Definitions of Pitch and Interval

Hello Monz, The definition of "Interval"
[see http://sonic-arts.org/dict/interval.htm]] goes like:

The size between two different pitches, or the section of the linearly-perceived pitch-continuum bounded by those two pitches.

That of "Pitch" [see http://sonic-arts.org/dict/pitch.htm]:

Our "vertical" perception of differences in the frequencies of musical tones, from lowest to highest over the audible continuum.

I am confused by the use of

[1] "linearly-perceived pitch-continuum" in the former, while the latter uses '"vertical" perception'. This is because the former definition uses the latter definition as its necesary part;

[2] And, why "linearly-perceived pitch-continuum', when we are using "audible continuum" in the definition of "Pitch" -- on which the definition of "Interval" depends? From whatever little I grasp,
"audible continuum" is perhaps more consistent and unambiguous.

My interest primarily arises from the relation those definitions have with "shruti".

Regards,
Haresh.

hi Haresh,

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

> Hello Monz, The definition of "Interval"
> [see http://sonic-arts.org/dict/interval.htm]] goes like:
>
> The size between two different pitches, or the section of
> the linearly-perceived pitch-continuum bounded by those
> two pitches.
>
> That of "Pitch" [see http://sonic-arts.org/dict/pitch.htm]:
>
> Our "vertical" perception of differences in the frequencies
> of musical tones, from lowest to highest over the audible
> continuum.
>
> I am confused by the use of
>
> [1] "linearly-perceived pitch-continuum" in the former,
> while the latter uses '"vertical" perception'. This is
> because the former definition uses the latter definition
> as its necesary part;
>
> [2] And, why "linearly-perceived pitch-continuum', when we
> are using "audible continuum" in the definition of "Pitch"
> -- on which the definition of "Interval" depends? From
> whatever little I grasp, "audible continuum" is perhaps
> more consistent and unambiguous.
>
> My interest primarily arises from the relation those
> definitions have with "shruti".

you're right to point out my inconsistent terminology
at this point. the definitions really should be re-worded thus:

------

interval:

The linearly-perceived size between two different pitches,
or the linearly-perceived section of the pitch-continuum
bounded by those two pitches.

pitch:

Our "vertical" linear perception of differences in the
frequencies of musical tones, from lowest to highest over
the audible continuum.

-------

the point that i am perhaps belaboring is that:

- our harmonic comprehension of relationships in the
pitch-continuum is exponential, in that it depends on
multiplication and division of the frequency-numbers, while ...

- our perception of "pitch-height" is linear in that it
depends on addition and subtraction of logarithmic frequency
values.

i'd like more feedback from you and others before i actually
change the Dictionary definitions.

-monz

>the point that i am perhaps belaboring is that:
>
>- our harmonic comprehension of relationships in the
>pitch-continuum is exponential, in that it depends on
>multiplication and division of the frequency-numbers, while ...
>
>- our perception of "pitch-height" is linear in that it
>depends on addition and subtraction of logarithmic frequency
>values.

There's no difference. Our perception of the pitch continuum
is logarithmic, not exponential. And adding or subtracting
logarithmic units is the same as multiplying or dividing
frequency numbers.

>i'd like more feedback from you and others before i actually
>change the Dictionary definitions.

>interval:
>
>The linearly-perceived size between two different pitches,
>or the linearly-perceived section of the pitch-continuum
>bounded by those two pitches.

Howabout just: "The distance between two pitches."? I don't
see what "linearly-perceived" adds, and the pitches don't
have to be different (a unison is an interval), and I don't
think we perceive sections of any continuum (in the sense
that we are aware of everything in between), just the size
of the section.

If you really want to make it longer, you might mention
something about units. Sometimes intervals are expressed
in frequency ratios, sometimes in cents, and sometimes in
scale degrees. An example of each should make it clear.

>pitch:
>
>Our "vertical" linear perception of differences in the
>frequencies of musical tones, from lowest to highest over
>the audible continuum.

Actually, pitch perception doesn't necessarily require
multiple frequencies or differences between them, as those
with absolute pitch can tell you. But even people without
absolute pitch experience pitch in isolated tones.

Howabout: "The sensation of frequency, usually described
as a 1-dimensional "height"."?

-Carl

hi Carl,

thanks for the feedback.

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> > the point that i am perhaps belaboring is that:
> >
> > - our harmonic comprehension of relationships in the
> > pitch-continuum is exponential, in that it depends on
> > multiplication and division of the frequency-numbers, while ...
> >
> > - our perception of "pitch-height" is linear in that it
> > depends on addition and subtraction of logarithmic frequency
> > values.
>
> There's no difference. Our perception of the pitch continuum
> is logarithmic, not exponential. And adding or subtracting
> logarithmic units is the same as multiplying or dividing
> frequency numbers.

you're right, but i guess i'm not making my points clear.

what i'm mainly trying to express is that we perceive
both pitch and interval-size logarithmically in a linear way,
but that our comprehension of harmonicity is based on
multiplicative properties of frequencies.

is that any better?

> > i'd like more feedback from you and others before i actually
> > change the Dictionary definitions.
>
> > interval:
> >
> > The linearly-perceived size between two different pitches,
> > or the linearly-perceived section of the pitch-continuum
> > bounded by those two pitches.
>
> Howabout just: "The distance between two pitches."? I don't
> see what "linearly-perceived" adds, and the pitches don't
> have to be different (a unison is an interval), and I don't
> think we perceive sections of any continuum (in the sense
> that we are aware of everything in between), just the size
> of the section.

yes, i didn't put enough thought into how i worded that
definition.

the point i was making here is that when musicians use
the term "interval", they can be referring to one of two
things: either 1) the two notes themselves, or 2) the
pitch-height distance between those two notes.

(and yes, in the case of a unison, the notes are the same
and the distance is zero, and that is indeed a valid interval.)

> If you really want to make it longer, you might mention
> something about units. Sometimes intervals are expressed
> in frequency ratios, sometimes in cents, and sometimes in
> scale degrees. An example of each should make it clear.

yes, i think that's a good idea. in fact, there's a *lot*
that i could add to the "interval" definition.

> > pitch:
> >
> > Our "vertical" linear perception of differences in the
> > frequencies of musical tones, from lowest to highest over
> > the audible continuum.
>
> Actually, pitch perception doesn't necessarily require
> multiple frequencies or differences between them, as those
> with absolute pitch can tell you. But even people without
> absolute pitch experience pitch in isolated tones.

you're right about these points too.

> Howabout: "The sensation of frequency, usually described
> as a 1-dimensional "height"."?

that's definitely a good definition, but a little *too*
succint, don't you think? ... let's see what others say.

-monz

>you're right, but i guess i'm not making my points clear.
>
>what i'm mainly trying to express is that we perceive
>both pitch and interval-size logarithmically in a linear way,
>but that our comprehension of harmonicity is based on
>multiplicative properties of frequencies.
>
>is that any better?

I'm afraid not. What's harmonicity?

>(and yes, in the case of a unison, the notes are the same
>and the distance is zero, and that is indeed a valid interval.)

So the word "different" shouldn't be in the definition.

>> Howabout: "The sensation of frequency, usually described
>> as a 1-dimensional "height"."?
>
>
>that's definitely a good definition, but a little *too*
>succint, don't you think? ... let's see what others say.

These are simple terms, so I think their definitions
should be short.

-Carl

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

> you're right to point out my inconsistent terminology
> at this point. the definitions really should be re-worded thus:
>
> ------
>
> interval:
>
> The linearly-perceived size between two different pitches,
> or the linearly-perceived section of the pitch-continuum
> bounded by those two pitches.
>
>
> pitch:
>
> Our "vertical" linear perception of differences in the
> frequencies of musical tones, from lowest to highest over
> the audible continuum.
>
> -------

monz, i think you're making things even more confusing here. why does
pitch have to involve "differences", when intervals are already
differences between pitches?

> the point that i am perhaps belaboring is that:
>
> - our harmonic comprehension of relationships in the
> pitch-continuum is exponential, in that it depends on
> multiplication and division of the frequency-numbers,
> while ...
>
> - our perception of "pitch-height" is linear in that it
> depends on addition and subtraction of logarithmic frequency
> values.

addition and subtraction of logarithmic frequency values is exactly
equivalent to multiplication and division of the frequency values
themselves. so you got a bit confused here trying to make this
distinction.