DINARRA (4)

Dear Tuners :
The term "Scala" in Italian languaje means "staircase" or "ladder".
The Spanish word "Escalera" has the same meaning.
I believe the term has a Latin origin.
If we try to define the word Scale we will inadvertently be hiding the
richness the word encloses. However, by avoiding a definition, it could
be
said, in poetic terms "Scale is the name given to a never ending musical

poem".

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The best
Eduardo

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> Dear Tuners :
> The term "Scala" in Italian languaje means "staircase" or "ladder".
> The Spanish word "Escalera" has the same meaning.
> I believe the term has a Latin origin.

It does: scalae, which means ladder. This root is relevant.

Dictionary.com gives the "traditional" or "common practice"
definition of scale: "An ascending or descending collection of
pitches proceeding by a specified scheme of intervals."

What many of you are discussing here, in my opinion, warrants the
invention of some new terms. You are attributing meanings to a word
that was never intended to contain them. The term "scale" is only
relevant in the framework of a composition, not in an abstract
mathematical sense. In terms of composition, a "scale" is a ladder
that ascends to/from and descends from/to a tonic note. A ladder is
not a ramp--it has a specified number of steps which are specified
distances from one another. In a certain sense, they are ordered, in
that each step has a specific distance from (and thus cardinal
relation to) the tonic. You can use a visual metaphor by imagining
an *actual* ladder: it is obvious which step is the first step, the
second, the third, etc.

Musical compositions traditionally start from the ground, climb
around the ladder for a while, and then get back to the ground.
Where I believe the dissent over "ordering" is arising is in the
presentation of a scale. When people see a list of notes (say C D E
F G A B C, to keep it simple), some see a definite ordered sequence
and others see a consequence of language. It is impossible to
represent the particular tones of a scale non-sequentially in a
language, even though they can be *conceptualized* non-sequentially.
I would like to argue here that tones in a scale are ordered but not
sequenced. The order is purely a result of the cardinality of the
step in respect to its distance from the tonic. This ordering is
atemporal, and has nothing necessarily to do with the use of a scale
in a composition. Basically you can jump or drop to and from any
step of the ladder you please, in any sequence you like, but the
ladder is still ordered in the same way.

This is why the atonalists use the term "tone row" instead
of "scale"; for them, the sequence was important and (theoretically)
the order was non-existant, because there was no tonic.

I think many of you here are trying to analyze scales as particular
subsets of the pitch continuum, abstract from any compositional
sense. This is fine (if a little impractical for answer to what
Aline probably thought was a simple question), but you must realize
your use of the word "scale" is misleading at this point. "Scale"
serves western common practice music fine, but beyond that it is
useful only as an analogue. Don't stretch it beyond its common
practice use; find a new term that will better serve your purposes!
Mr. Walker's proposed mathematical definition is much more
appropriate for the word "gamut" than for "scale", IMHO.

Regards to all,

-Igs

Hi there,

> > The term "Scala" in Italian languaje means "staircase" or "ladder".
> > The Spanish word "Escalera" has the same meaning.
> > I believe the term has a Latin origin.

> It does: scalae, which means ladder. This root is relevant.

Okay does seem we are stretching it quite a bit. It's
useful to know the origin, thanks! The word
has no particular association with ladders in English if one doesn't know the roots. One thinks perhaps of scales as in
a device for weighing things. Does it have that association in
Italian too? Or scales of a fish. However, I think the stretching is inevitable if you start
to think about scales geometrically. For instance,
the Hexany or any of those musical geometry type
scales - you can put all the notes into a single
ladder, but the ladder obscures the structure
of the scale. Going up / down the ladder one step
at a time is no longer a particularly useful way
to navigate the scale though of course you
can do it. Similarly also in the infinite Lambdoma,
it no longer is appropriate to go to the "next pitch" higher - because there is
no next pitch in fact, not in order
of pitch height - and the appropriate
thing to do is to go to the next pitch
in the same row of the Lambdoma - or
alternatively and equally good, to the
next pitch in the same column - which
follows the harmonic or subharmonic
series, which makes a lot of musical
sense. So now you have two directions for your ladders rather than just one.

In three dimensional scales, in effect
you have three ladders in three directions.
Each step of the horizontal ladder has
a ladder leading up from it vertically
and each of those has a ladder leading from
it in another horizontal direction - then
you may have yet another ladder leading into
the fourth dimension and higher dimensions.

Perhaps if one wants to coin a word
we could call these things
"multi-scales" or "multi-dimensional
scales", to mean that they are still
ordered, but not linearly ordered,
they don't have a one dimenstional order -
they have a two dimensional or higher
order on them. Usually I expect scales will
have some sort of natural order on them.
Though it doesn't have to coincide
with ordering in ascending pitch.

So the idea of abstracting away from
the order altogether is that then
you can allow scales with any
type of ordering the scales composer
desired, or none at all, it might
be useful to present a scale sometimes
as just a random juxtaposition of pitches
in no particular order at all to
kind of get one to approach it in a fresh fashion.

Hope this helps. I'm just presenting
this as a mathematical idea and
often mathematical ideas can
help to clear up or suggest other
ways of looking at things. But
they have no final authority,
there are nearly always many ways
of approaching a particular subject
mathemtaically, different ways of
axiomatising it though that gets obscured
because over time each area of the subject
tends to fall into a particular mode of
treatment that everyone uses by habit
and so they no longer see how much variety
is possible just in the basic ways
of looking at it (not new results, just
different ways of presenting the same
results and concepts). Sometimes though when it comes to applying the
ideas it can be useful to look at
other axiomatisations, for fun if nothing
else. So hopefully my idea will be
useful in that way. I won't be devastated if it doesn't get
taken up at all by anyone :-).

Robert

Or scales as in the scale of something, - small scale or
large scale etc.

Yes I can see, for instance the Lambdoma pitches as the
rationals would be a gamut - after you leave out all
the structure. As a 2D array it would be something
else, maybe one can call it a two dimensional scale.
So maybe my definition is of a gamut indeed, because
I wouldn't want to say that the set of all positive
rationals is a scale, but that's all you are left
with if you ignore the ordering on them altogether.

Then maybe the random pitches idea shows that
sometimes you can have a gamut which isn't
used as a basis for any type of ordering,
(or at least which is intended to kind
of get one to forget about orderings a bit, and look at it in another way
- e.g. that each pitch is an individual
personality for instance)

So, if we feel a scale must have some kind of
ladder type concept to it, maybe you can
have a gamut without any scale for it?

Robert

> Perhaps if one wants to coin a word
> we could call these things
> "multi-scales" or "multi-dimensional
> scales", to mean that they are still
> ordered, but not linearly ordered,
> they don't have a one dimenstional order -
> they have a two dimensional or higher
> order on them.

I would argue that these should be more properly regarded
as "gamuts", since they are so large that it is unlikely ALL members
would be used to imply a specific tonality in a composition.
Especially Lambdoma. Remember, when you take the word out of the
framework of composition, you're stretching the definition.

> Though it doesn't have to coincide
> with ordering in ascending pitch.

The point I was trying to make is that the *ordering* (not to be
confused with *sequencing*) of a scale is *always* based on pitch-
distance from a tonic note. It doesn't matter how you represent the
order, be it two-dimensional, 5-dimensional, or 1-dimensional; pitch
is absolute. In this sense you can think of "scale" also as a means
of measurement; same word, same root, same connotations.

> Hope this helps. I'm just presenting
> this as a mathematical idea and
> often mathematical ideas can
> help to clear up or suggest other
> ways of looking at things.

Mr. Walker, I respect your opinion very much, but I do not believe
this is a question of mathematics. I believe this is a question of
language/etymology. "Scale" is a word that predates much of the
mathematical approach that you are using. I understand that you wish
to form a "backwards compatible" definition of "scale" that is
consistent with the traditional meaning while incorporating the
developments of microtonal and JI theory, but frankly I believe that
that is unnecessary. Your definition is a better fit for the
word "gamut", in my opinion; in fact, it is absolutely fantastic for
that word.

> So, if we feel a scale must have some kind of
> ladder type concept to it, maybe you can
> have a gamut without any scale for it?

Yes! I think that's what I was trying to suggest. Simply, a gamut
does not *necessarily* imply a tonality (and thus an order) whereas a
scale does. A gamut could be used as a scale if a specific pitch was
chosen to be the tonic, and a scale could be used as a gamut if the
notion of tonality was removed from it.

Sound fair?

-Igs

Robert Walker wrote:

>Okay does seem we are stretching it quite a bit. It's
>useful to know the origin, thanks! The word
>has no particular association with ladders in English if
>one doesn't know the roots. One thinks perhaps of scales as in
>a device for weighing things. Does it have that association in
>Italian too? Or scales of a fish.
>
>

I doubt it since in Latin - where this learned words come from, not
Italian, a scale is a balance or a pound (£) (don't know about the fish).

>Similarly also in the infinite Lambdoma,
>it no longer is appropriate to go to the
>"next pitch" higher - because there is
>no next pitch in fact, not in order
>of pitch height - and the appropriate
>thing to do is to go to the next pitch
>in the same row of the Lambdoma - or
>alternatively and equally good, to the
>next pitch in the same column - which
>follows the harmonic or subharmonic
>series, which makes a lot of musical
>sense. So now you have two directions
>for your ladders rather than just one.
>
>

Infinite collections are not useful for scales, and your arguments re
multidimensional scales already apply to simple pythagorean.

Igs distinction of gamut and scale is very relevant here. Only by
limiting your tone generation, you get a gamut (e.g. seven fifths - the
white notes). From this (and, I would argue, any other [random]) ordered
and limited collection, you can make all kinds of scales by selecting a
tonic and melodic properties like authentic vs. plagal or preferred
intervals within the gamut, leading tones or special intervals beyond
the octave extending the gamut.

klaus

I can offer a fresh insight on this because, as of a few days ago, I
had no idea what a "scale" was, and so have no relevant preconceptions
;-) Feel free to disagree with anything I say, but try to back it up.

On 5/22/05, Igliashon Jones <igliashon@sbcglobal.net> wrote:
> Dictionary.com gives the "traditional" or "common practice"
> definition of scale: "An ascending or descending collection of
> pitches proceeding by a specified scheme of intervals."

It seems to me that there are 3 different meanings in common use. My
Collins Encyclopedia of Music does distinguish them, although I'll
still provide my own summary definitions:

1) A list of notes played in order as practice for an instrumentalist

2) A list of notes written out and enumerated

3) A set of notes

Meaning (1) is probably the most common in the real world, and the
least important one here. It should be obvious how to generalize it
to microtonality, right?

Meaning (2) is purely theoretical. At least one reference made this
explicit. The scale is the thing you write down, not something that
occurs in music. It certainly has an order, but I'm not sure what
that order means. At the least, it's so that you can refer to a
particular note as "the fifth of the scale" and so on. In this sense,
the order has nothing to do with actual music, except in that it
distinguishes a step from a leap, and groups together intervals as
"thirds", "fourths", etc.

Meaning (3) is the controversial one, and some definitions do leave it
out. I've found at least one reference to suggest that it exists in
the real world. It's a subtle thing where you have a finite number of
notes, as it would never do any harm to write them out in order to
give a scale as per definition (2). Hence it's only when we start
playing with a potentially infinite set that we have definitional
problems. I suggest that "the chromatic scale" often uses this
meaning. You can certainly say that such things should be called
"gamuts" but many people don't do this.

> What many of you are discussing here, in my opinion, warrants the
> invention of some new terms. You are attributing meanings to a word
> that was never intended to contain them. The term "scale" is only
> relevant in the framework of a composition, not in an abstract
> mathematical sense. In terms of composition, a "scale" is a ladder
> that ascends to/from and descends from/to a tonic note. A ladder is
> not a ramp--it has a specified number of steps which are specified
> distances from one another. In a certain sense, they are ordered, in
> that each step has a specific distance from (and thus cardinal
> relation to) the tonic. You can use a visual metaphor by imagining
> an *actual* ladder: it is obvious which step is the first step, the
> second, the third, etc.

I disagree with the relation to composition. Meaning (1) above
certainly has nothing to do with it.

Apart from that, I'm happy with this as meaning (2) except for the
word "tonic". A tonic is a feature of a key, not a scale.

> Musical compositions traditionally start from the ground, climb
> around the ladder for a while, and then get back to the ground.
> Where I believe the dissent over "ordering" is arising is in the
> presentation of a scale. When people see a list of notes (say C D E
> F G A B C, to keep it simple), some see a definite ordered sequence
> and others see a consequence of language. It is impossible to
> represent the particular tones of a scale non-sequentially in a
> language, even though they can be *conceptualized* non-sequentially.
> I would like to argue here that tones in a scale are ordered but not
> sequenced. The order is purely a result of the cardinality of the
> step in respect to its distance from the tonic. This ordering is
> atemporal, and has nothing necessarily to do with the use of a scale
> in a composition. Basically you can jump or drop to and from any
> step of the ladder you please, in any sequence you like, but the
> ladder is still ordered in the same way.

No to the first assertion. Initials and finals are features of modes
or keys, not scales, and needn't be the same or the lowest (or
highest) note in the scale.

Yes to order but not sequence, for meaning (2). That is, order but
not with respect to time.

Definitions are fairly consistent in giving scales an ordering but not
modes, so there's more than a conceptual difficulty. Modes have a
different ordering (initials, finals, and so on) and this should not
be confused with the ordering of a scale.

> This is why the atonalists use the term "tone row" instead
> of "scale"; for them, the sequence was important and (theoretically)
> the order was non-existant, because there was no tonic.

Maybe, but you still hear of "the chromatic scale" for atonal music.
Certainly a tone row has a sequence in a way a scale doesn't. Whole
tone scales are often used to avoid a sense of key center, but they're
still called "whole tone scales".

> I think many of you here are trying to analyze scales as particular
> subsets of the pitch continuum, abstract from any compositional
> sense. This is fine (if a little impractical for answer to what
> Aline probably thought was a simple question), but you must realize
> your use of the word "scale" is misleading at this point. "Scale"
> serves western common practice music fine, but beyond that it is
> useful only as an analogue. Don't stretch it beyond its common
> practice use; find a new term that will better serve your purposes!
> Mr. Walker's proposed mathematical definition is much more
> appropriate for the word "gamut" than for "scale", IMHO.

I'm wary of the Tuning List Fallacy here, that everybody else's
theories are detached from real music. The "gamut" as the full set of
notes available to the composer is compositionally relevant, and
sounds like useful concept. The difference between "gamut" and
"scale" could be that it has to be possible to give a single number to
an arbitrary note in a scale. I'm not sure if this should allow an
octave-equivalent meantone to be a scale enumerated by the spiral of
fifths. Really it shouldn't, but disallowing it by definition without
losing a desirable feature will be difficult.

I disagree with tying the word to common practice as well. Many of us
are influenced by medieval, renaissance, jazz, and other musics. The
word "scale" is used fairly liberally, and it would be plain eccentric
to avoid it where a common thread can be found.

Now, the specific difficulty with common practice music relates to
minor keys. If a minor key had two different scales, one ascending
and one descending (whatever that means) I'd be happy. But my
encyclopedia, at least, shows it as having a single scale. If that
only refers to meaning (1), no problem. If not, then I'm afraid we
need to fork meaning (2). One meaning would give us "the seventh
degree of the ascending minor scale" and the other would be ...
whatever that super-scale is supposed to refer to. I'd be happy to
call that second meaning a peculiarity of common practice music and
leave it out of the general definition.

And what would "the second degree of the descending minor scale" be?

Graham

Graham Breed wrote:

>I can offer a fresh insight on this because, as of a few days ago, I
>had no idea what a "scale" was, and so have no relevant preconceptions
>;-) Feel free to disagree with anything I say, but try to back it up.
> >

I'll do my best. Let me clarify a terminological problem that only occurred to me at hte very end: The meaning of mode in jaz theory (which many more people are familiar with than with the original meaning on Greek, medieval and renaissance music). The way I use it, Mode is a reach concept that gives you all the notes and tells you how to use them (like the major mode having leading tones). When you play "Dorian" on a chord of the second degree, you just think of the scale of the mode differently, but you are still playing the major mode. If this is not acceptable, it should at least help to clean up the other definitions that are lying around here.

klaus

>On 5/22/05, Igliashon Jones <igliashon@sbcglobal.net> wrote:
> >

>>What many of you are discussing here, in my opinion, warrants the
>>invention of some new terms. You are attributing meanings to a word
>>that was never intended to contain them. The term "scale" is only
>>relevant in the framework of a composition, not in an abstract
>>mathematical sense. In terms of composition, a "scale" is a ladder
>>that ascends to/from and descends from/to a tonic note. A ladder is
>>not a ramp--it has a specified number of steps which are specified
>>distances from one another. In a certain sense, they are ordered, in
>>that each step has a specific distance from (and thus cardinal
>>relation to) the tonic. You can use a visual metaphor by imagining
>>an *actual* ladder: it is obvious which step is the first step, the
>>second, the third, etc.
>> >>
>
>I disagree with the relation to composition. Meaning (1) above
>certainly has nothing to do with it.
>
>Apart from that, I'm happy with this as meaning (2) except for the
>word "tonic". A tonic is a feature of a key, not a scale.
> >

Disagree. A definite transposition of a scale is a key. A definite place for a tonic (which is what's relevant here) is a feature of a mode, which is a scale along with its instructions for use.

>
>Definitions are fairly consistent in giving scales an ordering but not
>modes, so there's more than a conceptual difficulty. Modes have a
>different ordering (initials, finals, and so on) and this should not
>be confused with the ordering of a scale.
> >

I would still call these modes scales. You may want to define a middle abstraction of a scale between gamuts and modes. It would still need a starting point and a direction, but have nothing else. However, I wonder what purpose such a soft definition could serve that leaves out all the cultural/stylistic infiormation about pitch ordering (but see below about the minor mode). The order of notes need not be any different than a scale, but the notes would be named for their function. (Ordering by initials and finals results in sample melodies, no?)

>
>I disagree with tying the word to common practice as well. >
... where functions of chords are more important than functions of tones. That is, I'm totally d'accord.

>
>Now, the specific difficulty with common practice music relates to
>minor keys.
>

Better terminology in my opinion: major and minor are modes.

> If a minor key had two different scales, one ascending
>and one descending (whatever that means) I'd be happy.
>

The melodic minor mode has two different scales. Still happy?

Melodic minor has a gamut of 9 tones, which in scalar order may look just the same as the mode of melodic minor. But as a mode you'd have the additional information that in music you skip notes in the upper tetrachord depending on your direction. When you practice, you extract two 7 note scales, but that's practice. I guess in theory scale is not a particularly useful concept.

> Apart from that, I'm happy with this as meaning (2) except for the
> word "tonic". A tonic is a feature of a key, not a scale.

You're right. My bad. I should have used the term "first ordinal
degree" instead of tonic...crikey, it's amazing how deep into my
thought processes tonal theory has dug its roots! But if you go back
and re-read my previous posts replacing "tonic" with "first ordinal
degree", I think you'll find less to debate about.

> Maybe, but you still hear of "the chromatic scale" for atonal
music.
> Certainly a tone row has a sequence in a way a scale doesn't. Whole
> tone scales are often used to avoid a sense of key center, but
they're
> still called "whole tone scales".

Whole tone and chromatic scales are members of that unique set
of "uniform" scales, such that they are exactly the same regardless
of which note is chosen to be their first ordinal degree. That does
not mean that they aren't defined as a specific pattern of steps
starting from a given first ordinal degree. Psychoacoustically they
don't imply a tonality, but in order to define a scale you logically
have to define every step in relation to a first degree.

> I disagree with tying the word to common practice as well. Many of
us
> are influenced by medieval, renaissance, jazz, and other musics.
The
> word "scale" is used fairly liberally, and it would be plain
eccentric
> to avoid it where a common thread can be found.

Perhaps you might find me an example in some music where "scale"
(specifically that word, not an "equivalent" like "rag" or "maqam")
is used other than to define an ordering of a set of note according
to their pitch-relationship to a given first degree? Even in JI,
every scale has a 1/1 which defines the other intervals by their
relation to it.

Hmm...maybe in that sense then the Lambdoma WOULD be a scale. This
is trickier than I thought!

-Igs

Hi all,

So many good points have been made!

When we've _finished_ this discussion ( if ever! :-) ), we can
take a couple of new terms over to the tuning-jargon list, eh?

I vote for -
gamut = a set of pitches (or equivalently, intervals)
lattice = a spatial arrangement of pitches in a gamut
metric = a measure of distance between pitches in a gamut
(may be defined in terms of the lattice, but need not)
scale = a gamut with a metric on it
raga = scale with (possibly probabilistic) rules for temporal
succession of pitches

No, I'm not trying to oversimplify this, but I am trying to
arrive at a workable set of terms that convey the most
appropriate connotations.

Anyone got an alternative set of short definitions?
Regards,
Yahya

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--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:

> I vote for -
> gamut = a set of pitches (or equivalently, intervals)
> lattice = a spatial arrangement of pitches in a gamut
> metric = a measure of distance between pitches in a gamut
> (may be defined in terms of the lattice, but need not)

I vote that lattice and metric retain their ordinary mathematical
definitions; to start revising mathematical definitions seems to me
likely to invite confusion.

Gamut is a set of pitches, with no additional properties? This would
make the set of all pitches a gamut, which seems like overdoing it.
Why not just call that a set of pitches?

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> I vote that lattice and metric retain their ordinary mathematical
> definitions; to start revising mathematical definitions seems to me
> likely to invite confusion.

lattice: http://tinyurl.com/dcts6
metric: http://tinyurl.com/coxmu

And, of course, fish have scales, as do most truck stops. I usually
try to work for over scale, but that all depends.

Many terms are overloaded. That's not confusion, that's just the way
it is.

Jon

--- In tuning@yahoogroups.com, "Jon Szanto" <jszanto@c...> wrote:
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> > I vote that lattice and metric retain their ordinary mathematical
> > definitions; to start revising mathematical definitions seems to me
> > likely to invite confusion.
>
> lattice: http://tinyurl.com/dcts6
> metric: http://tinyurl.com/coxmu
>
> And, of course, fish have scales, as do most truck stops. I usually
> try to work for over scale, but that all depends.
>
> Many terms are overloaded. That's not confusion, that's just the way
> it is.

No, in this case it is most definately confusion. Has it occurred to
you that we are *already* using "lattice" and "metric" rather
extensively in tuning theory?

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> No, in this case it is most definately confusion. Has it occurred to
> you that we are *already* using "lattice" and "metric" rather
> extensively in tuning theory?

Exactly my point: one simply understands that the word is being used
in a differing context. There isn't any confusion if one pays attention.

On 5/24/05, Gene Ward Smith <gwsmith@svpal.org> wrote:

> No, in this case it is most definately confusion. Has it occurred to
> you that we are *already* using "lattice" and "metric" rather
> extensively in tuning theory?

It may confuse you, because you're a mathematician with the peculiar
belief that other people are using mathematical terminology. "A
measure of distance between pitches" sounds like a metric to me. Are
you disagreeing with it? Algebraicists certainly don't have a
monopoly on lattices.

Graham

On 5/23/05, Igliashon Jones <igliashon@sbcglobal.net> wrote:

> Perhaps you might find me an example in some music where "scale"
> (specifically that word, not an "equivalent" like "rag" or "maqam")
> is used other than to define an ordering of a set of note according
> to their pitch-relationship to a given first degree? Even in JI,
> every scale has a 1/1 which defines the other intervals by their
> relation to it.

"A set of notes ordered by pitch" sounds right. You don't need the
"to a given first degree" because the ordering will always give you a
first degree.

There are cases where the order isn't specified, but you can always
say that it has one anyway. "Rag" and "maqam" are more an equivalant
of "mode" than "scale" anyway.

It may be problematic to use this definition in all cases for
microtonality. For example, the chromatic scale has the wrong
ordering in pelogic/mavila/whatever. In some cases, you can't assign
pitches to the notes, and so you can't impose an ordering. But the
rule for normal folks looks like an ordering by pitch.

> Hmm...maybe in that sense then the Lambdoma WOULD be a scale. This
> is trickier than I thought!

I don' t think there's much you can do about that.

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@g...> wrote:
> On 5/24/05, Gene Ward Smith <gwsmith@s...> wrote:
>
> > No, in this case it is most definately confusion. Has it occurred to
> > you that we are *already* using "lattice" and "metric" rather
> > extensively in tuning theory?
>
> It may confuse you, because you're a mathematician with the peculiar
> belief that other people are using mathematical terminology. "A
> measure of distance between pitches" sounds like a metric to me. Are
> you disagreeing with it?

The proposal was not that a measure of distance between pitches was a
metric, but that this was to be the definition of "metric", which
would mean nothing else would be a metric. A measure of distance
between pitches can be a metric under present standards, but Hahn
distance would no longer be a metric under this proposal, since it is
a measure of distance between pitch classes. Do you *really* want
that? Somehow I doubt it.

Algebraicists certainly don't have a
> monopoly on lattices.

We have to give geometers and analysts their due, I suppose.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> We have to give geometers and analysts their due, I suppose.

This completely ignores gardeners. I believe anti-gardenite behaviour
like this can, and *should*, cease in a civilized society.

Cheers,
Jon

(...gad, I hope they realize that was in jest...)

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> I vote that lattice and metric retain their ordinary mathematical
> definitions; to start revising mathematical definitions seems to me
> likely to invite confusion.

I vote that lattice and metric retain their ordinary tuning-theory
meanings on this list, which is after all the "tuning" list, not the
"math" list, or even the "tuning-math" list. I vote that scale retains
its ordinary musical meaning, fuzzy though that may be. In particular,
I think a scale is something we can hear, not a list of numbers, and
not something written on a staff, although scales may of course be
represented by either of these.

I think we are unlikely to ever capture what makes a good scale, in a
short description (mathematical or otherwise). However we do have
useful mathematical descriptions of several properties that seem to be
present in many traditional scales.

-- Dave Keenan

I concur with Igliashon entirely, save for the fact that a maqam of the Middle Eastern tradition is also composed of tones that warrant the definition of scale, as in minor scale with all its varieties.

Cordially,
Ozan
----- Original Message -----
From: Igliashon Jones
To: tuning@yahoogroups.com
Sent: 22 Mayıs 2005 Pazar 21:36
Subject: [tuning] Scales: an lengthy attempt at proper definition

> Dear Tuners :
> The term "Scala" in Italian languaje means "staircase" or "ladder".
> The Spanish word "Escalera" has the same meaning.
> I believe the term has a Latin origin.

It does: scalae, which means ladder. This root is relevant.

Dictionary.com gives the "traditional" or "common practice"
definition of scale: "An ascending or descending collection of
pitches proceeding by a specified scheme of intervals."

What many of you are discussing here, in my opinion, warrants the
invention of some new terms. You are attributing meanings to a word
that was never intended to contain them. The term "scale" is only
relevant in the framework of a composition, not in an abstract
mathematical sense. In terms of composition, a "scale" is a ladder
that ascends to/from and descends from/to a tonic note. A ladder is
not a ramp--it has a specified number of steps which are specified
distances from one another. In a certain sense, they are ordered, in
that each step has a specific distance from (and thus cardinal
relation to) the tonic. You can use a visual metaphor by imagining
an *actual* ladder: it is obvious which step is the first step, the
second, the third, etc.

Musical compositions traditionally start from the ground, climb
around the ladder for a while, and then get back to the ground.
Where I believe the dissent over "ordering" is arising is in the
presentation of a scale. When people see a list of notes (say C D E
F G A B C, to keep it simple), some see a definite ordered sequence
and others see a consequence of language. It is impossible to
represent the particular tones of a scale non-sequentially in a
language, even though they can be *conceptualized* non-sequentially.
I would like to argue here that tones in a scale are ordered but not
sequenced. The order is purely a result of the cardinality of the
step in respect to its distance from the tonic. This ordering is
atemporal, and has nothing necessarily to do with the use of a scale
in a composition. Basically you can jump or drop to and from any
step of the ladder you please, in any sequence you like, but the
ladder is still ordered in the same way.

This is why the atonalists use the term "tone row" instead
of "scale"; for them, the sequence was important and (theoretically)
the order was non-existant, because there was no tonic.

I think many of you here are trying to analyze scales as particular
subsets of the pitch continuum, abstract from any compositional
sense. This is fine (if a little impractical for answer to what
Aline probably thought was a simple question), but you must realize
your use of the word "scale" is misleading at this point. "Scale"
serves western common practice music fine, but beyond that it is
useful only as an analogue. Don't stretch it beyond its common
practice use; find a new term that will better serve your purposes!
Mr. Walker's proposed mathematical definition is much more
appropriate for the word "gamut" than for "scale", IMHO.

Regards to all,

-Igs

Dear Robert, why don't you use the term `lattice` instead of `scale` to
define a sound system which deviate from an ordered sequence of notes?

Cordially,
Ozan

----- Original Message -----
From: "Robert Walker" <robertwalker@ntlworld.com>
To: <tuning@yahoogroups.com>
Sent: 23 May�s 2005 Pazartesi 6:09
Subject: [tuning] Re: Scales: an lengthy attempt at proper definition

> Hi there,
>
> > > The term "Scala" in Italian languaje means "staircase" or "ladder".
> > > The Spanish word "Escalera" has the same meaning.
> > > I believe the term has a Latin origin.
>
> > It does: scalae, which means ladder. This root is relevant.
>
> Okay does seem we are stretching it quite a bit. It's
> useful to know the origin, thanks! The word
> has no particular association with ladders in English if
> one doesn't know the roots. One thinks perhaps of scales as in
> a device for weighing things. Does it have that association in
> Italian too? Or scales of a fish.
>
> However, I think the stretching is inevitable if you start
> to think about scales geometrically. For instance,
> the Hexany or any of those musical geometry type
> scales - you can put all the notes into a single
> ladder, but the ladder obscures the structure
> of the scale. Going up / down the ladder one step
> at a time is no longer a particularly useful way
> to navigate the scale though of course you
> can do it.
>
> Similarly also in the infinite Lambdoma,
> it no longer is appropriate to go to the
> "next pitch" higher - because there is
> no next pitch in fact, not in order
> of pitch height - and the appropriate
> thing to do is to go to the next pitch
> in the same row of the Lambdoma - or
> alternatively and equally good, to the
> next pitch in the same column - which
> follows the harmonic or subharmonic
> series, which makes a lot of musical
> sense. So now you have two directions
> for your ladders rather than just one.
>
> In three dimensional scales, in effect
> you have three ladders in three directions.
> Each step of the horizontal ladder has
> a ladder leading up from it vertically
> and each of those has a ladder leading from
> it in another horizontal direction - then
> you may have yet another ladder leading into
> the fourth dimension and higher dimensions.
>
> Perhaps if one wants to coin a word
> we could call these things
> "multi-scales" or "multi-dimensional
> scales", to mean that they are still
> ordered, but not linearly ordered,
> they don't have a one dimenstional order -
> they have a two dimensional or higher
> order on them. Usually I expect scales will
> have some sort of natural order on them.
> Though it doesn't have to coincide
> with ordering in ascending pitch.
>
> So the idea of abstracting away from
> the order altogether is that then
> you can allow scales with any
> type of ordering the scales composer
> desired, or none at all, it might
> be useful to present a scale sometimes
> as just a random juxtaposition of pitches
> in no particular order at all to
> kind of get one to approach it in
> a fresh fashion.
>
> Hope this helps. I'm just presenting
> this as a mathematical idea and
> often mathematical ideas can
> help to clear up or suggest other
> ways of looking at things. But
> they have no final authority,
> there are nearly always many ways
> of approaching a particular subject
> mathemtaically, different ways of
> axiomatising it though that gets obscured
> because over time each area of the subject
> tends to fall into a particular mode of
> treatment that everyone uses by habit
> and so they no longer see how much variety
> is possible just in the basic ways
> of looking at it (not new results, just
> different ways of presenting the same
> results and concepts).
>
> Sometimes though when it comes to applying the
> ideas it can be useful to look at
> other axiomatisations, for fun if nothing
> else. So hopefully my idea will be
> useful in that way. I won't be
> devastated if it doesn't get
> taken up at all by anyone :-).
>
> Robert
>
>

Dear Brother Yahya,

How about...

Scale: Staircase(s) of pitches

Gamut: Motion of ascent and descent within the staircase(s).

Tonic: Priority function ascribed to a degree of a scale.

Mode: A scale whose particular pitch is ascribed as tonic.

Key/Rag/Maqam: Staircase(s) - optionally transposed and modulated - with various functions assigned to certain degrees, where navigational routes are explicitly stated.

Cordially,
Ozan

----- Original Message -----
From: Yahya Abdal-Aziz
To: Tuning group at yahoo
Sent: 24 Mayıs 2005 Salı 8:28
Subject: [tuning] Re: Scales: an lengthy attempt at proper definition

Hi all,

So many good points have been made!

When we've _finished_ this discussion ( if ever! :-) ), we can
take a couple of new terms over to the tuning-jargon list, eh?

I vote for -
gamut = a set of pitches (or equivalently, intervals)
lattice = a spatial arrangement of pitches in a gamut
metric = a measure of distance between pitches in a gamut
(may be defined in terms of the lattice, but need not)
scale = a gamut with a metric on it
raga = scale with (possibly probabilistic) rules for temporal
succession of pitches

No, I'm not trying to oversimplify this, but I am trying to
arrive at a workable set of terms that convey the most
appropriate connotations.

Anyone got an alternative set of short definitions?
Regards,
Yahya

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I'll be brief: a scale is the scaffold from which music is built. Johnny

Gene,

Previously:
> > [YA]
> > I vote for -
> > gamut = a set of pitches (or equivalently, intervals)
> > lattice = a spatial arrangement of pitches in a gamut
> > metric = a measure of distance between pitches in a gamut
> > (may be defined in terms of the lattice, but need not)
>
> [GWS]
> I vote that lattice and metric retain their ordinary mathematical
> definitions; to start revising mathematical definitions seems to me
> likely to invite confusion.

[YA]
I'm not revising any mathematical definition, just trying to help
create useful musical ones. Yes, many terms are, as Jon pointed
out, overloaded - I had to grin as his first link sent me to:
"375 matches for lattice in Home & Garden"
none of them tunable, and all of them only mathematical in a
basic kind of way.

What I did do was ask for other people's short lists of terms and
definitions. So you don't like "lattice" and "metric" used as I did -
what are your alternative names for the same concepts?

Perhaps one of the reasons we all struggle with definitions and
clarity in this area is because of our determined use of metaphor
and simile. As often as it provides insight, a metaphor can cloud
real distinctions and bring irrelevant ones into prominence.
Metaphors mislead us quite as often as they guide us.

So it's worthwhile considering defining entirely new words, free
of connotations, whenever the connotations of existing terms
may be confusing. Maybe we should exchange "lattice" for
"grimble" and "metric" for "bleg"?

> Gamut is a set of pitches, with no additional properties? This would
> make the set of all pitches a gamut, which seems like overdoing it.

[YA]
But the gamut of the lambdoma is just that: the set of all pitches.
And the concept of the universal set, from which all other sets are
drawn, has a distinguished and useful career in maths. I don't see
that it is overdoing it, if any one musician finds a universal gamut of
practical use in making music.

> Why not just call that [a gamut] a set of pitches?

[YA]
1. For brevity.
2. For clarity of focus. We know we're talking about a set of
pitches _as a set and nothing more_ when we use the term "gamut".

Regards,
Yahya

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Hi Ozan,

Thank you for offering your own "... alternative set of short
definitions".

It's now clear that some people thought Aline's question,
on what constitutes a scale, was more complex than I do,
and some thought it less. Here's Johnny Reinhard's response
to the thread -
"a scale is the scaffold from which music is built."

While I don't disagree with that as a starting-point - defining
the _use_ of a scale, it's not particularly helpful in deciding
whether any given collection of pitches, pitch-classes,
directions, orders, rules ... whatever! is or is not a scale. More
to the point, it doesn't help us construct scales, or point out
features of our constructions which might make them more
or less useful in making music in various ways. On the other
hand, the kinds of concepts and measures canvassed in this
discussion - convexity, propriety and so on - and reported in
bewildering profusion by Scala, do help us by pointing out
many such features - if only we can get a grasp on which of
those features _we_ want. In case it's not obvious, I've
still got a long way to go before I'll be confident I
understand what most people on this list are talking about,
(what IS a CPS, anyway?) but I'll persevere because I'm
stubborn! And even those things I thought I understood
the "tuning-list orthodoxy" on, I may have misjudged based
purely on who's been vocal recently ... For example, I gave
Aline an "easy" answer as to what a JI scale is, and as might
be expected, provoked a reaction from someone else (Dave
Keenan) showing me it wasn't so easy ... :-) Still, I thought
Dave's answer (enabling tuning by ear without beats) was
equally facile, and a good deal harder to verify - How do I
know that two tuners hear the same thing? (Answer:
I don't, because there are "good tuners" and "bad tuners",
who get very different results; so according to Dave's
definition, one man's JI scale is another man's Poison ...)

Enough grumbling about how hard this all is! I still believe
that we ought to be able to come up, collectively, with a set
of tuning terms that make musical sense and are also
objectively demonstrable and verifiable - in other words,
belong to a science of musical tuning. I'm glad you seem
to share this belief, and I do thank you for offering your
own list (below).

On your usage, I suspect that you and I have opposite
notions of "scale" and "gamut". For me, the gamut is the
total set of notes you can play - it covers the whole range
from "gamma" to "ut". This usage seems to have historical
precedent too. The scale is the ascent or descent of pitches
in that gamut; they become steps in a ladder.

When the notion of octave-equivalence rules, specifying the
scale motion within the octave means automatically that you
have specified the scale motion throughout the entire gamut.
In this case, a scale is determined by its rising and falling
steps within any one octave of the gamut, and we can
consider a scale class as being the ascent and descent of
pitch-classes within an octave-reduced gamut, as I think
Gene did.

Tonic: Yes, thanks for defining this term. I think we would
also want, for some musical styles, to define dominant,
mediant, initial, final ... because of their specialised r�les
analogous to the specialised r�le of a tonic. However, I'm
unsure whether by "priority function" you simply mean that
the tonic is counted as "first step" in the scale (ladder), or
do you mean that the tonic is more important than other
pitches? And if the latter, melodically or harmonically?

Key/Rag/Maqam: OK for now.

Mode: I take it your definition is the relative one, as in
"the Dorian mode of ...", or "the Aeolian mode of ...", say,
C major? A common way of explaining modes in music
textbooks has been along the following lines -
"Take the white keys of the piano, starting at middle C.
Play an ascending scale of eight white notes until you
reach C above middle C. This is one mode, and its name
is .... Now start instead on the D above middle C, and play
an ascending scale of eight white notes until you reach
the D above that. This is another mode, and its name is
...." (The names vary depending on who you read or listen
to, or how classically Greek their inclinations are; some
prefer the names given by Glareanus.) Doesn't sound
like much more than transposing a given scale diatonically
(drawing on the same gamut), does it?

But in terms of ancient Greek practice, or of mediaeval
church practice, a mode was much more than that, and
the usual relationships we expect between notes of a
Western scale didn't always apply - for example, the
dominant wasn't always a fifth above the tonic. Because
of its rules about use of the notes in its gamut, a mode
was more akin to a raga or a maqam than to a scale.

Also, as another writer indicated recently on this list,
a "guitar mode" has rather more to do with fingering
than with an abstract selection of pitches. At least,
that's what I think they meant, and if I'm wrong,
someone's bound to correct me :-)

Surely a transposed scale is still a scale? To avoid
confusion with received musical usage, I think we need
to accept that the term "mode" has as least the following
four distinct meanings -
1. A Greek mode - An ancient Greek scale, with rules like a maqam.
2. An ecclesiastical mode - a mediaeval church scale, with rules
like a maqam.
3. The mode of the nth degree, or the nth mode, of a given key -
a diatonic transposition of a common-practice scale upwards by
n scale degrees.
4. A guitar mode - a fingering pattern on the guitar.

Possibly we could press the ancient Greek terms tonos (plural
tonoi) and tropos (plural tropoi) back into service to avoid using
terms that are now overladen with meaning. (I say "overladen",
because it's bad, like the straw that broke the camel's back,
rather than "overloaded", which is regarded as good practice in
object-oriented programming (OOP) circles. Come to think of it,
perhaps the OOP paradigm could be more fruitful for discussing
musical tuning than abstract algebra has been - it certainly offers
some suggestive terms, including "class" and "method". Perhaps
we should start a tuning-OOP list? I could hide all my gaffes
there ...)

But do tell me, Ozan, since you avoided the "metric" and "distance"
terms completely - what are your ideas on that subject?

Regards,
Yahya

-----Original Message-----

Dear Brother Yahya,

How about...

Scale: Staircase(s) of pitches

Gamut: Motion of ascent and descent within the staircase(s).

Tonic: Priority function ascribed to a degree of a scale.

Mode: A scale whose particular pitch is ascribed as tonic.

Key/Rag/Maqam: Staircase(s) - optionally transposed and modulated - with
various functions assigned to certain degrees, where navigational routes are
explicitly stated.

Cordially,
Ozan

----- Original Message -----
From: Yahya Abdal-Aziz
To: Tuning group at yahoo

Hi all,

So many good points have been made!

When we've _finished_ this discussion ( if ever! :-) ), we can
take a couple of new terms over to the tuning-jargon list, eh?

I vote for -
gamut = a set of pitches (or equivalently, intervals)
lattice = a spatial arrangement of pitches in a gamut
metric = a measure of distance between pitches in a gamut
(may be defined in terms of the lattice, but need not)
scale = a gamut with a metric on it
raga = scale with (possibly probabilistic) rules for temporal
succession of pitches

No, I'm not trying to oversimplify this, but I am trying to
arrive at a workable set of terms that convey the most
appropriate connotations.

Anyone got an alternative set of short definitions?
Regards,
Yahya

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Checked by AVG Anti-Virus.
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Yahya Abdal-Aziz wrote:

> Hi Ozan,

... just Klaus here ... if I may.

> On your usage, I suspect that you and I have opposite
> notions of "scale" and "gamut". For me, the gamut is the
> total set of notes you can play - it covers the whole range
> from "gamma" to "ut". This usage seems to have historical
> precedent too. The scale is the ascent or descent of pitches
> in that gamut; they become steps in a ladder.

The beautiful thing about the gamut is that, unlike the "white note
scale", it provides room for alterations. It is a system of seven note
names (a, b, c, d, e, f, g; doubled an octave higher and capitalized
an octave lower, with a lone Greek Gamma below the A) overlaid with
six "alteration indicators" (ut, re, mi, fa, sol, la: there has to be
a half step between mi and fa). Tones were identified by their name
and up to three "indicators". The lowest note was gamma ut (so the
name doesn't indicate any from-to idea), C could be fa or a new ut (so
must have been called C fa ut), F likewise, and G was ut again, but
also the sol in the hexachord on C or the re in the hexachord on F (G
ut sol re). B was B fa mi, a fourth from F or a ditonus from G, so
modern b and b flat were represented as one note. Finding the right
hexachord for a note was the medieval equivalen of accidentals.

>
> When the notion of octave-equivalence rules, specifying the
> scale motion within the octave means automatically that you
> have specified the scale motion throughout the entire gamut.

In the original gamut, it took a little more ...

> In this case, a scale is determined by its rising and falling
> steps within any one octave of the gamut, and we can
> consider a scale class as being the ascent and descent of
> pitch-classes within an octave-reduced gamut, as I think
> Gene did.

What about the scales that extend beyond the octave and where not
every note has an unaltered octave? I should say the gamut, in an
octave-reduced form, can hold them all, but the scale has to have the
"different" notes in their proper places.

> Also, as another writer indicated recently on this list,
> a "guitar mode" has rather more to do with fingering
> than with an abstract selection of pitches. At least,
> that's what I think they meant, and if I'm wrong,
> someone's bound to correct me :-)

I missed that, but I always thought the Berklee modes had something
like an excuse d'être for guitar players who may hold their
instruments by the "grip" for a certain chord and want to fill in some
diatonic nonchordal tones.

>
> Surely a transposed scale is still a scale? To avoid
> confusion with received musical usage, I think we need
> to accept that the term "mode" has as least the following
> four distinct meanings -
> 1. A Greek mode - An ancient Greek scale, with rules like a maqam.
> 2. An ecclesiastical mode - a mediaeval church scale, with rules
> like a maqam.
> 3. The mode of the nth degree, or the nth mode, of a given key -
> a diatonic transposition of a common-practice scale upwards by
> n scale degrees.
> 4. A guitar mode - a fingering pattern on the guitar.
>
> Possibly we could press the ancient Greek terms tonos (plural
> tonoi) and tropos (plural tropoi) back into service to avoid using
> terms that are now overladen with meaning.

I think 1. and 2. have enough in common to be called by the same names
(but I think it doesn't hurt when you stay with names of the original
cultures, if that culture bothered to theorize). Church modes
originally were mostly called "in the nth tone" originally, so why
not? (I have to admit that I'm not clear on the meaning of tonoi and
tropoi, though).

On the other hand, I think you might just as well replace the Berklee
modes by referring to the tonality and scale degrees directly. Jazz
theory is about chords whereas we are trying to talk about melody.

(I say "overladen",
> because it's bad, like the straw that broke the camel's back,
> rather than "overloaded", which is regarded as good practice in
> object-oriented programming (OOP) circles. Come to think of it,
> perhaps the OOP paradigm

Ah, I see it now; the explanation is right before the parentheses.
Would that be like me saying that you get a scale by applying a mode
to a gamut?

could be more fruitful for discussing
> musical tuning than abstract algebra has been - it certainly offers
> some suggestive terms, including "class" and "method". Perhaps
> we should start a tuning-OOP list? I could hide all my gaffes
> there ...)

I don't care where I make my blunders (and still hope that this time
my fingers didn't type their own words again).

kalus

My Dear Brother,

----- Original Message -----
From: Yahya Abdal-Aziz
To: tuning@yahoogroups.com
Sent: 26 Mayıs 2005 Perşembe 18:38
Subject: [tuning] Re: Scales: an lengthy attempt at proper definition

Hi Ozan,

Thank you for offering your own "... alternative set of short
definitions".

I hope I was fortunate enough to make sense this time.

It's now clear that some people thought Aline's question,
on what constitutes a scale, was more complex than I do,
and some thought it less. Here's Johnny Reinhard's response
to the thread -
"a scale is the scaffold from which music is built."

Most of the definitions I read aren't sinking in yet.

While I don't disagree with that as a starting-point - defining
the _use_ of a scale, it's not particularly helpful in deciding
whether any given collection of pitches, pitch-classes,
directions, orders, rules ... whatever! is or is not a scale. More
to the point, it doesn't help us construct scales, or point out
features of our constructions which might make them more
or less useful in making music in various ways. On the other
hand, the kinds of concepts and measures canvassed in this
discussion - convexity, propriety and so on - and reported in
bewildering profusion by Scala, do help us by pointing out
many such features - if only we can get a grasp on which of
those features _we_ want.

I surmise you will be interested to inquire as to how we pianists are educated about scales/modes/keys to begin with.

In case it's not obvious, I've
still got a long way to go before I'll be confident I
understand what most people on this list are talking about,
(what IS a CPS, anyway?) but I'll persevere because I'm
stubborn!

To say nothing of myself! However, I consider myself very obstinate in contrast.

And even those things I thought I understood
the "tuning-list orthodoxy" on, I may have misjudged based
purely on who's been vocal recently ... For example, I gave
Aline an "easy" answer as to what a JI scale is, and as might
be expected, provoked a reaction from someone else (Dave
Keenan) showing me it wasn't so easy ... :-) Still, I thought
Dave's answer (enabling tuning by ear without beats) was
equally facile, and a good deal harder to verify - How do I
know that two tuners hear the same thing? (Answer:
I don't, because there are "good tuners" and "bad tuners",
who get very different results; so according to Dave's
definition, one man's JI scale is another man's Poison ...)

That is a nightmare! A horrific prejudice which I have been fortunate enough to abondon only recently. I am finally very careful to remark that it is only myself who has a problem with the way things are explained, and can have little claims as to my opinion being universal. Far from it! My worthless comments are most likely having little impact in the world, and my influence as a musician is negligible. Grandiose conjectures elude me, and I'm a better, happier man, I assure you! Nevertheless, I feel that there can be no `culture` in the world which is inferior in `aesthetics` in comparison to its siblings. Hence, art is moot and ideals of supremacy futile, if not foolish. Any scale or interval may find/have found some use in the course of history. Thus, it's all a matter of taste. Who can prove that one is refined, and another is not?

Enough grumbling about how hard this all is! I still believe
that we ought to be able to come up, collectively, with a set
of tuning terms that make musical sense and are also
objectively demonstrable and verifiable - in other words,
belong to a science of musical tuning. I'm glad you seem
to share this belief, and I do thank you for offering your
own list (below).

Quite so dear fellow, quite so. But many problems will likely arise, not only in semantics, but also in etymology, epistemology, terminology, semiology and whatnot during our bold and daring quest to create a universal scientific ultra-comprehensive non-concise glossary of essential tuning terms and theoretical pharapharnalia!

On your usage, I suspect that you and I have opposite
notions of "scale" and "gamut". For me, the gamut is the
total set of notes you can play - it covers the whole range
from "gamma" to "ut". This usage seems to have historical
precedent too. The scale is the ascent or descent of pitches
in that gamut; they become steps in a ladder.

But this is not how we are taught! Maybe it matters little now that historical precedents override my arguments, but obviously this is not what I understand when asked to perform a `minor gamme`. I will definitely only choose the natural minor when writing the key signature, but will rarely, if at all, compose in it without alterating to the other minor scales.

My respected colleague, I can only think of the gamme as a dynamic, fluid, transitory passage of notes traversing the entire height of the 1st melodic minor scale, then falling back through the 2nd melodic minor scale. I cannot, in my right of mind, think of an ascending-descending scale, for that would mean that the ladder, or the each step, is moving!

If I may be allowed to iterate, I consider the scale to be an assortment of pitches from low to high with a beginning and an end, nothing more. The scale retains no information whatsoever as to which degrees function as tonic, dominant, leading tone, etc... and nothing can be inferred as to which mode or key such an assortment of pitches indicate!

When the notion of octave-equivalence rules, specifying the
scale motion within the octave means automatically that you
have specified the scale motion throughout the entire gamut.
In this case, a scale is determined by its rising and falling
steps within any one octave of the gamut, and we can
consider a scale class as being the ascent and descent of
pitch-classes within an octave-reduced gamut, as I think
Gene did.

How can this be? It is the gamut that is ascending-descending the scale(s). The scale is merely the foothold for whatever is moving over it. Or perhaps you are considering an escalator? But then there should be a constant glide of all the 7 notes played simultenously. This is certainly not the gamme that I know of. In simplest terms, the C major gamme is sounding the full extent of the C major scale by sounding each note succesively from low to high, and then high to low.

Tonic: Yes, thanks for defining this term. I think we would
also want, for some musical styles, to define dominant,
mediant, initial, final ... because of their specialised rôles
analogous to the specialised rôle of a tonic. However, I'm
unsure whether by "priority function" you simply mean that
the tonic is counted as "first step" in the scale (ladder), or
do you mean that the tonic is more important than other
pitches? And if the latter, melodically or harmonically?

All of them of course.

Key/Rag/Maqam: OK for now.

Mode: I take it your definition is the relative one, as in
"the Dorian mode of ...", or "the Aeolian mode of ...", say,
C major?

How else can one do it? You need first a scale to have a mode! The only scale you will ever need for all the Greek modes is the C major scale, whose successive degrees determine the nature of the mode. The scale itself bears no information as to which mode you desire, save for the faintest inclination that directs you to choosing the first degree by default. Thus, C major scale can be made synonymous with C major mode AKA Ionian, as mostly done, which I find obstructive to proper methodology.

A common way of explaining modes in music
textbooks has been along the following lines -
"Take the white keys of the piano, starting at middle C.
Play an ascending scale of eight white notes until you
reach C above middle C. This is one mode, and its name
is .... Now start instead on the D above middle C, and play
an ascending scale of eight white notes until you reach
the D above that. This is another mode, and its name is
...." (The names vary depending on who you read or listen
to, or how classically Greek their inclinations are; some
prefer the names given by Glareanus.) Doesn't sound
like much more than transposing a given scale diatonically
(drawing on the same gamut), does it?

But in terms of ancient Greek practice, or of mediaeval
church practice, a mode was much more than that, and
the usual relationships we expect between notes of a
Western scale didn't always apply - for example, the
dominant wasn't always a fifth above the tonic. Because
of its rules about use of the notes in its gamut, a mode
was more akin to a raga or a maqam than to a scale.

Of course! That is why a mode is so much more than a scale. It contains information as to which degree is the finalis, and which is the co-finalis, and what other functions are ascribed to several others.

Also, as another writer indicated recently on this list,
a "guitar mode" has rather more to do with fingering
than with an abstract selection of pitches. At least,
that's what I think they meant, and if I'm wrong,
someone's bound to correct me :-)

We digress. Let us regress.

Surely a transposed scale is still a scale?

A transposed scale in reference to a scale superimposed over itself? That would extend the range of the gamut as well as adding new pitches which must be dealt with. A scale is only a list of intervals, if you transpose the globule of pitches within the scale and overlap this over itself, the result is a scale which is bigger and more complicated to begin with.

I understand that you are referring to transposing the C major mode to another degree of the C major scale, at which point, the resulting mode will be identical in every way with the previous mode, its interval structure will be the same, while the scale itself is now extended. In such a case, and if the passage is fluid/dynamic/transient where certain degrees are given important roles, we are dealing with the Key of C Major, which is surely much more than the C major mode, let alone C major scale!

To avoid
confusion with received musical usage, I think we need
to accept that the term "mode" has as least the following
four distinct meanings -
1. A Greek mode - An ancient Greek scale, with rules like a maqam.
2. An ecclesiastical mode - a mediaeval church scale, with rules
like a maqam.
3. The mode of the nth degree, or the nth mode, of a given key -
a diatonic transposition of a common-practice scale upwards by
n scale degrees.
4. A guitar mode - a fingering pattern on the guitar.

I concur with all this information, save for the fact that a maqam is much more than a mode, simply because, like the key of C major, it contains information as to which modulations and transpositions are made available to the composer. For example, one can, with masterful articulation, use the fourth degree of Huzzam as a stepping stone to Nihavend like this:

Ed F G Ad Bd C Bd Ad G F Ed D/# Ed

G Ad Bb C Bb Ad G F

Where the comma-flats are most flexible. I never heard of a mode where one can suddenly enter the sphere of another mode.

Possibly we could press the ancient Greek terms tonos (plural
tonoi) and tropos (plural tropoi) back into service to avoid using
terms that are now overladen with meaning. (I say "overladen",
because it's bad, like the straw that broke the camel's back,
rather than "overloaded", which is regarded as good practice in
object-oriented programming (OOP) circles. Come to think of it,
perhaps the OOP paradigm could be more fruitful for discussing
musical tuning than abstract algebra has been - it certainly offers
some suggestive terms, including "class" and "method". Perhaps
we should start a tuning-OOP list? I could hide all my gaffes
there ...)

I am most excited about new terms. And, if it will clear the confusion, I will refer to gamut as gamme from this point forth.

But do tell me, Ozan, since you avoided the "metric" and "distance"
terms completely - what are your ideas on that subject?

Regards,
Yahya

I lack the technical capacity to fill in the details for those. Perhaps you might brief me on them.

Cordially,
Ozan

Hi "kalus" - OOPS! :-)

You wrote:
> ... just Klaus here ... if I may.
>
> > On your usage, I suspect that you and I have opposite
> > notions of "scale" and "gamut". For me, the gamut is the
> > total set of notes you can play - it covers the whole range
> > from "gamma" to "ut". This usage seems to have historical
> > precedent too. The scale is the ascent or descent of pitches
> > in that gamut; they become steps in a ladder.
>
> The beautiful thing about the gamut is that, unlike the "white note
> scale", it provides room for alterations. It is a system of seven note
> names (a, b, c, d, e, f, g; doubled an octave higher and capitalized
> an octave lower, with a lone Greek Gamma below the A) overlaid with
> six "alteration indicators" (ut, re, mi, fa, sol, la: there has to be
> a half step between mi and fa). Tones were identified by their name
> and up to three "indicators". The lowest note was gamma ut (so the
> name doesn't indicate any from-to idea), C could be fa or a new ut (so
> must have been called C fa ut), F likewise, and G was ut again, but
> also the sol in the hexachord on C or the re in the hexachord on F (G
> ut sol re). B was B fa mi, a fourth from F or a ditonus from G, so
> modern b and b flat were represented as one note. Finding the right
> hexachord for a note was the medieval equivalen of accidentals.

[YA] Sounds very complex ...! Where can I read more on the
_historical_ usage of gamut you're drawing on here? All I have to hand
on the subject is "The Pelican History of Music", bought decades ago
and probably mostly superseded by now.

> > When the notion of octave-equivalence rules, specifying the
> > scale motion within the octave means automatically that you
> > have specified the scale motion throughout the entire gamut.
>
> In the original gamut, it took a little more ...

> > In this case, a scale is determined by its rising and falling
> > steps within any one octave of the gamut, and we can
> > consider a scale class as being the ascent and descent of
> > pitch-classes within an octave-reduced gamut, as I think
> > Gene did.
>
> What about the scales that extend beyond the octave and where not
> every note has an unaltered octave? I should say the gamut, in an
> octave-reduced form, can hold them all, but the scale has to have the
> "different" notes in their proper places.
[YA] I think your "original gamut" is a structure with special
relationships between pitches over more than an octave, isn't
it? In which case, octave reductions is essentially foreign to
its nature. (As, for example, in a tuning system that contains
only the overtones of a given fundamental pitch C0, the notes
C1 an octave higher, G1 a twelfth higher, C2 two octaves higher,
E2, G2, Bb2, C3, D3, E3 ... belong to the system, but E1, Bb1 and
D1 don't.)

> > Also, as another writer indicated recently on this list,
> > a "guitar mode" has rather more to do with fingering
> > than with an abstract selection of pitches. At least,
> > that's what I think they meant, and if I'm wrong,
> > someone's bound to correct me :-)
>
> I missed that, but I always thought the Berklee modes had something
> like an excuse d'�tre for guitar players who may hold their
> instruments by the "grip" for a certain chord and want to fill in some
> diatonic nonchordal tones.
[YA] I like your "excuse d'�tre" ... :-)

> > Surely a transposed scale is still a scale? To avoid
> > confusion with received musical usage, I think we need
> > to accept that the term "mode" has as least the following
> > four distinct meanings -
> > 1. A Greek mode - An ancient Greek scale, with rules like a maqam.
> > 2. An ecclesiastical mode - a mediaeval church scale, with rules
> > like a maqam.
> > 3. The mode of the nth degree, or the nth mode, of a given key -
> > a diatonic transposition of a common-practice scale upwards by
> > n scale degrees.
> > 4. A guitar mode - a fingering pattern on the guitar.
> >
> > Possibly we could press the ancient Greek terms tonos (plural
> > tonoi) and tropos (plural tropoi) back into service to avoid using
> > terms that are now overladen with meaning.
>
> I think 1. and 2. have enough in common to be called by the same names
> (but I think it doesn't hurt when you stay with names of the original
> cultures, if that culture bothered to theorize). Church modes
> originally were mostly called "in the nth tone" originally, so why
> not? (I have to admit that I'm not clear on the meaning of tonoi and
> tropoi, though).
[YA] Good enough for me, but a trifle longwinded perhaps? Why not
just "the 4th tone" and so on?

> On the other hand, I think you might just as well replace the Berklee
> modes by referring to the tonality and scale degrees directly. Jazz
> theory is about chords whereas we are trying to talk about melody.
[YA] I guess calling them modes may have some practical benefits for
guitarists who frequently discuss them. Anyone care to comment?

> > (I say "overladen",
> > because it's bad, like the straw that broke the camel's back,
> > rather than "overloaded", which is regarded as good practice in
> > object-oriented programming (OOP) circles. Come to think of it,
> > perhaps the OOP paradigm
>
> Ah, I see it now; the explanation is right before the parentheses.
> Would that be like me saying that you get a scale by applying a mode
> to a gamut?
[YA] Yes. Your usage of "mode" and Ozan's seem to match, then.

> > could be more fruitful for discussing
> > musical tuning than abstract algebra has been - it certainly offers
> > some suggestive terms, including "class" and "method". Perhaps
> > we should start a tuning-OOP list? I could hide all my gaffes
> > there ...)
>
> I don't care where I make my blunders (and still hope that this time
> my fingers didn't type their own words again).
>
> kalus
[AY] !

Regards,
Yahya

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Hi Ozan,

You wrote:
> > Thank you for offering your own "... alternative set of short
> > definitions".

> I hope I was fortunate enough to make sense this time.

[YA] I believe I understood you well enough.

> > It's now clear that some people thought Aline's question,
> > on what constitutes a scale, was more complex than I do,
> > and some thought it less. Here's Johnny Reinhard's response
> > to the thread -
> > "a scale is the scaffold from which music is built."

> Most of the definitions I read aren't sinking in yet.

[YA] I find that some definitions "resonate" with my ...
sensibilities, or prejudices? ... while others leave me floundering.

> > While I don't disagree with that as a starting-point - defining
> > the _use_ of a scale, it's not particularly helpful in deciding
> > whether any given collection of pitches, pitch-classes,
> > directions, orders, rules ... whatever! is or is not a scale. More
> > to the point, it doesn't help us construct scales, or point out
> > features of our constructions which might make them more
> > or less useful in making music in various ways. On the other
> > hand, the kinds of concepts and measures canvassed in this
> > discussion - convexity, propriety and so on - and reported in
> > bewildering profusion by Scala, do help us by pointing out
> > many such features - if only we can get a grasp on which of
> > those features _we_ want.

> I surmise you will be interested to inquire as to how we pianists
> are educated about scales/modes/keys to begin with.

[YA] But of course. Or more specifically, how the education
of a pianist in a Francophone country differs from that in an
Anglophone country. You studied in Belgium, didn't you? And
I in Australia.

> > In case it's not obvious, I've
> > still got a long way to go before I'll be confident I
> > understand what most people on this list are talking about,
> > (what IS a CPS, anyway?) but I'll persevere because I'm
> > stubborn!

> To say nothing of myself! However, I consider myself very
> obstinate in contrast.

[YA] :-)

> > And even those things I thought I understood
> > the "tuning-list orthodoxy" on, I may have misjudged based
> > purely on who's been vocal recently ... For example, I gave
> > Aline an "easy" answer as to what a JI scale is, and as might
> > be expected, provoked a reaction from someone else (Dave
> > Keenan) showing me it wasn't so easy ... :-) Still, I thought
> > Dave's answer (enabling tuning by ear without beats) was
> > equally facile, and a good deal harder to verify - How do I
> > know that two tuners hear the same thing? (Answer:
> > I don't, because there are "good tuners" and "bad tuners",
> > who get very different results; so according to Dave's
> > definition, one man's JI scale is another man's Poison ...)

> That is a nightmare! A horrific prejudice which I have been fortunate
> enough to abondon only recently. I am finally very careful to remark
> that it is only myself who has a problem with the way things are
> explained, and can have little claims as to my opinion being universal.
> Far from it! My worthless comments are most likely having little impact
> in the world, and my influence as a musician is negligible. Grandiose
> conjectures elude me, and I'm a better, happier man, I assure you!
> Nevertheless, I feel that there can be no `culture` in the world which
> is inferior in `aesthetics` in comparison to its siblings. Hence, art is
> moot and ideals of supremacy futile, if not foolish. Any scale or interval
> may find/have found some use in the course of history. Thus, it's all a
> matter of taste. Who can prove that one is refined, and another is not?

[YA] I'm sure your humility far surpasses mine ...!

> > Enough grumbling about how hard this all is! I still believe
> > that we ought to be able to come up, collectively, with a set
> > of tuning terms that make musical sense and are also
> > objectively demonstrable and verifiable - in other words,
> > belong to a science of musical tuning. I'm glad you seem
> > to share this belief, and I do thank you for offering your
> > own list (below).

> Quite so dear fellow, quite so. But many problems will likely arise,
> not only in semantics, but also in etymology, epistemology,
> terminology, semiology and whatnot during our bold and daring
> quest to create a universal scientific ultra-comprehensive
> non-concise glossary of essential tuning terms and theoretical
> pharapharnalia!

[YA] Problems are science's raison d'�tre. Hmmm ... but why not
aim at conciseness too?

> > On your usage, I suspect that you and I have opposite
> > notions of "scale" and "gamut". For me, the gamut is the
> > total set of notes you can play - it covers the whole range
> > from "gamma" to "ut". This usage seems to have historical
> > precedent too. The scale is the ascent or descent of pitches
> > in that gamut; they become steps in a ladder.

> But this is not how we are taught! Maybe it matters little now
> that historical precedents override my arguments, but obviously
> this is not what I understand when asked to perform a `minor
> gamme`. I will definitely only choose the natural minor when
> writing the key signature, but will rarely, if at all, compose in it
> without alterating to the other minor scales.

[YA] On being asked to perform a "minor scale", I would of course
oblige the teacher with the notes, rising and falling, of the minor
scale in a fixed compass - whether one octave, or two, or more,
depending on the level of the class. If the teacher did not specify
the compass (or range), I would usually choose to play the scale over
two octaves as being the minimum that well demonstrates the melodic
flow about every degree of the scale. I think I'm right in saying that
French offers only "gamme" as a translation of the English "scale" or
Latin "scala"?

> My respected colleague, I can only think of the gamme as a dynamic,
> fluid, transitory passage of notes traversing the entire height of
> the 1st melodic minor scale, then falling back through the 2nd melodic
> minor scale. I cannot, in my right of mind, think of an ascending-
> descending scale, for that would mean that the ladder, or the each
> step, is moving!

[YA] I think we're talking at cross-purposes here ... As far as I recall,
my definitions did not imply that any scale moved, but that each scale
offered both one pattern for ascent and another for descent - two
ladders, side-by-side, if you will. Certainly that is what I meant!

> If I may be allowed to iterate, I consider the scale to be an
> assortment of pitches from low to high ... .

[YA] Which I called "gamut".

> .. with a beginning and an end,
> nothing more.

[YA] This is only halfway to being a scale as I understand it.
Or does your "C melodic minor scale" consist of 9 notes to every
octave, arranged in order of increasing pitch, so that it contains
both a minor sixth degree and a major sixth degree, and likewise
for sevenths? My "C melodic minor scale" consists of 7 notes to
every octave in one pattern ascending, and of 7 notes to every
octave in another pattern descending, so that it contains
only a major sixth degree when ascending, and only a minor sixth
degree when descending, and likewise for sevenths. My scale is
a set of patterns of melodic movement, built on a gamut of 9 notes.

> The scale retains no information whatsoever as to which degrees
> function as tonic, dominant, leading tone, etc... and nothing can be
> inferred as to which mode or key such an assortment of pitches
> indicate!

[YA] I understand that your halfway-scale (= gamut+pitch order)
does not distinguish a tonic starting-point. Certainly it contains a
lowest note of the gamut, which may have nothing to do with
anything but the pitch limitations of the instrument. A scale in my
sense also does not require a fixed starting-point; however, _in a
given context of musical practice_, the two patterns of notes
provided by my "C melodic minor scale" only occur in a key called
"C minor".

> > When the notion of octave-equivalence rules, specifying the
> > scale motion within the octave means automatically that you
> > have specified the scale motion throughout the entire gamut.
> > In this case, a scale is determined by its rising and falling
> > steps within any one octave of the gamut, and we can
> > consider a scale class as being the ascent and descent of
> > pitch-classes within an octave-reduced gamut, as I think
> > Gene did.

> How can this be? It is the gamut that is ascending-descending
> the scale(s). The scale is merely the foothold for whatever is
> moving over it.

[YA] In music, what moves? Melody, rhythm, harmony. A melody
in C minor moves over the notes of the C (melodic) minor scale.
A complex harmony in C minor moves over the notes of the
C (harmonic) minor scale. I don't think the gamut - the collection
of notes - moves at all. What you consider as moving is the "gamme"
- a melody consisting of many or all notes of a particular (say
C minor) scale. With enough fingers - or a long stick, I could play
all the notes of the C major gamut on the piano simultaneously.

> Or perhaps you are considering an escalator? But then there
> should be a constant glide of all the 7 notes played simultenously.
> This is certainly not the gamme that I know of. In simplest terms,
> the C major gamme is sounding the full extent of the C major scale
> by sounding each note succesively from low to high, and then high
> to low.

[YA] In my terms, that is a melody, not a scale.

> > Tonic: Yes, thanks for defining this term. I think we would
> > also want, for some musical styles, to define dominant,
> > mediant, initial, final ... because of their specialised r�les
> > analogous to the specialised r�le of a tonic. However, I'm
> > unsure whether by "priority function" you simply mean that
> > the tonic is counted as "first step" in the scale (ladder), or
> > do you mean that the tonic is more important than other
> > pitches? And if the latter, melodically or harmonically?

> All of them of course.

[YA] If so, I'd rather a definition that stated each of those
points explicitly.

> > Key/Rag/Maqam: OK for now.

> > Mode: I take it your definition is the relative one, as in
> > "the Dorian mode of ...", or "the Aeolian mode of ...", say,
> > C major?

> How else can one do it? You need first a scale to have a
> mode! The only scale you will ever need for all the Greek
> modes is the C major scale, whose successive degrees
> determine the nature of the mode. The scale itself bears
> no information as to which mode you desire, save for the
> faintest inclination that directs you to choosing the first
> degree by default. Thus, C major scale can be made
> synonymous with C major mode AKA Ionian, as mostly done,
> which I find obstructive to proper methodology.

[YA] It's certainly confusing terminology. For clarity, we
need to distinguish the C major scale from its first mode.

> > A common way of explaining modes in music
> > textbooks has been along the following lines -
> > "Take the white keys of the piano, starting at middle C.
> > Play an ascending scale of eight white notes until you
> > reach C above middle C. This is one mode, and its name
> > is .... Now start instead on the D above middle C, and play
> > an ascending scale of eight white notes until you reach
> > the D above that. This is another mode, and its name is
> > ...." (The names vary depending on who you read or listen
> > to, or how classically Greek their inclinations are; some
> > prefer the names given by Glareanus.) Doesn't sound
> > like much more than transposing a given scale diatonically
> > (drawing on the same gamut), does it?
> >
> > But in terms of ancient Greek practice, or of mediaeval
> > church practice, a mode was much more than that, and
> > the usual relationships we expect between notes of a
> > Western scale didn't always apply - for example, the
> > dominant wasn't always a fifth above the tonic. Because
> > of its rules about use of the notes in its gamut, a mode
> > was more akin to a raga or a maqam than to a scale.

> Of course! That is why a mode is so much more than a scale.
> It contains information as to which degree is the finalis, and
> which is the co-finalis, and what other functions are ascribed
> to several others.

[YA] So a gamut is a set of pitches, a scale is an ordering (or
maybe two) of a gamut, a gamme is a particular form of melody
made from a gamut, a mode is a scale plus functions for various
pitches within it.

> > Also, as another writer indicated recently on this list,
> > a "guitar mode" has rather more to do with fingering
> > than with an abstract selection of pitches. At least,
> > that's what I think they meant, and if I'm wrong,
> > someone's bound to correct me :-)

> We digress. Let us regress.

[YA] Where's the digression? That's all the word "mode"
means to most guitarists. Yes, I know they're not all
pianists, but we eschew cultural superiority, right? :-)

> > Surely a transposed scale is still a scale?

> A transposed scale in reference to a scale superimposed
> over itself? That would extend the range of the gamut as
> well as adding new pitches which must be dealt with.

[YA] Not at all what I meant! By "diatonic transposition"
I mean moving "thru the tones" - essentially choosing a
different starting point within the same set of notes.
Nothing more. No new notes are added.

> A scale is only a list of intervals,

[YA] Are you sure about that? This is almost where we
started ...

> if you transpose the globule of pitches within the scale
> and overlap this over itself, the result is a scale which
> is bigger and more complicated to begin with.

[YA] You are right, but no-one was talking about doing
that.

> I understand that you are referring to transposing the
> C major mode to another degree of the C major scale,

[YA] You misunderstand me. That would be a chromatic
transposition.

> at which point, the resulting mode will be identical in
> every way with the previous mode, its interval structure
> will be the same, while the scale itself is now extended.
> In such a case, and if the passage is fluid/dynamic/
> transient where certain degrees are given important
> roles, we are dealing with the Key of C Major, which is
> surely much more than the C major mode, let alone C
> major scale!

[YA] The Key of C Major has, perhaps greater and perhaps
merely different, harmonic implications than the C major
mode. But I wasn't talking about keys. At least, not yet.

> > To avoid
> > confusion with received musical usage, I think we need
> > to accept that the term "mode" has as least the following
> > four distinct meanings -
> > 1. A Greek mode - An ancient Greek scale, with rules like a maqam.
> > 2. An ecclesiastical mode - a mediaeval church scale, with rules
> > like a maqam.
> > 3. The mode of the nth degree, or the nth mode, of a given key -
> > a diatonic transposition of a common-practice scale upwards by
> > n scale degrees.
> > 4. A guitar mode - a fingering pattern on the guitar.

> I concur with all this information, save for the fact that a maqam
> is much more than a mode, simply because, like the key of C major,
> it contains information as to which modulations and transpositions
> are made available to the composer.

[YA] You're the expert on maqamat. Instead of saying -
"with rules like a maqam", perhaps I should just say "with rules
governing melodic succession".

> For example, one can, with masterful articulation, use the fourth
> degree of Huzzam as a stepping stone to Nihavend like this:
>
> Ed F G Ad Bd C Bd Ad G F Ed D/# Ed
>
> G Ad Bb C Bb Ad G F
>
> Where the comma-flats are most flexible.

[YA] Thank you for the example. I'd have to hear it to appreciate
it properly.

> I never heard of a mode where one can suddenly enter the
> sphere of another mode.

[YA] Or it wouldn't be a mode, would it? Same restriction governs
the use of ragas. One raga never changes to another within the same
composition. That you can or would do this with maqamat both
surprises and intrigues me. How is it possible to do so, I wonder,
without destroying the unity of mood that one maqam establishes?

> > Possibly we could press the ancient Greek terms tonos (plural
> > tonoi) and tropos (plural tropoi) back into service to avoid using
> > terms that are now overladen with meaning. (I say "overladen",
> > because it's bad, like the straw that broke the camel's back,
> > rather than "overloaded", which is regarded as good practice in
> > object-oriented programming (OOP) circles. Come to think of it,
> > perhaps the OOP paradigm could be more fruitful for discussing
> > musical tuning than abstract algebra has been - it certainly offers
> > some suggestive terms, including "class" and "method". Perhaps
> > we should start a tuning-OOP list? I could hide all my gaffes
> > there ...)

> I am most excited about new terms. And, if it will clear the confusion,
> I will refer to gamut as gamme from this point forth.

[YA] If "gamme" then means - for us at least! - the practice of playing
all the notes of a scale, from botom to top and back a gain, as a melody,
I'm content to use it that way. Trouble is, I think that most of our
Francophone friends wouldn't want it to no longer also mean "scale" in
all its musical senses ...

> > But do tell me, Ozan, since you avoided the "metric" and "distance"
> > terms completely - what are your ideas on that subject?
> > Regards,
> > Yahya

> I lack the technical capacity to fill in the details for those. Perhaps
> you might brief me on them.

[YA] There are several notions of distance in music. The simplest to
use just counts scale degrees. So a fifth is four notes (scale degrees)
away from a unison, three notes from a second, two notes from a third
and one note from a fourth.

A more complex one, such as the one given by James Tenney, give the
distance of a note (from a reference note) which is at a pitch n/d times
that of the reference note, as -
HD (n/d) = k . log (n . d)
Here n is the numerator and d the denominator of the pitch ratio, and
both are presumed to be integers. k is any convenient constant, and if
you want to measure harmonic distance along the chain of perfect
fifths, you could take it to be 1 / log (3 . 2). We take logs so that the
HD of, say, a fifth is unchanged by octave transposition of both pitches
in the interval. From this definition it follows that if a perfect fifth is
one step, a just major second is two steps, a major sixth is three and so
on. I draw my entire knowledge of this measure, or "metric", from the
paper Paul Erlich kindly sent me to study.

So much for the technical side ... on the side of musical feeling and
intuition, do you ever count, as I do, the number of melodic movements
away from the tonic? So that, for example, in C minor, Ab is only
related to the tonic note C in the second degree, wanting - if aiming at
arriving at C - to move first to G, F or possibly Bb. Whereas the G or
the F might move directly to the C, although still more likely to get
there in stages. I only get this sense in a more melismatic style of
composition, which precludes large leaps, except for effect. But in
such a style, I find that the distances of notes is determined firstly
by the number of scale steps intervening, and secondly by the number
of spiral-of-fifths steps intervening, between them. What exact
proportion each contributes, I couldn't say, and it does seem to vary
with the mood of the piece - not scientific, I know! But I do know that
a major or minor second is always closer than a third, and a third than
a fifth, while a fifth can sometimes be closer (melodically) than a fourth,
and other times not.

> Cordially,
> Ozan

Regards,
Yahya

Yahya Abdal-Aziz wrote:

>>The beautiful thing about the gamut is that, unlike the "white note
>>scale", it provides room for alterations. It is a system of seven note
>>names (a, b, c, d, e, f, g; doubled an octave higher and capitalized
>>an octave lower, with a lone Greek Gamma below the A) overlaid with
>>six "alteration indicators" (ut, re, mi, fa, sol, la: there has to be
>>a half step between mi and fa). Tones were identified by their name
>>and up to three "indicators". The lowest note was gamma ut (so the
>>name doesn't indicate any from-to idea), C could be fa or a new ut (so
>>must have been called C fa ut), F likewise, and G was ut again, but
>>also the sol in the hexachord on C or the re in the hexachord on F (G
>>ut sol re). B was B fa mi, a fourth from F or a ditonus from G, so
>>modern b and b flat were represented as one note. Finding the right
>>hexachord for a note was the medieval equivalen of accidentals.
> > > [YA] Sounds very complex ...! Where can I read more on the
> _historical_ usage of gamut you're drawing on here? All I have to hand
> on the subject is "The Pelican History of Music", bought decades ago
> and probably mostly superseded by now.

What are decades against the millennium that has apssed since Guido invented or described his system? Guido of Arezzo would be the obvious entry to look up, and if it doesn't say it all, solmisation and "ut queant laxis". And gamut of course (if your language allows; German doesn't seem to have a name for it and the English-German dictionaries just say "Skala, Tonleiter" which is getting rid of all the interesting cultural baggage).

Guido developed the method of notating music on a system of (four, in his case) lines. I have no idea if the finales of the church modes had already been thought of as being next to each other (where is Margo Schulter, by the way?) or if Guido wanted to have them compact; anyway they were on D (mode 1 and 2), E (3 and 4), F (5 and 6) and G (7 and 8) (the odd ones authentic, the even ones plagal). Since the placing of the half steps was determined by the ut-re-mi, the B was typically mi when starting on G ("Mixolydian", the Berkleeans say) and fa when starting on F ("But that makes it Ionian!" - making the point that you're bound to reap confusion when you mix terminologies). There were mixed modes, as in the obvious case when a melody exceeded an octave and you went like from authentic to plagal, or when a note changed its "interpretation". BTW, the infamous "mi contra fa, diabolus in musica" in the solmisation system described the "forbidden" interval class of the augmented second and the augmented fourth.

> > [YA] I think your "original gamut" is a structure with special
> relationships between pitches over more than an octave, isn't
> it? In which case, octave reductions is essentially foreign to
> its nature. (As, for example, in a tuning system that contains
> only the overtones of a given fundamental pitch C0, the notes
> C1 an octave higher, G1 a twelfth higher, C2 two octaves higher,
> E2, G2, Bb2, C3, D3, E3 ... belong to the system, but E1, Bb1 and
> D1 don't.)

Yes. The lowest B had no F under it and so could only be B mi=B natural. But since the same principle applies to all the octaves, I see no problem in generalizing "B can be soft or hard (flat or natural)". And no matter how many octaves and principles apply, I think you can octave recude anything if you only called it that.

>>>1. A Greek mode - An ancient Greek scale, with rules like a maqam.
>>>2. An ecclesiastical mode - a mediaeval church scale, with rules
>>>like a maqam.
>>>3. The mode of the nth degree, or the nth mode, of a given key -
>>>a diatonic transposition of a common-practice scale upwards by
>>>n scale degrees.
>>>4. A guitar mode - a fingering pattern on the guitar.
>>>
>>>Possibly we could press the ancient Greek terms tonos (plural
>>>tonoi) and tropos (plural tropoi) back into service to avoid using
>>>terms that are now overladen with meaning.
>>
>>I think 1. and 2. have enough in common to be called by the same names
>>(but I think it doesn't hurt when you stay with names of the original
>>cultures, if that culture bothered to theorize). Church modes
>>originally were mostly called "in the nth tone" originally, so why
>>not? (I have to admit that I'm not clear on the meaning of tonoi and
>>tropoi, though).
> > [YA] Good enough for me, but a trifle longwinded perhaps? Why not
> just "the 4th tone" and so on?

They really said "of the nth tone", and since they said it in Latin they had a case for that and didn't need a preposition. "'Ut queant laxis' cantus secundi toni est." A system very specific to the mediaval system of eight tones/modes; I wouldn't want to make this universal. But ...

>>On the other hand, I think you might just as well replace the Berklee
>>modes by referring to the tonality and scale degrees directly. Jazz
>>theory is about chords whereas we are trying to talk about melody.
> > [YA] I guess calling them modes may have some practical benefits for
> guitarists who frequently discuss them. Anyone care to comment?

The world in general is immersed in Berklee students. These are the only uses and names for "mode" that the vast majority is familiar with, and even if they have no practical value whatsoever (show me one), they will stick. However, I have been thinking before about a term that Ernst Krenek used for serial music (for putting the first note of a row at its end) and that I saw today in Dave Keenan's article "Optimising JI guitar designs ..." in the very same sense that we need to replace the Berklee modes: ROTATION. It has little cultural bagagge, it already seems to be in use, and it really means what it says, nothing more: that you start an ordered set at different places. Optimal term.

I would make a hierarchy of your modified four meanings-of-mode above:

A. gamut, tonal system: a repository of notes which may be derived from some tuning idea just come along with your instrument (like the overblown tone of a didgeridoo). The only demand is that to play these notes be possible

B. maqamat, modi, rags, melody types: describe the use of tones from a repository (I would use "mode" for the general term, but any other will do - just desribe its specific rules). It extracts scales from the gamut, but normally will have rules for other then scalar orderings.

C. rotations of the scale. A tonic stays a tonic, a leading tone stays a leading tone (sequences and underlying chords may momentarily suspend these functions). Can be used as an ornament, a practice pattern, and also (my concession to Berklee) to think of the mode in a certain way.

> > >>>(I say "overladen",
>>>because it's bad, like the straw that broke the camel's back,
>>>rather than "overloaded", which is regarded as good practice in
>>>object-oriented programming (OOP) circles. Come to think of it,
>>>perhaps the OOP paradigm
>>
>>Ah, I see it now; the explanation is right before the parentheses.
>>Would that be like me saying that you get a scale by applying a mode
>>to a gamut?
> > [YA] Yes. Your usage of "mode" and Ozan's seem to match, then.

<baffled> No they don't.

<After a while, and having read the other post written all the above> Of course, he has taken "gamut" for "gamme" all along, whereas in contemporary computer English it means palette, and a German will naturally refer to the original meaning since the word is extinct here. I also see how my sentence could be read in an Ozan-compatible way. Let me try again:

A scale is the result of extracting notes from a gamut (in the case of a piano: the 88 keys) using the rules of a mode.

I had thought that you, Yahya, had meant the same all along using more or less the same words. I also think that Ozan can live well with the statement, but he has "refused" to understand because he stuck to "contemporary western" usages of our words (in France/Belgium and the Berklee school) while you and I were trying to name musical phenomena in different cultures. If not, we will have to go a few more rounds. But first, let's think of a way to make sure we understand each other.

So hasta la proxima,

kLAus

Klaus,

Thank you for your thoughts.

My responses are interpolated below.

Regards,
Yahya

-----Original Message-----

Yahya Abdal-Aziz wrote:

>>The beautiful thing about the gamut is that, unlike the "white note
>>scale", it provides room for alterations. It is a system of seven note
>>names (a, b, c, d, e, f, g; doubled an octave higher and capitalized
>>an octave lower, with a lone Greek Gamma below the A) overlaid with
>>six "alteration indicators" (ut, re, mi, fa, sol, la: there has to be
>>a half step between mi and fa). Tones were identified by their name
>>and up to three "indicators". The lowest note was gamma ut (so the
>>name doesn't indicate any from-to idea), C could be fa or a new ut (so
>>must have been called C fa ut), F likewise, and G was ut again, but
>>also the sol in the hexachord on C or the re in the hexachord on F (G
>>ut sol re). B was B fa mi, a fourth from F or a ditonus from G, so
>>modern b and b flat were represented as one note. Finding the right
>>hexachord for a note was the medieval equivalen of accidentals.
>
>
> [YA] Sounds very complex ...! Where can I read more on the
> _historical_ usage of gamut you're drawing on here? All I have to hand
> on the subject is "The Pelican History of Music", bought decades ago
> and probably mostly superseded by now.

What are decades against the millennium that has apssed since Guido
invented or described his system? Guido of Arezzo would be the obvious
entry to look up, and if it doesn't say it all, solmisation and "ut
queant laxis". And gamut of course (if your language allows; German
doesn't seem to have a name for it and the English-German dictionaries
just say "Skala, Tonleiter" which is getting rid of all the
interesting cultural baggage).

[YA] My point was that later scholarship may have substantially revised
the conclusions drawn in the sixties about the gamut of Guido d'Arezzo
and those who used his system. Remember how plainchant became pop
music for a brief while, about a decade ago? Fashions come and go, and
new spins on old themes.

But certainly, I'll reread what I have here.

---

Guido developed the method of notating music on a system of (four, in
his case) lines. I have no idea if the finales of the church modes had
already been thought of as being next to each other (where is Margo
Schulter, by the way?) or if Guido wanted to have them compact; anyway
they were on D (mode 1 and 2), E (3 and 4), F (5 and 6) and G (7 and
8) (the odd ones authentic, the even ones plagal). Since the placing
of the half steps was determined by the ut-re-mi, the B was typically
mi when starting on G ("Mixolydian", the Berkleeans say) and fa when
starting on F ("But that makes it Ionian!" - making the point that
you're bound to reap confusion when you mix terminologies). There were
mixed modes, as in the obvious case when a melody exceeded an octave
and you went like from authentic to plagal, or when a note changed its
"interpretation". BTW, the infamous "mi contra fa, diabolus in musica"
in the solmisation system described the "forbidden" interval class of
the augmented second and the augmented fourth.

>
> [YA] I think your "original gamut" is a structure with special
> relationships between pitches over more than an octave, isn't
> it? In which case, octave reductions is essentially foreign to
> its nature. (As, for example, in a tuning system that contains
> only the overtones of a given fundamental pitch C0, the notes
> C1 an octave higher, G1 a twelfth higher, C2 two octaves higher,
> E2, G2, Bb2, C3, D3, E3 ... belong to the system, but E1, Bb1 and
> D1 don't.)

Yes. The lowest B had no F under it and so could only be B mi=B
natural. But since the same principle applies to all the octaves, I
see no problem in generalizing "B can be soft or hard (flat or
natural)". And no matter how many octaves and principles apply, I
think you can octave recude anything if you only called it that.

>>>1. A Greek mode - An ancient Greek scale, with rules like a maqam.
>>>2. An ecclesiastical mode - a mediaeval church scale, with rules
>>>like a maqam.
>>>3. The mode of the nth degree, or the nth mode, of a given key -
>>>a diatonic transposition of a common-practice scale upwards by
>>>n scale degrees.
>>>4. A guitar mode - a fingering pattern on the guitar.
>>>
>>>Possibly we could press the ancient Greek terms tonos (plural
>>>tonoi) and tropos (plural tropoi) back into service to avoid using
>>>terms that are now overladen with meaning.
>>
>>I think 1. and 2. have enough in common to be called by the same names
>>(but I think it doesn't hurt when you stay with names of the original
>>cultures, if that culture bothered to theorize). Church modes
>>originally were mostly called "in the nth tone" originally, so why
>>not? (I have to admit that I'm not clear on the meaning of tonoi and
>>tropoi, though).
>
> [YA] Good enough for me, but a trifle longwinded perhaps? Why not
> just "the 4th tone" and so on?

They really said "of the nth tone", and since they said it in Latin
they had a case for that and didn't need a preposition. "'Ut queant
laxis' cantus secundi toni est." A system very specific to the
mediaval system of eight tones/modes; I wouldn't want to make this
universal. But ...

[YA] So we should use a genitive constructins like "the 4th tone's"?
No, I don't think so ... :-)

>>On the other hand, I think you might just as well replace the Berklee
>>modes by referring to the tonality and scale degrees directly. Jazz
>>theory is about chords whereas we are trying to talk about melody.
>
> [YA] I guess calling them modes may have some practical benefits for
> guitarists who frequently discuss them. Anyone care to comment?

The world in general is immersed in Berklee students. These are the
only uses and names for "mode" that the vast majority is familiar
with, and even if they have no practical value whatsoever (show me
one), they will stick.

[YA] Berklee is a guitar method?

--------
However, I have been thinking before about a
term that Ernst Krenek used for serial music (for putting the first
note of a row at its end) and that I saw today in Dave Keenan's
article "Optimising JI guitar designs ..." in the very same sense that
we need to replace the Berklee modes: ROTATION. It has little cultural
bagagge, it already seems to be in use, and it really means what it
says, nothing more: that you start an ordered set at different places.
Optimal term.

[YA] A term very suitable to our purpose, I think.

-------

I would make a hierarchy of your modified four meanings-of-mode above:

A. gamut, tonal system: a repository of notes which may be derived
from some tuning idea just come along with your instrument (like the
overblown tone of a didgeridoo). The only demand is that to play these
notes be possible

B. maqamat, modi, rags, melody types: describe the use of tones from a
repository (I would use "mode" for the general term, but any other
will do - just desribe its specific rules). It extracts scales from
the gamut, but normally will have rules for other then scalar orderings.

C. rotations of the scale. A tonic stays a tonic, a leading tone stays
a leading tone (sequences and underlying chords may momentarily
suspend these functions). Can be used as an ornament, a practice
pattern, and also (my concession to Berklee) to think of the mode in a
certain way.

[YA] A useful and realistic hierarchy between tuning terms may prove
difficult to establish. Suppose we start with A. = gamut or tuning system.
More than just a set of pitches, it is a set related by being tunable or
playable on an (actual, or hypothetical?, or abstract?) instrument.
Then modes, in your sense B. of rules for the use of pitches in the
gamut, are built upon the gamut. Interestingly, one of the most important
rules of any mode is "don't use these notes at all!" But does the gamut of
the mode remain the whole set of notes playable on the instrument? That
seems counter-intuitive. That the mode (set of rules) extracts a scale
from a gamut is a useful alternative way of looking at scales. After all,
the set of notes in two different modes can be the same, while the modes
still differ in the _other_ rules they apply to the gamut.

I'd prefer to describe the structure as -
A. gamut - set of available pitches.
B. scale - set of subsets of the gamut for use in different melodic or
harmonic contexts. (*)
C. mode - set of rules for the use of notes of a scale.
D. rotation - a rule for rotating the interval pattern in a scale.

(*) For example, the major scale selects the LLsLLLs pattern in every
octave,
for both rising and falling melodies, and for all harmonisations;
while the melodic minor scale selects the LsLLLLs pattern in every octave
for rising melodies and the LLsLLsL pattern in every octave for falling
melodies.

In these terms, given any gamut, you can draw a number of scales from it;
you may apply as many different rules as your imagination permits to the
notes of a scale to create a mode; and a rotation is just a particular kind
of mode.

The only one of these notions that seems to be problematical is that a scale
is more than a set of pitches (or, equivalently, of intervals). The only
way
I see around the difficulty is to make the choice of different subsets of
my definition just one of the rules for a mode. That leaves us with a
9-tone
set of pitches in a minor scale, as Johnny says he teaches. Still, this is
contrary to my feeling that a minor scale has seven tones, two of which are
mutable, that is, take different forms depending on context.

-----

>>>(I say "overladen",
>>>because it's bad, like the straw that broke the camel's back,
>>>rather than "overloaded", which is regarded as good practice in
>>>object-oriented programming (OOP) circles. Come to think of it,
>>>perhaps the OOP paradigm
>>
>>Ah, I see it now; the explanation is right before the parentheses.
>>Would that be like me saying that you get a scale by applying a mode
>>to a gamut?
>
> [YA] Yes. Your usage of "mode" and Ozan's seem to match, then.

<baffled> No they don't.

<After a while, and having read the other post written all the above>
Of course, he has taken "gamut" for "gamme" all along, whereas in
contemporary computer English it means palette, and a German will
naturally refer to the original meaning since the word is extinct
here. I also see how my sentence could be read in an Ozan-compatible
way. Let me try again:

A scale is the result of extracting notes from a gamut (in the case of
a piano: the 88 keys) using the rules of a mode.

I had thought that you, Yahya, had meant the same all along using more
or less the same words. I also think that Ozan can live well with the
statement, but he has "refused" to understand because he stuck to
"contemporary western" usages of our words (in France/Belgium and the
Berklee school) while you and I were trying to name musical phenomena
in different cultures. If not, we will have to go a few more rounds.
But first, let's think of a way to make sure we understand each other.

So hasta la proxima,

kLAus

[YA] As� la proxima ...

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Yahya Abdal-Aziz wrote:

> [YA] So we should use a genitive constructins like "the 4th tone's"?
> No, I don't think so ... :-)

And actually, what I meant in the part above that I cut was that the modes were called tones when they applied to the interval structure, just like the Greek tonoi. So didn't want to introduce a numbering system.

>>>On the other hand, I think you might just as well replace the Berklee
>>>modes by referring to the tonality and scale degrees directly. Jazz
>>>theory is about chords whereas we are trying to talk about melody.
>>
>>[YA] I guess calling them modes may have some practical benefits for
>>guitarists who frequently discuss them. Anyone care to comment?
> > > The world in general is immersed in Berklee students. These are the
> only uses and names for "mode" that the vast majority is familiar
> with, and even if they have no practical value whatsoever (show me
> one), they will stick.
> > [YA] Berklee is a guitar method?

I'm on thin ice here. I strongly suspect that the D-7/G7/CM --> D Dorian/G Mixolydian/C Ionian way of thinking about cadences, which many jazz and pop musicians (including guitarists) use, was disseminated from the Berklee College of Music in Boston, aha, Massachusetts. Lawrence Berk, the founder, was a student of Joseph Schillinger, and from what I know about Schillinger he _must_ have had "diatonic transposition" among his bag of tricks. So it seems likely that he unearthed Glareans mode names, discarded the authentic/plagal opposition and the fact that Locrian was originally considered unusable and ended up with a somewhat highfalutin' way of saying "the major scale starting from this of that degree". I would like to know the exact history of these terms, but the few Schillinger books I've seen so far were all beyond my price range.

Diatonic transposition, of course, is a way of coming up with surprising melodies because you combine the melodic rules of one mode (in the original sense) with the interval structure of another.

> > --------
> However, I have been thinking before about a
> term that Ernst Krenek used for serial music (for putting the first
> note of a row at its end) and that I saw today in Dave Keenan's
> article "Optimising JI guitar designs ..." in the very same sense that
> we need to replace the Berklee modes: ROTATION. It has little cultural
> bagagge, it already seems to be in use, and it really means what it
> says, nothing more: that you start an ordered set at different places.
> Optimal term.
> > [YA] A term very suitable to our purpose, I think.

Which could be adapted to the jazz/pop terminology without hurt by just talking about the Dorian rotation instead of the Dorian mode. Yes, I like it.

> > -------
> > I would make a hierarchy of your modified four meanings-of-mode above:
> > A. gamut, tonal system: a repository of notes which may be derived
> from some tuning idea just come along with your instrument (like the
> overblown tone of a didgeridoo). The only demand is that to play these
> notes be possible
> > B. maqamat, modi, rags, melody types: describe the use of tones from a
> repository (I would use "mode" for the general term, but any other
> will do - just desribe its specific rules). It extracts scales from
> the gamut, but normally will have rules for other then scalar orderings.
> > C. rotations of the scale. A tonic stays a tonic, a leading tone stays
> a leading tone (sequences and underlying chords may momentarily
> suspend these functions). Can be used as an ornament, a practice
> pattern, and also (my concession to Berklee) to think of the mode in a
> certain way.
> > [YA] A useful and realistic hierarchy between tuning terms may prove
> difficult to establish. Suppose we start with A. = gamut or tuning system.
> More than just a set of pitches, it is a set related by being tunable or
> playable on an (actual, or hypothetical?, or abstract?) instrument.

Many musics have an archetypical instrument that will determine that. In Common Practice, it's the fiddler who has to adapt to the piano and not the piano that is considered deficient for its few and discrete pitches. For a didgeridoo, there is no tuning system. You have a fundamental and an overblown that theoretically should be a twelfth, but is usually bent god knows where. In Gagaku, every instrument has its own system from tuneable strings to fixed pipes to glissandos, and they all coexist in the same piece of music. Scales that follow a ratio (I'm not even talking about the mathematical sense here) are but a subset. So I would say, your scale in the hierarchy below is my gamut: an already limited selsction from the pitch continuum because of theoretical or practical considerations.

> Then modes, in your sense B. of rules for the use of pitches in the
> gamut, are built upon the gamut. Interestingly, one of the most important
> rules of any mode is "don't use these notes at all!"

Probably less if you have a primitive instrument (on a didgeridoo you have a fundamental and that other note and work with rhythm and pitch accents, and everything new you come up with will be idiomatic didgeridoo music) and more so if the instrument has more "universal" ambitions (like a piano that has had many idiomatic styles in the course of history and can still be used for playing orchestra scores - or like the trumpet before and after it had valves).

But does the gamut of
> the mode remain the whole set of notes playable on the instrument? That
> seems counter-intuitive.

What about the set of notes _expected_ from the instrument?

That the mode (set of rules) extracts a scale
> from a gamut is a useful alternative way of looking at scales. After all,
> the set of notes in two different modes can be the same, while the modes
> still differ in the _other_ rules they apply to the gamut.

We're _almost_ on the same wavelength. I keep the scales for later. My next step is the mode.

> > I'd prefer to describe the structure as -
> A. gamut - set of available pitches.
> B. scale - set of subsets of the gamut for use in different melodic or
> harmonic contexts. (*)
> C. mode - set of rules for the use of notes of a scale.
> D. rotation - a rule for rotating the interval pattern in a scale.
> > (*) For example, the major scale selects the LLsLLLs pattern in every
> octave,
> for both rising and falling melodies, and for all harmonisations;
> while the melodic minor scale selects the LsLLLLs pattern in every octave
> for rising melodies and the LLsLLsL pattern in every octave for falling
> melodies.
> > In these terms, given any gamut, you can draw a number of scales from it;
> you may apply as many different rules as your imagination permits to the
> notes of a scale to create a mode; and a rotation is just a particular kind
> of mode.

Here we have it: You take some selection from the gamut and then think about the kind of music you want to make. I say your idea of music determines the selection. Let's say your gamut is a series of 8 pitches arrived at by tuning consecutive fifths. You name them from A to G in pitch order, calling the two that are closest together both B. Theses pitches are expected in your musical culture, and all the modes share them (perhaps leaving out one note or another).

Then you decide to write a hymn in the first mode, later called Dorian by Glarean. You pick D as your finalis, probably start with the finalis itself or a melodic cadence approaching the finalis (like the tone below it), use the tones in the octave above D, have A and F as recitation tones, are free to jump from D up to A and further from A to C, and flatten the B if the notes before and after it are As. If you apply other rules (treating D, F, A and C as resting tones and the others as approaches) you are not playing the same mode.
> > The only one of these notions that seems to be problematical is that a scale
> is more than a set of pitches (or, equivalently, of intervals). The only
> way
> I see around the difficulty is to make the choice of different subsets of
> my definition just one of the rules for a mode. That leaves us with a
> 9-tone
> set of pitches in a minor scale, as Johnny says he teaches. Still, this is
> contrary to my feeling that a minor scale has seven tones, two of which are
> mutable, that is, take different forms depending on context.

With major and minor, I am still at mode level. Things are a little more complicated here since simultaneous tones may influence their respective functions (f in FM vs f in G7) and modulating to a transposition of the mode is an expected part of the tonal language, so the gamut is an open or circular meantone system.

Melodic minor as a mode has nine tones. Among its rules are "Skip the first and third tone if the melody goes from the fifth degree up to the tonic" and "Skip the first and third tone if the melody goes from the tonic down to the fifth degree". So the mode produces two different scales of seven tones each. Scales are just the outcome of the rules applied by the mode and are relatively uninteresting where there is only one scale (as in major).

Last part: These scales can be rotated.

Next round ...

klaus

Klaus,

Further replies to yours.
Are we getting close yet? :-)

Regards,
Yahya

-----Original Message-----
________________________________________________________________________
Date: Tue, 31 May 2005 17:51:54 +0200
From: klaus schmirler <KSchmir@...>

> [YA] So we should use a genitive constructins like "the 4th tone's"?
> No, I don't think so ... :-)

And actually, what I meant in the part above that I cut was that the
modes were called tones when they applied to the interval structure,
just like the Greek tonoi. So didn't want to introduce a numbering system.

[YA] So do you see a modern use for the terms tonos and tonoi?

...
> [YA] Berklee is a guitar method?

I'm on thin ice here. I strongly suspect that the D-7/G7/CM --> D
Dorian/G Mixolydian/C Ionian way of thinking about cadences, which
many jazz and pop musicians (including guitarists) use, was
disseminated from the Berklee College of Music in Boston, aha,
Massachusetts. Lawrence Berk, the founder, was a student of Joseph
Schillinger, and from what I know about Schillinger he _must_ have had
"diatonic transposition" among his bag of tricks. So it seems likely
that he unearthed Glareans mode names, discarded the authentic/plagal
opposition and the fact that Locrian was originally considered
unusable and ended up with a somewhat highfalutin' way of saying "the
major scale starting from this of that degree". I would like to know
the exact history of these terms, but the few Schillinger books I've
seen so far were all beyond my price range.

Diatonic transposition, of course, is a way of coming up with
surprising melodies because you combine the melodic rules of one mode
(in the original sense) with the interval structure of another.

[YA] And as a technique, far predates modern guitar methods, or
Schillnger for that matter ...

> --------
> However, I have been thinking before about a
> term that Ernst Krenek used for serial music (for putting the first
> note of a row at its end) and that I saw today in Dave Keenan's
> article "Optimising JI guitar designs ..." in the very same sense that
> we need to replace the Berklee modes: ROTATION. It has little cultural
> bagagge, it already seems to be in use, and it really means what it
> says, nothing more: that you start an ordered set at different places.
> Optimal term.
>
> [YA] A term very suitable to our purpose, I think.

Which could be adapted to the jazz/pop terminology without hurt by
just talking about the Dorian rotation instead of the Dorian mode.
Yes, I like it.

[YA] Aha! Agreed, then?

> -------
> I would make a hierarchy of your modified four meanings-of-mode above:
>
> A. gamut, tonal system: a repository of notes which may be derived
> from some tuning idea just come along with your instrument (like the
> overblown tone of a didgeridoo). The only demand is that to play these
> notes be possible
>
> B. maqamat, modi, rags, melody types: describe the use of tones from a
> repository (I would use "mode" for the general term, but any other
> will do - just desribe its specific rules). It extracts scales from
> the gamut, but normally will have rules for other then scalar orderings.
>
> C. rotations of the scale. A tonic stays a tonic, a leading tone stays
> a leading tone (sequences and underlying chords may momentarily
> suspend these functions). Can be used as an ornament, a practice
> pattern, and also (my concession to Berklee) to think of the mode in a
> certain way.
>
> [YA] A useful and realistic hierarchy between tuning terms may prove
> difficult to establish. Suppose we start with A. = gamut or tuning
system.
> More than just a set of pitches, it is a set related by being tunable or
> playable on an (actual, or hypothetical?, or abstract?) instrument.

Many musics have an archetypical instrument that will determine that.
In Common Practice, it's the fiddler who has to adapt to the piano and
not the piano that is considered deficient for its few and discrete
pitches. For a didgeridoo, there is no tuning system. You have a
fundamental and an overblown that theoretically should be a twelfth,
but is usually bent god knows where. In Gagaku, every instrument has
its own system from tuneable strings to fixed pipes to glissandos, and
they all coexist in the same piece of music. Scales that follow a
ratio (I'm not even talking about the mathematical sense here) are but
a subset. So I would say, your scale in the hierarchy below is my
gamut: an already limited selsction from the pitch continuum because
of theoretical or practical considerations.

[YA] No, I had the "theoretical or practical considerations" determine
the gamut; the scale (as I used it below) was drawn from the gamut.

> Then modes, in your sense B. of rules for the use of pitches in the
> gamut, are built upon the gamut. Interestingly, one of the most important
> rules of any mode is "don't use these notes at all!"

Probably less if you have a primitive instrument (on a didgeridoo you
have a fundamental and that other note and work with rhythm and pitch
accents, and everything new you come up with will be idiomatic
didgeridoo music) and more so if the instrument has more "universal"
ambitions (like a piano that has had many idiomatic styles in the
course of history and can still be used for playing orchestra scores -
or like the trumpet before and after it had valves).

But does the gamut of
> the mode remain the whole set of notes playable on the instrument? That
> seems counter-intuitive.

What about the set of notes _expected_ from the instrument?

[YA] Good! "A gamut is a set of notes expected from an
archetypical instrument based on certain theoretical and
practical considerations." Gee, it's almost legalese ...

That the mode (set of rules) extracts a scale
> from a gamut is a useful alternative way of looking at scales. After all,
> the set of notes in two different modes can be the same, while the modes
> still differ in the _other_ rules they apply to the gamut.

We're _almost_ on the same wavelength. I keep the scales for later. My
next step is the mode.

[YA] Yes, by all means let the mode (set of rules) come first;
by operating on the gamut, it determines the relevant scale or scales.

> I'd prefer to describe the structure as -
> A. gamut - set of available pitches.
> B. scale - set of subsets of the gamut for use in different melodic or
> harmonic contexts. (*)
> C. mode - set of rules for the use of notes of a scale.
> D. rotation - a rule for rotating the interval pattern in a scale.
>
> (*) For example, the major scale selects the LLsLLLs pattern in every
> octave,
> for both rising and falling melodies, and for all harmonisations;
> while the melodic minor scale selects the LsLLLLs pattern in every octave
> for rising melodies and the LLsLLsL pattern in every octave for falling
> melodies.
>
> In these terms, given any gamut, you can draw a number of scales from it;
> you may apply as many different rules as your imagination permits to the
> notes of a scale to create a mode; and a rotation is just a particular
kind
> of mode.

Here we have it: You take some selection from the gamut and then think
about the kind of music you want to make. I say your idea of music
determines the selection. Let's say your gamut is a series of 8
pitches arrived at by tuning consecutive fifths. You name them from A
to G in pitch order, calling the two that are closest together both B.
Theses pitches are expected in your musical culture, and all the modes
share them (perhaps leaving out one note or another).

Then you decide to write a hymn in the first mode, later called Dorian
by Glarean. You pick D as your finalis, probably start with the
finalis itself or a melodic cadence approaching the finalis (like the
tone below it), use the tones in the octave above D, have A and F as
recitation tones, are free to jump from D up to A and further from A
to C, and flatten the B if the notes before and after it are As. If
you apply other rules (treating D, F, A and C as resting tones and the
others as approaches) you are not playing the same mode.
>
> The only one of these notions that seems to be problematical is that a
scale
> is more than a set of pitches (or, equivalently, of intervals). The only
> way
> I see around the difficulty is to make the choice of different subsets of
> my definition just one of the rules for a mode. That leaves us with a
> 9-tone
> set of pitches in a minor scale, as Johnny says he teaches. Still, this
is
> contrary to my feeling that a minor scale has seven tones, two of which
are
> mutable, that is, take different forms depending on context.

With major and minor, I am still at mode level. Things are a little
more complicated here since simultaneous tones may influence their
respective functions (f in FM vs f in G7) and modulating to a
transposition of the mode is an expected part of the tonal language,
so the gamut is an open or circular meantone system.

[YA] And talking ofthe major mode or the minor mode has precedent.
So now we have this structure -
A. gamut - set of available pitches.
B. mode - set of rules for the use of notes from a gamut in different
melodic or harmonic contexts.
C. scale - set of subsets of the gamut selected by a mode. (*)
D. rotation - a rule for rotating the interval pattern in a scale.

(*) An example here ...

-----
Melodic minor as a mode has nine tones. Among its rules are "Skip the
first and third tone if the melody goes from the fifth degree up to
the tonic" and "Skip the first and third tone if the melody goes from
the tonic down to the fifth degree". So the mode produces two
different scales of seven tones each. Scales are just the outcome of
the rules applied by the mode and are relatively uninteresting where
there is only one scale (as in major).

[YA] You've lost me - "first and third tone"?

Last part: These scales can be rotated.
[YA] Sure.

Next round ...
... is here!

klaus

--
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Checked by AVG Anti-Virus.
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Yahya Abdal-Aziz wrote:
> Klaus,
> > Further replies to yours.
> Are we getting close yet? :-)

I think we're there. What does the rest of the world think?

(If anyone cares to read this without having followed the thread: I talk about "my ideas" below. They aren't mine, they are my interpretation of the meaning of "modes" and "gamut" in medieval Europe. I try to differentiate this from modern uses of "mode" , because I think these terms can be useful for talking about melodic organisation and tunings in general.)

klaus

> > Regards,
> Yahya
> > > -----Original Message-----
> ________________________________________________________________________
> Date: Tue, 31 May 2005 17:51:54 +0200
> From: klaus schmirler <KSchmir@...>

> [YA] So do you see a modern use for the terms tonos and tonoi?

I wouldn't mind, but I have a preference for sticking to culture specific terms which of course need to be introduced to outsiders from a "neutral" point of view at some time. Since I think that "tonal" and "modal" are well accepted adjectives for the description of cadence oriented and melody oriented music, I'd stick to the noun "mode" (although I talk about chords and chord functions instead of tones for that other principle). So you don't say "We'll call this rag tropos X" but stick to the rag's name and explain "It's a mode, tropos or even melody type that leaves out the seventh degree". (I abhor all that scale and temperament naming on this list that is for the most part not descriptive at all, or at best privately so.)

> Diatonic transposition, of course, is a way of coming up with
> surprising melodies because you combine the melodic rules of one mode
> (in the original sense) with the interval structure of another.
> > [YA] And as a technique, far predates modern guitar methods, or
> Schillnger for that matter ...

I think Schillinger used it for thematic invention, and I believe that interval structures and melody rules go hand in hand, so this is a very artificial and "postmodern" thing to do. Applied to motives, in sequences, sure.

> > >>--------
>>However, I have been thinking before about a
>>term that Ernst Krenek used for serial music (for putting the first
>>note of a row at its end) and that I saw today in Dave Keenan's
>>article "Optimising JI guitar designs ..." in the very same sense that
>>we need to replace the Berklee modes: ROTATION. It has little cultural
>>bagagge, it already seems to be in use, and it really means what it
>>says, nothing more: that you start an ordered set at different places.
>>Optimal term.
>>
>>[YA] A term very suitable to our purpose, I think.
> > > Which could be adapted to the jazz/pop terminology without hurt by
> just talking about the Dorian rotation instead of the Dorian mode.
> Yes, I like it.
> > [YA] Aha! Agreed, then?

I already used it last night. I, for one, will stick with it. But in the last post (I will probably snip that part) I was talking about rotating a mode which is messing up our hierarchy, or (unless you're Schillinger) nonsense. So I have to be careful about that.

>>A. gamut, tonal system: a repository of notes which may be derived
>>from some tuning idea just come along with your instrument (like the
>>overblown tone of a didgeridoo). The only demand is that to play these
>>notes be possible
>>
>>B. maqamat, modi, rags, melody types: describe the use of tones from a
>>repository (I would use "mode" for the general term, but any other
>>will do - just desribe its specific rules). It extracts scales from
>>the gamut, but normally will have rules for other then scalar orderings.
>>
>>C. rotations of the scale. A tonic stays a tonic, a leading tone stays
>>a leading tone (sequences and underlying chords may momentarily
>>suspend these functions). Can be used as an ornament, a practice
>>pattern, and also (my concession to Berklee) to think of the mode in a
>>certain way.
>>
>>[YA] A useful and realistic hierarchy between tuning terms may prove
>>difficult to establish. Suppose we start with A. = gamut or tuning
> > system.
> >>More than just a set of pitches, it is a set related by being tunable or
>>playable on an (actual, or hypothetical?, or abstract?) instrument.
> > > Many musics have an archetypical instrument that will determine that.
> In Common Practice, it's the fiddler who has to adapt to the piano and
> not the piano that is considered deficient for its few and discrete
> pitches. For a didgeridoo, there is no tuning system. You have a
> fundamental and an overblown that theoretically should be a twelfth,
> but is usually bent god knows where. In Gagaku, every instrument has
> its own system from tuneable strings to fixed pipes to glissandos, and
> they all coexist in the same piece of music. Scales that follow a
> ratio (I'm not even talking about the mathematical sense here) are but
> a subset. So I would say, your scale in the hierarchy below is my
> gamut: an already limited selsction from the pitch continuum because
> of theoretical or practical considerations.
> > [YA] No, I had the "theoretical or practical considerations" determine
> the gamut; the scale (as I used it below) was drawn from the gamut.

I misunderstood you there.

> >>Then modes, in your sense B. of rules for the use of pitches in the
>>gamut, are built upon the gamut. Interestingly, one of the most important
>>rules of any mode is "don't use these notes at all!"
> > > Probably less if you have a primitive instrument (on a didgeridoo you
> have a fundamental and that other note and work with rhythm and pitch
> accents, and everything new you come up with will be idiomatic
> didgeridoo music) and more so if the instrument has more "universal"
> ambitions (like a piano that has had many idiomatic styles in the
> course of history and can still be used for playing orchestra scores -
> or like the trumpet before and after it had valves).
> > But does the gamut of
> >>the mode remain the whole set of notes playable on the instrument? That
>>seems counter-intuitive.
> > > What about the set of notes _expected_ from the instrument?
> > [YA] Good! "A gamut is a set of notes expected from an
> archetypical instrument based on certain theoretical and
> practical considerations." Gee, it's almost legalese ...

I used the instrument to emphasize that the music and the instruments to play it were probably there before the theory. If you want to fix your intervals on a stringed instrument, you will probably tune third to second harmonics all the way and get a Pythagorean system. If you start out with an alpenhorn or a mouthbow, you don't even have much choice and build your melodies from the harmonic series. So a gamut can be just "a set of notes expected to occur in a musical culture."

> >>I'd prefer to describe the structure as -
>>A. gamut - set of available pitches.
>>B. scale - set of subsets of the gamut for use in different melodic or
>>harmonic contexts. (*)
>>C. mode - set of rules for the use of notes of a scale.
>>D. rotation - a rule for rotating the interval pattern in a scale.
>>
>>(*) For example, the major scale selects the LLsLLLs pattern in every
>>octave,
>>for both rising and falling melodies, and for all harmonisations;
>>while the melodic minor scale selects the LsLLLLs pattern in every octave
>>for rising melodies and the LLsLLsL pattern in every octave for falling
>>melodies.
>>
>>In these terms, given any gamut, you can draw a number of scales from it;
>>you may apply as many different rules as your imagination permits to the
>>notes of a scale to create a mode; and a rotation is just a particular
> > kind
> >>of mode.
> > > Here we have it: You take some selection from the gamut and then think
> about the kind of music you want to make. I say your idea of music
> determines the selection. Let's say your gamut is a series of 8
> pitches arrived at by tuning consecutive fifths. You name them from A
> to G in pitch order, calling the two that are closest together both B.
> Theses pitches are expected in your musical culture, and all the modes
> share them (perhaps leaving out one note or another).
> > Then you decide to write a hymn in the first mode, later called Dorian
> by Glarean. You pick D as your finalis, probably start with the
> finalis itself or a melodic cadence approaching the finalis (like the
> tone below it), use the tones in the octave above D, have A and F as
> recitation tones, are free to jump from D up to A and further from A
> to C, and flatten the B if the notes before and after it are As. If
> you apply other rules (treating D, F, A and C as resting tones and the
> others as approaches) you are not playing the same mode.
> >>The only one of these notions that seems to be problematical is that a
> > scale
> >>is more than a set of pitches (or, equivalently, of intervals). The only
>>way
>>I see around the difficulty is to make the choice of different subsets of
>>my definition just one of the rules for a mode. That leaves us with a
>>9-tone
>>set of pitches in a minor scale, as Johnny says he teaches. Still, this
> > is
> >>contrary to my feeling that a minor scale has seven tones, two of which
> > are
> >>mutable, that is, take different forms depending on context.

The Greeks thought of their tropoi from the instrument point of view, where you have a limited number of strings and tune some of them differently. But I think they mixed that with the other concept of moving tonics to another string, and the results are super complicated in my humble opinion (and to my humble mind). If you like to think like that, [big pause] you'd have to specify retunings in different contexts. This is at odds with my way of thinking, where all the notes that can be correct are provided at their specific pitches in the gamut, the modes provide the context for using some of them and leaving others. I think it isn't the case, but if you are more comfortable with thinking in terms of retuning instead of picking up a note, there may still be issues hidden.

> > > With major and minor, I am still at mode level. Things are a little
> more complicated here since simultaneous tones may influence their
> respective functions (f in FM vs f in G7) and modulating to a
> transposition of the mode is an expected part of the tonal language,
> so the gamut is an open or circular meantone system.
> > [YA] And talking ofthe major mode or the minor mode has precedent.
> So now we have this structure -
> A. gamut - set of available pitches.
> B. mode - set of rules for the use of notes from a gamut in different
> melodic or harmonic contexts.
> C. scale - set of subsets of the gamut selected by a mode. (*)
> D. rotation - a rule for rotating the interval pattern in a scale.
> > (*) An example here ...
> > -----
> Melodic minor as a mode has nine tones. Among its rules are "Skip the
> first and third tone if the melody goes from the fifth degree up to
> the tonic" and "Skip the first and third tone if the melody goes from
> the tonic down to the fifth degree". So the mode produces two
> different scales of seven tones each. Scales are just the outcome of
> the rules applied by the mode and are relatively uninteresting where
> there is only one scale (as in major).
> > [YA] You've lost me - "first and third tone"?

Excuse me, it's just the normal upward and downward scale. Melodic minor on the tonic C gives you G Ab A Bb B C from the gamut. Going down from C you skip B and A, going up from G you skip Ab and Bb. I thought since the mode provides more notes than are used in a scale, it was clearer describing the scale in terms of not playing certain notes. From a practical angle this is just one of the rules you, having learned it, have to forget.

> > > Last part: These scales can be rotated.
> [YA] Sure.

So we're done?

I was consciously thinking of this hierarchy when a was asking questions about blues tunings last night: you have a melodic prototype that gets distributed over (and beyond) the octave, that's the mode. The scales you get depend on the gamut (whether it's 7-limit, 11-limit, ET, combinations) and my hunch was that there are identifiable cultures that each use their own gamut.

And it's getting day where I sent it and the kids are as good as back from school. Gotta cook, bye.

klaus

--- In tuning@yahoogroups.com, klaus schmirler <KSchmir@o...> wrote:

> I think we're there. What does the rest of the world think?

I don't think you are going to convince people to call the things you
find in Scala scl files "gamuts" or "modes" unless there seems to be
some clear ultility for it.

Dear Brother Yahya,

Given my disagreement with certain points in this argument, I don't know if what I say will further my cause, but here goes.

Yes, I've studied in Belgium, with Yevgeny Moguilevsky, a brilliant virtuoso from Odessa, and first-prize winner of the Queen Elizabeth Competition. Thus, you might say that the influence I received was more Russian than Francophone. Besides, you may notice that my affliation is with the Anglo-Saxon culture rather than Frankish.

As for humility, you can see that I am very far behind in that respect as compared to you!

I always had problems with concise definitions. Something will eventually be missing from a term or a concept once rid of "redundant definitions". I am more comfortable with having something explained over and over in several ways, approaching the same problem from different angles. It's probably because I'm rather a dim light bulb.

As for the gamut wars, I rest my case. Nevertheless, I wonder why we allow this word to be overloaded when `compass` or `range` would do nicely in its stead to define the extent of pitches afforded by an instrument.

Equally unsettling is the the disunion of gamme-gamut-scale.

*

Here are some definition of `gamme` according to Le Robert & Collins Senior dictionary:

Gamme: Scale. Range. Gamut
Faire des gamme: To practice scales
Gamme ascendante/descendante: Rising/Falling scale
Toute la gamme: The whole lot
Gamme de produit: Range of products

*

Here is the definition of `scale` according to Microsoft Bookshelf British Reference Collection:

Scale: In music, a sequence of pitches that establishes a key, and in some respects the character of a composition. A scale is defined by its starting note and may be major or minor depending on the order of intervals. A chromatic scale is the full range of 12 notes. It has no key because there is no fixed starting point. = Listen to the ascending forms of the indicated scales as they sound when built on the pitch middle C: Diatonic Major Scale, Diatonic (Melodic Minor) Scale, Chromatic Scale, Whole Tone Scale, Pentatonic Scale.

Of course, the examples are given as (ascending-descending) subsets of 12tET and nothing remotely resembling microtonality can be discerned from this definition.

*

Here is the definition of scale(6) according to Merriam-Websters Collegiate Dictionary 10th Edition:

Scale: (ME, fr., LL scala ladder, staircase, fr. L scalae, pl., stairs, rungs, ladder; akin to L scandare to climb- more at SCAN)

1 a: LADDER b: archaic: a means of ascent

2 A graduated series of musical tones ascending or descending in order of pitch according to a specified scheme of their musical intervals

3 Something graduated esp. when used as a measure or rule: as a: a series of marks or points at knows intervals used to measure distances (as the height of the mercury in a thermometer) b: an indication of the relationship between the distances on a map and the corresponding actual distances c: RULER

4 a: a graduated series or scheme of rank or order (a scale of taxation) b: MINIMUM WAGE

5 a: a proportion between two sets of dimensions (as between those of a drawing and its original) b: A distinctive relative size, extent, or degree (projects done on a large scale)

6 a graded series of tests or of performances used in rating individual intelligence or achievement.

*

The best definition of `scale` is perhaps that of the Harvard Dictionary of Music 4th Edition:

Scale (Fr. gamme, échelle; Ger. Tonleiter, Skala; It. scala, gamma; Sp. escala gamma) A collection of pitches arranged in order from lowest to highest or from highest to lowest. The pitches of any music in which pitch is definable can be reduced to a scale. The concept and its pedagogical use have been especially prominent in the history of Western are music. The importance of the concept in non-Western systems varies considerably and is often associated with concepts of melody construction and internal pitch relationships that go well beyond any simple ordering of pitches from lowest to highest (see also Mode, Melody type). Even in Western tonal music, however, scales are only a reflection of compositional practice that includes notions of appropriate melodic progression and the functions of individual pitches in relation to one another. With respect to nontonal Western music, a scale is likely to be simply an arbitrary represantation of pitch content that contributes little to an understanding of a given work.

...

The rest of the definition tells us how the total pitch world of Western tonal music is consigned to 12 pitch-classes, how a scale out of these 12 pitches can be made to choose any one of the 12 tones as its starting point, how repetitions through any number of octaves may occur, how the diatonic scale is central to the idea of tonal music, how any of the seven pitches of such a scale can be taken as the starting point for rearranging the order of tones and semitones (thus resulting in what is called the `octave species` or `modes`), how all but one of these (starting with B) have been recognized in both theory and practice, thus, forming part of the system of modes, and how only two of these have gained prominence.

Moreover, there is hardly any distinction when it is said: "The major mode or major scale takes the pattern produced by starting upward through the diatonic scale from C." except for the fact that the minor scale or mode is distinguished in regards to its "starting point" and "hierarchical relationship (functions) of pitches".

Obviously, the "major mode" is made synonymous here with "major scale" just as it is the case with its minor counterpart.

To add insult to injury, let me confess that I'm so confused now that nothing makes sense anymore.

Here comes the greatest sentence: "A composition based PRIMARILY on a given scale is said to be the KEY of that scale."

This refutes the argument that maqams are modes, since everyone knows that a maqam is "a scale or several scales upon which a composition is PRIMARILY based upon"

The above-given definition of "maqam" is based on the premise that: "scales are simply abstractions from musical practice rather than musical objects with prior or independent standing." and that modes are "any of a series of loosely related concepts employed in the study and classification of both scales and melodies".

"Loosely related" is certainly not the proper term to brand maqams with. On the contrary, maqams are "very elaborately woven" with many many functions assigned to the pitches that aid in the melodic flow of music.

To make the distinction better, here is continuation of the definition of mode from the same source:

"The term (mode) is oftern restricted to scale types defined as collections of pitches arranged from lowest to highest, each including one pitch that is regarded as central. At another extreme, some concepts of mode emphasize melody types; any given mode is defined principally by characteristic melodic elements. Other concepts of mode range between these extremes. No single concept usefully embraces all that has been meant by the term throughout the the history of Western music as well as all that is meant by the terms associated with non-Western music that have at one time or another been translated as mode."

It is clear, that had non-Westerners knew of the wonderfully adequate term called "key" as a translation of "maqam/destgah/rag", they would never have attempted to stretch the definition of mode to what it has become today.

[YA] This is only halfway to being a scale as I understand it.
Or does your "C melodic minor scale" consist of 9 notes to every
octave, arranged in order of increasing pitch, so that it contains
both a minor sixth degree and a major sixth degree, and likewise
for sevenths? My "C melodic minor scale" consists of 7 notes to
every octave in one pattern ascending, and of 7 notes to every
octave in another pattern descending, so that it contains
only a major sixth degree when ascending, and only a minor sixth
degree when descending, and likewise for sevenths. My scale is
a set of patterns of melodic movement, built on a gamut of 9 notes.

[OZ] Indeed, I concur with the second definition where two kinds of "scales" (first to be ascended, the other to be descended) make the "gamme-mode-species?" of melodic minor.

[YA] I understand that your halfway-scale (= gamut+pitch order)
does not distinguish a tonic starting-point. Certainly it contains a
lowest note of the gamut, which may have nothing to do with
anything but the pitch limitations of the instrument. A scale in my
sense also does not require a fixed starting-point; however, _in a
given context of musical practice_, the two patterns of notes
provided by my "C melodic minor scale" only occur in a key called
"C minor".

[OZ] Does this mean that hundreds of Scala files need to be rid of the word scale, and replaced with gamut?

> How can this be? It is the gamut that is ascending-descending
> the scale(s). The scale is merely the foothold for whatever is
> moving over it.

[YA] In music, what moves? Melody, rhythm, harmony. A melody
in C minor moves over the notes of the C (melodic) minor scale.
A complex harmony in C minor moves over the notes of the
C (harmonic) minor scale. I don't think the gamut - the collection
of notes - moves at all. What you consider as moving is the "gamme"
- a melody consisting of many or all notes of a particular (say
C minor) scale. With enough fingers - or a long stick, I could play
all the notes of the C major gamut on the piano simultaneously.

[OZ] I still am overladen with the jumble of terms and concepts. But as I see, you are considering the static pile of pitches the gamut. OK. I can live with that I suppose. Never again will I refer to anything tonally mobile by the word starting with ga----!

> > Tonic: Yes, thanks for defining this term. I think we would
> > also want, for some musical styles, to define dominant,
> > mediant, initial, final ... because of their specialised rôles
> > analogous to the specialised rôle of a tonic. However, I'm
> > unsure whether by "priority function" you simply mean that
> > the tonic is counted as "first step" in the scale (ladder), or
> > do you mean that the tonic is more important than other
> > pitches? And if the latter, melodically or harmonically?

> All of them of course.

[YA] If so, I'd rather a definition that stated each of those
points explicitly.

[OZ] Please... I'm not very successful with that it seems. I'm sure someone else will be much more resourceful in defining the roles of pitches in a "gamut"?

[YA] It's certainly confusing terminology. For clarity, we
need to distinguish the C major scale from its first mode.

[OZ] And how would we do it exactly?

[YA] So a gamut is a set of pitches, a scale is an ordering (or
maybe two) of a gamut, a gamme is a particular form of melody
made from a gamut, a mode is a scale plus functions for various
pitches within it.

[OZ] Can a "gamut" be unordered? If so, how? And how would you define "key"?

> We digress. Let us regress.

[YA] Where's the digression? That's all the word "mode"
means to most guitarists. Yes, I know they're not all
pianists, but we eschew cultural superiority, right? :-)

[OZ] It is hard to drop prejudices! Sorry for that act of pretentiousness.

[YA] Not at all what I meant! By "diatonic transposition"
I mean moving "thru the tones" - essentially choosing a
different starting point within the same set of notes.
Nothing more. No new notes are added.

[OZ] That manoeuvre results in "octave species" or "modes". No?

> A scale is only a list of intervals,

[YA] Are you sure about that? This is almost where we
started ...

[OZ] Not anymore! I repent! I'm so confused with the chaos.

[YA] You're the expert on maqamat. Instead of saying -
"with rules like a maqam", perhaps I should just say "with rules
governing melodic succession".

[OZ] No, no, not at all. I'm merely a patron of this art form in my own perverse way. 8-)

> I never heard of a mode where one can suddenly enter the
> sphere of another mode.

[YA] Or it wouldn't be a mode, would it? Same restriction governs
the use of ragas. One raga never changes to another within the same
composition. That you can or would do this with maqamat both
surprises and intrigues me. How is it possible to do so, I wonder,
without destroying the unity of mood that one maqam establishes?

[OZ] That is so very easy to explain. How does one not destroy the C majorness of the key in C major although many other tonalities can be utilized through transpositions and modulations? Why does not the C minorness of the key in C minor is not destroyed although I frequent G Major?

[YA] If "gamme" then means - for us at least! - the practice of playing
all the notes of a scale, from botom to top and back a gain, as a melody,
I'm content to use it that way. Trouble is, I think that most of our
Francophone friends wouldn't want it to no longer also mean "scale" in
all its musical senses ...

[OZ] I renounce my evil ways! A thousand pardons to all the Franks!

[YA] There are several notions of distance in music. The simplest to
use just counts scale degrees. So a fifth is four notes (scale degrees)
away from a unison, three notes from a second, two notes from a third
and one note from a fourth.

A more complex one, such as the one given by James Tenney, give the
distance of a note (from a reference note) which is at a pitch n/d times
that of the reference note, as -
HD (n/d) = k . log (n . d)
Here n is the numerator and d the denominator of the pitch ratio, and
both are presumed to be integers. k is any convenient constant, and if
you want to measure harmonic distance along the chain of perfect
fifths, you could take it to be 1 / log (3 . 2). We take logs so that the
HD of, say, a fifth is unchanged by octave transposition of both pitches
in the interval. From this definition it follows that if a perfect fifth is
one step, a just major second is two steps, a major sixth is three and so
on. I draw my entire knowledge of this measure, or "metric", from the
paper Paul Erlich kindly sent me to study.

[OZ] Then, in simplest layman terms, can I define metric to be "any paradigm for interval measurment?"

So much for the technical side ... on the side of musical feeling and
intuition, do you ever count, as I do, the number of melodic movements
away from the tonic? So that, for example, in C minor, Ab is only
related to the tonic note C in the second degree, wanting - if aiming at
arriving at C - to move first to G, F or possibly Bb. Whereas the G or the F might move directly to the C, although still more likely to get there in stages.

[OZ] As in:

C-Eb-G-C
Ab-Eb-Ab-C-Eb-Ab
A-F-A-C-Eb-G
Bb-F-Bb-D-F
Ab-D-F#-C-D-F#
G-D-G-B-D-G
C-G-C-Eb-G

Intuitively, I count them as I improvise, so that I know what may come next, and where they may lead to.

I only get this sense in a more melismatic style of
composition, which precludes large leaps, except for effect.

[OZ] A pity... I am partial to large leaps, especially the major seventh!

But in such a style, I find that the distances of notes is determined firstly by the number of scale steps intervening, and secondly by the number of spiral-of-fifths steps intervening, between them. What exact
proportion each contributes, I couldn't say, and it does seem to vary
with the mood of the piece - not scientific, I know! But I do know that
a major or minor second is always closer than a third, and a third than
a fifth, while a fifth can sometimes be closer (melodically) than a fourth, and other times not.

[OZ] This has everything to do with counterpoint, the indispensible toolkit of a composer. The hidden meanings of the diatonical degrees can only be revealed by its power.

Regards,
Yahya

Cordially,
Ozan

My concern exactly.

----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 02 Haziran 2005 Perşembe 22:48
Subject: [tuning] Re: Scales: an lengthy attempt at proper definition

--- In tuning@yahoogroups.com, klaus schmirler <KSchmir@o...> wrote:

> I think we're there. What does the rest of the world think?

I don't think you are going to convince people to call the things you
find in Scala scl files "gamuts" or "modes" unless there seems to be
some clear ultility for it.

Ozan Yarman wrote:

> My concern exactly.
>
> ----- Original Message -----
> From: Gene Ward Smith
> To: tuning@yahoogroups.com
> Sent: 02 Haziran 2005 Perşembe 22:48
> Subject: [tuning] Re: Scales: an lengthy attempt at proper definition
>
>
> --- In tuning@yahoogroups.com, klaus schmirler <KSchmir@o...> wrote:
>
> > I think we're there. What does the rest of the world think?
>
> I don't think you are going to convince people to call the things you
> find in Scala scl files "gamuts" or "modes" unless there seems to be
> some clear ultility for it.
>
>

The utility arises as soon as you want to make music from these
scales. How many names are there for the same scales having their
origins in different cultures? Scala really only has a collection of
scales, to make culture specific music from them you have to know them
as modes.

I've mentioned Aeolian and Hypodorian before. As scales (running their
notes up and down the keyboard), they are identical. As modes, one of
them has its finalis at the bottom of its octave range and the primary
recitation tone is on the fifth degree, whereas the other one has the
finalis in the middle and the recitation tone on the third degree
(counting from the finalis) (and please don't hold me responsible for
errors in recitation tone placement; I'm no specialist in Gregoran
chant and go by old and little used memories). There may be an Indian
rag that looks exactly like the major scale, but has rules about
postponing the use of certain degrees that are totally foreign to the
major mode, just as the idea that you can end a piece on the tonic in
no matter which octave is foreign to the rag.

Apart from the loose usage of "scale" for any succession of pitches
which will always be there I see problems mainly for common practice
since most of its rules concern the succession of chords, not of
melody notes. But different melody types do exist, and you might want
to name them. They may all use the C major scale and tonality, but
your descriptions of the types will be different modes with stricter
rules than the plain vanilla major mode has.

klaus

Dear Ozan,

I'm sorry that you feel so disheartened. But your collection of
definitions below shows the state of affairs: so many terms and
definitions that can mean identical or different things. We were just
trying to extract a subset from them that expressed what might be
necessary in a few distinct terms.

I don't remember who introduced the term "gamut" in this discussion
and which meaning was intended. It was probably somewhere in the middle between your understanding, coming from French where gamme _is_
a scale plain and simple, and my German, where no cognate of "gamut"
exists, so that I naturally went back to the original meaning. And I
joined the discussion when I felt that the full potential of "gamut"
was being ignored.

> As for the gamut wars, I rest my case. Nevertheless, I wonder why
> we allow this word to be overloaded when `compass` or `range` would
> do nicely in its stead to define the extent of pitches afforded by
> an instrument.

Well, the word is overloaded in English. It can mean scale, it can
mean compass, but it also can mean the totality of "recognized"
pitches (according to the New Shorter Oxford). This was the original
meaning.

[French gamme, English scale: two catchall terms]

> *
>
> The best definition of `scale` is perhaps that of the Harvard
> Dictionary of Music 4th Edition:
> > Scale (Fr. gamme, échelle; Ger. Tonleiter, Skala; It. scala, gamma;
> Sp. escala gamma) A collection of pitches arranged in order from
> lowest to highest or from highest to lowest. The pitches of any
> music in which pitch is definable can be reduced to a scale. The
> concept and its pedagogical use have been especially prominent in
> the history of Western are music. The importance of the concept in
> non-Western systems varies considerably and is often associated
> with concepts of melody construction and internal pitch
> relationships that go well beyond any simple ordering of pitches
> from lowest to highest (see also Mode, Melody type). Even in
> Western tonal music, however, scales are only a reflection of
> compositional practice that includes notions of appropriate melodic
> progression and the functions of individual pitches in relation to
> one another. With respect to nontonal Western music, a scale is
> likely to be simply an arbitrary represantation of pitch content
> that contributes little to an understanding of a given work.

Note how this definition encompasses scale as an active ("concepts of
melody construction") and passive ("reflection of compositional
practice") principle. For the active principle, you are referred to
"mode". For the rest, the similarities to a mode are stressed, or it
is "an arbitrary representation of pitch content that contributes
little to an understanding of a given work."

>
> ...
>
> The rest of the definition tells us how the total pitch world of
> Western tonal music is consigned to 12 pitch-classes, how a scale
> out of these 12 pitches can be made to choose any one of the 12
> tones as its starting point, how repetitions through any number of
> octaves may occur, how the diatonic scale is central to the idea of
> tonal music, how any of the seven pitches of such a scale can be
> taken as the starting point for rearranging the order of tones and
> semitones (thus resulting in what is called the `octave species` or
> `modes`), how all but one of these (starting with B) have been
> recognized in both theory and practice, thus, forming part of the
> system of modes, and how only two of these have gained prominence.

This is Glarean's extension of the church modes. Notice the concluding
idea (which refers to "Ionian" and "Aeolian"): musical Darwinism at
its best. I don't think any of us wants that.

>
> Moreover, there is hardly any distinction when it is said: "The
> major mode or major scale takes the pattern produced by starting
> upward through the diatonic scale from C." except for the fact that
> the minor scale or mode is distinguished in regards to its
> "starting point" and "hierarchical relationship (functions) of
> pitches".
>
> Obviously, the "major mode" is made synonymous here with "major
> scale" just as it is the case with its minor counterpart.

Probably a reflection of what people call things. In the text, major
and minor were introduced in the context of Glarean's modes as modes
themselves (if only in the sense of octave species/placement of the
semitones), but music students today are taught to call them scales.

>
> To add insult to injury, let me confess that I'm so confused now
> that nothing makes sense anymore.

It's not you, it's the state of the world.

>
> Here comes the greatest sentence: "A composition based PRIMARILY on
> a given scale is said to be the KEY of that scale."

But they left out here that "a given scale" is (in our terminology)
the result of a mode transposed to a specific pitch height.

>
> This refutes the argument that maqams are modes, since everyone
> knows that a maqam is "a scale or several scales upon which a
> composition is PRIMARILY based upon"
>
> The above-given definition of "maqam" is based on the premise that:
> "scales are simply abstractions from musical practice rather than
> musical objects with prior or independent standing." and that modes
> are "any of a series of loosely related concepts employed in the
> study and classification of both scales and melodies".
>
> "Loosely related" is certainly not the proper term to brand maqams
> with. On the contrary, maqams are "very elaborately woven" with
> many many functions assigned to the pitches that aid in the melodic
> flow of music.

Take statements like "You play this rag fast", "There is no seventh
degree", "Introduce this note last", "Place a melisma here, here, and
there", "Always jump to this note from that other one, unless ..." Are
they related? Can a good singer avoid to weave them together?

>
> To make the distinction better, here is continuation of the
> definition of mode from the same source:
>
> "The term (mode) is oftern restricted to scale types defined as
> collections of pitches arranged from lowest to highest, each
> including one pitch that is regarded as central. At another
> extreme, some concepts of mode emphasize melody types; any given
> mode is defined principally by characteristic melodic elements.
> Other concepts of mode range between these extremes. No single
> concept usefully embraces all that has been meant by the term
> throughout the the history of Western music as well as all that is
> meant by the terms associated with non-Western music that have at
> one time or another been translated as mode."

Our main "innovation" is the resolution to call rotations of scales
rotations, not modes. Our modes make melodies from the "recognized"
notes of the gamut (the second definition above); operations on the
resluting scales are called something else.

>
> It is clear, that had non-Westerners knew of the wonderfully
> adequate term called "key" as a translation of "maqam/destgah/rag",
> they would never have attempted to stretch the definition of mode
> to what it has become today.

I'm not sure if you are being sarcastic or if I know that little about
maqams. A western key is a specific transposition of a scale; when a
march modulates to the subdominant for the trio, both parts may be in
major, but one is in C major and the other in F major, and both have
the same internal interval structure. In maqam, I thought, you tune to
the singer, don't modulate (=transpose the same mode to another pitch)
and have rules how to build your melody which a key doesn't have.

[...]

>
> [OZ] Does this mean that hundreds of Scala files need to be rid of
> the word scale, and replaced with gamut?

With some of them, like 12-ET, it makes sense. Most are really scales,
and we are given no information which mode brought them about. If
anything is called mode, it is probably a rotation of a scale.

[...]

Our central concept is the mode/rag/maqam. Its rules extract pitches
from the gamut, and the result is a scale, or several scales used in
different contexts. The notes of the scale can be rotated.

klaus

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:
> And even those things I thought I understood
> the "tuning-list orthodoxy" on, I may have misjudged based
> purely on who's been vocal recently ... For example, I gave
> Aline an "easy" answer as to what a JI scale is, and as might
> be expected, provoked a reaction from someone else (Dave
> Keenan) showing me it wasn't so easy ... :-) Still, I thought
> Dave's answer (enabling tuning by ear without beats) was
> equally facile, and a good deal harder to verify - How do I
> know that two tuners hear the same thing? (Answer:
> I don't, because there are "good tuners" and "bad tuners",
> who get very different results; so according to Dave's
> definition, one man's JI scale is another man's Poison ...)

To some degree that's true. But in my view that's far better than the
situation you get with the "tuning by ratios" definition. With that
definition I can play you any set of pitches (including a perfect
12-equal) and claim they constitute a JI scale and there is no way you
can prove me wrong, since there is always some ratio that's within the
accuracy of any measurement you can make.

At least with the "tunable by ear" definition, if someone claims to be
a super-tuner and able to hear near-beatlessness in say 12-equal, we
can subject them to randomised blind tests. Of course they may refuse,
but we can draw our own conclusions from that too. :-)

-- Dave Keenan

Klaus,

I think we may have baked a cake!
Is it too early to celebrate?

Yahya

-----Original Message-----
> Klaus,
>
> Further replies to yours.
> Are we getting close yet? :-)

I think we're there. What does the rest of the world think?

> So now we have this structure -
> A. gamut - set of available pitches.
> B. mode - set of rules for the use of notes from a gamut in different
> melodic or harmonic contexts.
> C. scale - set of subsets of the gamut selected by a mode.
> D. rotation - a rule for rotating the interval pattern in a scale.
>
...

So we're done?

... Gotta cook, bye.

klaus

--
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Version: 7.0.322 / Virus Database: 267.5.1 - Release Date: 2/6/05

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> My concern exactly.

I didn't express it well, since Scala actually gives an ordered scale
without the first note and whose last note is always the interval of
repitition, and I don't think there is even a name for that. The point
is, most of the time on these lists people really seem to mean by
"scale" more or less the same thing as "gamut". That is, most of the
time when coming up with a new "scale" we simply provide the notes
relative to some 1/1, along with the period if it isn't an octave.

--- In tuning@yahoogroups.com, klaus schmirler <KSchmir@o...> wrote:

> The utility arises as soon as you want to make music from these
> scales.

If I want to make music from the scale there's a lot more on my mind
than simply linear orderings. Two or more dimensional relationships,
and chords and how they connect with other chords, are major concerns.
If the scale is generated by generators, is that a part of the
definition of the scale? It isn't if you put it into Scala format, but
it is if you put it into Tonescape format, which might come up if you
use these for making music.

How many names are there for the same scales having their
> origins in different cultures?

That depends in good measure on what you count as being the same.

Scala really only has a collection of
> scales, to make culture specific music from them you have to know them
> as modes.

No, I don't think so. You have to know them as how you plan to make
use of them, and that can differ greatly. When there are a lot of
notes in your octave, the linear ordering becomes less relevant
anyway. You can't make much sense of 171 equal notes to the octave
just pondering it as an ascending scale. Given the vast differences in
the way the same set of notes can be organized and thought of, it
seems to me that equally vast problems arise if we insist on including
the organization and employment of the notes as part of the definition.

That was my argument since the beginning, to restrict the definition of scale to just what you said, reserve mode the function of what is inferred by `major scales` and `minor scales` (octave species), and extend further the definition for the increasing complexity of melody types by the usage of `key`, where transposition is and should be considered alien to modes.

And yes, maqams not only transpose, they modulate to other degrees and other maqams. So, they may not be called modes in the strictest sense that I adhere to.

Cordially,
Ozan
----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 03 Haziran 2005 Cuma 6:54
Subject: [tuning] Re: Scales: an lengthy attempt at proper definition

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> My concern exactly.

I didn't express it well, since Scala actually gives an ordered scale
without the first note and whose last note is always the interval of
repitition, and I don't think there is even a name for that. The point
is, most of the time on these lists people really seem to mean by
"scale" more or less the same thing as "gamut". That is, most of the
time when coming up with a new "scale" we simply provide the notes
relative to some 1/1, along with the period if it isn't an octave.

Gene Ward Smith wrote:
> --- In tuning@yahoogroups.com, klaus schmirler <KSchmir@o...> wrote:
> > >>The utility arises as soon as you want to make music from these >>scales.
> > > If I want to make music from the scale there's a lot more on my mind
> than simply linear orderings.

Exactly. I take it that orderings by pitch height and by generator distance are equally linear. (I should also take into account that you might not use "scale" in the narrower meaning Yahya and I tried to establish. But linearity is linearity, in scales or in gamuts.)

> Two or more dimensional relationships,

At least the way you say it does not imply that there is no linear ordering in these dimensions, too. In fact, I have difficulty imagining otherwise.

> and chords and how they connect with other chords, are major concerns.

In some musics, chords are no concern at all.

> If the scale is generated by generators, is that a part of the
> definition of the scale? It isn't if you put it into Scala format, but
> it is if you put it into Tonescape format, which might come up if you
> use these for making music.
> > How many names are there for the same scales having their > >>origins in different cultures? > > > That depends in good measure on what you count as being the same.

I meant that they are the same scale, but are used for different music. You snipped my example: Aeolian and Hypodorian both exist in a gamut generated by fifths (I suspect Glarean's sample compositions used thirds as consonants, so it would be meantone fifths - ahistorical for Hypodorian, but after all he invented Aeolian and put it in the same larger system as Hypodorian). As scales, both consist of "the white notes from A to a" and are undistinguishable from, say, natural minor which in contrast to both pays no concern to recitation tones, but divides its notes among the tonic, subdominant and dominant spheres.

> > Scala really only has a collection of > >>scales, to make culture specific music from them you have to know them >>as modes.
> > > No, I don't think so. You have to know them as how you plan to make
> use of them, and that can differ greatly. When there are a lot of
> notes in your octave, the linear ordering becomes less relevant
> anyway. You can't make much sense of 171 equal notes to the octave
> just pondering it as an ascending scale.

This is why we consider it a gamut. The mode - the ways - of the music we want to make will make a selection.

Given the vast differences in
> the way the same set of notes can be organized and thought of, it
> seems to me that equally vast problems arise if we insist on including
> the organization and employment of the notes as part of the definition.

Of what? Of the scale? That is our point, and that is why "scale" rarely is of much use. Of the mode? No, the organization and definition _are_ the mode.

> klaus

Yahya Abdal-Aziz wrote:
> Klaus,
> > I think we may have baked a cake!
> Is it too early to celebrate?
> > Yahya

Well, I waited before either celebrating or answering, and what I saw was a failure: People flaming each other for making too direct a connection between a minor "scale" and a twelve tone "scale" which could easily be avoided by referring specifically to a 12-ET gamut and Iglashion Jones reminding people that major and minor are modes. (I don't want to rule out a mode that has nothing to do with tonal music, yet produces a major scale upward and a minor scale downward or vv.; the size of the third from the tonic may be a good criterion for scales, but there is a better definition for major and minor as modes.)

None of our terms were newly invented, all we did was tie them to specific abstraction levels in place of using a large number of overlapping catch-alls. But it seems people like imprecision when no numbers are involved.

klaus

> > -----Original Message-----
> >>Klaus,
>>
>>Further replies to yours.
>>Are we getting close yet? :-)
> > > I think we're there. What does the rest of the world think?
> > >>So now we have this structure -
>>A. gamut - set of available pitches.
>>B. mode - set of rules for the use of notes from a gamut in different
>>melodic or harmonic contexts.
>>C. scale - set of subsets of the gamut selected by a mode.
>>D. rotation - a rule for rotating the interval pattern in a scale.
>>
> > ...
> > So we're done?

Dear Klaus,

At last, you would agree that my perception is equally valid amidst all this chaos? What with all the monkey business in "musical Darwinism", I'm sure I don't deserve being flogged for apostasy regarding the usage of modes/scales/gamuts and disregarding the usage of "rotations" (which I would rather call "octave species/modes").

As regards the "unrelatedness quotient" of melody types which according to you can be taken as modes, I disagree entirely that directions passed down from master to pupil can be taken for granted and the underlying pattern ignored when constructing/performing maqams/rags/destgahs. The connections, at least for maqams, are not "loose" in any sense of the word. Functions that correspond to Western keys are implemented to all the degrees of maqam scales, allowing a complete sweep of the entire tonal spectrum in Maqam Music. In fact, you are encouraged to a complete tour in Maqam City. It is considered a poor show if you stick to drinking coffee at Nihavend Cafe all day long.

If you thought that maqams do not modulate to other maqams, or transpose themselves within a given diapason, you are highly, if not grossly, mistaken. It's all about etiquette.

Cordially,
Ozan
----- Original Message -----
From: klaus schmirler
To: tuning@yahoogroups.com
Sent: 03 Haziran 2005 Cuma 5:03
Subject: Re: [tuning] Re: Scales: an lengthy attempt at proper definition

Dear Ozan,

I'm sorry that you feel so disheartened. But your collection of
definitions below shows the state of affairs: so many terms and
definitions that can mean identical or different things. We were just
trying to extract a subset from them that expressed what might be
necessary in a few distinct terms.

I don't remember who introduced the term "gamut" in this discussion
and which meaning was intended. It was probably somewhere in the
middle between your understanding, coming from French where gamme _is_
a scale plain and simple, and my German, where no cognate of "gamut"
exists, so that I naturally went back to the original meaning. And I
joined the discussion when I felt that the full potential of "gamut"
was being ignored.

> As for the gamut wars, I rest my case. Nevertheless, I wonder why
> we allow this word to be overloaded when `compass` or `range` would
> do nicely in its stead to define the extent of pitches afforded by
> an instrument.

Well, the word is overloaded in English. It can mean scale, it can
mean compass, but it also can mean the totality of "recognized"
pitches (according to the New Shorter Oxford). This was the original
meaning.

[French gamme, English scale: two catchall terms]

> *
>
> The best definition of `scale` is perhaps that of the Harvard
> Dictionary of Music 4th Edition:
>
> Scale (Fr. gamme, échelle; Ger. Tonleiter, Skala; It. scala, gamma;
> Sp. escala gamma) A collection of pitches arranged in order from
> lowest to highest or from highest to lowest. The pitches of any
> music in which pitch is definable can be reduced to a scale. The
> concept and its pedagogical use have been especially prominent in
> the history of Western are music. The importance of the concept in
> non-Western systems varies considerably and is often associated
> with concepts of melody construction and internal pitch
> relationships that go well beyond any simple ordering of pitches
> from lowest to highest (see also Mode, Melody type). Even in
> Western tonal music, however, scales are only a reflection of
> compositional practice that includes notions of appropriate melodic
> progression and the functions of individual pitches in relation to
> one another. With respect to nontonal Western music, a scale is
> likely to be simply an arbitrary represantation of pitch content
> that contributes little to an understanding of a given work.

Note how this definition encompasses scale as an active ("concepts of
melody construction") and passive ("reflection of compositional
practice") principle. For the active principle, you are referred to
"mode". For the rest, the similarities to a mode are stressed, or it
is "an arbitrary representation of pitch content that contributes
little to an understanding of a given work."

>
> ...
>
> The rest of the definition tells us how the total pitch world of
> Western tonal music is consigned to 12 pitch-classes, how a scale
> out of these 12 pitches can be made to choose any one of the 12
> tones as its starting point, how repetitions through any number of
> octaves may occur, how the diatonic scale is central to the idea of
> tonal music, how any of the seven pitches of such a scale can be
> taken as the starting point for rearranging the order of tones and
> semitones (thus resulting in what is called the `octave species` or
> `modes`), how all but one of these (starting with B) have been
> recognized in both theory and practice, thus, forming part of the
> system of modes, and how only two of these have gained prominence.

This is Glarean's extension of the church modes. Notice the concluding
idea (which refers to "Ionian" and "Aeolian"): musical Darwinism at
its best. I don't think any of us wants that.

>
> Moreover, there is hardly any distinction when it is said: "The
> major mode or major scale takes the pattern produced by starting
> upward through the diatonic scale from C." except for the fact that
> the minor scale or mode is distinguished in regards to its
> "starting point" and "hierarchical relationship (functions) of
> pitches".
>
> Obviously, the "major mode" is made synonymous here with "major
> scale" just as it is the case with its minor counterpart.

Probably a reflection of what people call things. In the text, major
and minor were introduced in the context of Glarean's modes as modes
themselves (if only in the sense of octave species/placement of the
semitones), but music students today are taught to call them scales.

>
> To add insult to injury, let me confess that I'm so confused now
> that nothing makes sense anymore.

It's not you, it's the state of the world.

>
> Here comes the greatest sentence: "A composition based PRIMARILY on
> a given scale is said to be the KEY of that scale."

But they left out here that "a given scale" is (in our terminology)
the result of a mode transposed to a specific pitch height.

>
> This refutes the argument that maqams are modes, since everyone
> knows that a maqam is "a scale or several scales upon which a
> composition is PRIMARILY based upon"
>
> The above-given definition of "maqam" is based on the premise that:
> "scales are simply abstractions from musical practice rather than
> musical objects with prior or independent standing." and that modes
> are "any of a series of loosely related concepts employed in the
> study and classification of both scales and melodies".
>
> "Loosely related" is certainly not the proper term to brand maqams
> with. On the contrary, maqams are "very elaborately woven" with
> many many functions assigned to the pitches that aid in the melodic
> flow of music.

Take statements like "You play this rag fast", "There is no seventh
degree", "Introduce this note last", "Place a melisma here, here, and
there", "Always jump to this note from that other one, unless ..." Are
they related? Can a good singer avoid to weave them together?

>
> To make the distinction better, here is continuation of the
> definition of mode from the same source:
>
> "The term (mode) is oftern restricted to scale types defined as
> collections of pitches arranged from lowest to highest, each
> including one pitch that is regarded as central. At another
> extreme, some concepts of mode emphasize melody types; any given
> mode is defined principally by characteristic melodic elements.
> Other concepts of mode range between these extremes. No single
> concept usefully embraces all that has been meant by the term
> throughout the the history of Western music as well as all that is
> meant by the terms associated with non-Western music that have at
> one time or another been translated as mode."

Our main "innovation" is the resolution to call rotations of scales
rotations, not modes. Our modes make melodies from the "recognized"
notes of the gamut (the second definition above); operations on the
resluting scales are called something else.

>
> It is clear, that had non-Westerners knew of the wonderfully
> adequate term called "key" as a translation of "maqam/destgah/rag",
> they would never have attempted to stretch the definition of mode
> to what it has become today.

I'm not sure if you are being sarcastic or if I know that little about
maqams. A western key is a specific transposition of a scale; when a
march modulates to the subdominant for the trio, both parts may be in
major, but one is in C major and the other in F major, and both have
the same internal interval structure. In maqam, I thought, you tune to
the singer, don't modulate (=transpose the same mode to another pitch)
and have rules how to build your melody which a key doesn't have.

[...]

>
> [OZ] Does this mean that hundreds of Scala files need to be rid of
> the word scale, and replaced with gamut?

With some of them, like 12-ET, it makes sense. Most are really scales,
and we are given no information which mode brought them about. If
anything is called mode, it is probably a rotation of a scale.

[...]

Our central concept is the mode/rag/maqam. Its rules extract pitches
from the gamut, and the result is a scale, or several scales used in
different contexts. The notes of the scale can be rotated.

klaus

Ozan Yarman wrote:
> Dear Klaus,

Hi Ozan,

> > At last, you would agree that my perception is equally valid amidst
> all this chaos?

I recognize that all these terms are in use, meaning more often than
not the same thing, and I try to take that into account. But I would
prefer if, at least in this community, people would try to make their
usage a bit more specific and restrict the terms that can refer to
different levels of musical abstraction to one level only.

What with all the monkey business in "musical
> Darwinism",

Should I have said "Spencerism"? By no means was that directed at you.
The text you quoted mentioned bit too matter-of-factly for my taste
that of all these 12 modes, only two survived. No word about the
historic change from modal to tonal music that was making itself felt,
no word about the fact that Glarean had just "invented" these two
survivors and their plagals.

I'm sure I don't deserve being flogged for apostasy
> regarding the usage of modes/scales/gamuts and disregarding the > usage of "rotations" (which I would rather call "octave > species/modes").

Octave species seems a safe term, but mode isn't, and I'd like to
restrict its meaning to the set of rules for making melodies.

This is Margo Schulter at http://www.medieval.org/emfaq/harmony/pyth4.html

> 4.3.2. Medieval modes in Pythagorean tuning
> > The term "mode" can have many meanings, but here is used simply to
> mean a scale or octave-species with a characteristic pattern of
> whole-steps and semitones. For theorists such as Johannes de
> Grocheio (c. 1300), the term could imply further a regular formula
> by which one may know the beginning, middle, and end of a melody -
> as in Gregorian chant with its reciting tones, as opposed to the
> world of polyphony and secular music. Thus Grocheio prefers to say
> that polyphonic music is based on various octave-species, but not
> on "modes" proper.

Polyphonic music was not in octaves only, so the melodies of other voices than the tenor couldn't adhere to the "mode" in its rich sense. Reason for Grocheo to come up with a different term.

> > As regards the "unrelatedness quotient" of melody types which > according to you can be taken as modes, I disagree entirely that > directions passed down from master to pupil can be taken for > granted and the underlying pattern ignored when > constructing/performing maqams/rags/destgahs.

I didn't say that, and I was insinuating that the author of the
article didn't mean that either. I have no way of looking into his
head, but I think he meant to say that there is no relation between a
rag emphasizing a note and it being a morning rag, except in a
specific culture. And that there is no requirement for modes in other
cultures to have a corresponding set of criteria.

The connections, at
> least for maqams, are not "loose" in any sense of the word. > Functions that correspond to Western keys are implemented to all > the degrees of maqam scales, allowing a complete sweep of the > entire tonal spectrum in Maqam Music.

I don't understand this. To use the precise terminology, keys in Western music can be transposed to every note of the gamut, not only some scale. Can you give an Arabic of Turkish term for "key"?

In fact, you are encouraged
> to a complete tour in Maqam City. It is considered a poor show if > you stick to drinking coffee at Nihavend Cafe all day long.

I've already started. Nihavend=the minor in that other thread :). And I stumbled upon an Arabic term for Gamma-Ut, the lowest note that gave its name to the medieval tone repository: yakah. So the 48 named tones are the equivalent of the gamut, a meantone spiral or 171-ET.

> > If you thought that maqams do not modulate to other maqams, or > transpose themselves within a given diapason, you are highly, if > not grossly, mistaken. It's all about etiquette.
> > Cordially, Ozan

Hi Klaus,

I concur that some definitions should be agreed upon in a community as compact as the tuning list, but there are certain issues that we haven't quite evaded yet it seems.

For example, I would rather reserve the term "rotations of the scale" for MOS, where the scale in question is a sub-set from your "gamut".

From my limited knowledge on Greek or Church modes, I cannot reach safe conclusions as much as you do, but I sense that mode is a poor substitute for the word Maqam. You can stretch the meaning, but why when there are better alternatives?

And just a minute, a key in C Minor in Classical Western Music cannot/does not have to/ transpose or modulate its scale everywhere over 12 notes. In fact, a traditional conception of key would limit its usage to a closed sphere of adjacent tones:

Cm-Fm-BM-Em-AM-Dm-GM-Cm

Maqams likewise sweep over many degrees of their scales in such a fashion throughout the piece, so as to indicate routes for microtonal harmonic progressions. Also, a maqam is certainly not restricted to its own default set of scales. Is it not evident that key is the best term to define the dynamic diatonical structure of maqams?

Besides, if the purpose is transposing the diapason for all 12 notes, there are 12 Ney Ahengs to do the job:

Bolaheng, Rast=D3
D# (Bolaheng-Davud Mabeyn=Between so and so)
Davud, E
Shah, F
F#
Mansur, G
G#
Kiz, A
A#
Mustahzen, B
Sipurde, C4 (260hz, standart diapason instrument)
C#
Bolahenk Nisfiye, D4 (half the size)

The equivalent of the gamut would then be `Kaba Rast to Treble Huseini`, or C3 to A5 for Sipurde Aheng.

Where did you get the idea of 171tET?

Cordially,
Ozan

----- Original Message -----
From: klaus schmirler
To: tuning@yahoogroups.com
Sent: 06 Haziran 2005 Pazartesi 3:24
Subject: Re: [tuning] Re: Scales: an lengthy attempt at proper definition

Ozan Yarman wrote:
> Dear Klaus,

Hi Ozan,

>
> At last, you would agree that my perception is equally valid amidst
> all this chaos?

I recognize that all these terms are in use, meaning more often than
not the same thing, and I try to take that into account. But I would
prefer if, at least in this community, people would try to make their
usage a bit more specific and restrict the terms that can refer to
different levels of musical abstraction to one level only.

What with all the monkey business in "musical
> Darwinism",

Should I have said "Spencerism"? By no means was that directed at you.
The text you quoted mentioned bit too matter-of-factly for my taste
that of all these 12 modes, only two survived. No word about the
historic change from modal to tonal music that was making itself felt,
no word about the fact that Glarean had just "invented" these two
survivors and their plagals.

I'm sure I don't deserve being flogged for apostasy
> regarding the usage of modes/scales/gamuts and disregarding the
> usage of "rotations" (which I would rather call "octave
> species/modes").

Octave species seems a safe term, but mode isn't, and I'd like to
restrict its meaning to the set of rules for making melodies.

This is Margo Schulter at http://www.medieval.org/emfaq/harmony/pyth4.html

> 4.3.2. Medieval modes in Pythagorean tuning
>
> The term "mode" can have many meanings, but here is used simply to
> mean a scale or octave-species with a characteristic pattern of
> whole-steps and semitones. For theorists such as Johannes de
> Grocheio (c. 1300), the term could imply further a regular formula
> by which one may know the beginning, middle, and end of a melody -
> as in Gregorian chant with its reciting tones, as opposed to the
> world of polyphony and secular music. Thus Grocheio prefers to say
> that polyphonic music is based on various octave-species, but not
> on "modes" proper.

Polyphonic music was not in octaves only, so the melodies of other
voices than the tenor couldn't adhere to the "mode" in its rich sense.
Reason for Grocheo to come up with a different term.

>
> As regards the "unrelatedness quotient" of melody types which
> according to you can be taken as modes, I disagree entirely that
> directions passed down from master to pupil can be taken for
> granted and the underlying pattern ignored when
> constructing/performing maqams/rags/destgahs.

I didn't say that, and I was insinuating that the author of the
article didn't mean that either. I have no way of looking into his
head, but I think he meant to say that there is no relation between a
rag emphasizing a note and it being a morning rag, except in a
specific culture. And that there is no requirement for modes in other
cultures to have a corresponding set of criteria.

The connections, at
> least for maqams, are not "loose" in any sense of the word.
> Functions that correspond to Western keys are implemented to all
> the degrees of maqam scales, allowing a complete sweep of the
> entire tonal spectrum in Maqam Music.

I don't understand this. To use the precise terminology, keys in
Western music can be transposed to every note of the gamut, not only
some scale. Can you give an Arabic of Turkish term for "key"?

In fact, you are encouraged
> to a complete tour in Maqam City. It is considered a poor show if
> you stick to drinking coffee at Nihavend Cafe all day long.

I've already started. Nihavend=the minor in that other thread :). And
I stumbled upon an Arabic term for Gamma-Ut, the lowest note that gave
its name to the medieval tone repository: yakah. So the 48 named tones
are the equivalent of the gamut, a meantone spiral or 171-ET.

>
> If you thought that maqams do not modulate to other maqams, or
> transpose themselves within a given diapason, you are highly, if
> not grossly, mistaken. It's all about etiquette.
>
> Cordially, Ozan

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Ozan Yarman wrote:

> Hi Klaus,
>
> I concur that some definitions should be agreed upon in a community
> as compact as the tuning list, but there are certain issues that we
> haven't quite evaded yet it seems.

Yes, in the end this was a thing between Yahya (get better!) and me.
If more people had participated, someone might have argued for very
different and maybe (just maybe, because I don't think this is
possible) truly culturally neutral terms. Also, keys and maybe a
couple of other terms could have been defined (as you might argue that
the notes of the maqamlar are taken from the gamut of the 48 tones,
but these are from a metamaqam like 55-equal that also needs a name
[my preferred solution would be to say that the gamut is in a tuning.
But if modulation transposes the 48 notes and maps them to different
tones in 55-equal, you must find a different term for the 48 or
abandon them as superceded by musical practice]).

>
> For example, I would rather reserve the term "rotations of the
> scale" for MOS, where the scale in question is a sub-set from your
> "gamut".
>
>> From my limited knowledge on Greek or Church modes, I cannot
>> reach safe conclusions as much as you do, but I sense that mode
>> is a poor substitute for the word Maqam. You can stretch the
>> meaning, but why when there are better alternatives?

Medieval modes are from a dead tradition, and deadness can serve as a
substitute to cultural neutrality ;O). Certainly maqamat and ragas
seem more refined, but what was important to me was to establish a
term for the process that defines the music - by picking notes from a
gamut, by giving them functions, and incidentally by producing scales.
The term "mode" was already there, the problem is to deprecate the use
of the same term for octave species or rotations.

>
> And just a minute, a key in C Minor in Classical Western Music
> cannot/does not have to/ transpose or modulate its scale everywhere
> over 12 notes. In fact, a traditional conception of key would limit
> its usage to a closed sphere of adjacent tones:

But it's not C minor that modulates, the music modulates to a new key
and away from C minor.

>
> Cm-Fm-BM-Em-AM-Dm-GM-Cm

Or Cm-C#minor, a common pop music device (which for some people is too
crude to deserve the name modulation).

>
> Maqams likewise sweep over many degrees of their scales in such a
> fashion throughout the piece, so as to indicate routes for
> microtonal harmonic progressions. Also, a maqam is certainly not
> restricted to its own default set of scales. Is it not evident that
> key is the best term to define the dynamic diatonical structure of
> maqams?

Is it possible that you are using "maqam" to mean the system of all
maqams _and_ specific maqam modes in that system? Then I would
understand that maqam music allows transpositions and modulations, and
you would have to specify whether you are using rast yakah (funny -
that's the melodic minor scale in its two directions) at the absolute
bottom of your vocal range (probably: "yakah in G") of higher up ("in
C"). If during all modulations you still can say that you are playing
rast yakah at the bottom of your range, then "maqam" overlaps into the
idea of "form" which may include stereotypical modulations or chord
progressions (as in the blues of a sonata). This needs an extra tem, I
think.

I'll try to get back to the part I snipped in 2 or 3 days; it has too
many foreign terms for me and I'll nedd time to research and digest
them. Also, it's time for bed if I want to take advantage of the night.

Güle güle,

klaus

'tis a late reply, but here goes.

When tuning definitions are concerned, is it just tea for two? Differences
of opinion lead to different directions, and hence, the foundation of
different schools of thought. This has been experienced once too often, with
quite regrettable results I might add. I think the tuning list should avoid
such segragations/secterianism whenever possible, even if it means complete
unresolution in most cases.

I am, as can be expected, still confused with your usage of the terms, and
am having difficulties drawing parallels to the world of maqams.

So, I may not be inclined to your usage of the word "mode".

Also, I am not at all inclined to use "modulation" synonymously with
"transposition", although chromatic modulation and transposition intersect
in both meaning and function. Especially since scales are generally subsets
of larger systems that you want to call gamuts, I object strongly to
the idea of "modulating within the gamut". How about "transposing through
the degrees of a gamut" instead?

Now, in order to understand Maqamat, one needs to consider the tonal music
of Europe, where modulations and transpositions of keys take place. Even in
a limited form such as I VI V, the tonal music differs from modes of the
Middle Ages. Perhaps it is the transition period from modality to tonality
that encourages you to adopt a more tonal perspective when scrutinizing
modality.

Anyway, the maqams not only modulate within the same diatonical scale, but
they also may transpose within the gamut. So, key seems to embrace the
concept pretty well.

Wherever did you get the idea for Rast Yegah? Maybe you can elaborate what
you mean?

Also, if you have been following the recent discussions about 79 MOS out of
159tET, perhaps you can suggest an approach that will clear the mess.

Cordially,
Ozan

----- Original Message -----
From: "klaus schmirler" <KSchmir@online.de>
To: <tuning@yahoogroups.com>
Sent: 08 Haziran 2005 �ar�amba 4:33
Subject: Re: [tuning] Re: Scales: an lengthy attempt at proper definition

Ozan Yarman wrote:

> Hi Klaus,
>
> I concur that some definitions should be agreed upon in a community
> as compact as the tuning list, but there are certain issues that we
> haven't quite evaded yet it seems.

Yes, in the end this was a thing between Yahya (get better!) and me.
If more people had participated, someone might have argued for very
different and maybe (just maybe, because I don't think this is
possible) truly culturally neutral terms. Also, keys and maybe a
couple of other terms could have been defined (as you might argue that
the notes of the maqamlar are taken from the gamut of the 48 tones,
but these are from a metamaqam like 55-equal that also needs a name
[my preferred solution would be to say that the gamut is in a tuning.
But if modulation transposes the 48 notes and maps them to different
tones in 55-equal, you must find a different term for the 48 or
abandon them as superceded by musical practice]).

>
> For example, I would rather reserve the term "rotations of the
> scale" for MOS, where the scale in question is a sub-set from your
> "gamut".
>
>> From my limited knowledge on Greek or Church modes, I cannot
>> reach safe conclusions as much as you do, but I sense that mode
>> is a poor substitute for the word Maqam. You can stretch the
>> meaning, but why when there are better alternatives?

Medieval modes are from a dead tradition, and deadness can serve as a
substitute to cultural neutrality ;O). Certainly maqamat and ragas
seem more refined, but what was important to me was to establish a
term for the process that defines the music - by picking notes from a
gamut, by giving them functions, and incidentally by producing scales.
The term "mode" was already there, the problem is to deprecate the use
of the same term for octave species or rotations.

>
> And just a minute, a key in C Minor in Classical Western Music
> cannot/does not have to/ transpose or modulate its scale everywhere
> over 12 notes. In fact, a traditional conception of key would limit
> its usage to a closed sphere of adjacent tones:

But it's not C minor that modulates, the music modulates to a new key
and away from C minor.

>
> Cm-Fm-BM-Em-AM-Dm-GM-Cm

Or Cm-C#minor, a common pop music device (which for some people is too
crude to deserve the name modulation).

>
> Maqams likewise sweep over many degrees of their scales in such a
> fashion throughout the piece, so as to indicate routes for
> microtonal harmonic progressions. Also, a maqam is certainly not
> restricted to its own default set of scales. Is it not evident that
> key is the best term to define the dynamic diatonical structure of
> maqams?

Is it possible that you are using "maqam" to mean the system of all
maqams _and_ specific maqam modes in that system? Then I would
understand that maqam music allows transpositions and modulations, and
you would have to specify whether you are using rast yakah (funny -
that's the melodic minor scale in its two directions) at the absolute
bottom of your vocal range (probably: "yakah in G") of higher up ("in
C"). If during all modulations you still can say that you are playing
rast yakah at the bottom of your range, then "maqam" overlaps into the
idea of "form" which may include stereotypical modulations or chord
progressions (as in the blues of a sonata). This needs an extra tem, I
think.

I'll try to get back to the part I snipped in 2 or 3 days; it has too
many foreign terms for me and I'll nedd time to research and digest
them. Also, it's time for bed if I want to take advantage of the night.

G�le g�le,

klaus

Ozan Yarman wrote:
> 'tis a late reply, but here goes.

And I promised to comment on the part I snipped a couple of days ago.
I can now say that I didn't find any of your terms except rast, but I
should have understood just by looking at their setup that they were
note names.

>
> When tuning definitions are concerned, is it just tea for two? Differences
> of opinion lead to different directions, and hence, the foundation of
> different schools of thought. This has been experienced once too often, with
> quite regrettable results I might add. I think the tuning list should avoid
> such segragations/secterianism whenever possible, even if it means complete
> unresolution in most cases.

I repeat, we didn't change anything except restricting the uses of
"mode" and "scale". Neither Yahya nor I introduced any new terms, and
what we drew attention to ("gamut" for a whole tonal system,
"rotation" for the "jazz modes") has all been in use before. "Key" or
"genus" might well have found a place in that terminology, but since
nobody else participated ...

>
> I am, as can be expected, still confused with your usage of the terms, and
> am having difficulties drawing parallels to the world of maqams.

Your gamut can be the classical 24 tones in 2 octaves (according to my
Arab-oriented source, that would be from yakah to ramal tuti). The
gamut can provide for an unequal distribution of the tones of for an
equal one like 24-et, which allows free and exact transposition. Or
you can have both, as in 53-et (How did 17-et fit into the picture?).
Or you can have an open system like JI that expands in the direction
your music wants to go (instruments permitting). And if you write for
an orchestra, you probably want a different gamut that is not
restricted to 2 octaves.

The mode sets the interval relations, final tone, mood, &c. Depending
on the contextual rules it provides, it selects one or more scales
from the gamut. (Actually it probably selects tones for a melody that
you can afterward arrange as a scale.) I mention two scales below that
look like F major. Since they are different modes, I assume that they
have different melodic rules; one may have the final on its upper F,
the other on the lower. And of course, if you refer to a specific
modal system like maqam, nobody wants to keep you from using that
specific term.

>
> So, I may not be inclined to your usage of the word "mode".
>
> Also, I am not at all inclined to use "modulation" synonymously with
> "transposition", although chromatic modulation and transposition intersect
> in both meaning and function.

I would say transposition is a restatement of a scale or melody on a
different degree of the gamut. This corresponds to "chromatic
transposition" in Western theory. A sequence in the modern sense is a
diatonic transposition that sticks to the notes of the scale, cycling
the motiv through different rotations of that scale.

"Modulation" is the procedure of going from one mode to another or a
different transposition of the same. So in the object oriented
paradigm, modulation, just like modes, is a method, not an object (Yahya?).

Especially since scales are generally subsets
> of larger systems that you want to call gamuts, I object strongly to
> the idea of "modulating within the gamut". How about "transposing through
> the degrees of a gamut" instead?

But the additional flat in the trio of a menuet or march was not part
of the scale before. It comes from the gamut. If you have unequal
steps between the 48 notes and transpose, you need new notes to keep the correct step sizes. They come from a gamut like 53-et.

>
> Now, in order to understand Maqamat, one needs to consider the tonal music
> of Europe, where modulations and transpositions of keys take place. Even in
> a limited form such as I VI V, the tonal music differs from modes of the
> Middle Ages. Perhaps it is the transition period from modality to tonality
> that encourages you to adopt a more tonal perspective when scrutinizing
> modality.

I don't think I do.

>
> Anyway, the maqams not only modulate within the same diatonical scale, but
> they also may transpose within the gamut. So, key seems to embrace the
> concept pretty well.
>
> Wherever did you get the idea for Rast Yegah? Maybe you can elaborate what
> you mean?

As for the part comparing it with harmonic minor, I simply didn't see
the slashes through the accidentals. As for its nontransposibility, as
far as I know Yakah is tuned to the lowest note in the range of the
singer. (My source is Habib Hassan Touma in a book on Arab music -
assuming that most of the classical heritage is Osmanic; it's the most
pertinent book I have access to - and a couple of essays by Frangis
Alizade that I read long ago). This would mean it is fixed in space
(at the low end of the gamut). Touma doesn't give the maqamat all on
the same note, which I would have expected if they are totally
transposable (you could see the differences easier by just looking at
accidentals). Instead, they start for the most part from G, C, and D,
half flat E seems common, some are on A. Furthermore, in the 'agam
group he gives a couple of major scales (I've looked hard for slashes
this time). Each transposition has its own name, including the ones on
low F (lower than yagah=G) and high F (s­ah war and gaharkah/mazmum
respectively). So a maqam seems to imply not only a sequence of
intervals, but also a position in the two octave gamut. Maybe Arabian
and Turkish music diverge in that respect. (But again, Alizade, from
north of Turkey, gave me the same ideas.)

>
> Also, if you have been following the recent discussions about 79 MOS out of
> 159tET, perhaps you can suggest an approach that will clear the mess.

I can't, although I'm reading along. If others have the same problems
I have, it may help if you state again what you are after, focussing
on the necessary notes instead of the notation. In traditional
notation, you have 24 notes per octave, like the Arabian system. If I
remember correctly, you need semitones, whole tones, 1 1/2 tones, and
pythagorean and just thirds. And it should be an et. Why does it need
to be a meantone system?

klaus

Dear Klaus,

I am not against restricting terms or their usage. In fact, proper
methodology requires it, unless we are not indulging in poetry or sophism.
Yet, I have made my objections from the point of view that Maqams should not
be consigned to the term "mode" even when this is expanded to embrace them.
It is simply not proper to insinuate that Greek-Christian theories have
similar bearings to Maqam Music. My rejection of the term is due to a
cultural issue alone.

Now, let us conclude then, that transposition is moving the tonic of a scale
to another degree of the gamut while preserving step sizes, while modulation
is rotating the scale itself. Modulation does not and cannot be forced to
mean the preservation of the correct step sizes of a scale. For example:

CDEFGABC

to

DEFGABCD

is a modulation from Ionian to Dorian. No?

And transposition would be:

CDEFGABC

FGABbCDEF

So, I would best restrict the term modulation and transposition to these
applications.

I appreciate your efforts in trying to understand Maqam Music. But know that
neither 24, nor 53 can suffice to explain the perde-system due to the nature
of the Ney that gives JI ratios close to that of Zarlino's diatonical scale
for Rast, the fundamental maqam and the first degree of the Ney at the same
time.

17ET? The misconception arises from the Ebjed system of 17 perdes per
octave, where the sharps and flats are individually represented on the
Halberstadt keyboard. The distinctions that are most important above all are
between those of segah-buselik and evdj-mahur.

Maqam Music should have the range of a piano, while the gamut of the perdes
can be transposed to the octave region according to the instrument chosen.

For example, each Ney has a different compass compared to the standart
diapason. Their registers are transposed even when their notation must
remain the same. That is because they are Transposing instruments like the
Clarinets or Trumpets.

Let me demonstrate. Sipurde Ney gives the following pitches for Rast
according to the international diapason:

CDEFGABC

However, third and seventh degrees can be flattened a notch depending on the
seyir of the maqam. Besides, in order to achieve the correct pitches (1 9/8
5/4 4/3 3/2 5/3 15/8 2), you need a meantone notation by default.

Barring the flattening nuances, you can express this maqam on the staff as:

Do-Re-Mi-Fa-Sol-La-Si-Do (principal major scale)

Where Do is around C4=260hz. Sipurde is the only Ney that can play in
concord with a symphony orchestra using this notation.

For other Neys, the same written notation results in the transposition of
the diapason itself. For example:

Mansur notation for Rast Maqam: Do-Re-Mi-Fa-Sol-La-Si-Do
Pitches heard: GABCDEF#G

Thus, the gamut of the perdes depends on the register of the instrument as
well as where you want to transpose them.

I hope this clears the misconception regarding perdes. Many think that they
correspond to frequencies, whereas they correspond only to flexible
step-sizes.

Cordially,
Ozan

----- Original Message -----
From: "klaus schmirler" <KSchmir@online.de>
To: <tuning@yahoogroups.com>
Sent: 11 Haziran 2005 Cumartesi 23:50
Subject: Re: [tuning] Re: Scales: an lengthy attempt at proper definition

Ozan Yarman wrote:
> 'tis a late reply, but here goes.

And I promised to comment on the part I snipped a couple of days ago.
I can now say that I didn't find any of your terms except rast, but I
should have understood just by looking at their setup that they were
note names.

>
> When tuning definitions are concerned, is it just tea for two? Differences
> of opinion lead to different directions, and hence, the foundation of
> different schools of thought. This has been experienced once too often,
with
> quite regrettable results I might add. I think the tuning list should
avoid
> such segragations/secterianism whenever possible, even if it means
complete
> unresolution in most cases.

I repeat, we didn't change anything except restricting the uses of
"mode" and "scale". Neither Yahya nor I introduced any new terms, and
what we drew attention to ("gamut" for a whole tonal system,
"rotation" for the "jazz modes") has all been in use before. "Key" or
"genus" might well have found a place in that terminology, but since
nobody else participated ...

>
> I am, as can be expected, still confused with your usage of the terms, and
> am having difficulties drawing parallels to the world of maqams.

Your gamut can be the classical 24 tones in 2 octaves (according to my
Arab-oriented source, that would be from yakah to ramal tuti). The
gamut can provide for an unequal distribution of the tones of for an
equal one like 24-et, which allows free and exact transposition. Or
you can have both, as in 53-et (How did 17-et fit into the picture?).
Or you can have an open system like JI that expands in the direction
your music wants to go (instruments permitting). And if you write for
an orchestra, you probably want a different gamut that is not
restricted to 2 octaves.

The mode sets the interval relations, final tone, mood, &c. Depending
on the contextual rules it provides, it selects one or more scales
from the gamut. (Actually it probably selects tones for a melody that
you can afterward arrange as a scale.) I mention two scales below that
look like F major. Since they are different modes, I assume that they
have different melodic rules; one may have the final on its upper F,
the other on the lower. And of course, if you refer to a specific
modal system like maqam, nobody wants to keep you from using that
specific term.

>
> So, I may not be inclined to your usage of the word "mode".
>
> Also, I am not at all inclined to use "modulation" synonymously with
> "transposition", although chromatic modulation and transposition intersect
> in both meaning and function.

I would say transposition is a restatement of a scale or melody on a
different degree of the gamut. This corresponds to "chromatic
transposition" in Western theory. A sequence in the modern sense is a
diatonic transposition that sticks to the notes of the scale, cycling
the motiv through different rotations of that scale.

"Modulation" is the procedure of going from one mode to another or a
different transposition of the same. So in the object oriented
paradigm, modulation, just like modes, is a method, not an object
(Yahya?).

Especially since scales are generally subsets
> of larger systems that you want to call gamuts, I object strongly to
> the idea of "modulating within the gamut". How about "transposing through
> the degrees of a gamut" instead?

But the additional flat in the trio of a menuet or march was not part
of the scale before. It comes from the gamut. If you have unequal
steps between the 48 notes and transpose, you need new notes to keep
the correct step sizes. They come from a gamut like 53-et.

>
> Now, in order to understand Maqamat, one needs to consider the tonal music
> of Europe, where modulations and transpositions of keys take place. Even
in
> a limited form such as I VI V, the tonal music differs from modes of the
> Middle Ages. Perhaps it is the transition period from modality to tonality
> that encourages you to adopt a more tonal perspective when scrutinizing
> modality.

I don't think I do.

>
> Anyway, the maqams not only modulate within the same diatonical scale, but
> they also may transpose within the gamut. So, key seems to embrace the
> concept pretty well.
>
> Wherever did you get the idea for Rast Yegah? Maybe you can elaborate what
> you mean?

As for the part comparing it with harmonic minor, I simply didn't see
the slashes through the accidentals. As for its nontransposibility, as
far as I know Yakah is tuned to the lowest note in the range of the
singer. (My source is Habib Hassan Touma in a book on Arab music -
assuming that most of the classical heritage is Osmanic; it's the most
pertinent book I have access to - and a couple of essays by Frangis
Alizade that I read long ago). This would mean it is fixed in space
(at the low end of the gamut). Touma doesn't give the maqamat all on
the same note, which I would have expected if they are totally
transposable (you could see the differences easier by just looking at
accidentals). Instead, they start for the most part from G, C, and D,
half flat E seems common, some are on A. Furthermore, in the 'agam
group he gives a couple of major scales (I've looked hard for slashes
this time). Each transposition has its own name, including the ones on
low F (lower than yagah=G) and high F (s�ah war and gaharkah/mazmum
respectively). So a maqam seems to imply not only a sequence of
intervals, but also a position in the two octave gamut. Maybe Arabian
and Turkish music diverge in that respect. (But again, Alizade, from
north of Turkey, gave me the same ideas.)

>
> Also, if you have been following the recent discussions about 79 MOS out
of
> 159tET, perhaps you can suggest an approach that will clear the mess.

I can't, although I'm reading along. If others have the same problems
I have, it may help if you state again what you are after, focussing
on the necessary notes instead of the notation. In traditional
notation, you have 24 notes per octave, like the Arabian system. If I
remember correctly, you need semitones, whole tones, 1 1/2 tones, and
pythagorean and just thirds. And it should be an et. Why does it need
to be a meantone system?

klaus

Ozan Yarman wrote:
> CDEFGABC
> > to
> > DEFGABCD
> > is a modulation from Ionian to Dorian. No?

THAT kind of modulation! I apologize and confess that I was only thinking of the tonal, Western definition. Actually, Gregorian chant modulates in this way (you could also say that the theory was too strict or simple to accomodate the actual traditional pieces ...).

> > I appreciate your efforts in trying to understand Maqam Music. The next Turk I see on the train with an istrument will be bombarded with questions.

all the best,

klaus