Diatonic Maqams

Now that the subject has come to one of my favorite arguments concerning Maqam Music, may I be allowed to comment that I find all Maqams to be diatonical (in that they are based on patterns of 7 appropriately spaced notes per octave per instant) rather than tetrachordal as propounded by the current Arel-Ezgi theory.

I interpret diatonical in a very broad context to mean any scale composed of 7 notes per octave per instance that makes use of common ratio harmonic and melodic intervals. I sure hope I do not stretch the definition.

Cordially,
Ozan
----- Original Message -----
From: Yahya Abdal-Aziz
To: tuning@yahoogroups.com
Sent: 01 Mart 2005 Salı 2:46
Subject: [tuning] Re: Diatonic

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

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

> I interpret diatonical in a very broad context to mean any scale
>composed of 7 notes per octave per instance that makes use of common
>ratio harmonic and melodic intervals. I sure hope I do not stretch
>the definition.

Hi Ozan,

I think most people would consider the Pythagorean[7], Meantone[7],
Dominant[7], Flattone[7], Helmholtz[7], Garibaldi[7], and Superpyth
[7] scales in the paper I mailed you to be diatonic. But I also think
most people would consider Porcupine[7], Amity[7], Beatles[7], Hanson
[7], Keemun[7], Liese[7], Magic[7], Myna[7], Tetracot[7], Wurschmidt
[7] and probably Dicot[7] and Mavila[7] to be non-diatonic -- even
though they have 7 notes per octave and are based just as much on
simple-integer ratio approximations.

Best,
Paul

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? Or should we just say that any 7-note scale that incorporates simple integer-ratios is "Septatonal" and only a few out of an infinite possibilities are recognized as "diatonical"?

Regards,
Ozan
----- Original Message -----
From: wallyesterpaulrus
To: tuning@yahoogroups.com
Sent: 01 Mart 2005 Salı 19:57
Subject: [tuning] Re: Diatonic Maqams

Hi Ozan,

I think most people would consider the Pythagorean[7], Meantone[7],
Dominant[7], Flattone[7], Helmholtz[7], Garibaldi[7], and Superpyth
[7] scales in the paper I mailed you to be diatonic. But I also think
most people would consider Porcupine[7], Amity[7], Beatles[7], Hanson
[7], Keemun[7], Liese[7], Magic[7], Myna[7], Tetracot[7], Wurschmidt
[7] and probably Dicot[7] and Mavila[7] to be non-diatonic -- even
though they have 7 notes per octave and are based just as much on
simple-integer ratio approximations.

Best,
Paul

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

> 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 and of one of the diatonics that I just
posted a lattice diagrams for! Look again at that post with the
lattice diagrams and see if you can figure out which scale I mean.

>Or should we just say that any 7-note scale that incorporates simple
>integer-ratios is "Septatonal" and only a few out of an infinite
>possibilities are recognized as "diatonical"?

A few, but still an infinite number :) But they're still only a
subset of the infinity of 7-note possibilities, yes. However, I
suspect most or all of the non-diatonic, 7-note possibilites are
quite unfamiliar to you -- refer my list below to the paper I sent
you and let me know.

> ----- Original Message -----
> From: wallyesterpaulrus
> To: tuning@yahoogroups.com
> Sent: 01 Mart 2005 Salý 19:57
> Subject: [tuning] Re: Diatonic Maqams
>
>
>
> Hi Ozan,
>
> I think most people would consider the Pythagorean[7], Meantone
[7],
> Dominant[7], Flattone[7], Helmholtz[7], Garibaldi[7], and
Superpyth
> [7] scales in the paper I mailed you to be diatonic. But I also
think
> most people would consider Porcupine[7], Amity[7], Beatles[7],
Hanson
> [7], Keemun[7], Liese[7], Magic[7], Myna[7], Tetracot[7],
Wurschmidt
> [7] and probably Dicot[7] and Mavila[7] to be non-diatonic --
even
> though they have 7 notes per octave and are based just as much on
> simple-integer ratio approximations.
>
> Best,
> Paul

Paul, do you consider certain two consequent notes in the following sequences:

C Db E F Gb A Bb C

and

C Db E F G Ab B C

to be "ditonic"? I can find no such instance to justify the traditional employment of the term diatonic to these scales, although I sense that they indeed are diatonical due to their septa-tonal nature (the same is true for the inherent structure of maqams). Is the Pythagorean 7-tone scale (Suz-i Dilara Maqam scale) the only ditonic scale which is also diatonical?

I can idenfiy the 1st sequence above the 10th lattice diagram in a glance:

D Eb F# G A Bb C# D

A Bb C# D Bb F# G A

I would appreciate it most if you could write a paper on what is diatonical and what is not in layman terms.

Cordially,
Ozan

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

> Paul, do you consider certain two consequent notes in the
>following sequences:
>
> C Db E F Gb A Bb C
>
> and
>
> C Db E F G Ab B C
>
> to be "ditonic"?

I don't understand the question.

>I can find no such instance to justify the traditional employment
>of the term diatonic to these scales, although I sense that they
>indeed are diatonical due to their septa-tonal nature (the same is
>true for the inherent structure of maqams).

As I remarked before (with examples from my paper) I don't think all
7-note scales are diatonic. There are quite a few 7-note scales with
two step sizes distributed evenly around the octave, and which are
conceived with consonant, near-small-integer-frequency-ratio
harmonies as the goal, which are nonetheless non-diatonic.

>Is the Pythagorean 7-tone scale (Suz-i Dilara Maqam scale) the only
>ditonic scale which is also diatonical?

Hmm . . . I don't know. How do you define "ditonic"?

> I can idenfiy the 1st sequence above the 10th lattice diagram in a
>glance:
>
> D Eb F# G A Bb C# D

Yup!

> A Bb C# D Bb F# G A

I think you meant 'Eb' for the fifth note there.

> I would appreciate it most if you could write a paper on what is
>diatonical and what is not in layman terms.

Have you read this paper of mine (please skip the optional sections)?
_The Forms Of Tonality: A Preview_
http://lumma.org/tuning/erlich/erlich-tFoT.pdf

I apologize if the relevant sections aren't in 'layman terms' --
this paper was directed toward a specific, JI-oriented, West-Coast-
USA audience. Please let's discuss the paper on- or off-list and
let's iron out any concepts/arguments/sections that are opaque to
you.

hi Ozan (and Paul),

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

>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...>
wrote:
>
> > Paul, do you consider certain two consequent notes in the
> > following sequences:
> >
> > C Db E F Gb A Bb C
> >
> > and
> >
> > C Db E F G Ab B C
> >
> > to be "ditonic"?
>
> I don't understand the question.

is "ditonic" is a typo for "diatonic"?

if not, then no, these scales are not "ditonic", because
"ditonic" means "two (whole) tones", and there is no
sequence of 2 whole-tones in either of these scales.

for example, one of Ptolemy's tunings was his
"ditonic diatonic genus":

(click "reply" to view properly on Yahoo web interface)

string-length proportions: 192 : 216 : 243 : 256

note ratio ~ cents

mese 1/1 0
> 8:9 ~ 203.9100017 cents
lichanos 8/9 - 203.9100017
> 8:9 ~ 203.9100017 cents
parhypate 64/81 - 407.8200035
> 243:256 ~ 90.22499567 cents
hypate 3/4 - 498.0449991

which equates to the descending sequence with ratios
A 1/1 - G 16/9 - F 128/81 - E 3/2

-monz

I entertained the idea that ditonic scales (beginning with 9:8+9:8) form the backbone of diatonic scales Paul. The most renown is the Pythagorean 7-tone ditonic-diatonic scale. I'm sure that not all 7-note scales are diatonic (let alone ditonic), but is there some algebraic process that can help us distinguish those which are, and those which are not?

I took a glance at Blackwood's work, but the techno-babble is beyond me. I can only verify by ear which scales resemble the `diatonic`s that I came to know.

I have read your paper, though I'm still in the dark as to some of the concepts you have produced. Nevertheless, the nice sloping lines tell me that there are certain zones within tolerable boundaries representing consonant dyads which equate to simple integer ratios as perceived by the human ear. Am I right?

Cordially,
Ozan

Thanks for the clarifications Monz.

is "ditonic" is a typo for "diatonic"?

if not, then no, these scales are not "ditonic", because
"ditonic" means "two (whole) tones", and there is no
sequence of 2 whole-tones in either of these scales.

for example, one of Ptolemy's tunings was his
"ditonic diatonic genus":

(click "reply" to view properly on Yahoo web interface)

string-length proportions: 192 : 216 : 243 : 256

note ratio ~ cents

mese 1/1 0
> 8:9 ~ 203.9100017 cents
lichanos 8/9 - 203.9100017
> 8:9 ~ 203.9100017 cents
parhypate 64/81 - 407.8200035
> 243:256 ~ 90.22499567 cents
hypate 3/4 - 498.0449991

which equates to the descending sequence with ratios
A 1/1 - G 16/9 - F 128/81 - E 3/2

That's the Pythagorean tetrachord!

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

> for example, one of Ptolemy's tunings was his
> "ditonic diatonic genus":
>
> (click "reply" to view properly on Yahoo web interface)
>
> string-length proportions: 192 : 216 : 243 : 256
>
> note ratio ~ cents
>
> mese 1/1 0
> > 8:9 ~ 203.9100017 cents
> lichanos 8/9 - 203.9100017
> > 8:9 ~ 203.9100017 cents
> parhypate 64/81 - 407.8200035
> > 243:256 ~ 90.22499567 cents
> hypate 3/4 - 498.0449991
>
>
> which equates to the descending sequence with ratios
> A 1/1 - G 16/9 - F 128/81 - E 3/2

i also meant to point out that Ptolemy's "ditonic diatonic"
genus is the same as the standard pythagorean tuning, which
persisted as "the" tuning (at least in theory) until c.1480.

-monz

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

> I entertained the idea that ditonic scales (beginning with 9:8+9:8)
>form the backbone of diatonic scales Paul. The most renown is the
>Pythagorean 7-tone ditonic-diatonic scale. I'm sure that not all 7-
>note scales are diatonic (let alone ditonic), but is there some
>algebraic process that can help us distinguish those which are, and
>those which are not?

Yes, if you mean which are diatonic and which aren't. Simply
speaking, if the scale is diatonic, it will be "correctly" spelled
with all 7 letter names, one letter per note . . . Of course, things
can be fuzzy if you're dealing with a "real" scale and an unfamiliar
musical usage . . . but I think my paper _The Forms Of Tonality: A
Preview_, which I think you've read, will help you see what I mean
by "diatonic".

> I took a glance at Blackwood's work, but the techno-babble is
>beyond me.

Oh dear, then surely my own techno-babble can only be
incomprehensible to you. Is there a passage in Blackwood's book that
you'd like me to try "laymanizing" for you?

> I have read your paper, though I'm still in the dark as to some of
>the concepts you have produced.

Allow me to shed light! Ask, ask, ask away . . .

>Nevertheless, the nice sloping lines
>tell me that there are certain zones within tolerable boundaries
>representing consonant dyads which equate to simple integer ratios
>as perceived by the human ear. Am I right?

Which chart are you looking at? Is this in _The Forms Of Tonality_,
or in a different paper?