Yahoo Tuning Groups Ultimate Backup tuning Scale Classification

When classifying a living species, they are usually arranged in a specific order: Domain, Kingdom, Phylum, Class, Order, Family, Genus, Species. Each lower category can be thought of as a subgroup of the former category.

I was wondering, what is the equivalent classification for scales? For example, consider the diatonic scale in 12-equal. I suppose the temperament family would be meantone, but I don't know much else beyond that.

If I were to try to arrange the categories of scales, I would probably do something like this:
Temperament family, temperament class, MOS, temperament, EDO (or a subset of..), Mode, MODMOS

Of course, I am pretty sure I made some categorizing mistakes as I am not an expert in this field. Could someone help point me in the right direction? And possibly explain what each of those terms above actually mean?

Ryan

🔗Mike Battaglia <battaglia01@...>

On Sat, Aug 6, 2011 at 3:16 PM, Ryan Avella <domeofatonement@...> wrote:
>
> When classifying a living species, they are usually arranged in a specific order: Domain, Kingdom, Phylum, Class, Order, Family, Genus, Species. Each lower category can be thought of as a subgroup of the former category.
>
> I was wondering, what is the equivalent classification for scales? For example, consider the diatonic scale in 12-equal. I suppose the temperament family would be meantone, but I don't know much else beyond that.
>
> If I were to try to arrange the categories of scales, I would probably do something like this:
> Temperament family, temperament class, MOS, temperament, EDO (or a subset of..), Mode, MODMOS
>
> Of course, I am pretty sure I made some categorizing mistakes as I am not an expert in this field. Could someone help point me in the right direction? And possibly explain what each of those terms above actually mean?

It hasn't been done yet, but I was suggesting something earlier called
a "paradigm" that would effectively classify temperaments by
generator. I guess if I were going to classify a temperament, it would
go something like this

Limit, rank, mapping matrix, MOS, mode, MODMOS, tuning

Hopefully we'll be able to get rid of the word "limit" one of these
days. I've been trying to shred the zeta function apart recently, with
some interesting results, but no time...

-Mike

🔗Ryan Avella <domeofatonement@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> Limit, rank, mapping matrix, MOS, mode, MODMOS, tuning
>
> Hopefully we'll be able to get rid of the word "limit" one of these
> days. I've been trying to shred the zeta function apart recently, with
> some interesting results, but no time...
>
> -Mike
>

Hmm, what exactly would the mapping matrix be? Is that the equivalent of the temperament/comma? And if you wanted to specify a EDO, that would fall under tuning right?

Limit isn't necessarily the bane of temperament. It creates somewhat of a link between Just Intonation and Equal Temperament. Back when Partch wrote "Genesis of a Music," these two were thought to have an unbridgeable dichotomy. That is how things were for a while, until Paul came along.

In my opinion, retaining the word "limit" in description of temperaments is important because it provides a link between Just and Equal. Rather than getting rid of it, maybe we could add another classification in addition to it? I'd be interested in seeing the results of your Zeta Fuction digression, in hope that it might improve (rather than replace) our understanding of regular temperaments and whatnot.

Ryan

🔗Mike Battaglia <battaglia01@...>

On Sat, Aug 6, 2011 at 3:57 PM, Ryan Avella <domeofatonement@...> wrote:
>
> Hmm, what exactly would the mapping matrix be? Is that the equivalent of the temperament/comma?

Yeah, I guess I could have just said "temperament." It's just that
some temperaments eliminate more than one comma, like miracle
temperament for example. Any rank-2 temperament in the 5-limit will
temper out only 1 comma (aka be "codimension 1"), any rank-2
temperament in the 7-limit will have to temper out 2 commas (aka be
codimension 2), etc.

> And if you wanted to specify a EDO, that would fall under tuning right?

Yeah.

> Limit isn't necessarily the bane of temperament. It creates somewhat of a link between Just Intonation and Equal Temperament. Back when Partch wrote "Genesis of a Music," these two were thought to have an unbridgeable dichotomy. That is how things were for a while, until Paul came along.

But there's no limit to the ear. I swear I'm close to some kind of
epic breakthrough with the stuff I've been doing with the zeta
function, which would remove the need for us to ever talk about limits
again, but I'm having trouble seeing the big picture, and no time to
put the whole thing together right now...

> In my opinion, retaining the word "limit" in description of temperaments is important because it provides a link between Just and Equal. Rather than getting rid of it, maybe we could add another classification in addition to it? I'd be interested in seeing the results of your Zeta Fuction digression, in hope that it might improve (rather than replace) our understanding of regular temperaments and whatnot.

It's not limits that link JI and equal temperament, it's the larger
regular mapping theory that links the two. If we were working within
an infinite limit (let's call it the w-limit, where w is "omega"),
we'd be tempering an infinite amount of commas from an
infinite-dimensional space to a 1-dimensional space. I'd like to say
that this means that our JI lattice would become a "Hilbert space,"
but I'm wary of saying anything about vector spaces these days for
fear of misusing terminology... But we could still link JI and equal
temperaments regardless.

-Mike

🔗Charles Lucy <lucy@...>

I have already made a database of all possible scales in 12tET, and some alternative Meantone spellings.

You can download it for Bento form here:

http://solutions.filemaker.com/database-templates/detail.jsp?serial=2551722014

or read about an older version here:

http://www.lucytune.com/scales/

Had your "friend" and hero Lumma not colluded with his Wikipedia cohorts to have anything about LucyTuning removed as of no value, you might have been able to find it more easily;-)

Perhaps some more fields could be added to show the categories that you suggest, so that the scales (tuning) could be sorted or grouped in diverse orders.

Further suggestions for fields and categories appreciated.

Are we falling into the old semantic trap of confusing the creatures called "tunings" with other living species which have "scales" ? ;-)

On 6 Aug 2011, at 20:16, Ryan Avella wrote:

> When classifying a living species, they are usually arranged in a specific order: Domain, Kingdom, Phylum, Class, Order, Family, Genus, Species. Each lower category can be thought of as a subgroup of the former category.
>
> I was wondering, what is the equivalent classification for scales? For example, consider the diatonic scale in 12-equal. I suppose the temperament family would be meantone, but I don't know much else beyond that.
>
> If I were to try to arrange the categories of scales, I would probably do something like this:
> Temperament family, temperament class, MOS, temperament, EDO (or a subset of..), Mode, MODMOS
>
> Of course, I am pretty sure I made some categorizing mistakes as I am not an expert in this field. Could someone help point me in the right direction? And possibly explain what each of those terms above actually mean?
>
> Ryan
>
>

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@...>

🔗Michael <djtrancendance@...>

>"Limit isn't necessarily the bane of temperament. It creates somewhat of
a link between Just Intonation and Equal Temperament. Back when Partch
wrote "Genesis of a Music," these two were thought to have an
unbridgeable dichotomy. That is how things were for a while, until Paul
came along."

I'd say limit is a bit of a bane for the following reasons

A) Often ratios from a higher odd limit sound cleaner than those of a lower odd limit...specifically with 11+ limit and with 9 vs. 7 limit (oddly enough, often 9 limit sounds less tense).
B) Furthermore, specifically with chords like 5:7:9...the chord sounds more tenser than its "limit" would imply. I recall Carl saying something about how many instruments often have stronger even overtones...and their overtones pile up in conflict with the "odd harmonic" 5:7:9 root tones.

>"I'd like to say that this means that our JI lattice would become a "Hilbert space,"

I know little about "Hilbert Spaces" (my calculus knowledge only extends to non-multivariable-calculus), but have some idea how what inner product space is and know how dot products work (how much of a vector is along/"makes directional movement along" another vector). I read the wiki on it and it sounds like a good idea in that it can extract data about individual harmonics from a waveform.

Now, if it were a Hilbert space...how would it work? Also...what would a "length" in Hilbert space translate to in JI theory.

>"but I'm wary of saying anything about vector spaces these days for

fear of misusing terminology"

On the side, why should we worry about terminology so much if we can find a pretty convincing answer...and then go back and find the correct way to name it once we know exactly where we're going?

🔗Steve Parker <steve@...>

On 6 Aug 2011, at 23:54, Michael wrote:

> On the side, why should we worry about terminology so much if we can find a pretty convincing answer...and then go back and find the correct way to name it once we know exactly where we're going?

Here's one reason...
I have a maths background and when I first came to the list (archives) I struggled with a lot of buzz words that didn't mean quite what they mean in maths.
Sometimes because they had been legitimately redefined, but often because the writer didn't get the difference.

Call it a 'gorilla' space if you need, but only call it a Hilbert space if it actually is.
In Mike's case I think he is clear!

Steve P.