Diatonic

Is a harmonic minor scale diatonic?

Lorenzo

hi Lorenzo,

--- In tuning@yahoogroups.com, "lorenzofrizzera" <lorenzo.frizzera@c..
.> wrote:
>
>
> Is a harmonic minor scale diatonic?
>
> Lorenzo

yes.

"diatonic" refers to a scale which is composed mostly
of "whole-steps" (often called "tones").

in 12-edo, using A-minor as an example, the
harmonic minor scale has this semitone pattern:

A B C D E F G# A
2 1 2 2 1 3 1

(if viewing on the Yahoo web interface, you'll have to
click "reply" to see it formatted properly)

where "2" is a whole-step, "1" is a half-step, and
"3" is one and a half steps.

so the harmonic minor scale has 3 whole-steps,
3 half-steps, and one big step which adds both.

of course, the harmonic minor scale originated within
a meantone context which was *not* 12-edo ... in that
context, the half-steps which i labeled "1" are all
diatonic semitones (~117 cents, also called "minor-2nd"),
the whole-steps labeled "2" are major-2nds (~193 cents),
and the step labeled "3" is an augmented-2nd (~269 cents)
which is a combination of a major-2nd and a chromatic
semitone (~76 cents).

you can look up a lot of these terms in the Encyclopedia
for more info.

-monz
http://tonalsoft.com

Ciao Monz.

If I well remember diatonic means "through (all) the notes" so I've tought
that a diatonic scale is a collection of seven notes with seven different
names. But this explanation would be strange since C Db Ebb F Gx A# B would
be diatonic and it seems really chromatic.

Reading tonalsoft enciclopedia I've found that "diatonic" refers to a scale
with 5 tones and 2 half-tones and I was confused since I consider a harmonic
minor as a diatonic scale.

So it would be useful to me if you would define better this statement:

>"diatonic" refers to a scale which is composed mostly
>of "whole-steps" (often called "tones").

So a whole tones scale would be diatonic?

Do you think that it is possible to measure the minimum of tones and/or
halftones to say "diatonic" instead of "chromatic"? Or, instead of a measure
of intervals, is necessary to refers to a structure of them?

My personal opinion is that any interval in a chain of seven fifths is
diatonic while any other is chromatic. So something in a harmonic minor is
diatonic (harmonization of 2, 4, 5, 6 degree) and something other is
chromatic (1, 3, 7 degree). In hexatonal scale some chords are diatonic (7
without fifth) while a lot of others are not.

Lorenzo

hi Lorenzo,

hmmm ... yes, you do bring up some interesting points.
i'll address the ones i can.

--- In tuning@yahoogroups.com, "Lorenzo Frizzera" <lorenzo.frizzera@c.
..> wrote:

> Ciao Monz.
>
> If I well remember diatonic means "through (all) the notes"

not the generic "through the notes", but rather,
"through tones", with the definition of "tone" which
means "whole-step" as opposed to "semitone" (half-step).

the name comes from the ancient Greek genera, which
were classified into three broad groups: diatonic,
chromatic, and enharmonic:

. the enharmonic was considered the theoretical "ideal",
and its name means basically "in proper attunement".
it used quarter-tones or intervals close to that.

. the chromatic was characterized by its use of many
semitones, and its name means "through the colors" or
"through the shades", in the sense of different shades
or colors from the enharmonic or diatonic.

. the diatonic was characterized by its use of 5 whole-tones
and 2 semitones.

> so I've tought that a diatonic scale is a collection
> of seven notes with seven different names.

exactly, as i just said.

> But this explanation would be strange since
> C Db Ebb F Gx A# B would be diatonic and it seems
> really chromatic.

yes, well ... that is a scale which you constructed
and it really does fall outside the typical diatonic usage.
i can't really give any solid rules on this kind of thing.
the best thing to do is look at the historical perspective,
because that shows how our standard music theory has evolved,
and the names make more sense when you look at the "big picture"
going far back in time.

> Reading tonalsoft enciclopedia I've found that "diatonic"
> refers to a scale with 5 tones and 2 half-tones and I was
> confused since I consider a harmonic minor as a diatonic scale.

Boethius wrote his book on music c.505 AD, and his purpose
was to transmit the ancient Greek theory to the Latin world
at a time when he was watching the Roman Empire crumble
before his eyes.

Boethius's book is generally presumed to be mostly a
translation of a lost work by Nicomachus, and also a
summary and commentary on both the Euclidean _Sectio Canonis_
and on Ptolemy's book on music. He does discuss and give
monochord measurements for all three genera.

Almost immediately after Boethius, the "dark ages" ensued,
and there is a complete break in music theory at this point.
we have nothing substantial until the Frankish theorists
began writing treatises around 800 AD. but while the
medieval theorists continued to uphold Boethius's treatise
as the ultimate reference on music theory all the way up
about 1450, there are significant differences between
Boethius and their own work -- primarily, the fact that
they never discuss the chromatic or enharmonic genera again,
basing everything on the diatonic. it was only after the
Crusades that European theorists rediscovered the ancient
Greek theory and experimented with actually tuning up the
chromatic and enharmonic genera.

so the *natural* minor scale became the standard source
scale for medieval theory, which has continued to develop
in an unbroken line up to the present day. the natural
minor scale does indeed contain 5 tones and 2 semitones.

it was only later, during the "common-practice" period
of standard tonality, that the harmonic minor scale came
into recognition and regular use. it's still considered
"diatonic" because it uses all 7 letters and repeats none
of them. regardless of what i wrote before, that sentence
really states the hallmark of all diatonic scales.

> So it would be useful to me if you would define better
> this statement:
>
> > "diatonic" refers to a scale which is composed mostly
> > of "whole-steps" (often called "tones").
>
> So a whole tones scale would be diatonic?

no ... the definition says "mostly". perhaps i need to
add the words "but not entirely". it is crucial to a
diatonic scale that there are at least two different
step sizes, and that the one which is used less is about
half the size of the one which is used more. any scale
which follows that pattern will sound diatonic.

> Do you think that it is possible to measure the minimum
> of tones and/or halftones to say "diatonic" instead of
> "chromatic"? Or, instead of a measure of intervals, is
> necessary to refers to a structure of them?
>
> My personal opinion is that any interval in a chain of
> seven fifths is diatonic while any other is chromatic.
> So something in a harmonic minor is diatonic (harmonization
> of 2, 4, 5, 6 degree) and something other is chromatic
> (1, 3, 7 degree). In hexatonal scale some chords are
> diatonic (7 without fifth) while a lot of others are not.

yes, your explanations sound good to me too. unfortunately,
i'm far too busy these days to really get deeply into new
theory. it was easy for me to say all that i did about the
ancient Greeks, Boethius, and the Franks, because i spent
years studying that stuff. these days, i'm extremely busy
converting web pages. :)

(and as i wrote before, i've also been spending the whole
week moving my residence. as the years go by, my library
keeps getting bigger and bigger ...)

-monz

Hi Monz.

>it is crucial to a diatonic scale that there are at least two different
>step sizes, and that the one which is used less is about
>half the size of the one which is used more.
>any scale which follows that pattern will sound diatonic.

So you confirm that a minor harmonic scale is'nt diatonic since it has three
tones, three
half-tones and one tone and a half?

Anyway I find hard to consider diatonic C Db Eb F G A B even if there are 5L
and 2s.

Lorenzo

--- In tuning@yahoogroups.com, "lorenzofrizzera"
<lorenzo.frizzera@c...> wrote:
>
>
> Is a harmonic minor scale diatonic?
>
> Lorenzo

I would say so, because the harmonic minor scale is a periodicity
block (though not of the Fokker variety) with unison vectors 81:80
and 25:24.

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
>
> hi Lorenzo,
>
>
> --- In tuning@yahoogroups.com, "lorenzofrizzera"
<lorenzo.frizzera@c..
> .> wrote:
> >
> >
> > Is a harmonic minor scale diatonic?
> >
> > Lorenzo
>
>
> yes.
>
> "diatonic" refers to a scale which is composed mostly
> of "whole-steps" (often called "tones").

The whole-tone scale is composed entirely of whole-steps, but it
isn't diatonic.

> in 12-edo, using A-minor as an example, the
> harmonic minor scale has this semitone pattern:
>
> A B C D E F G# A
> 2 1 2 2 1 3 1

A minority of the steps here are whole-steps anyway. :)

--- In tuning@yahoogroups.com, "Lorenzo Frizzera"
<lorenzo.frizzera@c...> wrote:
> Ciao Monz.
>
> If I well remember diatonic means "through (all) the notes" so I've
tought
> that a diatonic scale is a collection of seven notes with seven
different
> names.

Yes, that's another way of saying what I said before.

> But this explanation would be strange since C Db Ebb F Gx A# B would
> be diatonic and it seems really chromatic.

Harmonically this would be a highly disconnected periodicity block,
rather unlikely to arise in the first place.

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:

> > > "diatonic" refers to a scale which is composed mostly
> > > of "whole-steps" (often called "tones").
> >
> > So a whole tones scale would be diatonic?
>
>
> no ... the definition says "mostly". perhaps i need to
> add the words "but not entirely".

That still wouldn't help, since the harmonic scals isn't mostly
composed of whole-steps, while plenty of scales that are mostly
composed of "whole-steps" of one kind or another aren't diatonic.

> it is crucial to a
> diatonic scale that there are at least two different
> step sizes, and that the one which is used less is about
> half the size of the one which is used more. any scale
> which follows that pattern will sound diatonic.

I completely disagree with this last statement. In the paper I mailed
you, you'll find plenty of scales with two step sizes where the one
used less is about half the size of the one used more. Most of these
aren't diatonic.

hi Paul and Lorenzo,

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:

>
> --- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
>
> > > > "diatonic" refers to a scale which is composed mostly
> > > > of "whole-steps" (often called "tones").
> > >
> > > So a whole tones scale would be diatonic?
> >
> >
> > no ... the definition says "mostly". perhaps i need to
> > add the words "but not entirely".
>
> That still wouldn't help, since the harmonic scals isn't mostly
> composed of whole-steps, while plenty of scales that are mostly
> composed of "whole-steps" of one kind or another aren't diatonic.
>
> > it is crucial to a
> > diatonic scale that there are at least two different
> > step sizes, and that the one which is used less is about
> > half the size of the one which is used more. any scale
> > which follows that pattern will sound diatonic.
>
> I completely disagree with this last statement. In the
> paper I mailed you, you'll find plenty of scales with two
> step sizes where the one used less is about half the size
> of the one used more. Most of these aren't diatonic.

yes, correct. i should have specified that the one which
is used more is a "tone" of some sort, i.e., approximately
200 cents or approximately a 9:8 ratio.

in fact, since i wrote so much in this thread about the
historical meaning of "diatonic", it should be emphasized
that *all* ancient and medieval writers -- with the single
exception of Aristoxenus and his followers -- defined the
"tone" (i.e., "whole-step") as a 9:8 ratio.

(for Aristoxenus a "tone" was a logarithmic 2/5 of a
"perfect-4th", and a perfect-4th was defined as the smallest
musical consonance, and so was determined solely by ear.)

it wasn't until temperament entered the picture c.1500 that
a tone ever became any other size. specifically, it became
the mean-tone of 1/4-comma meantone, ~193.1568569 cents,
and then the size shifted up or down a bit as other meantones
were devised and popularized.

Blackwood wrote a whole book on the subject, _The Structure
of Recognizable Diatonic Tunings_, and i know that you (Paul)
have read it and thoroughly digested what he says. give us
some more insight.

(i have Blackwood's book too, but don't know where it is
right now.)

-monz

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:

> Blackwood wrote a whole book on the subject, _The Structure
> of Recognizable Diatonic Tunings_, and i know that you (Paul)
> have read it and thoroughly digested what he says. give us
> some more insight.

Well, a lot of the book is concerned with the vanishing of the
syntonic comma, and you yourself reproduced some of the examples from
his book at the bottom of your Vicentino page:

http://sonic-arts.org/monzo/vicentino/vicentino.htm

Any sort of meantone temperament (or meantone-based adaptive-JI) is
an appropriate diatonic tuning for the music of Lasso and his
contemporaries and successors. Try *strict* JI or a non-meantone ET
like 22, 34, or 53, and you'll be saddled with some unsuitable shifts
or drifts rather than using a stable, clear diatonic structure
throughout.

Of course Benedetti in the 16th century and Woolhouse in the 19th had
already explained similar points. But it's a point that needs to be
made from many angles, and I think Blackwood's arguments add to the
picture. I wasn't too impressed with other aspects of Blackwood's
book, but found it a worthwhile study overall.

>> Is a harmonic minor scale diatonic?
>>
>I would say so, because the harmonic minor scale is a periodicity
>block (though not of the Fokker variety) with unison vectors 81:80
>and 25:24.

A chromatic scale can stay inside a periodicity block too but it is not diatonic.
What is the difference?

Lorenzo

--- In tuning@yahoogroups.com, "Lorenzo Frizzera"
<lorenzo.frizzera@c...> wrote:
>
> >> Is a harmonic minor scale diatonic?
> >>
> >I would say so, because the harmonic minor scale is a periodicity
> >block (though not of the Fokker variety) with unison vectors 81:80
> >and 25:24.
>
> A chromatic scale can stay inside a periodicity block too but it is
not
> diatonic.
> What is the difference?
>
> Lorenzo

Lorenzo, only 7 notes (and not just any 7 notes) can live inside a
periodicity block with unison vectors 81:80 and 25:24. These are the
smallest 5-limit superparticular ratios, if that helps you justify
your feeling that the diatonic scale is "special" in some way.

Hi Monz,

I'm sure Aristoxenus wouldn't have expressed it in those
concise terms ... However did he arrive at such a strange
measure?

Yahya

-----Original Message-----
______________________________________________________________________
Date: Mon, 28 Feb 2005 10:18:10 -0000
From: "monz" <monz@tonalsoft.com>
Subject: Re: Diatonic

hi Paul and Lorenzo,

[YA] ...

. i should have specified that the one which
is used more is a "tone" of some sort, i.e., approximately
200 cents or approximately a 9:8 ratio.

in fact, since i wrote so much in this thread about the
historical meaning of "diatonic", it should be emphasized
that *all* ancient and medieval writers -- with the single
exception of Aristoxenus and his followers -- defined the
"tone" (i.e., "whole-step") as a 9:8 ratio.

(for Aristoxenus a "tone" was a logarithmic 2/5 of a
"perfect-4th", and a perfect-4th was defined as the smallest
musical consonance, and so was determined solely by ear.)

[YA] ...

-monz

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>Lorenzo, only 7 notes (and not just any 7 notes) can live inside a
>periodicity block with unison vectors 81:80 and 25:24.

Can you make a list of all seven notes scale which stay in this particular periodicity block?

>These are the
>smallest 5-limit superparticular ratios, if that helps you justify
>your feeling that the diatonic scale is "special" in some way.

I love to play chromatic.... :)
But I find strange that anybody has an idea of what is "diatonic" and nobody can tell exactly what does it mean.
I'm waiting your list of 7 notes scale to see if anybody agree in consider them all diatonic.

Lorenzo

--- In tuning@yahoogroups.com, "Lorenzo Frizzera"
<lorenzo.frizzera@c...> wrote:
> >Lorenzo, only 7 notes (and not just any 7 notes) can live inside a
> >periodicity block with unison vectors 81:80 and 25:24.
>
> Can you make a list of all seven notes scale which stay in this
particular
> periodicity block?

We have to set some conditions on what is a "compact enough"
periodicity block, or else the list becomes infinitely long (though
not exhaustive of 7 note scales by any means). And that's only
considering JI -- temperament adds a whole multiverse of additional
possibilities. But let's see . . . how about we insist that each note
and each consonant dyad belong to at least one consonant triad, and
that the graph of consonances is connected? To view this correctly,
click on "Reply":

1)
A-----E-----B
/ \ / \ / \
/ \ / \ / \
F-----C-----G-----D

2)
D-----A-----E-----B
\ / \ / \ /
\ / \ / \ /
F-----C-----G

3)
A B
/ \ / \
/ \ / \
F-----C-----G-----D
\ /
\ /
Eb

4)
C#
/ \
/ \
D-----A-----E-----B
\ / \ /
\ / \ /
F G

5)
E-----B
/ \ / \
/ \ / \
F-----C-----G-----D
\ /
\ /
Ab

6)
F#
/ \
/ \
D-----A-----E-----B
\ / \ /
\ / \ /
C-----G

7)
A-----E
/ \ / \
/ \ / \
F-----C-----G-----D
\ /
\ /
Bb

8)
G#
/ \
/ \
D-----A-----E-----B
\ / \ /
\ / \ /
F-----C

9)
E-----B
\ / \
\ / \
G-----D-----A
\ / \
\ / \
F-----C

10)
F#----C#
/ \ /
/ \ /
G-----D-----A
/ \ /
/ \ /
Eb----Bb

And of course all transpositions of these. There ten are all distinct
in JI, as you'll see if you put ratios in place of the letter names.
Did I miss anything?

> >These are the
> >smallest 5-limit superparticular ratios, if that helps you justify
> >your feeling that the diatonic scale is "special" in some way.
>
> I love to play chromatic.... :)
> But I find strange that anybody has an idea of what is "diatonic"
and nobody
> can tell exactly what does it mean.

I don't think the whole world has been using the term in a completely
cut-and-dried, consistent manner.

hi Yahya,

oh yes, that's exactly how Aristoxenus described the
size of the "tone". he was very careful to completely
avoid any reference to string length (and hence, ratios),
instead making use of the concept of string tension.

this is why i have argued that it's time to stop translating
_syntonon_ as "intense" and _malakon_ as "soft" (which is
what was picked up and transmitted by Partch), preferring
instead _syntonon_ = "tense" and _malakon_ = "relaxed".

Aristoxenus specified the _diatessaron_ (= perfect-4th)
as the smallest musical consonance, which is true in
pythagorean tuning where it is the 4:3 ratio. but he
also used a method of "tuning by concords" to arrive at
a 12-tone scale in which temperament is unavoidable in
order to have all the "concords" he specifies. in other
words, if you assume that the concords must all be exactly
4:3's and 3:2's, you will end up with a "wolf 5th" at the
end, whereas Aristoxenus specified that that 5th was also
a consonance and thus created a closed circular tuning.

when describing smaller intervals, Aristoxenus specifies
that the semitone is what is left over after you subtract
two tones from the _diatessaron_ (4th). thus, a tone is
2/5 of a perfect-4th.

-monz

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

>
> Hi Monz,
>
> I'm sure Aristoxenus wouldn't have expressed it in those
> concise terms ... However did he arrive at such a strange
> measure?
>
> Yahya
>
> -----Original Message-----
>
______________________________________________________________________
> Date: Mon, 28 Feb 2005 10:18:10 -0000
> From: "monz" <monz@t...>
> Subject: Re: Diatonic
>
> <snip>
>
> (for Aristoxenus a "tone" was a logarithmic 2/5 of a
> "perfect-4th", and a perfect-4th was defined as the smallest
> musical consonance, and so was determined solely by ear.)

> I don't think the whole world has been using the term in a
completely
> cut-and-dried, consistent manner.

Ibn sina said ( in arabic ), "when no one of the tetrachord ratios is
bigger than the sum of the two other ratios, the tetrachord is said to
be diatonic"

Ibn sina based his musical writings on greek writings. I think all
uses of this term have similar meaning.

in modern church byzantine music the diatonic scale is the 5-limit
scale :
9/8 10/9 16/15 9/8 9/8 10/9 16/15

in western music as you know the term "diatonic" means scale
containing five tones and two half-tones.

rami vitale

I've taked some ideas from the answers to this topic by various people:

>it's still considered "diatonic" because it uses all 7
>letters and repeats none of them.

This is really weak.
Sometimes it works... B C# D# E F# G# A#
and sometimes not C D# E# F# G# A# B.

>Ibn sina based his musical writings on greek writings. I think all
>uses of this term have similar meaning.
>in western music as you know the term "diatonic" means scale
>containing five tones and two half-tones.

>the diatonic was characterized by its use of 5 whole-tones
>and 2 semitones.

This is strange since a melodic minor would be diatonic but not an harmonic minor.
I don't see any reason for this distinction.

>only 7 notes (and not just any 7 notes) can live inside a
>periodicity block with unison vectors 81:80 and 25:24. These are the
>smallest 5-limit superparticular ratios

>how about we insist that each note
>and each consonant dyad belong to at least one consonant triad, and
>that the graph of consonances is connected?

In this context beneath major, harmonic minor, melodic minor, harmonic major
scales, the double harmonic (s, Ts, s, T, s, Ts, s) would be diatonic too.
To me this contradicts the history of the term (there is just one single
whole tone!) and the common concept of "diatonic" usually referred to
triadic consonant music (it's hard to consider a triad on 5 and 7 degree of
a double harmonic scale).

So I try now my own definition of diatonic:
a scale of seven notes where each note has a major or minor third.

Lorenzo

--- In tuning@yahoogroups.com, "Lorenzo Frizzera"
<lorenzo.frizzera@c...> wrote:
>
> I've taked some ideas from the answers to this topic by various
people:
>
> >it's still considered "diatonic" because it uses all 7
> >letters and repeats none of them.
>
> This is really weak.
> Sometimes it works... B C# D# E F# G# A#
> and sometimes not C D# E# F# G# A# B.
>
> >Ibn sina based his musical writings on greek writings. I think all
> >uses of this term have similar meaning.
> >in western music as you know the term "diatonic" means scale
> >containing five tones and two half-tones.
>
> >the diatonic was characterized by its use of 5 whole-tones
> >and 2 semitones.
>
> This is strange since a melodic minor would be diatonic but not an
harmonic
> minor.
> I don't see any reason for this distinction.
>
> >only 7 notes (and not just any 7 notes) can live inside a
> >periodicity block with unison vectors 81:80 and 25:24. These are
the
> >smallest 5-limit superparticular ratios
>
> >how about we insist that each note
> >and each consonant dyad belong to at least one consonant triad,
and
> >that the graph of consonances is connected?
>
> In this context beneath major, harmonic minor, melodic minor,
harmonic major
> scales, the double harmonic (s, Ts, s, T, s, Ts, s) would be
diatonic too.
> To me this contradicts the history of the term (there is just one
single
> whole tone!) and the common concept of "diatonic" usually referred
to
> triadic consonant music (it's hard to consider a triad on 5 and 7
degree of
> a double harmonic scale).
>
> So I try now my own definition of diatonic:
> a scale of seven notes where each note has a major or minor third.
>
> Lorenzo

Yes, these familiar words with fuzzy meanings make life difficult.

According to the American Heritage Dictionary in my office, it
means "Using only the eight tones of a standard major or minor scale
without chromatic variation"; Greek "diatonos" = "at the interval
of a tone".

Personally, I think it means a scale composed from 3 linked chords
on the circle of 5ths. For example, f, c and g are 3 adjacent notes
on the cirlce of 5ths,
the key of C major is the major chords F, C ,G.
C natural minor is Cm, Fm, Gm;
C harmonic minor is Cm, Fm, G
C melodic minor ascending is Cm, F, G

Another, possibly better but related definition is a chain of 7 5ths
(3rd harmonics!) f - c - g - d - a - e - b; this would be what
the ancient Greeks were familiar with and is probably what the
word "diatonic" means. It approximates the acoustically pure chords
I mentioned above for the major scale; harmonic minor is a little
problematic, but the Greeks probably didn't have that.

--Jeff

Lorenzo, your definition of the diatonic does not include this scale which sounds diatonic to me:

D Eb F# G Ab B C D

Where F# and Ab does not equate to any major or minor thirds, but a diminished third.

Ozan
----- Original Message -----
From: Lorenzo Frizzera
To: tuning@yahoogroups.com
Sent: 21 Mart 2005 Pazartesi 2:39
Subject: [tuning] Re: Diatonic

So I try now my own definition of diatonic:
a scale of seven notes where each note has a major or minor third.

Lorenzo

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> Lorenzo, your definition of the diatonic does not include this scale
which sounds diatonic to me:
>
> D Eb F# G Ab B C D
>
> Where F# and Ab does not equate to any major or minor thirds, but a
diminished third.
>
> Ozan
> -----

Diatonic was the Greek tetrachord divided "through tones",
whole-tones. Medieval praxis overtook this term for a 7-tone scale
based also on diatonic tetrachords. Ozan Yarman's scale has two
conjunct _chromatic_ tetrachords in the semitone-small third-semitone
rotation.

tetrachord 1: D Eb F# G
tetrachord 2: G Ab B C
disjunction: C D'

The diminished third F#-Ab is a result of the conjunction, not an
interval in the tetrachords.

Daniel Wolf says also that this tetrachordal scale, in disjunct form
is "Mayamalavagoulai" the first scale learned by musicians in Karnatic
music, part of the 72 melakarta system. The conjunct form given by
Ozan Yarman is not possible in the melakarta system, as SA-PA cannot
be diminished.

Gabor

As I already wrote I would not consider this scale (which is a mode of the what I call "double harmonic") as diatonic since it permits only 5 traditional triads instead of 7 (we can go deeper in what means traditional triad...). More, there is just one single whole tone and for a scale which is dia-"tonic" is quite strange.
So I consider a *complete* circle of third a base for diatonicism. Maybe I'm wrong...

Other scales in 12-et such diminished (1 2 1 2 1 2 1 2), exatonal (2 2 2 2 2 2) and augmented (1 3 1 3 1 3) have a third for every note but these are'nt linked and it is impossible to do a *complete* circle of third.
In the scales of seven note is possible.

An augmented triad or a diminished tetrad have this characteristic. And maybe we can consider them as a subset of a diatonic scale.

A complete circle of fifths is a subset of a compete circle of third and this includes the definition of Jeff.

Of course this is my way to consider diatonicism and if to you, Ozan, a double harmonic sounds "diatonic" is just a question of words meaning. I think, since this word is often used here, it would be good if we would give the same meaning to "diatonic". Do you think is possible?

Ciao

Lorenzo

----- Original Message -----
From: Ozan Yarman
To: tuning@yahoogroups.com
Sent: Monday, March 21, 2005 10:20 AM
Subject: Re: [tuning] Re: Diatonic

Lorenzo, your definition of the diatonic does not include this scale which sounds diatonic to me:

D Eb F# G Ab B C D

Where F# and Ab does not equate to any major or minor thirds, but a diminished third.

Ozan
----- Original Message -----
From: Lorenzo Frizzera
To: tuning@yahoogroups.com
Sent: 21 Mart 2005 Pazartesi 2:39
Subject: [tuning] Re: Diatonic

So I try now my own definition of diatonic:
a scale of seven notes where each note has a major or minor third.

Lorenzo

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From: "jjensen142000":

> Yes, these familiar words with fuzzy meanings make life difficult.
>
> According to the American Heritage Dictionary in my office, it
> means "Using only the eight tones of a standard major or minor scale
> without chromatic variation"; Greek "diatonos" = "at the interval
> of a tone".

What's a "standard minor"? Natural and harmonic would fit the definition, but melodic minor has "chromatic variation", with two notes flatted on the descending scale.

> Personally, I think it means a scale composed from 3 linked chords
> on the circle of 5ths. For example, f, c and g are 3 adjacent notes
> on the cirlce of 5ths,
> the key of C major is the major chords F, C ,G.
> C natural minor is Cm, Fm, Gm;
> C harmonic minor is Cm, Fm, G
> C melodic minor ascending is Cm, F, G

The seven medieval/ecclesiastical modes are diatonic by the modern definition. Arabic and Turkish maqams are diatonic, but some have different notes descending, and Sab� has a diminished octave, which I would consider a form of chromaticism. Indian modes are also diatonic, but some of the Carnatic melas have groups of prime-minor second-diminished third, so I don't know if you can rightfully call those diatonic. I also consider pentatonic and hexatonic scales incomplete diatonic scales, with the blues scale (pentatonic minor plus tritone) a mixed diatonic-chromatic.

To me, a diatonic scale can be expressed by taking "do-re-mi", using flats, sharps, double flats/sharps and quarter-tone flats/sharps, and using each of the seven solfege syllables once; any chromaticity scale requires one of these solfege syllables to be repeated using different accidentals.

I also understand the steps C to D-flat as diatonic, C to C-sharp as chromatic, and C-sharp to D-flat as enharmonic.

But as it's already been said here, diatonic, chromatic and enharmonic had different meanings to the ancient Greeks.

> Another, possibly better but related definition is a chain of 7 5ths
> (3rd harmonics!) f - c - g - d - a - e - b; this would be what
> the ancient Greeks were familiar with and is probably what the
> word "diatonic" means. It approximates the acoustically pure chords
> I mentioned above for the major scale; harmonic minor is a little
> problematic, but the Greeks probably didn't have that.

I get the impression that harmonic minor is of Arabic (and ultimately Persian) origin, as Maqam Nahawand is essentially harmonic minor ascending (but natural minor descending). It's a scale with the last four notes forming a Hij�z tetrachord, which is commonly [1/1 16/15 5/4 4/3] in just intervals. Ozan's scale is made up of two conjunct Hij�z tetrachords, and looks like Maqam Hijaz Kar [1/1 16/15 5/4 4/3 3/2 8/5 15/8 2/1] but you start on the fifth note instead of the first.

Or *did* the ancient Greeks have tetrachords with a wide middle interval?

I realize perfectly well that F# and Ab are conjuct tones to the pivot of the two tetrachords you mentioned. This just happens to be one of the maqams we are familiar with. I gave this as an example to a certain inconsistency I observed with Lorenzo's definition that each note in a diatonic scale should have its major or minor third partner.
----- Original Message -----
From: alternativetuning
To: tuning@yahoogroups.com
Sent: 21 Mart 2005 Pazartesi 13:49
Subject: [tuning] Re: Diatonic

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> Lorenzo, your definition of the diatonic does not include this scale
which sounds diatonic to me:
>
> D Eb F# G Ab B C D
>
> Where F# and Ab does not equate to any major or minor thirds, but a
diminished third.
>
> Ozan
> -----

Diatonic was the Greek tetrachord divided "through tones",
whole-tones. Medieval praxis overtook this term for a 7-tone scale
based also on diatonic tetrachords. Ozan Yarman's scale has two
conjunct _chromatic_ tetrachords in the semitone-small third-semitone
rotation.

tetrachord 1: D Eb F# G
tetrachord 2: G Ab B C
disjunction: C D'

The diminished third F#-Ab is a result of the conjunction, not an
interval in the tetrachords.

Daniel Wolf says also that this tetrachordal scale, in disjunct form
is "Mayamalavagoulai" the first scale learned by musicians in Karnatic
music, part of the 72 melakarta system. The conjunct form given by
Ozan Yarman is not possible in the melakarta system, as SA-PA cannot
be diminished.

Gabor

It seems to me that you are ignoring the practice to fit the definition you gave Lorenzo. D Eb F# G Ab B C D most certainly sounds to me like a diatonic scale. As a matter of fact, all maqams can be reduced to instances of one or more diatonic scales.

Safiyuddin Urmewi of Baghdad also considered such intervals as Eb-F# whole tones, no matter how augmented. It would not be wrong to assume that augmented whole tones function similarly as whole tones in a tetrachord. Thus, I cannot possibly accept the claim that the above-mentioned scale in not diatonic.

Cordially,
Ozan
----- Original Message -----
From: Lorenzo Frizzera
To: tuning@yahoogroups.com
Sent: 21 Mart 2005 Pazartesi 15:15
Subject: [tuning] Re: Diatonic

As I already wrote I would not consider this scale (which is a mode of the what I call "double harmonic") as diatonic since it permits only 5 traditional triads instead of 7 (we can go deeper in what means traditional triad...). More, there is just one single whole tone and for a scale which is dia-"tonic" is quite strange.
So I consider a *complete* circle of third a base for diatonicism. Maybe I'm wrong...

Other scales in 12-et such diminished (1 2 1 2 1 2 1 2), exatonal (2 2 2 2 2 2) and augmented (1 3 1 3 1 3) have a third for every note but these are'nt linked and it is impossible to do a *complete* circle of third.
In the scales of seven note is possible.

An augmented triad or a diminished tetrad have this characteristic. And maybe we can consider them as a subset of a diatonic scale.

A complete circle of fifths is a subset of a compete circle of third and this includes the definition of Jeff.

Of course this is my way to consider diatonicism and if to you, Ozan, a double harmonic sounds "diatonic" is just a question of words meaning. I think, since this word is often used here, it would be good if we would give the same meaning to "diatonic". Do you think is possible?

Ciao

Lorenzo

Daniel, just a correction.... The Saba scale can be defined as a diatonical scale with a triadic appendix below the fundamental:

C Db E F G Ad B C'
C Bd A

The misconception arises from comparing A to Ad, which is indeed a diminished octave, but hardly the focal point of the scale.

The scale D Eb F# G Ab B C D is reminiscent of Maqam Neveser modulated a whole tone above C.

BTW, I like your definition of the diatonic.

Cordially,
Ozan
----- Original Message -----
From: Daniel A. Wier
To: tuning@yahoogroups.com
Sent: 21 Mart 2005 Pazartesi 16:04
Subject: Re: [tuning] Re: Diatonic

From: "jjensen142000":

> Yes, these familiar words with fuzzy meanings make life difficult.
>
> According to the American Heritage Dictionary in my office, it
> means "Using only the eight tones of a standard major or minor scale
> without chromatic variation"; Greek "diatonos" = "at the interval
> of a tone".

What's a "standard minor"? Natural and harmonic would fit the definition,
but melodic minor has "chromatic variation", with two notes flatted on the
descending scale.

> Personally, I think it means a scale composed from 3 linked chords
> on the circle of 5ths. For example, f, c and g are 3 adjacent notes
> on the cirlce of 5ths,
> the key of C major is the major chords F, C ,G.
> C natural minor is Cm, Fm, Gm;
> C harmonic minor is Cm, Fm, G
> C melodic minor ascending is Cm, F, G

The seven medieval/ecclesiastical modes are diatonic by the modern
definition. Arabic and Turkish maqams are diatonic, but some have different
notes descending, and Sabâ has a diminished octave, which I would consider a
form of chromaticism. Indian modes are also diatonic, but some of the
Carnatic melas have groups of prime-minor second-diminished third, so I
don't know if you can rightfully call those diatonic. I also consider
pentatonic and hexatonic scales incomplete diatonic scales, with the blues
scale (pentatonic minor plus tritone) a mixed diatonic-chromatic.

To me, a diatonic scale can be expressed by taking "do-re-mi", using flats,
sharps, double flats/sharps and quarter-tone flats/sharps, and using each of
the seven solfege syllables once; any chromaticity scale requires one of
these solfege syllables to be repeated using different accidentals.

I also understand the steps C to D-flat as diatonic, C to C-sharp as
chromatic, and C-sharp to D-flat as enharmonic.

But as it's already been said here, diatonic, chromatic and enharmonic had
different meanings to the ancient Greeks.

> Another, possibly better but related definition is a chain of 7 5ths
> (3rd harmonics!) f - c - g - d - a - e - b; this would be what
> the ancient Greeks were familiar with and is probably what the
> word "diatonic" means. It approximates the acoustically pure chords
> I mentioned above for the major scale; harmonic minor is a little
> problematic, but the Greeks probably didn't have that.

I get the impression that harmonic minor is of Arabic (and ultimately
Persian) origin, as Maqam Nahawand is essentially harmonic minor ascending
(but natural minor descending). It's a scale with the last four notes
forming a Hijâz tetrachord, which is commonly [1/1 16/15 5/4 4/3] in just
intervals. Ozan's scale is made up of two conjunct Hijâz tetrachords, and
looks like Maqam Hijaz Kar [1/1 16/15 5/4 4/3 3/2 8/5 15/8 2/1] but you
start on the fifth note instead of the first.

Or *did* the ancient Greeks have tetrachords with a wide middle interval?

Hi Ozan and Daniel.

> According to the American Heritage Dictionary in my office, it
> means "Using only the eight tones of a standard major or minor scale
> without chromatic variation"; Greek "diatonos" = "at the interval
> of a tone".

Eight?

This is a narrow concept of diatonicism. Maybe in this way we could consider
that "diatonic" is a synonim of MOS. Infact in 12-et any MOS is a subset of
a diatonic scale: 1, 2, 3, 5, 7 (12 is obviously chromatic).

>To me, a diatonic scale can be expressed by taking "do-re-mi", using flats,
>sharps, double flats/sharps and quarter-tone flats/sharps, and using each
>of
>the seven solfege syllables once; any chromaticity scale requires one of
>these solfege syllables to be repeated using different accidentals.

In this way you consider diatonic almost any scale with seven notes.
If this scale is diatonic please define what is chromatic for you: Cx D# E F
G A# B.

>It seems to me that you are ignoring the practice to fit the definition you
>gave Lorenzo.

It could be.

>It would not be wrong to assume that augmented whole tones function
>similarly as whole tones in a >tetrachord. Thus, I cannot possibly accept
>the claim that the above-mentioned scale in not diatonic.

This is true melodically. But I'm not sure that everybody consider the word
"diatonic" only in a melodic context. Harmonically the scale C Db E F G Ab B
has four consonant triad but only two of these are chained by fifth. This
gives less possibility of harmonic cadences and this is an important
difference compared with major, harmonic major and harmonic minor.

Ciao

Lorenzo

--- In tuning@yahoogroups.com, "Lorenzo Frizzera"
<lorenzo.frizzera@c...> wrote:

> This is a narrow concept of diatonicism. Maybe in this way we could
consider
> that "diatonic" is a synonim of MOS. Infact in 12-et any MOS is a
subset of
> a diatonic scale: 1, 2, 3, 5, 7 (12 is obviously chromatic).

Blackwood considers it to mean a MOS with a period of an octave and a
generator a fifth with some tempering, which can be sharp.

From: "Lorenzo Frizzera"

> In this way you consider diatonic almost any scale with seven notes.
> If this scale is diatonic please define what is chromatic for you: Cx D# E > F
> G A# B.

Ew, that's a gray area if I've ever seen one.

And we might have different ideas of what "diatonic" means. I was taught that diatonic scales were seven-note scales, and chromatic scales ran the whole twelve-note gamut.

I do wonder if the Carnatic mela (forgot the name) with the notes C Db Ebb F# G Ab Bbb C would rightfully be considered diatonic or chromatic. How would that be tuned using 22-tone sruti?

Dear Lorenzo, I disagree entirely. The scale C Db E F Gb A Bb is most perfect for Jazz harmonies (you modulated it wrongly saying C Db E F G Ab B
).

Cordially,
Ozan
----- Original Message -----
From: Lorenzo Frizzera
To: tuning@yahoogroups.com
Sent: 22 Mart 2005 Salı 2:03
Subject: [tuning] Re: Diatonic

This is true melodically. But I'm not sure that everybody consider the word
"diatonic" only in a melodic context. Harmonically the scale C Db E F G Ab B
has four consonant triad but only two of these are chained by fifth. This
gives less possibility of harmonic cadences and this is an important
difference compared with major, harmonic major and harmonic minor.

Ciao

Lorenzo

That is a weird diatonic scale with a double augmented whole tone between Ebb-F# and Bbb C. Nevertheless, it is still diatonic.
----- Original Message -----
From: Daniel A. Wier
To: tuning@yahoogroups.com
Sent: 22 Mart 2005 Salı 4:56
Subject: Re: [tuning] Re: Diatonic

From: "Lorenzo Frizzera"

> In this way you consider diatonic almost any scale with seven notes.
> If this scale is diatonic please define what is chromatic for you: Cx D# E
> F
> G A# B.

Ew, that's a gray area if I've ever seen one.

And we might have different ideas of what "diatonic" means. I was taught
that diatonic scales were seven-note scales, and chromatic scales ran the
whole twelve-note gamut.

I do wonder if the Carnatic mela (forgot the name) with the notes C Db Ebb
F# G Ab Bbb C would rightfully be considered diatonic or chromatic. How
would that be tuned using 22-tone sruti?

Ozan Yarman wrote:

>It seems to me that you are ignoring the practice to fit the definition you gave Lorenzo. D Eb F# G Ab B C D most certainly sounds to me like a diatonic scale. >
I think you are trying to reconcile different meanings of "diatonic" with different musical backgrounds, and maybe you think a "good" scale has to be diatonic. In Ancient Greek theory, the above is definitely "chromatic".

The harmonic minor "scale" consists of a diatonic and a harmonic tetrachord. You should keep in mind that its typical use in Western music is harmonic. If it is used as a scale per se, it is meant to sound exotic. A diatonic scale doesn't do that for western ears.

klaus

klaus schmirler wrote:

>Ozan Yarman wrote:
>
> >
>>It seems to me that you are ignoring the practice to fit the definition you gave Lorenzo. D Eb F# G Ab B C D most certainly sounds to me like a diatonic scale. >>
>> >>
>I think you are trying to reconcile different meanings of "diatonic" >with different musical backgrounds, and maybe you >
definitely a "or your sources" has to go in there

>think a "good" scale >has to be diatonic. In Ancient Greek theory, the above is definitely >"chromatic".
>
>The harmonic minor "scale" consists of a diatonic and a harmonic >tetrachord. You should keep in mind that its typical use in Western >music is harmonic. If it is used as a scale per se, it is meant to sound >exotic. A diatonic scale doesn't do that for western ears.
>
>klaus
>
> >

Klaus, I'm perfectly aware of the role Western tonality ascribed for melodic and harmonic minor scales. I'm also aware how Western tonality has superceded ancient Greek theory so as to render modal configurations obsolete in many ways. In this context, it would not be out of place to re-define what we understand of diatonic, chromatic and enharmonic genera. I think Daniel summed it up neatly, saying:

I also understand the steps C to D-flat as diatonic, C to C-sharp as chromatic, and C-sharp to D-flat as enharmonic.

You should know that Western ears do not have monopoly over what is diatonical and what is not. Al-Qindi, Al-Farabi, Ibn Sina and Safiyuddin Urmewi all precede Western theorists in promulgating Hellenic tetrachord calculations. The Maqams of then and today most certainly sound diatonical to me, in that, each instance is made up of 7 steps whose intervals function as half-tones and whole-tones in a given tetrachord.

Cordially,
Ozan
----- Original Message -----
From: klaus schmirler
To: tuning@yahoogroups.com
Sent: 22 Mart 2005 Salı 10:54
Subject: Re: [tuning] Re: Diatonic

Ozan Yarman wrote:

>It seems to me that you are ignoring the practice to fit the definition you gave Lorenzo. D Eb F# G Ab B C D most certainly sounds to me like a diatonic scale.
>
I think you are trying to reconcile different meanings of "diatonic"
with different musical backgrounds, and maybe you think a "good" scale
has to be diatonic. In Ancient Greek theory, the above is definitely
"chromatic".

The harmonic minor "scale" consists of a diatonic and a harmonic
tetrachord. You should keep in mind that its typical use in Western
music is harmonic. If it is used as a scale per se, it is meant to sound
exotic. A diatonic scale doesn't do that for western ears.

klaus

Ozan Yarman wrote:

>Klaus, I'm perfectly aware of the role Western tonality ascribed for melodic and harmonic minor scales. I'm also aware how Western tonality has superceded ancient Greek theory so as to render modal configurations obsolete in many ways. In this context, it would not be out of place to re-define what we understand of diatonic, chromatic and enharmonic genera. I think Daniel summed it up neatly, saying:
>
>I also understand the steps C to D-flat as diatonic, C to C-sharp as chromatic, and C-sharp to D-flat as enharmonic.
>
>You should know that Western ears do not have monopoly over what is diatonical and what is not. Al-Qindi, Al-Farabi, Ibn Sina and Safiyuddin Urmewi all precede Western theorists in promulgating Hellenic tetrachord calculations. The Maqams of then and today most certainly sound diatonical to me, in that, each instance is made up of 7 steps whose intervals function as half-tones and whole-tones in a given tetrachord.
> >
Well, actually I wanted to insist that Western tonality has not superceded Ancient Greek theory, it just concerns a different music.

In Greece, diatonic, chromatic, and enharmonic concerned independent tunings with steps around 200 and 100, 300 and 100, and 400 and 50 cents. In Western harmony, the terms concern harmonic relations, and the enharmonic relation is the difference between the diatonic and chromatic halfsteps in a given tuning. In a modal context, I think that Greek theory gives you a better handle in classifying tetrachords of heptatonic scales. Western music (apart from the harmonic relations emntioned above) essentially differentiates between music in scales, which are diatonic except for the harmonic minor, which is explained as having a "borrowed tone", and music which uses all the tones of 12-ET. Middle Eastern music has steps of around 150 cents that neither the West nor the Greeks know about, so there are probably Arabic terms going around that fit better than the Greek ones.

Your scale with the adjacent half steps is not diatonic in the Western of the Greek sense. Since it can be analyzed as two tetrachords with two half steps and large second, it is a perfect chromatic scale for the Greeks, but not to Western theory. Not being diatonic makes it a bad scale for anybody who needs consonant chords and movement by fifths,; it does not make it an inherently bad scale. So why call it diatonic?

klaus

>> This is a narrow concept of diatonicism. Maybe in this way we could >> consider
>> that "diatonic" is a synonim of MOS. Infact in 12-et any MOS is a subset >> of
>> a diatonic scale: 1, 2, 3, 5, 7 (12 is obviously chromatic).
>
>Blackwood considers it to mean a MOS with a period of an octave and a
>generator a fifth with some tempering, which can be sharp.

I dont' understand why it can be sharp. Please can you explain me?

Lorenzo

Maybe this is not important but on my italian dictionary I have a definition very similar to that of the American Heritage Dictionary of Jeff. Here is the same: http://en.wikipedia.org/wiki/Diatonic

So it seems that the classical definition of diatonic in West concerns major and natural minor scales and relative modes (anyway I still don't know if a melodic minor scale is considered "diatonic" in a conservatory; I would like to know it).

Ozan (and a lot of other people I think) has a different way to use the term:

>The Maqams of then and today most certainly sound diatonical
>to me, in that, each instance is made up of 7 steps whose intervals
>function as half-tones and whole-tones in a given tetrachord.

If I've well understood he considers diatonic any composition of any
tetrachords, which means essentially any scale with seven notes.

It seems that this two ways to consider the term are related to the harmonic/tonal or melodic/modal context. So there is a "melodic diatonicism" and a "harmonic diatonicism" both regarding scales with seven notes. The scales with more notes has to be considered chromatic.

Anyway the chromatic tetrachord of the ancient Greeks gives scales with seven notes "melodically diatonic" and this makes some confusion... :)

Lorenzo

--- In tuning@yahoogroups.com, "Lorenzo Frizzera"
<lorenzo.frizzera@c...> wrote:

> >> This is a narrow concept of diatonicism. Maybe in this way we could
> >> consider
> >> that "diatonic" is a synonim of MOS. Infact in 12-et any MOS is a
subset
> >> of
> >> a diatonic scale: 1, 2, 3, 5, 7 (12 is obviously chromatic).
> >
> >Blackwood considers it to mean a MOS with a period of an octave and a
> >generator a fifth with some tempering, which can be sharp.
>
> I dont' understand why it can be sharp. Please can you explain me?

Blackwood considered that a diatonic tuning, which was the subject of
his book, should lead to something you could call a diatonic scale in
some sense if you took a chain of six fifths. At the very outside,
that would bound you by 7-equal on the flat side, and 5-equal on the
sharp side, which corresponds to his ratio running from 1 to infinity.
However, he wouldn't really allow it to range quite this far, but I
can't recall the details. He also recognized that a meantone fifth, a
little flat, corresponded to the usual Western idea of what "diatonic"
meant, and was merely willing to push the envelope a little and
consider sharp tunings.

From: Ozan Yarman

> That is a weird diatonic scale with a double augmented whole tone between > Ebb-F# and Bbb C. Nevertheless, it is still diatonic.

The second interval is only a single augmented whole tone. The first interval is also some sort of ditone, which in meantone (definitely not used in Indian music) is around 350 cents.

The ragam I referred to is called S�lagam, BTW. A list of all 72 modes in Carnatic music and other info can be found here: http://www.geocities.com/vasudevanvrv/carnatic/music.htm. (All these modes can be expressed in 12-tone equal temperament, but a 22-tone JI scale can also be used - essentially Yekta Bey's scale with schismic alterations, minus the perfect prime and perfect fifth a comma flat.)

Another correction needed...

> The ragam I referred to is called S�lagam, BTW. A list of all 72 modes in
> Carnatic music and other info can be found here:
> http://www.geocities.com/vasudevanvrv/carnatic/music.htm. (All these modes
> can be expressed in 12-tone equal temperament, but a 22-tone JI scale can
> also be used - essentially Yekta Bey's scale with schismic alterations,
> minus the perfect prime and perfect fifth a comma flat.)

Not Yekta Bey, Arel-Ezgi-�zdilek.

It is an extremely wrong inclination to think that the revisionists Arel and
Ezgi have proposed the perfect theory to represent maqam music. We measure
here with our electronic devices 13/12, 12/11 and 11/10 in many maqams,
exotic intervals which, contrary to what Yekta or his successors have
proposed, are clearly undefined and unacknowledged as yet. It would be a
fallacy to map maqams to 12-tone equal temperament and claim that they can
be expressed with strictly Western tones. We have heard many times the
compositions from the Kemalist era, feigning ignorance of this very fact.
The plethora of maqams can hardly be represented by 12-EQ. I believe the
same is also true for Persian Destgah, Hindustani Sangeet and Karnatic
Sangeet.

Ozan Yarman

----- Original Message -----
From: "Danny Wier" <dawiertx@sbcglobal.net>
To: <tuning@yahoogroups.com>
Sent: 23 Mart 2005 �ar�amba 4:25
Subject: Re: [tuning] Re: Diatonic

>
> Another correction needed...
>
> > The ragam I referred to is called S�lagam, BTW. A list of all 72 modes
in
> > Carnatic music and other info can be found here:
> > http://www.geocities.com/vasudevanvrv/carnatic/music.htm. (All these
modes
> > can be expressed in 12-tone equal temperament, but a 22-tone JI scale
can
> > also be used - essentially Yekta Bey's scale with schismic alterations,
> > minus the perfect prime and perfect fifth a comma flat.)
>
> Not Yekta Bey, Arel-Ezgi-�zdilek.
>

Danny, you are correct. But Ebb-F# is still a double augmented whole-tone.

In response to Lorenzo, here is the definition of a diatonic scale from Paul
Erlich dated 02-03-2005:

> Paul, do you think C Db E F Gb A Bb C or C Db E F G Ab B C can be
>categorized as diatonical scales?

"Yes, in the sense I mentioned earlier, because they contain one and
only one instance of each of the 7 letter names, and they're even
relatively compact harmonically. In fact, these two scales are merely
transpositions of one another..."

I wish Paul would come and back me up on this one, with reasons as to why
and how the scale I gave is diatonic. I do not wish to be blockhead going up
against centuries of Western practice here.

Cordially,
Ozan

----- Original Message -----
From: "Danny Wier" <dawiertx@sbcglobal.net>
To: <tuning@yahoogroups.com>
Sent: 23 Mart 2005 �ar�amba 1:34
Subject: Re: [tuning] Re: Diatonic

>
> From: Ozan Yarman
>
> > That is a weird diatonic scale with a double augmented whole tone
between
> > Ebb-F# and Bbb C. Nevertheless, it is still diatonic.
>
> The second interval is only a single augmented whole tone. The first
> interval is also some sort of ditone, which in meantone (definitely not
used
> in Indian music) is around 350 cents.
>
> The ragam I referred to is called S�lagam, BTW. A list of all 72 modes in
> Carnatic music and other info can be found here:
> http://www.geocities.com/vasudevanvrv/carnatic/music.htm. (All these modes
> can be expressed in 12-tone equal temperament, but a 22-tone JI scale can
> also be used - essentially Yekta Bey's scale with schismic alterations,
> minus the perfect prime and perfect fifth a comma flat.)
>
>