Ragalike Dorian mode -- for Haresh Bakshi

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Hello, there, Haresh Bakshi and everyone.

From time to time there have been discussions on the Tuning List about
"raga-like" scales which may draw their inspiration from the classical
raga music of India and yet take other musical directions. For
example, the 22 srutis of the Indian tradition have prompted some
quite different systems on the part of European or other musicians
such as 22-tone equal temperament or intonational schemes involving
septimal ratios.

Here I would like to describe what I call a "raga-like" scale which
could be called a version of the medieval European Dorian mode, but
using ratios different from those of the Indian srutis based on ratios
of 3 and 5. While I actually use a tempered version of this raga-like
mode, I shall also give near-equivalent just intonation ratios for
this version of medieval European Dorian.

In describing this scale as "raga-like," I refer both to the spiritual
qualities I find in the music it invites, and to certain musical
traits reflected in or facilitated by the intonational nuances:

(1) The scale is typically used for essentially
monophonic music with a single melodic line;

(2) This melodic line typically flows above a fixed
drone consisting of the final (or 1/1) and fifth;
and

(3) Certain steps of the scale are tuned so as to
maximize consonance or "simplicity of ratio"
in relation to this drone.

In a tempered realization, the scale is as follows, with note names
showing the layout on a 24-note keyboard with two manuals at
approximately 58.680 cents apart, an interval which serves as the
diatonic semitone of this scale. An asterisk (*) shows a note played
on the upper manual: having the fingers of the right hand move fluidly
between notes on the two manuals, while the left hand maintains the
drone on the lower manual, is part of the performance practice for
this scale.

1/1 ~44/39 7/6 ~4/3 ~3/2 ~22/13 ~7/4 2/1
D4 E4 E*4 G4 A4 B4 B*4 D5
0 208.19 266.87 495.90 704.10 912.29 970.97 1200
208.19 58.68 229.03 208.19 208.19 58.68 229.03

In this tuning, fifths are wide and fourths narrow by about 2.14
cents; the small semitones of this scale, E4-E*4 and B4-B*4, are
narrower than the just septimal ratio of 28:27 (~62.96 cents) by twice
this amount, or about 4.28 cents. Likewise, the major seconds D4-E4
and A4-B4 are wider than a pure 9:8 (~203.91 cents) by about 4.28
cents, or twice the tempering of the fifth.

Followers of ancient Greek and medieval Arabic or European theory
might note that this scale could be described as a kind of tempered
variation on the diatonic of Archytas (steps of 9:8, 8:7, and 28:27)
with two tetrachords so arranged (28:27 as middle step) as to produce
a medieval European Dorian pattern.[1]

Let consider first the melodic qualities of this scale, and then the
aspect of vertical consonance above a drone. From a melodic view,
there is an engaging contrast between the narrow semitones and the
spacious septimal whole-tones near 8:7 (E*-G, B*-D); the whole-tones
D4-E4, G4-A4, and A4-B4 are also quite generously sized, being
slightly larger than the Pythagorean 9:8.

More specifically, the Dorian qualities of the mode are often
communicated in a melody by the major sixth and minor seventh degrees
above the final or 1/1. Here the major sixth is rather wide, with a
size of around 22:13, or somewhat larger than the Pythagorean 27:16
(~905.87 cents), while the narrow minor seventh is very close to a
just 7:4 (actually about 2.14 cents larger). Between these two
important modal degrees is a narrow 58.68-cent semitone, which might
be described as a kind of tempered 28:27 "thirdtone."

Since the quality of these sixth and seventh degrees of Dorian is felt
vertically as well as melodically in relation to a drone, this raises
the topic of vertical consonance. A "raga-like" property of this scale
is that many of the notes form highly consonant ratios, or reasonably
close tempered equivalents, in relation to a drone of final and fifth.

In the above diagram, the scale is shown in the octave D4-D5, and for
this usual range the drone would typically be sounded at D3-A3. Above
this drone, the final D4 (the lowest note of the melodic modal octave)
sounds D3-A3-D4, a tempered 2:3:4, the "threefold perfection of
harmony" in medieval European theory with its 2:1 octave, 2:3 fifth,
and 4:3 fourth.

The second degree of the mode, E4, sounds a highly favored sonority of
D3-A3-E4, with a tempered ratio of 4:6:9; often medieval or
neo-medieval melodies in Dorian tend to emphasize this degree, for
example by dwelling upon it at internal cadences. While the second
degree is actually about 4.28 cents higher than a pure 9:8 or 9:4, and
closer to 44:39 or 88:39, the consonant impression of 4:6:9 can still
be very effective.

The third degree, E*4, at a pure 7/6, forms with the tempered fifth of
the drone a sonority of D3-A3-E*4, or approximately 6:9:14, with the
outer interval of a just 7:3 minor third.

The fourth degree, G4, at a tempered 4/3, forms with the drone a very
pleasing combination of the fourth (or eleventh) and fifth above the
lowest note, or D3-A3-G4, a tempered ratio of 6:9:16. The effect is
similar to that of the common 13th-century European 6:8:9.

The fifth degree, A4, at a tempered 3/2, yields in relation to the
drone an approximate 2:3:6.

The sixth degree, B4, at approximately 22/13, yields a somewhat more
complex and active type of sonority than the other steps of the mode:
this could be taken as a tempered 26:39:88, or the fifth of the drone
plus a major sixth rather wider than the Pythagorean 27/16. However,
this rather large major sixth and also the major second or ninth
between the fifth of the drone and this sixth degree are both
intervals with some degree of "compatibility" or "concord," so that
this degree may also be described as somewhat consonant in effect.

The seventh degree, B*4, at approximately 7/4, forms with the drone a
tempered 2:3:7, with this degree and the upper note of the drone at a
pure 3:7 septimal minor tenth.

The eighth degree or octave, D5, at 2/1, forms with the drone a
tempered 2:3:8, an octave extension of the approximate 2:3:4 formed by
the modal final D4 an octave below.

Thus the first, fifth, and eighth degrees of the mode form tempered
versions of 3-odd-limit concords (2:3:4, 2:3:6, 2:3:8). The third and
seventh degrees form approximate 7-prime-limit or 9-odd-limit
concords, with 7:6 or 7:3 pure (6:9:14, 2:3:7). The second and fourth
degrees form temperd 3-prime-limit or 9-odd-limit concords (4:6:9,
6:9:16) of a "quartal/quintal" kind favored in medieval European and
various other world musical traditions. The sixth degree forms a
rather more complex but still somewhat "compatible" sonority
(approximating 26:39:88) lending a bit of contrast to this general
picture of vertical simplicity.

Of course, the two dimensions interact in musical practice to give an
overall impression of what I might call stateliness, as when the
seventh degree forming a 2:3:7 or 4:6:7 sonority (the latter if it is
sounded at B*3, the step below the final of the modal octave) resolves
by a majestically large whole-tone step near 8:7 to the final or its
octave (2:3:4 or 2:3:8).

I find the effect very pleasing for medieval or neo-medieval melodies
in a European kind of style: a very different tradition than that of
India, but yet bringing into play melodic patterns along with elements
of drone and consonance which might somehow seem related.

One might also take the idea of an already hybrid style yet further by
using this scale for polyphonic music. There are fascinating
resources, including the narrow fourth at a near-21:16 between the
fourth and seventh degrees (4/3 and 7/4), thus making possible the
sonority of 16:21:24:28 (4/3-7/4-2/1-7/3), which is among the most
awesome and beautiful things in music.

However, the most characteristic use of this scale, and the one which
typifies its "raga-like" characteristics, is the setting of a single
melody above a drone, with the element of vertical consonance.

In conclusion, I would like warmly to thank Haresh Bakshi for his many
generous contributions to this list, and for his role in promoting
both knowledge and friendship among musicians of many cultures and
traditions.

-----------
Scala files
-----------

Here is a Scala file for this tempered scale:

! ragaldor.scl
!
Raga-like medieval European Dorian mode with ~7/6 and ~7/4, tempered version
7
!
208.191213 cents
7/6
495.904393 cents
704.095607 cents
912.286820 cents
970.966512 cents
2/1

Here is a near-equivalent just intonation tuning:

! ragaldoj.scl
!
Raga-like medieval European Dorian mode with 7/6 and 7/4, just version
7
!
44/39
7/6
4/3
3/2
22/13
7/4
2/1

----
Note
----

1. A just intonation version of the Archytan diatonic realization of
medieval European Dorian corresponding to this scale is as follows:

1/1 9/8 7/6 4/3 3/2 27/16 7/4 2/1
D4 E4 F4 G4 A4 B4 C4 D5
0 203.91 266.87 498.04 701.96 905.87 968.83 1200
9:8 28:27 8:7 9:8 9:8 28:27 8:7
203.91 62.96 231.17 203.91 203.91 62.96 231.17

Most appreciatively,

Margo Schulter
mschulter@value.net

--- In tuning@yahoogroups.com, "M. Schulter" <MSCHULTER@V...> wrote:

> In this tuning, fifths are wide and fourths narrow by about 2.14
> cents; the small semitones of this scale, E4-E*4 and B4-B*4, are
> narrower than the just septimal ratio of 28:27 (~62.96 cents) by
twice
> this amount, or about 4.28 cents. Likewise, the major seconds D4-E4
> and A4-B4 are wider than a pure 9:8 (~203.91 cents) by about 4.28
> cents, or twice the tempering of the fifth.
>
> Followers of ancient Greek and medieval Arabic or European theory
> might note that this scale could be described as a kind of tempered
> variation on the diatonic of Archytas (steps of 9:8, 8:7, and 28:27)
> with two tetrachords so arranged (28:27 as middle step) as to
produce
> a medieval European Dorian pattern.[1]

This size of fifth sounds like it fits the 46-et pretty well, but in
terms of the 13-limit approximations which seem to be implied, I'm
more inclined to link it to the Hemififth temperament and the 58 et.
Hemififth is a temperament with a neutral third generator
approximating 11/9, and this generator has a "poptimal" 13-limit
version of 17/58. Your scale could be regarded as a non-MOS scale of
Hemififths, which has MOS scales of size 7, 10, 17 and 24. A basis
for the commas is [144/143, 196/195, 243/242, 364/363], and these, I
think, are relevant to your scale.

> Let consider first the melodic qualities of this scale, and then the
> aspect of vertical consonance above a drone. From a melodic view,
> there is an engaging contrast between the narrow semitones and the
> spacious septimal whole-tones near 8:7 (E*-G, B*-D); the whole-tones
> D4-E4, G4-A4, and A4-B4 are also quite generously sized, being
> slightly larger than the Pythagorean 9:8.

The 58-et version of your scale goes [10, 3, 11, 10, 10, 3, 11],
which we might compare to the MOS [7, 10, 7, 10, 7, 10, 7].

--- In tuning@yahoogroups.com, "M. Schulter" <MSCHULTER@V...> wrote:
...........

Hello Margo, thanks for a very learned and lucid "Raga-like Dorian mode": the exposition was, indeed, stimulating and informative. It whetted up my appetite to re-visit several pentatonic raga-s in a new light. Thanks once again.

The Dorian mode can be spoken of as a homologous of the Kafi Thaat:
C D Eb F G A Bb C'

I am putting aside the distinction between the shruti system and the
tempered scale, for a while; as also the distinction between the Thaat and the raga. This means that you can play the notes of the scale, in a raga-like fashion, and create spiritual, even mystical, ambiance. The result of such an approach is not a raga technically -- it is "mood", "air", atmosphere, having a distinctive but intangible quality, having its own attributes and ethos. It is eminently disposed and willing to comply with the dictates of the flights of imagination, whether we are performing singly or severally. It is particularly amenable to nascent improvisations and even the question-answer type "jugalbandhi". I think this will also lend itself well to flexible harmonization, especially because of the absence of the leading note. The recurring melodic line acts as the motif, the unifying theme or design providing a contrast to the free-flowing
patterns.

You have referred to the drone. In the case of the Dorian mode, the drone (I mean Tanpura here) would be tuned like G3 C4 C4 C3. This will, of course, vary with the mode we select. For example, the NOTES of the raga Malkaus:
C Eb F Ab Bb will require the drone to be tuned in F3 C4 C4 C3. If, in a mode, both F and G are absent, the drone tuning will have to be
B3 C4 C4 C3. [In the latter case, F# will be present in the mode].

You also mention: "Certain steps of the scale are tuned so as to
maximize consonance or 'simplicity of ratio' in relation to this drone." This becomes complicated with the simultaneous sounding of the four strings of the drone (I mean Tanpura), because of too many combinational tones. -- Or, have I got it wrong?

Like the muurchchhana, the modes keep changing their "Sa", giving rise to several Indian scales, all of which would make for interesting improvisations. Likewise, the notes of several pentatonic raga-s [Bhupali, Deshkar, Shuddha Kalyan, Durga, Bairagi Bhairav, Gunakri, Bhupal Todi, Bhinna Shadja, Madhu Kaus, Sarang -- the list goes on] can be taken to form the respective scales, and elaborated for sheer joy.

In conclusion, I want to thank you and all the members of this illustrious group, who have been patient with me, and treated me with excessive indulgence, forgetting and forgiving my gross ignorance of the subject matter of the Tuning group.

Regards,
Haresh.

--- In tuning@yahoogroups.com, "Haresh BAKSHI <hareshbakshi@h...>"
<hareshbakshi@h...> wrote:

> You also mention: "Certain steps of the scale are tuned so as to
> maximize consonance or 'simplicity of ratio' in relation to this
>drone." This becomes complicated with the simultaneous sounding of
>the four strings of the drone (I mean Tanpura), because of too many
>combinational tones. -- Or, have I got it wrong?

well, i don't think one would normally worry about combinational
tones explicitly, because if two notes form a simple ratio, or three
or more notes form an otonal chord, then all the combinational tones
will "line up" and add to the sensation of consonance. also, the vast
majority of combinational tones get louder nonlinearly with the
loudness of the "real" tones, and so only become important at quite
loud volume levels -- not a typical feature of raga as i know it.

however, there can certainly be competing forces involved in
maximizing the consonance of a note with respect to the various drone
strings. for example, A5 can be tuned low to form a 10/3 ratio above
C4, or tuned high to form a 9/4 ratio above G4. it is my
understanding that one or the other tuning of A may be found in
different ragas, though i'm not sure if the low tuning of A is ever
actually used with a G in the drone . . . haresh?

but margo was only tuning *certain* notes this way, and as i recall,
left some of the potentially conflicted notes in non-
consonant, "spicy" relationship with the drone . . . margo?

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

>>>> however, there can certainly be competing forces involved in
maximizing the consonance of a note with respect to the various drone
strings. for example, A5 can be tuned low to form a 10/3 ratio above
C4, or tuned high to form a 9/4 ratio above G4. it is my
understanding that one or the other tuning of A may be found in
different ragas, though i'm not sure if the low tuning of A is ever
actually used with a G in the drone . . . haresh? >>>>

Hello, the tanpura is tuned in either
G3 C4 C4 C3 or
F3 C4 C4 C3 or
B3 C4 C4 C3.

So, the note A does not take part in the tanpura tuning. The only exception I have heard about is for the raga Todi [C Dbb Ebb F# (G) Abb B], the use of "bb" implying that the note is lower than usual. Here, the theoretically preferred tuning, though never followed in practice, is
Abb3 C4 C4 C3.

Regards,
Haresh.

--- In tuning@yahoogroups.com, "Haresh BAKSHI <hareshbakshi@h...>"
<hareshbakshi@h...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus
<wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:
>
> >>>> however, there can certainly be competing forces involved in
> maximizing the consonance of a note with respect to the various
drone
> strings. for example, A5 can be tuned low to form a 10/3 ratio
above
> C4, or tuned high to form a 9/4 ratio above G4. it is my
> understanding that one or the other tuning of A may be found in
> different ragas, though i'm not sure if the low tuning of A is ever
> actually used with a G in the drone . . . haresh? >>>>
>
> Hello, the tanpura is tuned in either
> G3 C4 C4 C3 or
> F3 C4 C4 C3 or
> B3 C4 C4 C3.
>
> So, the note A does not take part in the tanpura tuning.

right, i was asking about the *scale* tuning. anyone know?