Raga-s and Drone Harmonics

As stated in an earlier message in the past, we can tune the tanpura
in one of the three ways, depending upon whether the raga (i)
includes G as one of the notes or not; (ii) includes a weak or a
strong F; (iii) excludes both G and F, but includes F#. So, we have
three methods of tuning.
In all three cases, 2nd and 3rd strings are tonic; the 4th string is
tonic in the lower octave. The 1st string is either G in the lower
octave, or F in the lower octave, or B in the lower octave. The four
strings are plucked, one at a time, slowly, softly, consistently.

I attempted some elementary calculations to find out which of the
notes were possible as harmonics, for all three types of tuning
mentioned above. I assumed the Indian gamut to be --
1/1 16/15 9/8 6/5 5/4 4/3 45/32 3/2 8/5 27/16 9/5 15/8 2/1.

In the calculations above, I did not come across at least two notes
(as possible harmonics): Db [16/15], and Ab [8/5].

Further, I excluded the possibility of the existence of combinational
tones. This is because, combinational tones are heard when two
musical tones of different pitches are sounded together, LOUDLY AND
CONTINUOUSLY. The tanpura is neither loud (it is very soft), nor
continuous (it is plucked at a very slow rate, one string at a time).

The raga relation. Let us assume our tonic to be in the note of C.
The significant harmonics are those that would arise from the C
(middle and lower octaves). They are:
1 2 3 4 5 6 7 8
c c' g' c" e" g" b"b c"'
0 1200 1902 2400 2786 3102 3369 3500 [cents]

Even if we were to take into consideration all the modes of tuning
and do all the calculation as shown in the example above, we still
will not come across Db [16/15], and Ab [8/5].

The conclusion. The ragas with Db and/or Ab will not get any
support from the harmonics of the tanpura. There ar several such
raga-s, like Bhairava, Poorvi, Bibhas .... the number is very large.

Any comments? Corrections?

Regards,
Haresh.

--- In tuning@y..., "Haresh BAKSHI" <hareshbakshi@h...> wrote:
> As stated in an earlier message in the past, we can tune the
tanpura
> in one of the three ways, depending upon whether the raga (i)
> includes G as one of the notes or not; (ii) includes a weak or a
> strong F; (iii) excludes both G and F, but includes F#. So, we
have
> three methods of tuning.
> In all three cases, 2nd and 3rd strings are tonic; the 4th string
is
> tonic in the lower octave. The 1st string is either G in the lower
> octave, or F in the lower octave, or B in the lower octave. The
four
> strings are plucked, one at a time, slowly, softly, consistently.
>
> I attempted some elementary calculations to find out which of the
> notes were possible as harmonics, for all three types of tuning
> mentioned above. I assumed the Indian gamut to be --
> 1/1 16/15 9/8 6/5 5/4 4/3 45/32 3/2 8/5 27/16 9/5 15/8 2/1.

Haresh - this is great!

>
> In the calculations above, I did not come across at least two notes
> (as possible harmonics): Db [16/15], and Ab [8/5].
>
>
> Further, I excluded the possibility of the existence of
combinational
> tones. This is because, combinational tones are heard when two
> musical tones of different pitches are sounded together, LOUDLY AND
> CONTINUOUSLY. The tanpura is neither loud (it is very soft), nor
> continuous (it is plucked at a very slow rate, one string at a
time).
>
>
> The raga relation. Let us assume our tonic to be in the note of
C.
> The significant harmonics are those that would arise from the C
> (middle and lower octaves). They are:
> 1 2 3 4 5 6 7 8
> c c' g' c" e" g" b"b c"'
> 0 1200 1902 2400 2786 3102 3369 3500 [cents]

Haresh, the 8th pitch should be 3600 cents.

Harmonics Ratio Cents
1 0
2 1200
3 1901.955001
4 2400
5 2786.313714
6 3101.955001
7 3368.825906
8 3600

I would like to say that I would consider harmonics above this point
to be "significant".

If we look at the next octave of the harmonic series we see other
useful treasures:

8 3600 8/7 231.1740935
9 3803.910 9/8 203.9100017
10 3986.313 10/9 182.4037121
11 4151.317 11/10 165.0042285
12 4301.955 12/11 150.6370585
13 4440.527 13/12 138.5726609
14 4568.825 14/13 128.2982447
15 4688.268 15/14 119.4428083
16 4800 16/15 111.7312853

Is the ratio 9/8 an important interval on Indian string instruments?
Between 4/3 and 3/2 vertically?

>
> Even if we were to take into consideration all the modes of tuning
> and do all the calculation as shown in the example above, we still
> will not come across Db [16/15], and Ab [8/5].
>
> The conclusion. The ragas with Db and/or Ab will not get any
> support from the harmonics of the tanpura. There ar several such
> raga-s, like Bhairava, Poorvi, Bibhas .... the number is very large.

One comment, is that I've found I can fill in the area of the minor
third and major third, as well as their inversions, with an extremely
wide variety of ratios, and still sound correct over a harmonic
drone. Especially where I leave the 1/1, 4/3, 3/2, 2/1 stable. 11
Limit intervals for instance are not found in the first 8 harmonics,
yet 11/9 @ 347.408 and 18/11 @ 852.592, are incredibly powerful
melodic intervals. Neutral intervals are very exotic, but I've seen
again and again that they can be sang. I conjecture that the reason
this will work is because these exotic intervals are found by
addition of the successive members of the harmonic series, so
therefore sound correct over the harmonic drone. And where they may
not be found in the first eight harmonics, gives one wonderful
tensions and emotional flavors for melodic improvisation. Harmonic
intervals seem to work in a relative way to me; not requiring all
members of a scale to be a direct member of the linear harmonic
series (but perhaps found by addition of its members) drone.

Thanks again for the posts - I'm learning allot from them,

Jacky Ligon

--- In tuning@y..., "Haresh BAKSHI" <hareshbakshi@h...> wrote:
> As stated in an earlier message in the past, we can tune the
tanpura
> in one of the three ways, depending upon whether the raga (i)
> includes G as one of the notes or not; (ii) includes a weak or a
> strong F; (iii) excludes both G and F, but includes F#. So, we
have
> three methods of tuning.
> In all three cases, 2nd and 3rd strings are tonic; the 4th string
is
> tonic in the lower octave. The 1st string is either G in the lower
> octave, or F in the lower octave, or B in the lower octave. The
four
> strings are plucked, one at a time, slowly, softly, consistently.
>

If the first 8 harmonics are the most significant, then if the
Tanpura is playing a drone with 1/1 and 3/2 for C and G, then the
complimentary harmonic scale would be:

Ratios Cents
1/1 0.000
8/7 231.174
7/6 266.871
6/5 315.641
5/4 386.314
4/3 498.045
3/2 701.955
12/7 933.129
7/4 968.826
9/5 1017.596
15/8 1088.269
2/1 1200.000

If the Tanpura is playing 1/1 and 4/3 for C and F, then the
complimentary harmonic scale would be:

Ratios Cents
1/1 0.000
8/7 231.174
7/6 266.871
6/5 315.641
5/4 386.314
4/3 498.045
3/2 701.955
32/21 729.219
14/9 764.916
8/5 813.686
5/3 884.359
7/4 968.826
16/9 996.090
9/5 1017.596
15/8 1088.269
2/1 1200.000

If the Tanpura is playing 1/1 and 45/32 for C and F#, then the
complimentary harmonic scale would be:

Ratios Cents
1/1 0.000
135/128 92.179
8/7 231.174
7/6 266.871
6/5 315.641
5/4 386.314
4/3 498.045
45/32 590.224
3/2 701.955
45/28 821.398
105/64 857.095
27/16 905.865
225/128 976.537
15/8 1088.269
2/1 1200.000

I can see there are many possible shadings when we consider the
combination of the first eight harmonics for two tanpura strings

Haresh, I would like to ask about the occurance of 7/5 in Indian
music. Have you encountered this interval in Raaga?

Many thanks,

Jacky Ligon

--- In tuning@y..., ligonj@n... wrote:
> --- In tuning@y..., "Haresh BAKSHI" <hareshbakshi@h...> wrote:

...........

> > (iii) excludes both G and F, but includes F#. So, we
> have
> > three methods of tuning.
> >

.........

Hi jacky, thanks for this message. In the third case of tuning,
mentioned above, the tanpura is tuned as under:
1st string: lower B
2nd and 3rd strings: C
4th string: lower C.
We dont use F# in tuning the tanpura. So, your third list will
change: What will it be, now?

The second query is about the use of 7/5. I will write separately
about that.

Regards,
Haresh.

--- In tuning@y..., "Haresh BAKSHI" <hareshbakshi@h...> wrote:
> --- In tuning@y..., ligonj@n... wrote:
> > --- In tuning@y..., "Haresh BAKSHI" <hareshbakshi@h...> wrote:
>
> ...........
>
> > > (iii) excludes both G and F, but includes F#. So, we
> > have
> > > three methods of tuning.
> > >
>
> .........
>
> Hi jacky, thanks for this message. In the third case of tuning,
> mentioned above, the tanpura is tuned as under:
> 1st string: lower B
> 2nd and 3rd strings: C
> 4th string: lower C.
> We dont use F# in tuning the tanpura. So, your third list will
> change: What will it be, now?

Haresh,

Good Morning!

I'll try to get this in before I head to the office.

Sorry I misunderstood the use of F#.

If we assume the "B" to be 15/8, then the complimentary harmonic
scale would be:

1/1 0.000
15/14 119.443
35/32 155.140
9/8 203.910
8/7 231.174
7/6 266.871
75/64 274.582
6/5 315.641
5/4 386.314
4/3 498.045
45/32 590.224
3/2 701.955
15/8 1088.269
2/1 1200.000

It's interesting to note the appearance of 45/32 here, which turns
out to be a member of the harmonics afterall.

>
> The second query is about the use of 7/5. I will write separately
> about that.
>
> Regards,
> Haresh.

I will look forward to your comments about 7/5.

Thanks,

Jacky Ligon