shruti-s at the lower end

The Octave 22Hz -- 44 Hz
========================

Here each shruti would be exactly 1 Hz apart. The shruti-s would be
equidistant.

The shruti distances between notes (shadja gram) are:

Sa Re Ga Ma Pa Dha Ni Sa
4 3 2 4 4 3 2

And the shruti intervals would be: [fractions, in decimal, in cents]

22/22, 26/22, 29/22, 31/22, 35/22, 39/22, 42/22,
1/1 1.181818 1.318181 1.409090 1.59090 1.772727 1.909090
0 0.07255 0.119975 0.148939 0.201643 0.248642 0.280826
0 289.207 478.2579 593.7176 803.8122 991.1650 1119.4605

44/22
2/1
o.301030
1200.

Do these ratios give rise to an octave with a new sound? Has anyone
tried this?

We CANNOT accommodate 22 shruti-s in an octave, if the scale starts
below 22 Hz.

Is this some kind of limit? Is this the reason why the human ear
cannot hear below 22 Hz?

Haresh.

Haresh wrote,

>Here each shruti would be exactly 1 Hz apart. The shruti-s would be
>equidistant.

That's not perceptually equidistant. We hear logarthmically. At 22 Hz, an
increment of 1 Hz is a small semitone. At 440 Hz, the increment of 1 Hz
becomes melodically imperceptible. In higher and higher ranges, 1 Hz means
less and less.

Dividing the span from 22 Hz to 44 Hz in 1 Hz increments would result in an
otonal scale that happens to be very far from the Indian scale. As you
showed, Ga is almost as high as the usual Ma and Pa becomes a komal Dha.
Meanwhile, dividing the span from 22 Hz to 44 Hz using equally-spaced frets
on a string instrument or equally-spaced holes on a wind instrument can
result in a utonal scale, also very far from the Indian scale, but in the
opposite direction.

A perceptually equal division would be 22-tone equal temperamen, leading to
a scale much closer, though still noticeably different, from the Indian
scale.

22-tET quantization of sa-grama:

Sa Re Ga Ma Pa Dha Ni Sa
4 3 2 4 4 3 2

0 218 384 491 709 927 1091 1200

I wouldn't use this, but it's still a lot closer than either the otonal or
the utonal versions.

>We CANNOT accommodate 22 shruti-s in an octave, if the scale starts
>below 22 Hz.

What do you mean?

>Is this some kind of limit? Is this the reason why the human ear
>cannot hear below 22 Hz?

Yes -- that's just the physiology of the ear. You can _feel_ frequencies
below that, of course -- but they won't be perceived as having _pitch_.

Hi Haresh,

I've tried listening to your scales at 22-44 Hz.

Used the ocarina voice in midi as a sine wave approximation.

I think if one could play only the note itself, then I prob. wouldn't be able to distinguish
the 44-tet notes. However, not so easy to tell because those low
notes set higher notes resonating quietly, and one can use those
instead, and when one notices them, fine distinctions of pitch then become
easy.

I'm not sure if they are partials in the midi ocarina voice as they are rather high
in pitch, up in the middle c octave kind of range, perhaps resonances in the speaker or room?

Might be quite hard to generate a 22 hz sine wave with no give-away
higher resonances.

Here is a little example midi clip. Uses ocarina voice, as prob. closest
approx to sinewave in midi.

http://members.nbci.com/tune_smithy/partials/22hz_44notes_fig.mid

It uses notes 0.5 hz apart in the range from 22 hz to 44 hz.

Ratios:
44/44 45/44 46/44 47/44 48/44 49/44 50/44 51/44 52/44 53/44 54/44 55/44
56/44 57/44 58/44 59/44 60/44 61/44 62/44 63/44 64/44 65/44 66/44 67/44 68/44
69/44 70/44 71/44 72/44 73/44 74/44 75/44 76/44 77/44 78/44 79/44 80/44 81/44
82/44 83/44 84/44 85/44 86/44 87/44 88/44

Can one tell which way it's going all the time? (uses a figuration that goes
up / down)

If so, is one using higher partials or higher pitched resonances in ones
speaker or room to tell, or the notes themselves.

Can you tell which way the lowest partials are going (imagining the higher
pitches as a separate tune)?

Here is your 22 note shruti in the same figuration:

http://members.nbci.com/tune_smithy/partials/22hz_22_notes_shruti_fig.mid

22/22 23/22 24/22 25/22 26/22 27/22 28/22 29/22 30/22 31/22 32/22 33/22 34/22
35/22 36/22 37/22 38/22 39/22 40/22 41/22 42/22 43/22 44/22

Here is your 22 hz shadja gram, again in the same fig.

http://members.nbci.com/tune_smithy/partials/22hz_shadja_gram_fig.mid

1/1 13/11 29/22 31/22 35/22 39/22 21/11 2/1

And here, for fun, is a little fractal tune using your /22 shadja gram
transposing up into higher pitches as well.

http://members.nbci.com/tune_smithy/partials/22hz_shruti_shadja_gram_1_min.mid
(27 Kb)

or if one wants to hear more:
http://members.nbci.com/tune_smithy/partials/22hz_shruti_shadja_gram_10_mins.zip
(17 Kb, unzips to 507 Kb)

http://members.nbci.com/tune_smithy/partials/22hz_shruti_shadja_gram.ts
(for fractal tune smithy)

Robert