The master scale?

I took a sitar lesson last night which was quite an experience in and
of itself. Anyway, my teacher said that there are 22 discernable
notes between octaves in music. I'm not sure if this is an Indian
concept or if this is a universal rule.

This started me on a line of thought that I hadn't really considered
lately: There has to be a finite number of discernable pitches
between octaves; there are numerous frequencies that have no
perceptable audible difference from it's ajacent frequency.

Maybe it's slightly different to the trained ear and the amature ear.

So here's my question: Assuming that you have a fundemental tone and
it's octave, how many perceptable tones are between them to the ear
of the average perfessional musician?

In a message dated 4/4/03 11:55:43 AM Eastern Standard Time,
hand_of_kaal@hotmail.com writes:

> So here's my question: Assuming that you have a fundemental tone and
> it's octave, how many perceptable tones are between them to the ear
> of the average perfessional musician?

1200 equal divisions of the octave are discernible to the professional
musician thoroughly trained.

best, Johnny Reinhard

--- In tuning@yahoogroups.com, Afmmjr@a... wrote:
> In a message dated 4/4/03 11:55:43 AM Eastern Standard Time,
> hand_of_kaal@h... writes:
>
>
> > So here's my question: Assuming that you have a fundemental tone
and
> > it's octave, how many perceptable tones are between them to the
ear
> > of the average perfessional musician?
>
>
>
> 1200 equal divisions of the octave are discernible to the
professional
> musician thoroughly trained.
>
> best, Johnny Reinhard

i would qualify this by saying that few musicians have demonstrated
the ability to detect *melodic* differences of 1/1200 or even 5/1200
(=1/240) octave, while *anyone* can detect *harmonic* differences
even smaller than 1/1200 octave, at least for certain intervals, by
noting how the rate of beating changes and by listening to the
interval's combinational tones which generally move considerably
further in pitch.

In a message dated 4/4/03 3:31:55 PM Eastern Standard Time,
wallyesterpaulrus@yahoo.com writes:

> i would qualify this by saying that few musicians have demonstrated
> the ability to detect *melodic* differences of 1/1200 or even 5/1200
> (=1/240) octave, while *anyone* can detect *harmonic* differences
> even smaller than 1/1200 octave, at least for certain intervals, by
> noting how the rate of beating changes and by listening to the
> interval's combinational tones which generally move considerably
> further in pitch.

I would qualify further by saying that listening for beats is not necessarily
the same thing as hearing the distinctiveness of an interval. Beats are
everything BUT the interval resounding. Counting beats to determine
intervals is kind of like cheating.

Also, There are all kinds of professional musicians, to be sure. But
wouldn't you want to bet on the best of them? Stick to a cent and you won't
be disappointed. More musicians can hear this difference than cannot. They
just haven't studied the issue well enough. That's been my experience.

best, Johnny Reinhard
AFMM

--- In tuning@yahoogroups.com, Afmmjr@a... wrote:
> In a message dated 4/4/03 3:31:55 PM Eastern Standard Time,
> wallyesterpaulrus@y... writes:
>
>
> > i would qualify this by saying that few musicians have
demonstrated
> > the ability to detect *melodic* differences of 1/1200 or even
5/1200
> > (=1/240) octave, while *anyone* can detect *harmonic* differences
> > even smaller than 1/1200 octave, at least for certain intervals,
by
> > noting how the rate of beating changes and by listening to the
> > interval's combinational tones which generally move considerably
> > further in pitch.
>
>
> I would qualify further by saying that listening for beats is not
necessarily
> the same thing as hearing the distinctiveness of an interval.
Beats are
> everything BUT the interval resounding. Counting beats to
determine
> intervals is kind of like cheating.
>
> Also, There are all kinds of professional musicians, to be sure.
But
> wouldn't you want to bet on the best of them? Stick to a cent and
you won't
> be disappointed. More musicians can hear this difference than
cannot. They
> just haven't studied the issue well enough. That's been my
experience.
>
> best, Johnny Reinhard
> AFMM

when repeated listening tests on these lists have shown that everyone
who tried is unable to reliably distinguish pitches (melodically)
when they differ by less than 4 cents, what is the "hearing this
difference" that is supposedly present and the "study of the issue"
that is supposedly lacking?

In a message dated 4/4/03 5:14:32 PM Eastern Standard Time,
wallyesterpaulrus@yahoo.com writes:

> that is supposedly lacking?

Paul, come over for a lesson and you'll get the training necessary to
distinguish a single cent. It doesn't work over the internet as I have
stated several times before.

best, Johnny

> (=1/240) octave, while *anyone* can detect *harmonic* differences
> even smaller than 1/1200 octave, at least for certain intervals, by
> noting how the rate of beating changes and by listening to the
> interval's combinational tones which generally move considerably
> further in pitch.

Remember that beat rate is a function of frequency, as in Hertz rather
than logarithmic pitch. So small cents values can cause a considerable
difference at high frequencies-including the _overtones of low
pitches_ in some cases.

/Ö

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

> when repeated listening tests on these lists have shown that everyone
> who tried is unable to reliably distinguish pitches (melodically)
> when they differ by less than 4 cents, what is the "hearing this
> difference" that is supposedly present and the "study of the issue"
> that is supposedly lacking?

There you go. I vote for the 311-et as the Master Scale.

wallyesterpaulrus wrote :

> what is the "hearing this
> difference" that is supposedly present and the "study of the issue"
> that is supposedly lacking?

That reminds me of the story of the blind men and the elephant, tuning list version :
Once upon a time there was two frequencies, one of 1730 hz, the other of 1731hz.
A debate was raging about wether or not musicians could detect such small
difference of pitch.
Johnny pretended he could (but he said nothing about 1731-1732 and over,
which was strange), while Paul said :
� repeated listening tests have shown that everyone who tried is unable to reliably
distinguish pitches (melodically) that differ by less than 433 / 432 �, etc.
So, as they were having this debate, Jacques passed by and offered them to hear
the two pitches along with a third one of 1298 hz.
� You hear ? I was right said Johnny : 1730 and 1731 sound different. �
� You hear ? I was right said Paul : NOW they sound different. �
Jacques said nothing,
but he proposed to lower the bar next time, at least to 1728-1729, or any others,
which would be more fun to experiment with.

The issue is to gear things to the more accurate in pitch details, or to
average it out for those with less acuity. As a professional musician
interested in the further development of microtonal music, I hope the cent
can be treated as a threshold in pitch attention. Larger amounts do not take
into account the top musicians.

Elephants are a different story. They hear lower pitch than humans can.

best, Johnny

Hello Michael, the basic issue is this:
The number of discernable pitches in an octave is VERY large; but the number of such pitches which are musically useful is 22. The former is a matter of physiology; the latter, of aesthetics.

Regards,
Haresh.

--- In tuning@yahoogroups.com, "Michael" <hand_of_kaal@h...> wrote:
> I took a sitar lesson last night which was quite an experience in and
> of itself. Anyway, my teacher said that there are 22 discernable
> notes between octaves in music. I'm not sure if this is an Indian
> concept or if this is a universal rule.
>
> This started me on a line of thought that I hadn't really considered
> lately: There has to be a finite number of discernable pitches
> between octaves; there are numerous frequencies that have no
> perceptable audible difference from it's ajacent frequency.
>
> Maybe it's slightly different to the trained ear and the amature ear.
>
> So here's my question: Assuming that you have a fundemental tone and
> it's octave, how many perceptable tones are between them to the ear
> of the average perfessional musician?

--- In tuning@yahoogroups.com, "Haresh BAKSHI" <hareshbakshi@h...> wrote:
> Hello Michael, the basic issue is this:
> The number of discernable pitches in an octave is VERY large; but
the number of such pitches which are musically useful is 22. The
former is a matter of physiology; the latter, of aesthetics.

You use 22, and I'll use 311.

Hello, in the message #43253, you had mentioned:

**** I vote for the 311-et as the Master Scale. ****

Will you please tell me more about that? A comparasion will be very instructive for me.

Thanks and regards,
Haresh.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Haresh BAKSHI" <hareshbakshi@h...> wrote:
> > Hello Michael, the basic issue is this:
> > The number of discernable pitches in an octave is VERY large; but
> the number of such pitches which are musically useful is 22. The
> former is a matter of physiology; the latter, of aesthetics.
>
> You use 22, and I'll use 311.

--- In tuning@yahoogroups.com, "Haresh BAKSHI" <hareshbakshi@h...> wrote:
> Hello, in the message #43253, you had mentioned:
>
> **** I vote for the 311-et as the Master Scale. ****
>
> Will you please tell me more about that? A comparasion will be very
instructive for me.

Paul suggested we can't hear melodic distictions beyond the 300-et, so
I'm having fun with 311, which as far as I can tell I was the first to
notice, so I feel obligated.

The reason for calling it a "master scale" of sorts is that it
consistently handles everything up to the 41 limit, and is just above
Paul's cutoff.

Here are the errors in cents for all the primes to 41:

[.295803, -.461623, -.337160, .450546, .629896, -.775345, -.406907,
.664560, .647886, .945136, -.540180, -.766586]

These are all under Johnny's magic 1 cent figure, and while that is
not true for all of the 41-limit consonances, none are worse than 2
cents off.

In a message dated 4/6/03 9:35:35 PM Eastern Daylight Time, gwsmith@svpal.org
writes:

> These are all under Johnny's magic 1 cent figure,

Gene, please, it is the approach of my group, now entering its 23rd year. If
your system is just higher than "Paul's cutoff" (whatever that means) ((do
you want it known this way, Paul)), why not respect the performing groups
accuracy specializing in your specialty...microtonality. What I do is under
public display...and this year I did "Hearing a Cent" before an audience.
Try to imagine value in a more accurate system that is eminently experienced
by professional instrumentalists.

best, Johnny Reinhard
AFMM

>Paul suggested we can't hear melodic distictions beyond the 300-et, so
>I'm having fun with 311, which as far as I can tell I was the first to
>notice, so I feel obligated.

Paul Hahn noticed 311 some years back.

http://library.wustl.edu/~manynote/consist5.txt

-Carl

Hi there,

Just to mention something to consider here.

Suppose you can distinguish 8 cents but not 4 cents.

- here choose an appropriate interval depending on
what you can easily distinguish, e.g.
20 and 10, or in the case of Johnny, 1 and 0.5 perhaps,
or whatever.

Set up a scale of 4 cent steps, i.e. 480 steps to an
octave.

Now you can distinguish degree 0 from degree 2 and
1 from 3, but not 0 from 1 or 1 from 2.

But, you _can_ distinguish 1 from 2 now melodically
if you add enough notes to give it some extra
context because if you play, in scale degrees, say:

0 1 0 2 0 1 0 2
then the 1 and 2 can be distinguished from each other
in the trill because the 1 sounds the same as the 0
while the 2 doesn't, okay. But you could say - yes
but that is just because the 0 and 1 sound the same
and are in one pitch "category" while the 2 is in
another, But that won't work, because try

0 1 -1 0 2 0 1 -1 0 2 0 1 -1 0 2

then supposing you can hear steps of 2 units and not 1 unit steps,
you will hear the steps as:

0 1 -1 0 2 0 1 -1 0 2 0 1 -1 0 2
0 -2 0 2 -2 0 -2 0 2 -2 0 -2 0 2

In fact, should seem to go down twice for every step up
- as a kind of Esher endlessly descending staircase.

Here it is with a bit of rhythm to make the wider steps
more noticeable.
notes
0 1 : -1 0 : 2 :0 1 : -1 0 : 2
beats
2 1 : 2 1 : 3 2 1 : 2 1 : 3 :

I've done them for a wide variety of step sizes to hopefully
have one for nearly anyone whatever your cents resolution:

http://tunesmithy.netfirms.com/Escher_stair_case_melody_0.125_cents.mid
http://tunesmithy.netfirms.com/Escher_stair_case_melody_0.25_cents.mid
http://tunesmithy.netfirms.com/Escher_stair_case_melody_0.5_cents.mid
http://tunesmithy.netfirms.com/Escher_stair_case_melody_1_cents.mid
http://tunesmithy.netfirms.com/Escher_stair_case_melody_2_cents.mid
http://tunesmithy.netfirms.com/Escher_stair_case_melody_4_cents.mid
http://tunesmithy.netfirms.com/Escher_stair_case_melody_8_cents.mid
http://tunesmithy.netfirms.com/Escher_stair_case_melody_16_cents.mid

Of course your midi player also has to be up to the cents resolution,
and another thing - sometimes the timbre of the midi instrument
or a real instrunent may also vary a fair amount depending on the pitch played,
enabling one to distinguish notes one couldn't distinguish as pure sine
waves say, so I suppose these should be done as audio files really
with a suitable FM timbre that doesn't vary with pitch. Anyway here they are

One thing I've noticed - I can hear a difference between one clip
and the previous one well before the point at which the individual
notes begin to reach what I normally think as my usual pitch discrimination.
But - sounds rather like a difference in the rhythm or amplitude at that
point which I remember Kraig remarking on at one poitn.

thanks,

Robert

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:

> I'm having fun with 311, which as far as I can tell I was the first
to
> notice,

it came up as an ultra-consistent (41-limit) ET early on this list.

> so I feel obligated.
>
> The reason for calling it a "master scale" of sorts is that it
> consistently handles everything up to the 41 limit, and is just
above
> Paul's cutoff.

i said 1/1200 octave or even 5/1200 (1/240) octave . . . lots of
people have independently come up with the same rough figure,
including marc jones . . .

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >Paul suggested we can't hear melodic distictions beyond the 300-et, so
> >I'm having fun with 311, which as far as I can tell I was the first to
> >notice, so I feel obligated.
>
> Paul Hahn noticed 311 some years back.

Back in the sixties?

i've proposed 152-equal as a "universal tuning" -- universal enough
for most of my music anyway. mary beth ackerley psyched me out by
guessing that 153-equal would have some special significance for me
(presumably based on numerology, astrology, or sum'm) . . . her
spirits must have counted the octave!

--- In tuning@yahoogroups.com, "Haresh BAKSHI" <hareshbakshi@h...>
wrote:
> Hello Michael, the basic issue is this:
> The number of discernable pitches in an octave is VERY large; but
the number of such pitches which are musically useful is 22. The
former is a matter of physiology; the latter, of aesthetics.
>
> Regards,
> Haresh.

surely this must be a subjective judgment, haresh . . . the musicians
of so many musical cultures divide their octaves in so many different
ways . . . 22-tone scales, for example, tend to lack neutral thirds
relative to the tonic, yet such pitches are characteristic of much of
the musical world from egypt to thailand.

In a message dated 4/7/03 2:43:52 AM Eastern Daylight Time,
wallyesterpaulrus@yahoo.com writes:

> i said 1/1200 octave or even 5/1200 (1/240) octave . . . lots of
> people have independently come up with the same rough figure,
> including marc jones . . .
>
>
>

Maybe this is not a voting question. Rather, it requires acquiescence that
we should make a cultural decision, taken at the higher end of the music
makers.

best, Johnny Reinhard

--- In tuning@yahoogroups.com, "wallyesterpaulrus"

/tuning/topicId_43234.html#43277

<wallyesterpaulrus@y...> wrote:
> i've proposed 152-equal as a "universal tuning" -- universal enough
> for most of my music anyway. mary beth ackerley psyched me out by
> guessing that 153-equal would have some special significance for me
> (presumably based on numerology, astrology, or sum'm) . . . her
> spirits must have counted the octave!

***Hi Paul,

That's not too far from 144-tET that was "hashed out" with Dan
Stearns a couple of years ago, right?? Well, I think 72-tET is
enought for me: I can neither hear nor use many more steps than
that...

Joseph

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:

> ***Hi Paul,
>
> That's not too far from 144-tET that was "hashed out" with Dan
> Stearns a couple of years ago, right??

monz and dan discussed notating 144, with some "hashes" . . .

> Well, I think 72-tET is
> enought for me: I can neither hear nor use many more steps than
> that...

it's not a question of more steps -- you certainly don't have
anywhere near 72 tones on any of your instruments or in any of your
compositions -- but i think you might find that your shakespearean
music won't sound so good in 72-equal.

--- In tuning@yahoogroups.com, Afmmjr@a... wrote:

> Try to imagine value in a more accurate system that is eminently
experienced
> by professional instrumentalists.

1200 is more accurate than 311, but perhaps not to the extent you
think it is. In any case, why treat 1200 as a fact of nature and not
something Alexander Ellis came up with because it seemed convenient?

Here are the errors in cents for odd primes to 41 in 311 equal:

[.295803, -.461623, -.337160, .450546, .629896, -.775345, -.406907,
.664560, .647886, .945136, -.540180, -.766586]

Here are those same error in 1200-equal:

[.044999, -.313713, .174094, -.317943, .472340, .044591, .486984,
-.274347, .422806, -.35571e-1, -.344039, -.062406]

Clearly better, but not four times better as one might naively suppose.

Here are the errors in cents for 1171-equal:

[.009132, .022752, -.422832, .005712, -.220230, -.429363,
-.331120, -.093305, .311790, -.372890, -.276575, .314195]

It is better in all limits up to the 59-limit, and much better in the
5-limit.

In a message dated 4/8/03 3:44:57 AM Eastern Daylight Time, gwsmith@svpal.org
writes:

> 1200 is more accurate than 311, but perhaps not to the extent you
> think it is. In any case, why treat 1200 as a fact of nature and not
> something Alexander Ellis came up with because it seemed convenient?

Hi Gene,

First off, if you are doing electronics and you can get more accuracy than a
cent, especially for slow just intonation harmonies, by all means, please use
more accurate numbers.

Regarding the convenience of cents, they have become obvious through previous
posts. But they are real intervals for me, and my musicians. To deny this
is not possible. If they are not necessary for one's particular music is a
choice to be made. But for players that CAN hear them, they need to be
accounted for.

Today I want to compare the 31-tET scale with the extended quarter-comma
meantone of Vivaldi, and with Paul's just intonation thoughts. The
differences between them are measured in cents conveniently. And I can hear
these differences.

I don't have mathematical gifts. It is basically because I can hear and
produce cents that I argue for their proper place in measuring different
tunings and temperaments.

best, Johnny Reinhard

On Monday, April 7, 2003, at 10:25 , tuning@yahoogroups.com wrote:

> The master scale?

No such thing.

"The ear, Galilei argued, had no regard for systems. Only the octave itself could be critically determined. All other intervals were flexible, part of a continuum." - D. Barolsky

http://humanities.uchicago.edu/classes/zbikowski/week9sum.html

- Joel

--- In tuning@yahoogroups.com, "wallyesterpaulrus"

/tuning/topicId_43234.html#43288

<wallyesterpaulrus@y...> wrote:
> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
> wrote:
>
> > ***Hi Paul,
> >
> > That's not too far from 144-tET that was "hashed out" with Dan
> > Stearns a couple of years ago, right??
>
> monz and dan discussed notating 144, with some "hashes" . . .
>
> > Well, I think 72-tET is
> > enought for me: I can neither hear nor use many more steps than
> > that...
>
> it's not a question of more steps -- you certainly don't have
> anywhere near 72 tones on any of your instruments or in any of your
> compositions -- but i think you might find that your shakespearean
> music won't sound so good in 72-equal.

***Yes, I remember now the discussion of meantone emulation with 144-
tET...

JP

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"

> ***Yes, I remember now the discussion of meantone emulation with
144-
> tET...
>
> JP

it isn't very good -- you either have 12-equal or almost 2/5-comma
meantone, neither of which sound very good if you've bathed yourself
in nice meantone harmonies for a while (yup, i've been playing my 31-
tone guitar a lot lately)

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

> it isn't very good -- you either have 12-equal or almost 2/5-comma
> meantone, neither of which sound very good if you've bathed yourself
> in nice meantone harmonies for a while (yup, i've been playing my 31-
> tone guitar a lot lately)

311 can do 1/6-comma meantone, so Mozart is taken care of.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> 311 can do 1/6-comma meantone, so Mozart is taken care of.

And 612 can do 1/11-comma, (aka 12-equal), 2/11-comma, 3/11-comma ...