=-1 regardless
of the choice of g.

-Mike

🔗dkeenanuqnetau <d.keenan@...>

🔗Mike Battaglia <battaglia01@...>

On Tue, Nov 15, 2011 at 7:31 PM, dkeenanuqnetau <d.keenan@...> wrote:
>
> > I would say that the tonic is still C
> > throughout (unless I modulate to some other key).
>
> That may be the case, but how can we tell that from the list of chord names. If we saw it on the staff, or with additional annotations of the kind you mentioned previously "F phryg" etc) it might show otherwise. Excuse me while I replace the LYD of my ION MIXture, and shut the DOR of AEOL PHRYG and LOC it. :-)

I was just assuming, that if you played that progression, you'd hear
it centered around C. I guess you could hear it centered around
something else. C ionian | A aeolian | D dorian | G mixolydian | C
ionian is something you'd probably hear as C major, I'll wager.

> > and that the mode at any moment is the scale you'd play to flesh out
> > each of those chords, which means it's defined with respect to the
> > same root as the chord.
>
> The chord sequence alone doesn't tell us that.

The chord sequence alone gives you a set of possible modes that you
can play. You'll probably want to play ones that are Rothenberg
proper. For example, C7#11 could be C lydian dominant (4|2 #4), or C
octatonic (0|4(4). If we're in the key of F, then I have to be able to
have a definition of "mode" that allows me to refer to something like
"C octatonic" without insinuating that the tonic has switched to C.

> But if you tell me that this specific genre requires that the scale change to one whose name begins with the same note name that the chord name begins with

this/DT specific/JJ genre/NN requires/VBZ that/IN the/DT scale/NN
change/VBP to/TO one/CD whose/WP$ name/NN begins/VBZ with/IN the/DT
same/JJ note/NN name/NN that/IN the/DT chord/NN name/NN begins/VBZ
with/IN

(ROOT
(S
(NP (DT this) (JJ specific) (NN genre))
(VP (VBZ requires)
(SBAR (IN that)
(S
(NP (DT the) (NN scale))
(VP (VBP change)
(PP (TO to)
(NP
(NP (CD one))
(SBAR
(WHNP (WP$ whose) (NN name))
(S
(VP (VBZ begins)
(PP (IN with)
(NP (DT the) (JJ same) (NN note) (NN name)))
(SBAR (IN that)
(S
(NP (DT the) (NN chord) (NN name))
(VP (VBZ begins)
(PP (IN with))))))))))))))))

So then yes.

> then yes I would say that the tonic changes from C -> A -> D -> G -> C, because I'm taking "tonic" to mean nothing more than "the note the scale is named after", just as the "root" need be nothing more than "the note the chord is named after". However the tonal centre of the piece as a whole may be considered to remain as C throughout, or it may have no tonal centre.
//snip
> > I've been using the term "tonic" synonymously with "tonal center."
> > How are you using it and how is it different from a root?
>
> I don't know how to explain that better than in my previous message. Maybe reread it now that you understand that I _am_ using the two terms differently. And maybe try substituting the word "scale" for the word "key". And hopefully the above will help.
//snip
> I'm not saying this is common usage. I just think it will cause less confusion relative to common usage than will adopting the term "root" for a property of a scale, since it has previously only been the property of a chord.

The way I used "root" is the way it was taught to me in music school.
When you build a triad in some scale, you play root, third, fifth of
the scale. So in this usage, the word "root" is already used to mean
the lowest note in the scale (although I wonder if in Gregorian chant
that'd be different for the hypo-modes, where the main note is in the
middle of the scale).

Modes are effectively a way to generalize triadic harmony to heptadic
harmony, except to avoid critical band effects you just don't play all
of the notes at the same time in closed voicing.

> The correspondence that you point to, between the roots of chords and the notes which the scales are named after, seems to me to belong only to one specific musical genre.

I'm not sure what you mean by this. Nothing I've said is genre
specific. What exactly is a note that a scale is named after?

-Mike

🔗Mike Battaglia <battaglia01@...>

On Tue, Nov 15, 2011 at 11:03 PM, dkeenanuqnetau
<d.keenan@...> wrote:
>
> I note that a direct reading of the inevitable diagrams leads naturally to a D|U(P) notation, whereas you have been using U|D(P). I notice the wiki page has only been up for two weeks and would guess that the number of people already using the notation could be counted on the fingers of one hand, so it's not too late to save posterity from possibly decades of needless confusion.
>
> Is there any reason to prefer U|D to D|U?

It only leads naturally to a D|U(P) notation because I chose to
arrange the periodicity block going from left to right in
pitch-ascending order, because that's the direction in which we as
English readers tend to read things. If I had arranged the block going
from up to down, so that it looked more like this

Ionian: 5|1

B
E
A
D
G
C <---
F

then such diagrams would lead naturally to a U|D(P) notation, because
we also tend to read from up to down instead of from left to right.
And this way would probably be more illustrative for pedagogical
purposes, because it makes it so that more generators "up" is actually
"up." So I'd rather change the diagrams than the notation, but this
was just something quick.

-Mike

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> > Octave-reduced generator chains is the standard way to look at a MOS. I prefer not to use either of your "paradigms" and work with periodic scales.
>
> I don't understand. Octave-reduced generator chains are the second way
> I said. You just said that the second way I said is the standard way
> to look at an MOS, but that you prefer to not look at them in either
> of the ways I've said, and instead prefer to work with them in the
> first way I said.

No, I said I prefer not to work with them in either way, and use periodic scales instead. That means no octave reduced anything.

> > Nothing I said has anything to do with changing Ionian to Dorian in one step. Note I did not say shift up or down by U or D, but by mU or mD, where m what you need to get to the generator.
>
> That's not what you originally said, but I see that you've changed it.

I only changed it so that it's mD up and mU down.

> It looks like modal shifts by successive values of "n" will result in
> successive cyclic rotations of the scale.

That's true, but it's irrelevant since I look at shifts spaced by m rather than by 1.

Then you say that depending
> on the choice of g, all of the shifts of positive n will either be
> "up" or "down," depending on whether the generator is sharpened or
> not. However, this isn't true; if you're in ionian mode then modal
> shifting by n=1 is dorian, which is down, and modal shifting by n=-1
> is locrian, which is also down.

OK, have to fix that.

🔗genewardsmith <genewardsmith@...>

🔗dkeenanuqnetau <d.keenan@...>

🔗genewardsmith <genewardsmith@...>

🔗dkeenanuqnetau <d.keenan@...>

🔗Charles Lucy <lucy@...>

I fail to understand why you are wasting everybody's time with this chaining of fourths and fifths naming.
You seem to be re-inventing the wheel; it was already worked out years ago:
see:
http://www.harmonics.com/scales/
and
http://www.lucytune.com/new_to_lt/pitch_05.html

On 16 Nov 2011, at 06:08, dkeenanuqnetau wrote:

> I'd prefer to use 0|6 for Lydian too, but surely "D" is intended to stand for "down" and "U" for "up" (in generators from the tonic), so that should be called D|U.
>
> /tuning/files/MikeBattaglia/UDPTable.gif
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> > --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> > > --- In tuning@yahoogroups.com, "dkeenanuqnetau" <d.keenan@> wrote:
> > >
> > > > Is there any reason to prefer U|D to D|U?
> > >
> > > I'd prefer to use 6|0 for Lydian and call that U|D.
> >
> > Sorry, I meant 0|6.
>
>

Charles Lucy
lucy@...

-- Promoting global harmony through LucyTuning --

For more information on LucyTuning go to:

http://www.lucytune.com

LucyTuned Lullabies (from around the world) can found at:

http://www.lullabies.co.uk

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

I have a problem with all of this, which is that I and others have
already been using it this way for about 3 months now and nobody
bothered to complain when I first introduced it. I introduced it on XA
even prior to this, but on tuning-math first posted about it here:

/tuning-math/message/19404

I even asked at the time for feedback on it, for example whether or
not ssLssssLss Pajara should be 4|4(2) or 2|2(2) (the thread left off
with 2|2(2), but we later decided 4|4(2) was better on XA).

I've since been using it for random posts on tuning-math and on the
wiki in the way I described. I don't see why I should have to change
my notes, the random wiki pages in which I've used it, and make the
archives be incorrect just because you all like it the other way to
match the quick half-assed diagrams I threw together to explain this
to Gene. I also know of at least 4-5 people on XA who already know
this notation and have used it, so they'd all be incorrect as well.
(I'm telling you, [tuning] is dead. Everything happens on tuning-math
and XA these days.)

Well, I prefer it this way because it says M|m, aka Major vs minor
scale degrees, and U|D, generators up vs down, and I find both of
those more intutive than m|M, minor vs Major, and D|U, down vs up. Is
there a reason why the switched version overrides these? If it's just
arbitrary, then it might as well be the arbitrary way that it already
is. If there really is a legit reason which overrides all of that
above, then I'll change it.

-Mike

On Wed, Nov 16, 2011 at 3:16 AM, dkeenanuqnetau <d.keenan@...> wrote:
>
> Ah. So that's what that was all about. No wonder I couldn't follow it. That's the opposite of Mike's use of "up" and "down" on the rest of that page. Note for example that Meantone[7] Ionian (major) is described in U|D terms as 5|1.
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> >
> > I gave a perfectly reasonable interpretation (up to the top mode, down to the bottom mode) which leads to just the opposite conclusion.

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

On Wed, Nov 16, 2011 at 12:31 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > I have a problem with all of this, which is that I and others have
> > already been using it this way for about 3 months now and nobody
> > bothered to complain when I first introduced it.
>
> Do we call your way D|U or U|D? If we call it U|D, it makes the explanation of U and D weird in the "mathematical definition" section.

That's why I didn't want to define it in terms of periodic scales.
Here's how I'd do it:

1) Let S be a convex set on a lattice which defines an MOS.
2) Let c be the point on that lattice which corresponds to the
interval (L-s) for that MOS.
3) Arrange the axes so that c is on the positive side.
4) Pick a point in that lattice, and call it the "root." Translate the
lattice so that the "root" is now the origin. It doesn't have to be in
S but probably will be.
5) Let n be the coordinate for the negative-most point in the block,
and let p be the coordinate for the positive-most point in the block.
6) Let P be the number of periods per equivalence interval.
6) Let U = p*P, D = -n*P.
7) The UDP notation for the mode is U|D(P).

This also means that 7|-1 is something like C# locrian, but where you
still consider C to be the root (and hence maybe you'd play C in the
bass with C# locrian on top). That'd probably be useful for scales
like myna[7], where 10|-4 will probably catch on.

-Mike

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

On Wed, Nov 16, 2011 at 5:31 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > 1) Let S be a convex set on a lattice which defines an MOS.
>
> Bad start. You don't need either lattices or convex sets.

How can the start to a definition be "bad?"

> > 2) Let c be the point on that lattice which corresponds to the
> > interval (L-s) for that MOS.
>
> > 3) Arrange the axes so that c is on the positive side.
> You'd need to explain that better.
>
> What axes?
>
> I give up. Sorry, Mike, this is a total mess.

Alright, I don't know how I got sucked into a game where I repeatedly
give you definitions for the same thing and you tell me that they're
"not mathematical enough," but I'm ducking out for now. It's defined
to my satisfaction on the wiki, and everyone seems to understand that
definition just fine. If you'd like to take the initiative in
mathematically formalizing it in a way that's consistent with the
definitions that I gave, I'll leave that to you.

-Mike

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Wed, Nov 16, 2011 at 5:31 PM, genewardsmith
> <genewardsmith@...> wrote:
> >
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > > 1) Let S be a convex set on a lattice which defines an MOS.
> >
> > Bad start. You don't need either lattices or convex sets.
>
> How can the start to a definition be "bad?"

Because you introduce two mathematical concepts--lattices and convex sets--which are not only completely unnecessary, they don't serve to clear anything up. You don't need the language of lattices or convex sets to talk about one-dimensional lattices and convex sets, so why bring it in?

> Alright, I don't know how I got sucked into a game where I repeatedly
> give you definitions for the same thing and you tell me that they're
> "not mathematical enough," but I'm ducking out for now. It's defined
> to my satisfaction on the wiki, and everyone seems to understand that
> definition just fine.

I don't. I think it verges on being gibberish.

🔗Mike Battaglia <battaglia01@...>

On Nov 17, 2011, at 2:24 PM, "genewardsmith" <genewardsmith@...>
wrote:

Because you introduce two mathematical concepts--lattices and convex
sets--which are not only completely unnecessary, they don't serve to clear
anything up. You don't need the language of lattices or convex sets to talk
about one-dimensional lattices and convex sets, so why bring it in?

How can I talk about one dimensional lattices and convex sets without using
the language of one dimensional lattices and convex sets?

I don't. I think it verges on being gibberish.

Can you be as precise in your criticisms of my definition as you'd like me
to be in the actual definition?

-Mike

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

On Thu, Nov 17, 2011 at 8:18 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > How can I talk about one dimensional lattices and convex sets without using
> > the language of one dimensional lattices and convex sets?
>
> You are just talking about a generator chain, so why not call it that?

How do I define a generator "up" vs "down" then? Do I just say in the
positive direction on the chain? What's "positive?"

How about this:

1) Let M be an MOS.
2) Let g be the generator for that MOS which, when iterated in the
positive direction, eventually passes through the chroma L-s, which
means it also eventually passes through L.
3) Pick a point along the chain, one which doesn't necessarily have to
be in the scale, and call it the "root" or "tonic."
4) Let n be the number of generators required to go down from the
tonic to get to the negative-most point in the block,
and let p be the number of generators required to go up from the tonic
to get to the positive-most point in the block.
5) Let P be the number of periods per equivalence interval.
6) Let U = p*P, D = -n*P.
7) The UDP notation for the mode is U|D(P).

So here we get

> > Can you be as precise in your criticisms of my definition as you'd like me
> > to be in the actual definition?
>
> I could write a revised version, and then restore your version and you could have a look at it if you like.

Alright.

-Mike