Sagittal notation article updated

Dear tuning revolutionaries,

George Secor and I have recently updated the Sagittal article at
http://dkeenan.com/sagittal/Sagittal.pdf

The significant changes are:

1. Mentioned and gave an example of the ASCII _shorthand_ (for 72-
ET).

2. Changed the recommended notations for the following equal
divisions of the octave: 10, 13, 14, 21, 43, 53, due to feedback
from users and readers, particularly Jacob Barton and Ozan Yarman.

3. Told readers about the free Sagittal truetype font and some of
the other things they can find on the Sagittal website. (For those
who might be reading a paper copy.)

4. Moved the description of the extreme superset, of symbols that
almost nobody except Gene Ward Smith will ever need ;-), to the very
end of the article, to try to mitigate its "freakout factor". Thanks
to Yahya Abdal-Aziz and Joseph Pehrson for prompting this.

5. Removed two symbols (determined to be unnecessary) from the
abovementioned superset.

[Note: There may be other changes to this superset in the wind. This
may unfortunately require changing the font mapping, but may allow
us to notate more tunings below 612-ET without using accents and may
allow us to include our version of the Tartini-Couper quartertone
symbols (see Figure 1). These are used in conjunction with Sagittal
symbols in Herman Miller's MOS-nominal notations for (multi-)linear
temperaments.]

6. Mentioned the use of right accents, if needed, to differentiate
13-limit pitches from the 7-limit ones that are only 0.4 cents away
(and other uses).

7. Added four more names to the acknowledgements, Yahya Abdal-Aziz,
Jacob Barton, Prent Rodgers, Ozan Yarman.

Thanks again to everyone who has contributed to Sagittal over the
years.

-- Dave Keenan

Cool!

-Carl

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>
> Dear tuning revolutionaries,
>
> George Secor and I have recently updated the Sagittal article at
> http://dkeenan.com/sagittal/Sagittal.pdf
>
> The significant changes are:
>
> 1. Mentioned and gave an example of the ASCII _shorthand_ (for 72-
> ET).
>
> 2. Changed the recommended notations for the following equal
> divisions of the octave: 10, 13, 14, 21, 43, 53, due to feedback
> from users and readers, particularly Jacob Barton and Ozan Yarman.
>
> 3. Told readers about the free Sagittal truetype font and some of
> the other things they can find on the Sagittal website. (For those
> who might be reading a paper copy.)
>
> 4. Moved the description of the extreme superset, of symbols that
> almost nobody except Gene Ward Smith will ever need ;-), to the
very
> end of the article, to try to mitigate its "freakout factor".
Thanks
> to Yahya Abdal-Aziz and Joseph Pehrson for prompting this.
>
> 5. Removed two symbols (determined to be unnecessary) from the
> abovementioned superset.
>
> [Note: There may be other changes to this superset in the wind.
This
> may unfortunately require changing the font mapping, but may allow
> us to notate more tunings below 612-ET without using accents and
may
> allow us to include our version of the Tartini-Couper quartertone
> symbols (see Figure 1). These are used in conjunction with Sagittal
> symbols in Herman Miller's MOS-nominal notations for (multi-)linear
> temperaments.]
>
> 6. Mentioned the use of right accents, if needed, to differentiate
> 13-limit pitches from the 7-limit ones that are only 0.4 cents away
> (and other uses).
>
> 7. Added four more names to the acknowledgements, Yahya Abdal-Aziz,
> Jacob Barton, Prent Rodgers, Ozan Yarman.
>
> Thanks again to everyone who has contributed to Sagittal over the
> years.
>
> -- Dave Keenan

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:

> 4. Moved the description of the extreme superset, of symbols that
> almost nobody except Gene Ward Smith will ever need ;-), to the very
> end of the article, to try to mitigate its "freakout factor". Thanks
> to Yahya Abdal-Aziz and Joseph Pehrson for prompting this.

At the moment I'm working with 224-et, which for some reason you seem
to have a better handle on that 99. For 99, what is the problem with
simply using the symbol set of 130-et? Take the 99-note MOS of 21/130,
notate it, and you have all notes of 99-et. I suppose it isn't
fifths-based enough for you.

> These are used in conjunction with Sagittal
> symbols in Herman Miller's MOS-nominal notations for (multi-)linear
> temperaments.]

I've been suggesting this approach--where is it documented?

On Sat, 18 Feb 2006, Dave Keenan wrote:
>
> Dear tuning revolutionaries,
>
> George Secor and I have recently updated the Sagittal article at
> http://dkeenan.com/sagittal/Sagittal.pdf
>
> The significant changes are:
>
> 1. Mentioned and gave an example of the ASCII _shorthand_ (for 72-
> ET).
>
> 2. Changed the recommended notations for the following equal
> divisions of the octave: 10, 13, 14, 21, 43, 53, due to feedback
> from users and readers, particularly Jacob Barton and Ozan Yarman.
>
> 3. Told readers about the free Sagittal truetype font and some of
> the other things they can find on the Sagittal website. (For those
> who might be reading a paper copy.)
>
> 4. Moved the description of the extreme superset, of symbols that
> almost nobody except Gene Ward Smith will ever need ;-), to the very
> end of the article, to try to mitigate its "freakout factor". Thanks
> to Yahya Abdal-Aziz and Joseph Pehrson for prompting this.
>
> 5. Removed two symbols (determined to be unnecessary) from the
> abovementioned superset.
>
> [Note: There may be other changes to this superset in the wind. This
> may unfortunately require changing the font mapping, but may allow
> us to notate more tunings below 612-ET without using accents and may
> allow us to include our version of the Tartini-Couper quartertone
> symbols (see Figure 1). These are used in conjunction with Sagittal
> symbols in Herman Miller's MOS-nominal notations for (multi-)linear
> temperaments.]
>
> 6. Mentioned the use of right accents, if needed, to differentiate
> 13-limit pitches from the 7-limit ones that are only 0.4 cents away
> (and other uses).
>
> 7. Added four more names to the acknowledgements, Yahya Abdal-Aziz,
> Jacob Barton, Prent Rodgers, Ozan Yarman.
>
> Thanks again to everyone who has contributed to Sagittal over the
> years.

Dave & George,

Well done, guys! This is a significant revision and goes
a long way towards making the Sagittal notation more
accessible. Thanks once again for all the effort and
thought you've put into devising practical ways to
notate truly micro differences well.

Regards,
Yahya

--
No virus found in this outgoing message.
Checked by AVG Free Edition.
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Gene Ward Smith wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
> >>These are used in conjunction with Sagittal >>symbols in Herman Miller's MOS-nominal notations for (multi-)linear >>temperaments.]
> > > I've been suggesting this approach--where is it documented?

On the tuning-math list from around a year ago: from discussion in the thread "Suggestion for a linear temperament notation system".

/tuning-math/message/11629

Specific recommendations for some common 5-limit and 7-limit temperaments are summed up here:

/tuning-math/message/11673
/tuning-math/message/11676

> On the tuning-math list from around a year ago: from discussion
> in the thread "Suggestion for a linear temperament notation system".
>
> /tuning-math/message/11629
>
> Specific recommendations for some common 5-limit and 7-limit
> temperaments are summed up here:
>
> /tuning-math/message/11673
> /tuning-math/message/11676

Hi Herman,

It looks to me like that deserves to be collected on a web
page somewhere... (hint, hint :)

-Carl

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
> Gene Ward Smith wrote:
> > I've been suggesting this approach--where is it documented?
>
> On the tuning-math list from around a year ago: from discussion in
> the thread "Suggestion for a linear temperament notation system".
>
> /tuning-math/message/11629

Thanks Herman,

I don't mean to be immodest but I feel I should point out that at
least one important branch of that discussion thread (tree) seems to
have become disconnected from the rest. This branch starts at
/tuning-math/message/11654

This thread is very long. It would be great if you would edit it
into an article that just gives the final resulting system. I'd be
happy to put it, or a link to it, on the Sagittal site.

-- Dave Keenan

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
>
> /tuning-math/message/11673
> /tuning-math/message/11676

What's a pseudo-nominal? Are you proposing to notate the nominals
themselves with Sagittal?

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, Herman Miller <hmiller@> wrote:
> >
> > /tuning-math/message/11673
> > /tuning-math/message/11676
>
> What's a pseudo-nominal?

I think we concluded later that "compound nominal" was a better
term. It means a nominal that consists of more than one character or
glyph.

> Are you proposing to notate the nominals
> themselves with Sagittal?

No. The nominals are notated as the nearest pitches of 24-ET using
the letters A thru G (or corresponding staff positions) and the
Tartini-Couper quartertone symbols (including conventional flats and
sharps).

To make it clear that these are conceptually grouped with the
letter, and not with any accidentals (which _are_ sagittal), we put
them on the "wrong" side (i.e. to the left of the letter), e.g. #F
and pronounce them like "sharp F".

You also have the option of using non-compound nominals where 24-ET
is notated OHAPWIBJCRXKDSYLETFUZNGV, which looks completely random
until you see it laid out this way, and look down the columns.

O H A P
W I B
. J C R X
. K D S
Y L E T
. . F U Z
. N G V O

The corresponding compound nominals are:

bA vA A ^A
bB vB B
. vC C ^C #C
. vD D ^D
bE vE E ^E
. . F ^F #F
. vG G ^G #G

Where v and ^ (when placed to the left of the letter) stand for the
Tartini-Couper semiflat and semisharp, and "vA" is
pronounced "semiflat A".

-- Dave Keenan

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:

> No. The nominals are notated as the nearest pitches of 24-ET using
> the letters A thru G (or corresponding staff positions) and the
> Tartini-Couper quartertone symbols (including conventional flats and
> sharps).

Sounds convenient when you have halves of fifths or fourths as
generators. And you could notate all of Shrutar[24] with just
nominals, I guess.

> You also have the option of using non-compound nominals where 24-ET
> is notated OHAPWIBJCRXKDSYLETFUZNGV, which looks completely random
> until you see it laid out this way, and look down the columns.

Fairly grisly, but I'll keep this in mind. My proposal to notate 99
via hemififths could now go FHCLGID for nominals, so we'd have H in
place of A, L in place of E and I in place of B.

Oops!

I wrote:
> Where v and ^ (when placed to the left of the letter) stand for the
> Tartini-Couper semiflat and semisharp, and "vA" is
> pronounced "semiflat A".

"vA" is pronounced "down-A" and "^A" is pronounced "up-A". But don't
forget that when you're not limited to ASCII you don't use up and down
arrows for these, but the Tartini half sharp and Couper backwards flat
symbols.

-- Dave Keenan

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@> wrote:
> > You also have the option of using non-compound nominals where 24-
> > ET is notated OHAPWIBJCRXKDSYLETFUZNGV, which looks completely
> > random until you see it laid out this way, and look down the
> > columns.
>
> Fairly grisly, but I'll keep this in mind. My proposal to notate 99
> via hemififths could now go FHCLGID for nominals, so we'd have H in
> place of A, L in place of E and I in place of B.

Right. Except the default is that D should be at the center of the
chain (unless there's a good reason for it not to be). This allows
the system to automatically generate the conventional notation for
meantone.

I don't think Herman and I ever agreed on the best thing to do when
there is an even number in the chain. We agreed that D should be one
of the two middle ones and that the rule should favour #G over bA
(which are both "O") in the case of a 12 note chain of fourths.

-- Dave Keenan

> On the tuning-math list from around a year ago: from discussion
> in the thread "Suggestion for a linear temperament notation system".
>
> /tuning-math/message/11629
>
> Specific recommendations for some common 5-limit and 7-limit
> temperaments are summed up here:
>
> /tuning-math/message/11673
> /tuning-math/message/11676

Hi Herman,

It looks to me like that deserves to be collected on a web
page somewhere... (hint, hint :)

-Carl

Dave Keenan wrote:
> I don't think Herman and I ever agreed on the best thing to do when > there is an even number in the chain. We agreed that D should be one > of the two middle ones and that the rule should favour #G over bA > (which are both "O") in the case of a 12 note chain of fourths.

I've been including both options in my notes: for instance, the sensipent notation uses 8 nominals:

(vA) ^C F ^A D vG B vE (^G)

where optionally either vA or ^G is included (but not both). But in order to be consistent with the #G notation, the simplest rule is to always pick the one on the left.

(#G) #C #F B E A D G C F bB bE (bA)

An alternative rule would be to always pick sharps over flats (or semisharps over semiflats). In that case, the sensipent notation would use ^G instead of vA. But it's easy enough to include both as options and let the composer decide which one is preferable.

Carl Lumma wrote:
>>On the tuning-math list from around a year ago: from discussion
>>in the thread "Suggestion for a linear temperament notation system".
>>
>>/tuning-math/message/11629
>>
>>Specific recommendations for some common 5-limit and 7-limit >>temperaments are summed up here:
>>
>>/tuning-math/message/11673
>>/tuning-math/message/11676
> > > Hi Herman,
> > It looks to me like that deserves to be collected on a web
> page somewhere... (hint, hint :)

I agree that would be a nice thing to have. I suppose I should start writing one....

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>
> Oops!
>
> I wrote:
> > Where v and ^ (when placed to the left of the letter) stand for the
> > Tartini-Couper semiflat and semisharp, and "vA" is
> > pronounced "semiflat A".
>
> "vA" is pronounced "down-A" and "^A" is pronounced "up-A". But don't
> forget that when you're not limited to ASCII you don't use up and down
> arrows for these, but the Tartini half sharp and Couper backwards flat
> symbols.
>
> -- Dave Keenan
>
If you're not limited to ASCII, you can rotate letters, etc., to obtain single symbols for the nominals. Anyway, since in notated music, the nominals are just the lines and spaces on the staff, what to call them is a whole different order of question than the questions of visible notation which Sagittal seeks to address. Still, I'm not too crazy about these "pseudo-accidentals", since they seem to imply a chromatic unison relationship between different nominals, where in fact none exists.

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
> I've been including both options in my notes: for instance, the
> sensipent notation uses 8 nominals:
>
> (vA) ^C F ^A D vG B vE (^G)
>
> where optionally either vA or ^G is included (but not both). But
in
> order to be consistent with the #G notation, the simplest rule is
to
> always pick the one on the left.
>
> (#G) #C #F B E A D G C F bB bE (bA)
>
> An alternative rule would be to always pick sharps over flats (or
> semisharps over semiflats). In that case, the sensipent notation
would
> use ^G instead of vA. But it's easy enough to include both as
options
> and let the composer decide which one is preferable.

Sounds like a good idea.

-- Dave Keenan

wallyesterpaulrus wrote:
> If you're not limited to ASCII, you can rotate letters, etc., to obtain single symbols for the nominals. Anyway, since in notated music, the nominals are just the lines and spaces on the staff, what to call them is a whole different order of question than the questions of visible notation which Sagittal seeks to address. Still, I'm not too crazy about these "pseudo-accidentals", since they seem to imply a chromatic unison relationship between different nominals, where in fact none exists.

Dave Keenan proposed a naming convention using letters from the Greek and Hebrew alphabets; I made a suggestion that extends the traditional "do re mi" solfa names for the notes to include names for all 24 pitches. (The problem with the Hebrew letters is that they can activate the bidirectional text algorithm in systems that support right-to-left text, so a sequence of Hebrew letters may appear in a different order from one text editor to another. But if that problem can be overcome, that convention would be useful in cases where the semisharp and semiflat symbols are unavailable, such as web pages.)

I also have issues with the compound nominals, such as the fact that you can have a "semiflat" symbol used in conjunction with a Sagittal up-arrow of some kind or other, and I've considered alternative notations (such as special staffs for each different kind of temperament, or distinct shapes of note heads). I have a sample of notation that I intended for a page on lemba temperament, which uses a specialized 7-line staff (with unequal line spacing):

http://www.io.com/~hmiller/png/lemba-notation.png

But I found that this system was hard to read in practice: it doesn't have any familiar landmarks. (Note that this was done before I decided to use the sagittal arrows; I was still using sharp and flat symbols for the accidentals.) Probably after using it for a while it would become familiar, but the same process of familiarization would have to occur for each temperament. Still, the configuration of the staff would make it clear that you're not dealing with traditional notation, and give you a rough idea of the pitches.

Herman Miller wrote:
> wallyesterpaulrus wrote:
> >>If you're not limited to ASCII, you can rotate letters, etc., to obtain single symbols for the nominals. Anyway, since in notated music, the nominals are just the lines and spaces on the staff, what to call them is a whole different order of question than the questions of visible notation which Sagittal seeks to address. Still, I'm not too crazy about these "pseudo-accidentals", since they seem to imply a chromatic unison relationship between different nominals, where in fact none exists.
> > > Dave Keenan proposed a naming convention using letters from the Greek > and Hebrew alphabets; I made a suggestion that extends the traditional > "do re mi" solfa names for the notes to include names for all 24 > pitches. (The problem with the Hebrew letters is that they can activate > the bidirectional text algorithm in systems that support right-to-left > text, so a sequence of Hebrew letters may appear in a different order > from one text editor to another. But if that problem can be overcome, > that convention would be useful in cases where the semisharp and > semiflat symbols are unavailable, such as web pages.)

24 you say? 24? Well, you can use the 24 directions. See

http://en.wikipedia.org/wiki/Earthly_Branches

about 2/3 of the way down. It's a big table, you can't miss it. All common symbols and lelft-right ordering.

Graham

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@...> wrote:
> If you're not limited to ASCII, you can rotate letters, etc., to
obtain single symbols for the nominals.

Sure.

> Anyway, since in notated music, the nominals are just the lines
and spaces on the staff, what to call them is a whole different
order of question than the questions of visible notation which
Sagittal seeks to address.

Yes.

> Still, I'm not too crazy about these "pseudo-accidentals", since
they seem to imply a chromatic unison relationship between different
nominals, where in fact none exists.

Yes, pseudo-accidentals used to create compound-nominals. The only
place where there remains a chromatic unison between different
compound nominals is between #G and bA. Would you be happier if we
just eliminated bA altogether, so there is a strict set of 24 unique
compound nominals?

-- Dave Keenan

Woops! I think i may have misunderstood you Paul. What's a chromatic
unison? Examples of the problem in the case of the 24-ET compound
nominals?

- Dave Keenan

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>
> Dear tuning revolutionaries,
>
> George Secor and I have recently updated the Sagittal article at
> http://dkeenan.com/sagittal/Sagittal.pdf
>

***Congrats to Dave Keenan and George Secor. It seems that moving
the "Spartan Symbol Set" to earlier in the article made a lot of
sense, leaving the "Engineered Evolution" with all its "twists and
turns" for the conclusion. For me, personally, I am still only
using 6 Sagittal symbols from the Sagittal-Wilson notation for
Blackjack. (Obviously quarter tones, sixth-tones and twelfth-tones)
A recent electronic piece had cues transcribed in this notation for
live percussionists. Similarly, I'm in the middle of a piece for
piano and Blackjack electronic accompaniment cues in Sagittal-Wilson
notation. I enjoy using Blackjack for combination with live
instruments and even with 12-equal when it is necessary (such
as the piano) since I have at least the pitches C, G, D and A in
common! (And, of course, other "quasi just" intervals from
corresponding triads). I plan to do some more experimental work with
other tuning systems, but they may be entirely electronic with no
notation other than that of graphic sequencer notation, if I ever
wanted to project that... since live performers may not be involved.

J. Pehrson

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>
> Woops! I think i may have misunderstood you Paul. What's a chromatic
> unison?

A typical example is the classical augmented unison, the interval from C to C-sharp, for instance.

> Examples of the problem in the case of the 24-ET compound
> nominals?
>
> - Dave Keenan

There seems to be a relationship between compound nominals which share the same letter, but there isn't.

Dave, I'm glad to contribute however little.

Cordially,
Ozan

----- Original Message -----
From: "Dave Keenan" <d.keenan@bigpond.net.au>
To: <tuning@yahoogroups.com>
Sent: 18 �ubat 2006 Cumartesi 9:06
Subject: [tuning] Sagittal notation article updated

> Dear tuning revolutionaries,
>
> George Secor and I have recently updated the Sagittal article at
> http://dkeenan.com/sagittal/Sagittal.pdf
>
> The significant changes are:
>
> 1. Mentioned and gave an example of the ASCII _shorthand_ (for 72-
> ET).
>
> 2. Changed the recommended notations for the following equal
> divisions of the octave: 10, 13, 14, 21, 43, 53, due to feedback
> from users and readers, particularly Jacob Barton and Ozan Yarman.
>
> 3. Told readers about the free Sagittal truetype font and some of
> the other things they can find on the Sagittal website. (For those
> who might be reading a paper copy.)
>
> 4. Moved the description of the extreme superset, of symbols that
> almost nobody except Gene Ward Smith will ever need ;-), to the very
> end of the article, to try to mitigate its "freakout factor". Thanks
> to Yahya Abdal-Aziz and Joseph Pehrson for prompting this.
>
> 5. Removed two symbols (determined to be unnecessary) from the
> abovementioned superset.
>
> [Note: There may be other changes to this superset in the wind. This
> may unfortunately require changing the font mapping, but may allow
> us to notate more tunings below 612-ET without using accents and may
> allow us to include our version of the Tartini-Couper quartertone
> symbols (see Figure 1). These are used in conjunction with Sagittal
> symbols in Herman Miller's MOS-nominal notations for (multi-)linear
> temperaments.]
>
> 6. Mentioned the use of right accents, if needed, to differentiate
> 13-limit pitches from the 7-limit ones that are only 0.4 cents away
> (and other uses).
>
> 7. Added four more names to the acknowledgements, Yahya Abdal-Aziz,
> Jacob Barton, Prent Rodgers, Ozan Yarman.
>
> Thanks again to everyone who has contributed to Sagittal over the
> years.
>
> -- Dave Keenan
>
>

wallyesterpaulrus escreveu:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
> >> Woops! I think i may have misunderstood you Paul. What's a
>> chromatic unison?
> > > A typical example is the classical augmented unison, the interval
> from C to C-sharp, for instance.

Paul Hindemith has suggested the term `augmented first'.

--
'-------------------------------------------------------------------.
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*N�o deixe seu voto sumir! http://www.votoseguro.org/
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== THE WAR IN IRAQ COSTS ==
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.-------------------------------------------------------------------'
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_______________________________________________________
Yahoo! Acesso Gr�tis - Internet r�pida e gr�tis. Instale o discador agora!
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Hudson Lacerda wrote:
> wallyesterpaulrus escreveu:
>> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>>
>>> Woops! I think i may have misunderstood you Paul. What's a
>>> chromatic unison?
>>
>> A typical example is the classical augmented unison, the interval
>> from C to C-sharp, for instance.
> > Paul Hindemith has suggested the term `augmented first'.
> Or, actually, "augmented prime", which should be recognizable in musical circles of the entire Western world. I was also thrown off by the "unison", which in my opinion can be impure, sloppy, or detuned, but is always at least meant to consist of two tones identical in theory.

klaus

Thanks for the correction: *augmented prime*.

klaus schmirler escreveu:
> Hudson Lacerda wrote:
[...]
>>Paul Hindemith has suggested the term `augmented first'.
>>
> > > Or, actually, "augmented prime", which should be recognizable in musical > circles of the entire Western world. I was also thrown off by the > "unison", which in my opinion can be impure, sloppy, or detuned, but is > always at least meant to consist of two tones identical in theory.
> > klaus

--
'-------------------------------------------------------------------.
Hudson Lacerda <http://geocities.yahoo.com.br/hfmlacerda/>
*N�o deixe seu voto sumir! http://www.votoseguro.org/
*Ap�ie o Manifesto: http://www.votoseguro.com/alertaprofessores/

== THE WAR IN IRAQ COSTS ==
http://nationalpriorities.org/index.php?option=com_wrapper&Itemid=182
.-------------------------------------------------------------------'
--

_______________________________________________________
Yahoo! Acesso Gr�tis - Internet r�pida e gr�tis. Instale o discador agora!
http://br.acesso.yahoo.com

--- In tuning@yahoogroups.com, klaus schmirler <KSchmir@...> wrote:
>
> Hudson Lacerda wrote:
> > wallyesterpaulrus escreveu:
> >> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@> wrote:
> >>
> >>> Woops! I think i may have misunderstood you Paul. What's a
> >>> chromatic unison?
> >>
> >> A typical example is the classical augmented unison, the interval
> >> from C to C-sharp, for instance.
> >
> > Paul Hindemith has suggested the term `augmented first'.
> >
>
> Or, actually, "augmented prime", which should be recognizable in
musical
> circles of the entire Western world. I was also thrown off by the
> "unison", which in my opinion can be impure, sloppy, or detuned,
but is
> always at least meant to consist of two tones identical in theory.
>
> klaus

I don't agree, any more than "octave" always means "perfect octave"
and never "augmented octave" -- in truth, both are found.

wallyesterpaulrus wrote:

> I don't agree, any more than "octave" always means "perfect octave"
> and never "augmented octave" -- in truth, both are found.

Looking it up, it seems that unison in English is used at least as often
as an interval name as prime, if not more so. But even then, my New Oxford Companion to Music (PA, 1983) defines "unison" as "the interval
between the same two notes" and "prime" as "the interval formed by two
notes written on the same line or space, e.g. F and F#". Besides, prime
is derived from an ordinal like rest of the interval names, so it
deserves the same treatment as seconds, octaves, and the non-latin ones.

Nevertheless, what I corrected (not your usage, but Hudson's choice of
words) may have been totally correct. I have never read Hindemith in
English; all I know is that he stuck to the traditional interval names
in German and that Hudson may have read a Portuguese translation and
wanted to convey "prima" (o primeira? Can't tell from my chico Aurélio).

klaus

It is meaningless to say, in my opinion, that an interval of a unison can
exist when unison itself is none other than a distance of 0 units between a
frequency of an instrument and another performing simultaneously. In other
words, it is the sound of the same pitch with octave equivalances taken into
consideration.

----- Original Message -----
From: "klaus schmirler" <KSchmir@online.de>
To: <tuning@yahoogroups.com>
Sent: 23 �ubat 2006 Per�embe 2:57
Subject: Re: [tuning] Re: Sagittal notation article updated

wallyesterpaulrus wrote:

> I don't agree, any more than "octave" always means "perfect octave"
> and never "augmented octave" -- in truth, both are found.

Looking it up, it seems that unison in English is used at least as often
as an interval name as prime, if not more so. But even then, my New
Oxford Companion to Music (PA, 1983) defines "unison" as "the interval
between the same two notes" and "prime" as "the interval formed by two
notes written on the same line or space, e.g. F and F#". Besides, prime
is derived from an ordinal like rest of the interval names, so it
deserves the same treatment as seconds, octaves, and the non-latin ones.

Nevertheless, what I corrected (not your usage, but Hudson's choice of
words) may have been totally correct. I have never read Hindemith in
English; all I know is that he stuck to the traditional interval names
in German and that Hudson may have read a Portuguese translation and
wanted to convey "prima" (o primeira? Can't tell from my chico Aur�lio).

klaus

Hi Oz,

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> It is meaningless to say, in my opinion, that an interval
> of a unison can exist when unison itself is none other than
> a distance of 0 units between a frequency of an instrument
> and another performing simultaneously. In other words,
> it is the sound of the same pitch with octave equivalances
> taken into consideration.

Indeed, the name "unison" is Latin for "one sound".

I see nothing wrong with considering "unison" to
be an interval like all others. It's akin to the
use of zero in math.

However, note that some instruments are capable of
producing unisons by themself.

For example, on a guitar:

* it's a trivial matter to play a unison interval
(i.e., dyad) by playing one open string and fretting
the next lowest string at the same pitch;

* it's also very easy to play one string open and both
of the next adjacent lower strings fretted to a unison with
that, so there's a "unison triad";

* i can even contrive to put the guitar in my lap and
use three fingers on adjacent strings with my hand over
the fretboard, with one open string, to play a
"unison tetrad" ... but i do have long fingers :) .

In terms of theory, there's probably not much use
for any of this -- but it does become an important
aspect of instrumental technique on instruments like
this, and that's something that can be exploited by
a composer or performer too.

-monz
http://tonalsoft.com
Tonescape microtonal music software

monz wrote:

> Indeed, the name "unison" is Latin for "one sound".
> > I see nothing wrong with considering "unison" to
> be an interval like all others. It's akin to the > use of zero in math.
> > > However, note that some instruments are capable of
> producing unisons by themself. I guess none of us foreigners take issue with unison in the context of a musical setting (where the unison might as well be an octave). What we found funny was its use as an interval name, where most languages would use some equivalent of latin "prima", "first (note)".

Getting up to look for that smaller music dictionary ...

The concise Oxford I have has unison as a voice leading device without mentioning the possibility of octaves. No prime at all. The list of intervals begins with the second. But the Oxford Companion had the additional unison definition of "same sound", wheres primes were "written on the same line", i.e. sharing the same nominal. Exactly as in the non-English-speaking Western world. But then, the list of intervals in the same book (well, other volume) contradicts this and goes "unison, second, third, ...," mixing the "same sound" with all the intervals that can be diminished and augmented.

So I have learned and will forthwith humbly suffer that in the old Empire, people are not very consistent in naming the first interval, but I won't never ever use this myself.

klaus

klaus schmirler escreveu:
[...]
> The concise Oxford I have has unison as a voice leading device without > mentioning the possibility of octaves. No prime at all. The list of > intervals begins with the second. But the Oxford Companion had the > additional unison definition of "same sound", wheres primes were > "written on the same line", i.e. sharing the same nominal. Exactly as in > the non-English-speaking Western world. But then, the list of intervals > in the same book (well, other volume) contradicts this and goes "unison, > second, third, ...," mixing the "same sound" with all the intervals that > can be diminished and augmented.
> > So I have learned and will forthwith humbly suffer that in the old > Empire, people are not very consistent in naming the first interval [...]

No way to be consistent, because the pitch naming is not trully consistent, except for the diatonic intervals. (Besides, it is very strange taking in account the reference point for an interval. Interval 0 is already 1 unit length -- prime...)

Now, between `chromatic unisson' (or `augmented unisson' or so) and `augmented prime', I choose `augmented prime', and I use 'unisson' only for `the same'. Optimal? Not of course.

Regards,

--
'-------------------------------------------------------------------.
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klaus schmirler wrote:

> Getting up to look for that smaller music dictionary ...
> > The concise Oxford I have has unison as a voice leading device without > mentioning the possibility of octaves. No prime at all. The list of > intervals begins with the second. But the Oxford Companion had the > additional unison definition of "same sound", wheres primes were > "written on the same line", i.e. sharing the same nominal. Exactly as in > the non-English-speaking Western world. But then, the list of intervals > in the same book (well, other volume) contradicts this and goes "unison, > second, third, ...," mixing the "same sound" with all the intervals that > can be diminished and augmented.

I looked this up in my Collins Encyclopedia of Music a few weeks ago -- I don't have it to hand now. But the entry for "unison" says the same sound and the entry for "augmented" gives a list of intervals that can be augmented that doesn't include the unison. However, there's an accompanying table that does include the augmented unison. Hence, inconsistency abounds.

My other essential reference, "The Right Way to Read Music" (hardly authoritative, but an indication of what's being taught to children) uses "chromatic semitone" throughout for this interval.

Graham

Hi klaus,

--- In tuning@yahoogroups.com, klaus schmirler <KSchmir@...> wrote:

> I guess none of us foreigners take issue with unison
> in the context of a musical setting (where the unison
> might as well be an octave). What we found funny was
> its use as an interval name, where most languages would
> use some equivalent of latin "prima", "first (note)".

Oh yes, i had forgotten about the "augmented prime"
vs. "augmented unison" business ... i had intended to
post something about that before.

I find it fascinating that we use the modern vernacular
languages (and their equivalent numeral abbreviations)
for all intervals 2nd thru 7th, but that we retain the
old Latin names for 1st and 8th, which are "prime" and
"octave" respectively. I always took that to be an
implicit recognition of the importance of those two
intervals (and i'm considering "prime" to be an interval).

-monz
http://tonalsoft.com
Tonescape microtonal music software

Hi Graham,

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:

> I looked this up in my Collins Encyclopedia of Music
> a few weeks ago -- I don't have it to hand now. But
> the entry for "unison" says the same sound and the
> entry for "augmented" gives a list of intervals that
> can be augmented that doesn't include the unison.
> However, there's an accompanying table that does
> include the augmented unison. Hence, inconsistency
> abounds.
>
> My other essential reference, "The Right Way to
> Read Music" (hardly authoritative, but an indication
> of what's being taught to children) uses
> "chromatic semitone" throughout for this interval.

"Augmented unison", "augmented prime", and "chromatic
semitone" are all basically synonymous. Here's how i
see it:

* "unison" and "prime" are pretty much synonymous to
begin with;

* "augmented prime" places the interval into the
hierarchy of the complete set of diatonic/chromatic
intervals;

* "chromatic semitone" puts more emphasis on the
fact of its being one of the basic step-sizes of
diatonic/chromatic music -- the others being the
"diatonic semitone" and the "whole tone".

-monz
http://tonalsoft.com
Tonescape microtonal music software

Hi Hudson,

--- In tuning@yahoogroups.com, Hudson Lacerda <hfmlacerda@...> wrote:

> No way to be consistent, because the pitch naming is
> not trully consistent, except for the diatonic intervals.
> (Besides, it is very strange taking in account the
> reference point for an interval. Interval 0 is already
> 1 unit length -- prime...)

Yes, this is one of those unfortunate circumstances. We've
discussed it here before: the discrepancy stems from the
fact that the interval names "prime, 2nd, 3rd, 4th,..." etc.
date from before the recognition of the concept of zero.
So musicians and music-theorists just naturally began
counting the intervals with "one".

It's difficult for us today to realize what human perception
of the natural world is like without zero, because we're
so used to it. But it took a long time for recognition to
occur, well into the second half of the 1st millenium AD.

-monz
http://tonalsoft.com
Tonescape microtonal music software

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

> "Augmented unison", "augmented prime", and "chromatic
> semitone" are all basically synonymous. Here's how i
> see it:
>
> * "unison" and "prime" are pretty much synonymous to
> begin with;
>
> * "augmented prime" places the interval into the
> hierarchy of the complete set of diatonic/chromatic
> intervals;
>
> * "chromatic semitone" puts more emphasis on the
> fact of its being one of the basic step-sizes of
> diatonic/chromatic music -- the others being the
> "diatonic semitone" and the "whole tone".

http://tonalsoft.com/enc/c/chromatic-semitone.aspx

-monz
http://tonalsoft.com
Tonescape microtonal music software

monz,

----- Original Message -----
From: "monz" <monz@tonalsoft.com>
To: <tuning@yahoogroups.com>
Sent: 24 �ubat 2006 Cuma 10:15
Subject: [tuning] unison as an interval (was: Sagittal notation article
updated)

> Hi Oz,
>
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > It is meaningless to say, in my opinion, that an interval
> > of a unison can exist when unison itself is none other than
> > a distance of 0 units between a frequency of an instrument
> > and another performing simultaneously. In other words,
> > it is the sound of the same pitch with octave equivalances
> > taken into consideration.
>
>
> Indeed, the name "unison" is Latin for "one sound".
>

Clearly so.

> I see nothing wrong with considering "unison" to
> be an interval like all others. It's akin to the
> use of zero in math.
>

Now there is a serious problem with unison in the mathematical sense.
Consider a clock and another running at twice the pace compared to the
former. There will be a moment when the two clocks will be synchronized in
an instant of time. Since `interval` according to Merriam-Webster's
Collegiate Dictionary is `a space of time between events or states` in this
context, you will see that there is no space of time in that particular
instant when the two clocks are synchronized, and thus no interval to speak
of then. This is pretty much analogous to interval in the musical sense:
`Difference in pitch between tones` where there is actually a `difference`
to speak of.

However, the definition seems to be broadened by some to include
`simultaneously occuring phenomena` which should not ordinarily correspond
to `a space of time/distance/tone`.

For preserving the coherence of meaning, I am forced to say that unison is
not an `interval`, since there is no `difference of tones` to mention where
difference is defined as: `dissimilarity or the quality distinguishing one
thing from another`.

>
> However, note that some instruments are capable of
> producing unisons by themself.
>
> For example, on a guitar:
>
> * it's a trivial matter to play a unison interval
> (i.e., dyad) by playing one open string and fretting
> the next lowest string at the same pitch;
>

By instrument, I meant the medium for producing sound. Certainly the two
seperate strings of a guitar are seperate instruments by which sound is
produced.

> * it's also very easy to play one string open and both
> of the next adjacent lower strings fretted to a unison with
> that, so there's a "unison triad";

I would rather say that you play a unison trichord, much like a hammer
striking three strings tuned to a single tone.

>
> * i can even contrive to put the guitar in my lap and
> use three fingers on adjacent strings with my hand over
> the fretboard, with one open string, to play a
> "unison tetrad" ... but i do have long fingers :) .
>
>

Likewise, it would be a tetra-chord, not to be confused with the `division
of the fourth`.

> In terms of theory, there's probably not much use
> for any of this -- but it does become an important
> aspect of instrumental technique on instruments like
> this, and that's something that can be exploited by
> a composer or performer too.
>

We both agree that its usage is essential. I just do not agree that it is an
`interval`. There is no perceptible difference to speak of!

>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>
>
>

Ozan Yarman escreveu:
[...]
> Now there is a serious problem with unison in the mathematical sense.

???

The interval i between two pitches a and b can be defined as:

i=a-b

If a==b (unisson), then:

i=0

The interval i between two (non-zero) frequencies a and b can be defined as:

i=a/b

If a==b (unisson), then:

i=1

Where is the problem?

> Consider a clock and another running at twice the pace compared to the
> former. There will be a moment when the two clocks will be synchronized in
> an instant of time. Since `interval` according to Merriam-Webster's
> Collegiate Dictionary is `a space of time between events or states` in this
> context,

That *is not* a mathematical definition of interval.

To compare pitches os frequencies, interval should be defined respectivelly as a difference or a ratio of two numbers.

> you will see that there is no space of time in that particular
> instant when the two clocks are synchronized, and thus no interval to speak
> of then. This is pretty much analogous to interval in the musical sense:
> `Difference in pitch between tones` where there is actually a `difference`
> to speak of.
> > However, the definition seems to be broadened by some to include
> `simultaneously occuring phenomena` which should not ordinarily correspond
> to `a space of time/distance/tone`.
> > For preserving the coherence of meaning, I am forced to say that unison is
> not an `interval`, since there is no `difference of tones` to mention where
> difference is defined as: `dissimilarity or the quality distinguishing one
> thing from another`.

That is not a mathematical definition of `difference' either.

Idiosyncrasies... :-)

---

`Unisson' is a musical interval, it is the same as `prime'. But, due the word origin, it makes no sense to say `augmented unisson' although `augmented prime' is correct.

Cheers,
Hudson

--
'-------------------------------------------------------------------.
Hudson Lacerda <http://geocities.yahoo.com.br/hfmlacerda/>
*N�o deixe seu voto sumir! http://www.votoseguro.org/
*Ap�ie o Manifesto: http://www.votoseguro.com/alertaprofessores/

== THE WAR IN IRAQ COSTS ==
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.-------------------------------------------------------------------'
--

_______________________________________________________
Yahoo! Acesso Gr�tis - Internet r�pida e gr�tis. Instale o discador agora!
http://br.acesso.yahoo.com

Hudson, you are simply repeating what I said in mathematical terms without
realizing their gravity. Indeed, unison is but the re-statement of the same
pitch:

If subtracting frequency A produced on a string from frequency B produced on
another string yields 0, it simply means that there is NO difference and
that the interval between the two frequencies is absent, which is to say
that there is NO interval to speak of!

A hz - B hz = 0 = no difference = absence of any interval = unison.

Thus it is useless, redundant, or worse, in vain to speak of an `interval of
a unison` when it is a mathematical fact that there is 0 (hence, NO)
interval between the two frequencies given above.

It is like asking `what is the time interval between two simultaenous
events?`. It is an absurd question, since the events are already stated as
simultaenous. Similarly, by describing unison, we admit that the frequencies
are the same - with or without octave equivalances (equating 0 cents with
1200 cents) taken into consideration.

Thus, it is baseless to speak of an `interval of a unison`, since there is
no musical interval to mention here.

Moreover, you yourself admit to the contradiction that there cannot be an
`augmented unison`, since unison by definition is ONE SOUND.

Would you say that there are `unisonic intervals` between the three strings
of a piano tuned to the same pitch? Would anyone say that a pianist has
played the interval of a unison when he stroke a single key that sounded
these three strings together?

Certainly not. We would rather say that he played a certain pitch with a
pre-defined letter-designation, even though three strings resonate
simultaneously.

Therefore, it would be nothing less than a daft suggestion to speak of
unison as a musical interval here, or anywhere else for that matter, unless
we are talking about a performance based on one or more synchronized
octaves.

As for `augmented prime`, it signifies a substantial quantity between a
statement of two distinct pitches denoted by the same basic note/letter
designation such as C and C#.

Ozan

----- Original Message -----
From: "Hudson Lacerda" <hfmlacerda@yahoo.com.br>
To: <tuning@yahoogroups.com>
Sent: 28 �ubat 2006 Sal� 17:17
Subject: Re: [tuning] unison as an interval

> Ozan Yarman escreveu:
> [...]
> > Now there is a serious problem with unison in the mathematical sense.
>
> ???
>
> The interval i between two pitches a and b can be defined as:
>
> i=a-b
>
> If a==b (unisson), then:
>
> i=0
>
> The interval i between two (non-zero) frequencies a and b can be defined
as:
>
> i=a/b
>
> If a==b (unisson), then:
>
> i=1
>
> Where is the problem?
>
> > Consider a clock and another running at twice the pace compared to the
> > former. There will be a moment when the two clocks will be synchronized
in
> > an instant of time. Since `interval` according to Merriam-Webster's
> > Collegiate Dictionary is `a space of time between events or states` in
this
> > context,
>
> That *is not* a mathematical definition of interval.
>
> To compare pitches os frequencies, interval should be defined
> respectivelly as a difference or a ratio of two numbers.
>
> > you will see that there is no space of time in that particular
> > instant when the two clocks are synchronized, and thus no interval to
speak
> > of then. This is pretty much analogous to interval in the musical sense:
> > `Difference in pitch between tones` where there is actually a
`difference`
> > to speak of.
> >
> > However, the definition seems to be broadened by some to include
> > `simultaneously occuring phenomena` which should not ordinarily
correspond
> > to `a space of time/distance/tone`.
> >
> > For preserving the coherence of meaning, I am forced to say that unison
is
> > not an `interval`, since there is no `difference of tones` to mention
where
> > difference is defined as: `dissimilarity or the quality distinguishing
one
> > thing from another`.
>
> That is not a mathematical definition of `difference' either.
>
> Idiosyncrasies... :-)
>
> ---
>
> `Unisson' is a musical interval, it is the same as `prime'. But, due the
> word origin, it makes no sense to say `augmented unisson' although
> `augmented prime' is correct.
>
>
> Cheers,
> Hudson
>

In my opinion, prime is only a starting note from where other intervals can
be formed. Intervals in European common practice start with augmented prime.

----- Original Message -----
From: "monz" <monz@tonalsoft.com>
To: <tuning@yahoogroups.com>
Sent: 24 �ubat 2006 Cuma 19:04
Subject: [tuning] Re: unison as an interval

> Hi Hudson,
>
>
> --- In tuning@yahoogroups.com, Hudson Lacerda <hfmlacerda@...> wrote:
>
> > No way to be consistent, because the pitch naming is
> > not trully consistent, except for the diatonic intervals.
> > (Besides, it is very strange taking in account the
> > reference point for an interval. Interval 0 is already
> > 1 unit length -- prime...)
>
>
> Yes, this is one of those unfortunate circumstances. We've
> discussed it here before: the discrepancy stems from the
> fact that the interval names "prime, 2nd, 3rd, 4th,..." etc.
> date from before the recognition of the concept of zero.
> So musicians and music-theorists just naturally began
> counting the intervals with "one".
>
> It's difficult for us today to realize what human perception
> of the natural world is like without zero, because we're
> so used to it. But it took a long time for recognition to
> occur, well into the second half of the 1st millenium AD.
>
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>
>

Ozan Yarman escreveu:
> Hudson, you are simply repeating what I said in mathematical terms without
> realizing their gravity. Indeed, unison is but the re-statement of the same
> pitch:

I have only questioned your argument on a possible ``serious problem with unison in the mathematical sense''.

I don't mean unison as *the same* pitch (or originary `the same sound'), but as the relation (or interval) between two (or more) sounds with *equal* pitch.

In other words: when the interval between two pitches is zero, we call this an unison. `Unison' is just a name for a particular interval of value zero.

[...]
> Thus it is useless, redundant, or worse, in vain to speak of an `interval of
> a unison` when it is a mathematical fact that there is 0 (hence, NO)
> interval between the two frequencies given above.

Think of unison as part of answer to a question like: ``What are the intervals between this reference pitch and the ten first pitches of that melody?''

> > It is like asking `what is the time interval between two simultaenous
> events?`. It is an absurd question, since the events are already stated as
> simultaenous.
[...]

I don't think this question is absurd.
Its answer is simply zero.
There is no mathematical inconsistency.
This case is very different of zero divide or expecting a real result of sqrt(-2) or like.

Hudson

--
'-------------------------------------------------------------------.
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*N�o deixe seu voto sumir! http://www.votoseguro.org/
*Ap�ie o Manifesto: http://www.votoseguro.com/alertaprofessores/

== THE WAR IN IRAQ COSTS ==
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.-------------------------------------------------------------------'
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_______________________________________________________
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http://br.acesso.yahoo.com

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:

> If subtracting frequency A produced on a string from frequency B
produced on
> another string yields 0, it simply means that there is NO difference and
> that the interval between the two frequencies is absent, which is to say
> that there is NO interval to speak of!

You are treating zero as if it is not a number. If you have an oboe at
pitch p1, and a violin at pitch p2, and if it happens that p1=p2, then
the pitch of the violin and the pitch of the oboe are zero cents apart.

Indeed. They are not apart to begin with, so you admit. There is NO interval
between them.

zero ze�ro,
noun a cipher; nothing; the point from which the reckoning begins on scales,
such as those of the barometer, etc; the lowest point (figurative); zero
hour.

(c) Larousse plc. All rights reserved

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
To: <tuning@yahoogroups.com>
Sent: 28 �ubat 2006 Sal� 20:07
Subject: [tuning] Re: unison as an interval

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> > If subtracting frequency A produced on a string from frequency B
> produced on
> > another string yields 0, it simply means that there is NO difference and
> > that the interval between the two frequencies is absent, which is to say
> > that there is NO interval to speak of!
>
> You are treating zero as if it is not a number. If you have an oboe at
> pitch p1, and a violin at pitch p2, and if it happens that p1=p2, then
> the pitch of the violin and the pitch of the oboe are zero cents apart.
>
>
>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Indeed. They are not apart to begin with, so you admit. There is NO
interval
> between them.

This is all so tedious and silly. If I have two players in front of
me, and one plays an a natural (speaking in 12tet for the moment) and
the other plays a b natural, we say they are playing a major second
apart. If the second player then moves to an a natural (we are
assuming computer-like precision of pitch...) we then say that they
are playing a unison a natural. It is a term of convenience, and most
reasonable people would understand that to refer to the interval that
they are playing as being a unison is not an absurdity, but a term for
the one condition where the two players are playing the exact same
frequency.

For those two players, every other pair of notes in the entire
universe could be referred to as an interval, and I can't see the
problem of calling the unison an interval, since it only requires the
understanding of an interval of no distance.

White is a color, yet while in white light it is the combination of
all colors, in pigment it is the complete absence of all colors. We
still think of it as white, and call it a color.

Only on the tuning list...

Cheers,
Jon

Jon Szanto wrote:

>--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
>>Indeed. They are not apart to begin with, so you admit. There is NO
>> >>
>interval
> >
>>between them.
>> >>
>
>This is all so tedious and silly. >Only on the tuning list...
> >
It IS the tuning list...

--
* David Beardsley
* microtonal guitar
* http://biink.com/db

db,

--- In tuning@yahoogroups.com, David Beardsley <db@...> wrote:
> It IS the tuning list...

Gad, you're right! Never mind. I hope everyone finds a definition that
they are happy with!!

Cheers,
Jon

Jon, tedious and silly are everywhere as far as the eye can see, such as the
phrase you coined: `interval of no distance`.

Does it not strike you as queer? Let me translate it in other words:

`Pitch difference between two frequencies that are one and the same`.

(where there is no pitch difference worth mentioning of course.)

And I don't see what colours have to do with unison.

My verdict:

1. Zero is not a counting number, it's the absence of any quantity or
qualification.
2. A distance of zero units between any two notes is no distance at all.
3. Unison is the name for two or more simultaneously sounding tones that are
the same.
4. Unison is the absence of any interval in music, barring octave
equivalances.

See:
http://en.wikipedia.org/wiki/0_(number)

----- Original Message -----
From: "Jon Szanto" <jszanto@cox.net>
To: <tuning@yahoogroups.com>
Sent: 28 �ubat 2006 Sal� 21:05
Subject: [tuning] Re: unison as an interval

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > Indeed. They are not apart to begin with, so you admit. There is NO
> interval
> > between them.
>
> This is all so tedious and silly. If I have two players in front of
> me, and one plays an a natural (speaking in 12tet for the moment) and
> the other plays a b natural, we say they are playing a major second
> apart. If the second player then moves to an a natural (we are
> assuming computer-like precision of pitch...) we then say that they
> are playing a unison a natural. It is a term of convenience, and most
> reasonable people would understand that to refer to the interval that
> they are playing as being a unison is not an absurdity, but a term for
> the one condition where the two players are playing the exact same
> frequency.
>
> For those two players, every other pair of notes in the entire
> universe could be referred to as an interval, and I can't see the
> problem of calling the unison an interval, since it only requires the
> understanding of an interval of no distance.
>
> White is a color, yet while in white light it is the combination of
> all colors, in pigment it is the complete absence of all colors. We
> still think of it as white, and call it a color.
>
> Only on the tuning list...
>
> Cheers,
> Jon
>
>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:

> 1. Zero is not a counting number, it's the absence of any quantity or
> qualification.

Zero is in fact the smallest cardinal number. It is the number of
elements in the empty set.

> 2. A distance of zero units between any two notes is no distance at all.

No, it's a distance of zero.

> 3. Unison is the name for two or more simultaneously sounding tones
that are
> the same.

No, it's the name for one or more simultaneously sounding tones that
are not the same, but are of the same pitch.

> > 1. Zero is not a counting number, it's the absence of any quantity or
> > qualification.
>
> Zero is in fact the smallest cardinal number. It is the number of
> elements in the empty set.
>

It is the absence of any elements in a set, which qualifies the set as
empty.

> > 2. A distance of zero units between any two notes is no distance at all.
>
> No, it's a distance of zero.
>

That is equal to no distance. You are playing with words to distort the
meaning of zero, attempting to convince us that zero and null are different
values.

Zero distance = No distance
Zero difference = No difference
Zero interval = No interval

> > 3. Unison is the name for two or more simultaneously sounding tones
> that are
> > the same.
>
> No, it's the name for one or more simultaneously sounding tones that
> are not the same, but are of the same pitch.
>
>

Maybe I am missing the irony in your words, but here goes:

Tones that are the same = Tones of the same pitch.

You once again repeated what I said, save admitting to the only possible
logical conclusion:

1. Unison =
2. Difference between two or more simultaneously sounding tones tuned to the
same frequency =
3. Lack of difference between two or more simultaneously sounding tones =
4. An intervallic value of 0 =
5. Absence of an interval =
6. Sameness of simultaneously sounding two or more tones.

Zip, nada, null, zilch.

A value of 0 equals the absence of that value. The only logically consistent
definition of a unison is `Sameness in pitch of simultaneously sounding two
or more tones` where octave equivalances are disregarded.

As for the trick question, the answer is already contained within, so it is
absurd to ask it in the first place. The question itself is a mockery of
logical consistency.

----- Original Message -----
From: "Hudson Lacerda" <hfmlacerda@yahoo.com.br>
To: <tuning@yahoogroups.com>
Sent: 28 �ubat 2006 Sal� 20:00
Subject: Re: [tuning] unison as an interval

> Ozan Yarman escreveu:
> > Hudson, you are simply repeating what I said in mathematical terms
without
> > realizing their gravity. Indeed, unison is but the re-statement of the
same
> > pitch:
>
> I have only questioned your argument on a possible ``serious problem
> with unison in the mathematical sense''.
>
> I don't mean unison as *the same* pitch (or originary `the same sound'),
> but as the relation (or interval) between two (or more) sounds with
> *equal* pitch.
>
> In other words: when the interval between two pitches is zero, we call
> this an unison. `Unison' is just a name for a particular interval of
> value zero.
>
> [...]
> > Thus it is useless, redundant, or worse, in vain to speak of an
`interval of
> > a unison` when it is a mathematical fact that there is 0 (hence, NO)
> > interval between the two frequencies given above.
>
> Think of unison as part of answer to a question like: ``What are the
> intervals between this reference pitch and the ten first pitches of that
> melody?''
>
> >
> > It is like asking `what is the time interval between two simultaenous
> > events?`. It is an absurd question, since the events are already stated
as
> > simultaenous.
> [...]
>
> I don't think this question is absurd.
> Its answer is simply zero.
> There is no mathematical inconsistency.
> This case is very different of zero divide or expecting a real result of
> sqrt(-2) or like.
>
> Hudson
>

On 2/28/06, Ozan Yarman <ozanyarman@ozanyarman.com> wrote:
> You once again repeated what I said, save admitting to the only possible
> logical conclusion:
>
> 1. Unison =
> 2. Difference between two or more simultaneously sounding tones tuned to the
> same frequency =
> 3. Lack of difference between two or more simultaneously sounding tones =
> 4. An intervallic value of 0 =
> 5. Absence of an interval =
> 6. Sameness of simultaneously sounding two or more tones.
>
> Zip, nada, null, zilch.
>
> A value of 0 equals the absence of that value. The only logically consistent
> definition of a unison is `Sameness in pitch of simultaneously sounding two
> or more tones` where octave equivalances are disregarded.
>
> As for the trick question, the answer is already contained within, so it is
> absurd to ask it in the first place. The question itself is a mockery of
> logical consistency.

I don't want to get too involved in this discussion, I just want to
ask you one question: What (if any) is the difference between the two
sets {} (the empty set) and {0} (the set containing only the number
zero)?

Keenan

Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
> > 3. Unison is the name for two or more simultaneously sounding tones
> that are
> > the same.
>
> No, it's the name for one or more simultaneously sounding tones that
> are not the same, but are of the same pitch.

Oh man, elegantly put! Wish I could have said it, but that is
certainly what was in my head - thanks.

Cheers,
Jon

So, who's made a home run then?

Simultaneously sounding tones that are the same = Tones sharing a common
pitch.

> >
> > No, it's the name for one or more simultaneously sounding tones that
> > are not the same, but are of the same pitch.
>
> Oh man, elegantly put! Wish I could have said it, but that is
> certainly what was in my head - thanks.
>
> Cheers,
> Jon
>
>

>
> I don't want to get too involved in this discussion, I just want to
> ask you one question: What (if any) is the difference between the two
> sets {} (the empty set) and {0} (the set containing only the number
> zero)?
>
> Keenan
>

I see no difference in between as long as the sets are subject to the same
terms and operations.

A set that contains zero amount of whatnot equals a set that is devoid of
that whatnot. Nothingness! Seeing as zero is the absence of
value/quantity/qualification, both sets are categorically empty, they
contain nothing.

Do you treat zero as if it were a substantial figure? The answer to your
question is zero.

Then again, I'm a total ignorant in math.

Cordially,
Oz.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:

> That is equal to no distance. You are playing with words to distort the
> meaning of zero, attempting to convince us that zero and null are
different
> values.

I'm simply saying what any mathematician anywhere would say.

--- In tuning@yahoogroups.com, "Jon Szanto" <jszanto@...> wrote:
>
> Gene,
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@>
> wrote:
> > > 3. Unison is the name for two or more simultaneously sounding tones
> > that are
> > > the same.
> >
> > No, it's the name for one or more simultaneously sounding tones that
> > are not the same, but are of the same pitch.
>
> Oh man, elegantly put! Wish I could have said it, but that is
> certainly what was in my head - thanks.

Thanks, Jon. It would have been even more elegant if I had said what I
intended, namely "two or more".

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
> Thanks, Jon. It would have been even more elegant if I had said what I
> intended, namely "two or more".

Well, it must say something that I actually read "two" in place of
"one" in my mind!

J

I'm agree with gene.

My experience : when I want to tune a string with sound of my tombak as
unison , it is related to tombak-sound spectrum. Pitch of tombak is
related to one durable and powerful partial in inharmonic structure ,
other partials decay rapidly and in my tombak the third partial and some
other remain sounding which third is the refrence to recognize pitch.

So unison must be defined in perception process of sound pitch .

Shaahin Mohaajeri

Tombak Player & Researcher , Composer

www.geocities.com/acousticsoftombak

My tombak musics : www.rhythmweb.com/gdg

My articles in ''Harmonytalk'':

www.harmonytalk.com/archives/000296.html
<http://www.harmonytalk.com/archives/000296.html>

www.harmonytalk.com/archives/000288.html
<http://www.harmonytalk.com/archives/000288.html>

My article in DrumDojo:

www.drumdojo.com/world/persia/tonbak_acoustics.htm
<http://www.drumdojo.com/world/persia/tonbak_acoustics.htm>

________________________________

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf
Of Gene Ward Smith
Sent: Wednesday, March 01, 2006 12:49 AM
To: tuning@yahoogroups.com
Subject: [tuning] Re: unison as an interval

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:

> 1. Zero is not a counting number, it's the absence of any quantity or
> qualification.

Zero is in fact the smallest cardinal number. It is the number of
elements in the empty set.

> 2. A distance of zero units between any two notes is no distance at
all.

No, it's a distance of zero.

> 3. Unison is the name for two or more simultaneously sounding tones
that are
> the same.

No, it's the name for one or more simultaneously sounding tones that
are not the same, but are of the same pitch.

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An analogy: Consider the different ways one can transform a square in
such a way as to leave it looking the same as when you started. You
can rotate it 90 degrees clockwise. Or 180 degrees. Or 270 degrees
clockwise. You can pick it up and turn it over along a horizontal,
vertical, or either diagonal axis. You can also pick it up, wave it
over your head, throw it on the floor and jump over it, pick it up,
and put it down 90 degrees rotated from where it started, but that
(for our purposes) is considered the same thing as just rotating it.
What matters is what orientation the square ends up in, not the
process by which it got there. Given that definition, the above seven
transformations are *almost* all the transformations that leave a
square invariant.

Now these transformations *almost* have a certain property, which is
this: The result of applying any two of these transformations is the
same as one of thes transformations. For example, a clockwise
rotation of 90 degrees followed by a clockwise rotation of 90 degrees
is a rotation of 180 degrees. A flip on the horizontal axis followed
by a flip on a diagonal axis is a 90 or 270 degree rotation, depending
on which diagonal. (It's not the same *process* as a rotation, but it
results in the same *orientation*, so it counts as the same.) And so
forth.

But... a 180 degree rotation followed by a 180 degree rotation, or a
90 degree followed by a 270 degree, or a horizontal flip followed by a
horizontal flip (et cetera) all leave the square oriented as it was
when you started, which is no transformation at all...

Unless you define it to be yet another a tranformation, the null or
identity transformation. Why would you do so? Because then *every*
combination of these 8 transformations is one of these 8
transformations, and then it becomes much easier to develop
definitions and theorems about such transformations. When you include
the null transformation, these transformations, along with the
operation consisting of doing one transformation followed by another,
form a mathematical group. And once you have a group, the methods and
theorems of group theory can be brought to bear on the situation.

This is why, to a mathematician, doing nothing to a square counts as a
transformation of that square: because by considering it so the
apparatus of group theory can be used.

There are lots of other groups, finite and infinite. For instance,
the positive rational numbers, along with the operation of
multiplication, form a group.

Of course, in music theory, positive rational numbers (considered as
frequency ratios) correspond to just intervals, and multiplication of
rational numbers corresponds to addition of intervals. So musical
intervals, and the operation of adding intervals, also form a group.

But only if the combination of any two rational intervals is a
rational interval; and the combination of an upward fifth, say, and a
downward fifth is a unison. So the rational intervals form a group
only if the unison is defined to be an interval.

It's not just wordplay; it's defining terms in such a way as to make
things like group theory applicable to the problem.

- Rich Holmes

Hi Oz,

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:

> We both agree that its usage is essential. I just do not
> agree that it is an `interval`. There is no perceptible
> difference to speak of!

OK, then i guess we just look at it in two different ways.

To me, saying that unison is not an interval because there
is no difference, is exactly like saying that zero is not
a number because there is no difference.

This point of view is exactly what held mathematics back
for millenia, until people finally realized that not only
could they treat zero as a number like all others, but
also that employing its use made many kinds of mathematical
problems "work" in ways that they couldn't before.

-monz
http://tonalsoft.com
Tonescape microtonal music software

Are you accusing me of being a reactionary monz? I simply state the
obvious... zero represents the absence of value. It has the numerical value
of void in the world of numbers. One can very well utilize this parameter in
any mathematical equation without encountering an error. This is all very
clearly explained in this link:

http://en.wikipedia.org/wiki/0_%28number%29

I know not what prevents you or the others from accepting the fact that
unison (in an ideal world) represents the absence of an interval. How can
one speak of an interval of a unison, when unison is the absence of an
interval?

I'm truly gobsmacked.

Cordially,
Oz.

----- Original Message -----
From: "monz" <monz@tonalsoft.com>
To: <tuning@yahoogroups.com>
Sent: 01 Mart 2006 �ar�amba 23:48
Subject: [tuning] Re: unison as an interval (was: Sagittal notation article
updated)

> Hi Oz,
>
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> > We both agree that its usage is essential. I just do not
> > agree that it is an `interval`. There is no perceptible
> > difference to speak of!
>
>
> OK, then i guess we just look at it in two different ways.
>
> To me, saying that unison is not an interval because there
> is no difference, is exactly like saying that zero is not
> a number because there is no difference.
>
> This point of view is exactly what held mathematics back
> for millenia, until people finally realized that not only
> could they treat zero as a number like all others, but
> also that employing its use made many kinds of mathematical
> problems "work" in ways that they couldn't before.
>
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>
>
>

Hi Monz.

You wrote:

> To me, saying that unison is not an interval because there
> is no difference, is exactly like saying that zero is not
> a number because there is no difference.
>
> This point of view is exactly what held mathematics back
> for millenia, until people finally realized that not only
> could they treat zero as a number like all others, but
> also that employing its use made many kinds of mathematical
> problems "work" in ways that they couldn't before.

First of all, I totally agree. Then, I think we're trying to turn two
questions into a single one and I'm a bit surprised noone has pointed this
out yet.
Q1: Is 1/1 an interval?
A1: Certainly.
Q2: How should we call the 1/1?
A2: Whatever your view is, here's mine.
If we want to stress the fact that it's the smallest of all intervals (i.e.
the first degree of a [diatonic] scale), we call it a "prime". Then the
second degree of a diatonic scale is a second and so on. If we want to
stress the fact that the pitches of "these two tones" are identical, we call
it a "unison".
So I'd conclude like this: Prime is an interval. That means 1/1 is an
interval. Unison is a prime taken from a different point of view. That means
the word "unison" doesn't explain the prime as an interval of zero distance
but rather as two tones of the same pitch (or one tone produced by two
"instruments").
That's why "augmented prime" works OK for me, but "augmented unison" does
not.

Petr

What? You want me to believe that zero has a value?

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
To: <tuning@yahoogroups.com>
Sent: 01 Mart 2006 �ar�amba 3:59
Subject: [tuning] Re: unison as an interval

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> > That is equal to no distance. You are playing with words to distort the
> > meaning of zero, attempting to convince us that zero and null are
> different
> > values.
>
> I'm simply saying what any mathematician anywhere would say.
>
>
>

Ozan Yarman wrote:

> > I know not what prevents you or the others from accepting the fact that
> unison (in an ideal world) represents the absence of an interval. How can
> one speak of an interval of a unison, when unison is the absence of an
> interval?
> > I'm truly gobsmacked.

What does an interval describe? Which values can this thing described take?

The penultimate notes in a piece of music form a minor third. What does it resolve to?

klaus

Goodness gracious Petr, of course 1/1 is not an interval, it's a ratio
denoting a pitch the frequency of which is divided by itself to yield a
fundamental reference point for all the intervals you may like to have in a
Just Intonation scheme. You could just as well say 1 - as Gene does most of
the time - instead of specifying a ratio, which amounts to the same thing.
It is in relation to THIS pitch that intervals are determined.

A relative frequency value of 1 is equal to the intervallic value of 0. That
is, the absence of an interval, for it means that there is no difference
between the frequencies in question. It is therefore only natural to refer
to this relative frequency as the reference tone.

More to the point, the first degree of a diatonical scale (prime) does not
correspond an interval, since there is no mention of another note with which
to compare. Unlike unison, it is a stand-alone pitch by itself. Only in
`augmented prime` do you reproduce another instance of the same note a
little further away with an accidental to form an interval.

Even sounding two instances of the same pitch on two seperate instruments,
still yields no difference, and hence, no interval. What makes it a unison
is, you can tell from the timbre of the instruments that unison is actually
being played.

Oz.

----- Original Message -----
From: "Petr Par�zek" <p.parizek@chello.cz>
To: <tuning@yahoogroups.com>
Sent: 02 Mart 2006 Per�embe 0:43
Subject: Re: [tuning] Re: unison as an interval (was: Sagittal notation
article updated)

> Hi Monz.
>
> You wrote:
>
> > To me, saying that unison is not an interval because there
> > is no difference, is exactly like saying that zero is not
> > a number because there is no difference.
> >
> > This point of view is exactly what held mathematics back
> > for millenia, until people finally realized that not only
> > could they treat zero as a number like all others, but
> > also that employing its use made many kinds of mathematical
> > problems "work" in ways that they couldn't before.
>
> First of all, I totally agree. Then, I think we're trying to turn two
> questions into a single one and I'm a bit surprised noone has pointed this
> out yet.
> Q1: Is 1/1 an interval?
> A1: Certainly.
> Q2: How should we call the 1/1?
> A2: Whatever your view is, here's mine.
> If we want to stress the fact that it's the smallest of all intervals
(i.e.
> the first degree of a [diatonic] scale), we call it a "prime". Then the
> second degree of a diatonic scale is a second and so on. If we want to
> stress the fact that the pitches of "these two tones" are identical, we
call
> it a "unison".
> So I'd conclude like this: Prime is an interval. That means 1/1 is an
> interval. Unison is a prime taken from a different point of view. That
means
> the word "unison" doesn't explain the prime as an interval of zero
distance
> but rather as two tones of the same pitch (or one tone produced by two
> "instruments").
> That's why "augmented prime" works OK for me, but "augmented unison" does
> not.
>
> Petr
>
>

An interval describes a substantial quantity seperating tones from one
another. It can have any value one likes it to have, as long as it is a
value.

Absence of value does not count as a value. It's a parameter only.

Unison is the absence of intervallic value. Which part is so hard to
understand?

What do you want the minor third to resolve to?

----- Original Message -----
From: "klaus schmirler" <KSchmir@online.de>
To: <tuning@yahoogroups.com>
Sent: 02 Mart 2006 Per�embe 0:56
Subject: Re: [tuning] Re: unison as an interval

> Ozan Yarman wrote:
>
> >
> > I know not what prevents you or the others from accepting the fact that
> > unison (in an ideal world) represents the absence of an interval. How
can
> > one speak of an interval of a unison, when unison is the absence of an
> > interval?
> >
> > I'm truly gobsmacked.
>
> What does an interval describe? Which values can this thing described
take?
>
> The penultimate notes in a piece of music form a minor third. What does
> it resolve to?
>
> klaus
>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> What? You want me to believe that zero has a value?

It has a value if you follow the usage of mathematicians. In the
context of music, musicians are generally agreed in calling two
instruments playing at zero cents apart an interval of a unison, and
not the lack of an interval, so it seems musicians and mathematicians
for the most part see eye to eye on this. Your milage, obviously, varies.

That is more than I can say for your milage. Dare I suggest that you are
confusing `parameter` with `value`?

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
To: <tuning@yahoogroups.com>
Sent: 02 Mart 2006 Per�embe 3:22
Subject: [tuning] Re: unison as an interval

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > What? You want me to believe that zero has a value?
>
> It has a value if you follow the usage of mathematicians. In the
> context of music, musicians are generally agreed in calling two
> instruments playing at zero cents apart an interval of a unison, and
> not the lack of an interval, so it seems musicians and mathematicians
> for the most part see eye to eye on this. Your milage, obviously, varies.
>
>
>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> That is more than I can say for your milage. Dare I suggest that you are
> confusing `parameter` with `value`?

Considering I'm a mathematician and you are not, it seems likely I
have a better grasp of mathematical language than you do. If I
understand you correctly, you think I'm confusing the value of a
function, f(x), with the argument of a function, x. How?

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
To: <tuning@yahoogroups.com>
Sent: 02 Mart 2006 Per�embe 4:07
Subject: [tuning] Re: unison as an interval

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > That is more than I can say for your milage. Dare I suggest that you are
> > confusing `parameter` with `value`?
>
> Considering I'm a mathematician and you are not,

Obviously. I'm a total ignorant in mathematics, but I have some powerful
friends in high places.

it seems likely I
> have a better grasp of mathematical language than you do.

We are all trusting on that.

If I
> understand you correctly, you think I'm confusing the value of a
> function, f(x), with the argument of a function, x. How?
>
>

Not having a clue as to what you might be referring to, I'll give it my best
shot. You treat zero as if it has a value (substantial quantity or
qualification) when it is simply meant to denote the absence of it:

http://mathworld.wolfram.com/Zero.html

http://home.ubalt.edu/ntsbarsh/zero/ZERO.HTM

If zero had a value as you claim it to have, simple arithmetic operations
would have yielded material results:

1+0 is 1.
1-0 is still 1.
1*0 is the absence of 1, hence 0.
1/0 is impossible to realize, or worse, the collapse of mathematics.

What number times 0 can yield a non-zero number anyway?

I don't see anyone coming up with a solid argument yet, so I'll stick to my
version of the story.

Down with the tradition!

Hi Ozan.

You wrote:

> Not having a clue as to what you might be referring to, I'll give it my
best
> shot. You treat zero as if it has a value (substantial quantity or
> qualification) when it is simply meant to denote the absence of it:
>
> http://mathworld.wolfram.com/Zero.html
>
> http://home.ubalt.edu/ntsbarsh/zero/ZERO.HTM
>
> If zero had a value as you claim it to have, simple arithmetic operations
> would have yielded material results:
>
> 1+0 is 1.
> 1-0 is still 1.
> 1*0 is the absence of 1, hence 0.
> 1/0 is impossible to realize, or worse, the collapse of mathematics.
>
> What number times 0 can yield a non-zero number anyway?

What number? I'll tell you. The infinity.
Let's look at it from the other side. If you're saying that a value cannot
be infinitely small, then, what is infinity? If I treated zero as a
non-value (i.e. something too small to be called a value), then I had to
treat infinity as a "supervalue" (i.e. something too large to be called a
value). Or, in other words, if zero can't be a value because it's the
smallest of all, then neither infinity can be a value because it's the
largest of all.
In the same way as any regular number times zero makes zero, similarly any
regular number times infinity makes infinity. That means zero times infinity
is actually an uncertain value denoting the range between these two rather
than a single position in that range. Or, if put more simply (though not
exactly what I mean), zero times infinity can be virtually any value but
neither zero nor infinity.

Petr

Ozan Yarman wrote:
> An interval describes a substantial quantity seperating tones from one
> another. It can have any value one likes it to have, as long as it is a
> value.

My answer would be: An interval describes the pitch relationship between two parts of music (voices). It occurs to me now that it can also describe notes in succession, but that doesn't really change things.

> > Absence of value does not count as a value. It's a parameter only.

Only? It's the value of this parameter that tells you if the interval is consonant or dissonant, upwards or downwards (or a repetition), and you certainly want a complete set of values for it. The inversion of the third is the sixth, the inversion of the second is the seventh, the inveriosn of the octave is the prime. [I wrote in a different post that I am not going to use "unison" for intervals since English doesn't seem to use much, but allows the alternative term.]

> > Unison is the absence of intervallic value. No, its value is the zero operator for pitch shift (ouch. Gene, am I making sense? Probably not. Perhaps "neutral element" or something?)

> > What do you want the minor third to resolve to?

You know that. One part has B, the other D. The next note is the last one. No matter the mode, they will (both!) go on to some form of ...

Ozan Yarman wrote:

> Not having a clue as to what you might be referring to, I'll give it my best
> shot. You treat zero as if it has a value He doesn't treat 0 as if it had a value of course it is useful, so it has a value), he treats it as if it _was_ a value (and it is).

klaus

Total gibberish. Every sane person knows that zero is the absence of value.

----- Original Message -----
From: "klaus schmirler" <KSchmir@online.de>
To: <tuning@yahoogroups.com>
Sent: 02 Mart 2006 Per�embe 16:24
Subject: Re: [tuning] Re: unison as an interval

> Ozan Yarman wrote:
>
> > Not having a clue as to what you might be referring to, I'll give it my
best
> > shot. You treat zero as if it has a value
>
> He doesn't treat 0 as if it had a value of course it is useful, so it
> has a value), he treats it as if it _was_ a value (and it is).
>
> klaus
>

Petr,

> >
> > What number times 0 can yield a non-zero number anyway?
>
> What number? I'll tell you. The infinity.

What? That's a fallacious statement. Dividing by zero is an illegal
operation. Even the simplest calculator will validate me, just run your
windows calculator and divide any number by 0 and see what I mean, unless of
course you are dividing zero by zero, which yields a result the function of
which is undefined.

Have you not read http://home.ubalt.edu/ntsbarsh/zero/ZERO.HTM

"Act of Dividing by Zero Is a Meaningless Operation:
Forget Its Result"

"While zero is a concept and a number, Infinity is not a number; it is the
name for a concept."

> Let's look at it from the other side. If you're saying that a value cannot
> be infinitely small, then, what is infinity?

You can define both infinetesimal and infinitely large in mathematics as
long as you remain faithful to the terminology. Infinitely small does not
equal 0. You are decreasing in size perpetually, but you never reach zero.
In contrast, you can increase in size perpetually, and never reach an end.

Examples:

1. You can keep shrinking your atoms (provided that there is no longer a
repellent force to keep you from doing so) indefinitely, constantly reducing
the size of your body.

2. You can likewise travel in any direction in space forever, provided that
you have the means to do so.

If I treated zero as a
> non-value (i.e. something too small to be called a value),

What? Zero is not something too small to be called a value, it is the
absence of value proper, or rather, the absence of whatever it is you want
to count.

then I had to
> treat infinity as a "supervalue" (i.e. something too large to be called a
> value).

According to John Wallis, "Infinitely means more than any Finite number
assignable". It is the impossibility of assigning a substantial quantity.

Or, in other words, if zero can't be a value because it's the
> smallest of all, then neither infinity can be a value because it's the
> largest of all.

The smallest value is still a value, just as the largest value is still a
value. Neither zero nor infinity can be conceived as tangible quantities.
Zero is not the smallest value, it is the lack of quantization. Likewise
infinity is not the largest value, it is the impossibility of descerning a
finite value.

> In the same way as any regular number times zero makes zero, similarly any
> regular number times infinity makes infinity.

That is because they invalidate actual values.

That means zero times infinity
> is actually an uncertain value denoting the range between these two rather
> than a single position in that range.

It is not only uncertain, but also indeterminable.

Or, if put more simply (though not
> exactly what I mean), zero times infinity can be virtually any value but
> neither zero nor infinity.
>

Certainly not.

1/x times x^2 - when x goes to infinity - tends to yield infinity. When x
goes to 0, it tends to yield 0, simply because, the product is x itself.

> Petr
>
>

Oz.

----- Original Message -----
From: "klaus schmirler" <KSchmir@online.de>
To: <tuning@yahoogroups.com>
Sent: 02 Mart 2006 Per�embe 15:06
Subject: Re: [tuning] Re: unison as an interval

> Ozan Yarman wrote:
> > An interval describes a substantial quantity seperating tones from one
> > another. It can have any value one likes it to have, as long as it is a
> > value.
>
> My answer would be: An interval describes the pitch relationship between
> two parts of music (voices). It occurs to me now that it can also
> describe notes in succession, but that doesn't really change things.
>

Interval literally means `time or space between`. The lack thereof does not
count as an interval.

> >
> > Absence of value does not count as a value. It's a parameter only.
>
> Only? It's the value of this parameter that tells you if the interval is
> consonant or dissonant, upwards or downwards (or a repetition), and you
> certainly want a complete set of values for it. The inversion of the
> third is the sixth, the inversion of the second is the seventh, the
> inveriosn of the octave is the prime. [I wrote in a different post that
> I am not going to use "unison" for intervals since English doesn't seem
> to use much, but allows the alternative term.]
>

Let me refine my statement then: In a world where years are determined
according to the conceived birth-date of Yeshua the Messiah, the Christians
say that 1 B.C is immediately proceeded by 1 Anno Domini. The common mistake
here is, a year was not yet fulfilled when Yeshua was 0 years old (hence,
new-born), yet it was assigned the year 1, whereas it should have been
assigned the year 0, meaning that the period of a year had not yet elapsed.
This is equivalent to saying that the year did not exist until the calendar
pointed to 1 A.D.

Following this logic, only after 1 A.D is it possible to say that the first
year begins.

Your confusion with intervals is analogous to the nonsense of Gregorian
years.

Your definition of inversion is likewise lacking. An interval can only be
inverted if the base pitch is flipped over to its octave. Likewise, chords
are inverted in this fashion. Since unison is two same pitches at the base,
flipping over the pitches that form a unison will only carry them both to
their octave. But somehow, you expect one of them to remain while you carry
the other away. This is fallacious. The inversion of the unison is not the
interval of an octave, but another unison an octave higher than previous.

Any other way of conceiving it is illogical. One is at most entitled to say
that a pitch and its octave are psycho-acoustically the same, so one can try
to imagine that the interval of an octave does not exist... which is not a
very convincing argument either.

> >
> > Unison is the absence of intervallic value.
>
> No, its value is the zero operator for pitch shift (ouch. Gene, am I
> making sense? Probably not. Perhaps "neutral element" or something?)
>

Do you need someone else to come to the rescue? I don't see anyone making
relevant statements powerful enough to defeat my valid arguments.

> >
> > What do you want the minor third to resolve to?
>
> You know that. One part has B, the other D. The next note is the last
> one. No matter the mode, they will (both!) go on to some form of ...
>
>
>

Unison. They will resolve to a state of zero interval, hence the absence
thereof.

Cordially,
Ozan

You are mayhap confusing timbre with pitch when defining unison my brother in Islam?
----- Original Message -----
From: Mohajeri Shahin
To: tuning@yahoogroups.com
Sent: 01 Mart 2006 Çarşamba 6:30
Subject: RE: [tuning] Re: unison as an interval

I'm agree with gene.

My experience : when I want to tune a string with sound of my tombak as unison , it is related to tombak-sound spectrum. Pitch of tombak is related to one durable and powerful partial in inharmonic structure , other partials decay rapidly and in my tombak the third partial and some other remain sounding which third is the refrence to recognize pitch.

So unison must be defined in perception process of sound pitch .

Shaahin Mohaajeri

Tombak Player & Researcher , Composer

www.geocities.com/acousticsoftombak

My tombak musics : www.rhythmweb.com/gdg

My articles in ''Harmonytalk'':

www.harmonytalk.com/archives/000296.html

www.harmonytalk.com/archives/000288.html

My article in DrumDojo:

www.drumdojo.com/world/persia/tonbak_acoustics.htm

----- Original Message -----
From: "Rich Holmes" <rsholmes@mailbox.syr.edu>
To: <tuning@yahoogroups.com>
Sent: 01 Mart 2006 �ar�amba 6:38
Subject: Re: [tuning] Re: unison as an interval

> An analogy: Consider the different ways one can transform a square in
> such a way as to leave it looking the same as when you started. You
> can rotate it 90 degrees clockwise. Or 180 degrees. Or 270 degrees
> clockwise. You can pick it up and turn it over along a horizontal,
> vertical, or either diagonal axis. You can also pick it up, wave it
> over your head, throw it on the floor and jump over it, pick it up,
> and put it down 90 degrees rotated from where it started, but that
> (for our purposes) is considered the same thing as just rotating it.
> What matters is what orientation the square ends up in, not the
> process by which it got there. Given that definition, the above seven
> transformations are *almost* all the transformations that leave a
> square invariant.
>
> Now these transformations *almost* have a certain property, which is
> this: The result of applying any two of these transformations is the
> same as one of thes transformations. For example, a clockwise
> rotation of 90 degrees followed by a clockwise rotation of 90 degrees
> is a rotation of 180 degrees. A flip on the horizontal axis followed
> by a flip on a diagonal axis is a 90 or 270 degree rotation, depending
> on which diagonal. (It's not the same *process* as a rotation, but it
> results in the same *orientation*, so it counts as the same.) And so
> forth.
>
> But... a 180 degree rotation followed by a 180 degree rotation, or a
> 90 degree followed by a 270 degree, or a horizontal flip followed by a
> horizontal flip (et cetera) all leave the square oriented as it was
> when you started, which is no transformation at all...
>
> Unless you define it to be yet another a tranformation, the null or
> identity transformation. Why would you do so? Because then *every*
> combination of these 8 transformations is one of these 8
> transformations, and then it becomes much easier to develop
> definitions and theorems about such transformations. When you include
> the null transformation, these transformations, along with the
> operation consisting of doing one transformation followed by another,
> form a mathematical group. And once you have a group, the methods and
> theorems of group theory can be brought to bear on the situation.
>

I don't see the relevance of this analogy. The simpler ones I produced still
expect to be refuted, provided that they can actually be refuted.

> This is why, to a mathematician, doing nothing to a square counts as a
> transformation of that square: because by considering it so the
> apparatus of group theory can be used.
>
> There are lots of other groups, finite and infinite. For instance,
> the positive rational numbers, along with the operation of
> multiplication, form a group.
>
> Of course, in music theory, positive rational numbers (considered as
> frequency ratios) correspond to just intervals, and multiplication of
> rational numbers corresponds to addition of intervals. So musical
> intervals, and the operation of adding intervals, also form a group.
>
> But only if the combination of any two rational intervals is a
> rational interval; and the combination of an upward fifth, say, and a
> downward fifth is a unison. So the rational intervals form a group
> only if the unison is defined to be an interval.
>
> It's not just wordplay; it's defining terms in such a way as to make
> things like group theory applicable to the problem.
>

I hardly see what all this has to do with unison, which is a state of
interval-lessness.

> - Rich Holmes
>
>

Oz.

Ozan Yarman escreveu:
> Petr,
> > > >>>What number times 0 can yield a non-zero number anyway?
>>
>>What number? I'll tell you. The infinity.
> > > > What? That's a fallacious statement. Dividing by zero is an illegal
> operation. Even the simplest calculator will validate me, just run your
> windows calculator and divide any number by 0 and see what I mean, unless of
> course you are dividing zero by zero, which yields a result the function of
> which is undefined.

The first software piece I tried gave me a different result... Why?

octave:1> 1/0
warning: division by zero
ans = Inf
octave:2> 0/0
warning: division by zero
ans = NaN

Anyway, considering the perfect prime or unisson as an interval -- even if one can put its status under question -- is an useful thing.

Bye,
Hudson

--
'-------------------------------------------------------------------.
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*N�o deixe seu voto sumir! http://www.votoseguro.org/
*Ap�ie o Manifesto: http://www.votoseguro.com/alertaprofessores/

== THE WAR IN IRAQ COSTS ==
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_______________________________________________________
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Hi Oz,

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Petr wrote:
> > Let's look at it from the other side. If you're
> > saying that a value cannot be infinitely small,
> > then, what is infinity?
>
>
> You can define both infinetesimal and infinitely large
> in mathematics as long as you remain faithful to the
> terminology. Infinitely small does not equal 0. You
> are decreasing in size perpetually, but you never reach
> zero. In contrast, you can increase in size perpetually,
> and never reach an end.

> > If I treated zero as a non-value (i.e. something
> > too small to be called a value),
>
>
> What? Zero is not something too small to be called a
> value, it is the absence of value proper, or rather,
> the absence of whatever it is you want to count.

This issue is becoming confused because you (Oz) are
only looking at the use of zero in one way, as an
absence of value for measureable quantities.

But if you take into account the use of zero as a
midpoint in the negative-positive continuum, its
usefulness becomes apparent. This is the means of
using zero as part of a measurement scale ... and
after all, the notes we're measuring do come from
what musicians call a "scale" too.

So if a musician thinks of the pitch gamut as being
centered on middle-C (which is a very common conception),
then all treble notes are positive, all bass notes
are negative, and middle-C itself is zero.

Anything wrong with that?

In fact, this is exactly how the scale of prime-factor
exponents works (in any number of dimensions) in the
notation i proposed here:

http://sonic-arts.org/monzo/article/article.htm#reference

where middle-C has the value that i like to call "n^0"
-- it's the 1/1.

-monz
http://tonalsoft.com
Tonescape microtonal music software

On 3/2/06, Hudson Lacerda <hfmlacerda@yahoo.com.br> wrote:
> > What? That's a fallacious statement. Dividing by zero is an illegal
> > operation. Even the simplest calculator will validate me, just run your
> > windows calculator and divide any number by 0 and see what I mean, unless of
> > course you are dividing zero by zero, which yields a result the function of
> > which is undefined.
>
> The first software piece I tried gave me a different result... Why?
>
> octave:1> 1/0
> warning: division by zero
> ans = Inf
> octave:2> 0/0
> warning: division by zero
> ans = NaN
>
> Anyway, considering the perfect prime or unisson as an interval -- even
> if one can put its status under question -- is an useful thing.
>
> Bye,
> Hudson

This is getting really off topic, but there's something seriously
wrong with your world view if you depend on a calculator as your
source of mathematical truth. I had a calculator (a TI-89) that would
print an infinity sign when you told it to evaluate 10^1000.

Keenan

It relation to microtonality the works of Giomento Scelsi stand as an example of unison writing. His four pieces on a single tone ( i paraphrase the title as i run out the door)
He broaden the meaning of a unison to expand beyond such mundane scientific definitions into something that can broaden around a single frequency.
Take heavy vibrato on a tone, it is a still a tone but he frequency varies. His work has more to offer us than any metamathematical concept.
Let us also remember how the Greeks rejected the idea of zero as a place holder , arguing that zero cannot occupy a space.
It slowed down the mathematics for 2,000 years.
I say the more zeros and types of zeros the better ( the Jewish kaballist were master of these, and have gain much by their insights) .
>
> -- Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

One should ask that question to the software designers who inserted those
statements there.

According to:

http://en.wikipedia.org/wiki/0_%28number%29

"Division: 0 / x = 0, for nonzero x. But x / 0 is undefined, because 0 has
no multiplicative inverse, a consequence of the previous rule. For positive
x, as y in x / y approaches zero from positive values, its quotient
increases toward positive infinity, but as y approaches zero from negative
values, the quotient increases toward negative infinity. The different
quotients confirms that division by zero is undefined."

> >
> >
> > What? That's a fallacious statement. Dividing by zero is an illegal
> > operation. Even the simplest calculator will validate me, just run your
> > windows calculator and divide any number by 0 and see what I mean,
unless of
> > course you are dividing zero by zero, which yields a result the function
of
> > which is undefined.
>
> The first software piece I tried gave me a different result... Why?
>
> octave:1> 1/0
> warning: division by zero
> ans = Inf
> octave:2> 0/0
> warning: division by zero
> ans = NaN
>
> Anyway, considering the perfect prime or unisson as an interval -- even
> if one can put its status under question -- is an useful thing.
>
> Bye,
> Hudson
>
> --

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> One should ask that question to the software designers who inserted
those
> statements there.

Here's Wikipedia on Nan. What do you suppose the software designers
had in mind?

http://en.wikipedia.org/wiki/NaN

monz,

> >
> > What? Zero is not something too small to be called a
> > value, it is the absence of value proper, or rather,
> > the absence of whatever it is you want to count.
>
>
>
> This issue is becoming confused because you (Oz) are
> only looking at the use of zero in one way, as an
> absence of value for measureable quantities.
>

And what is wrong with that? Do you suggest that we assign any other meaning
to zero?

> But if you take into account the use of zero as a
> midpoint in the negative-positive continuum, its
> usefulness becomes apparent. This is the means of
> using zero as part of a measurement scale ... and
> after all, the notes we're measuring do come from
> what musicians call a "scale" too.
>

Goodness gracious monz! I did not deny at all the need for negative numbers
in a continuum of integers. I merely pointed out the significance of zero in
that continuum... that it is a point denoting the absence of a quality or
quantity, as in 0 degrees Celcius, denoting (ideally) the absence of liquid
water, or Absolute Zero temperature, denoting (ideally) the absence of
molecular motion, or 0 Watts, denoting (ideally) the absence of power.

Now, it is terribly hard for me to understand what it is that prevents you
and the rest from accepting the undeniable fact that 0 Cents denote the
absence of an interval.

And you still insist on calling the absence of an interval an interval. I
find it horrid and implausible.

> So if a musician thinks of the pitch gamut as being
> centered on middle-C (which is a very common conception),
> then all treble notes are positive, all bass notes
> are negative, and middle-C itself is zero.
>
> Anything wrong with that?
>

Nothing is wrong with that. And still you do not follow the course of logic?

> In fact, this is exactly how the scale of prime-factor
> exponents works (in any number of dimensions) in the
> notation i proposed here:
>
> http://sonic-arts.org/monzo/article/article.htm#reference
>
> where middle-C has the value that i like to call "n^0"
> -- it's the 1/1.
>
>

So? All this agrees with my arguments thus far.

>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>
>
>

Oz.

And your point being?

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
To: <tuning@yahoogroups.com>
Sent: 02 Mart 2006 Per�embe 20:58
Subject: [tuning] Re: unison as an interval

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > One should ask that question to the software designers who inserted
> those
> > statements there.
>
> Here's Wikipedia on Nan. What do you suppose the software designers
> had in mind?
>
> http://en.wikipedia.org/wiki/NaN
>
>

Ozan Yarman wrote:

[counting of years without the 0]

> Following this logic, only after 1 A.D is it possible to say that the first
> year begins.
> > Your confusion with intervals is analogous to the nonsense of Gregorian
> years.

My confusion about your example begins and ends with not comprehending whether you are saying that the year 1 or the year 0 doesn't exist. By your logic, the "Gregorian" count seems to be the only sensible one. What about a temperature of 0 degrees?

> > Your definition of inversion is likewise lacking. An interval can only be
> inverted if the base pitch is flipped over to its octave. Likewise, chords
> are inverted in this fashion. Since unison is two same pitches at the base,

You are already assuming to much. Intervals have no inherent direction, there is no base. Flip one or the other, the outcome will be the same. In order to prevent you form bringing up that "flip" is not defined for isolated primes, please think of two melodies in double counterpoint and flip one of these over. Watch what happens to primes and octaves.

> flipping over the pitches that form a unison will only carry them both to
> their octave. But somehow, you expect one of them to remain while you carry
> the other away. This is fallacious. The inversion of the unison is not the
> interval of an octave, but another unison an octave higher than previous.
> > Any other way of conceiving it is illogical. One is at most entitled to say
> that a pitch and its octave are psycho-acoustically the same, so one can try
> to imagine that the interval of an octave does not exist... which is not a
> very convincing argument either.
> > >>> Unison is the absence of intervallic value.
>> No, its value is the zero operator for pitch shift (ouch. Gene, am I
>> making sense? Probably not. Perhaps "neutral element" or something?)
>>
> > > Do you need someone else to come to the rescue?

When I'm making up words to translate concepts I only learned in German, yes.

I don't see anyone making
> relevant statements powerful enough to defeat my valid arguments.

So many drivers, all on the wrong lane.

> > >>> What do you want the minor third to resolve to?
>> You know that. One part has B, the other D. The next note is the last
>> one. No matter the mode, they will (both!) go on to some form of ...
>>
>>
>>
> > Unison. They will resolve to a state of zero interval, hence the absence
> thereof.

They were in an interval relationship before, but aren't any more? Shedding samsara to go to interval nirwana?

klaus

Ozan Yarman wrote:

> Goodness gracious monz! I did not deny at all the need for negative numbers
> in a continuum of integers. I merely pointed out the significance of zero in
> that continuum... that it is a point denoting the absence of a quality or
> quantity, as in 0 degrees Celcius, denoting (ideally) the absence of liquid
> water, or Absolute Zero temperature, denoting (ideally) the absence of
> molecular motion, or 0 Watts, denoting (ideally) the absence of power.

No, you are (in this analogy) defining it as the absence of a number.

klaus

> > Now, it is terribly hard for me to understand what it is that prevents you
> and the rest from accepting the undeniable fact that 0 Cents denote the
> absence of an interval.
> > And you still insist on calling the absence of an interval an interval. I
> find it horrid and implausible.

> [counting of years without the 0]
>
> > Following this logic, only after 1 A.D is it possible to say that the
first
> > year begins.
> >
> > Your confusion with intervals is analogous to the nonsense of Gregorian
> > years.
>
> My confusion about your example begins and ends with not comprehending
> whether you are saying that the year 1 or the year 0 doesn't exist. By
> your logic, the "Gregorian" count seems to be the only sensible one.
> What about a temperature of 0 degrees?
>

I'm saying that neither the Julian nor the Gregorian calendars acknowledge
the existance of a 0 point in the integer continuum of negative and positive
numbers, whereas they ordinarily should have.

FYI, according to MY logic, the true way of counting years is fixing a point
in time whereby not even a mili-second has passed in reference to that
point, which renders that point the glorious title of `the 0th year of the
0th century`, where neither a year nor a century is yet fulfilled.

Let's try to imagine an Eclipse-calendar which started on the latest total
solar eclipse. The moment the sun was completely covered on 11 August 1999
according to the Gregorian calendar, and when the totality was visible from
Elazig-Turkey, this marked that day as the zeroth day of the zeroth year of
E.C. After 24 hours have elapsed, we will proceed into day 1 E.C. After 12
months have elapsed, we will proceed into year 1 E.C. After a 100 years have
elapsed, we will proceed into the 1st century E.C.

See:

http://www.mreclipse.com/Special/SEprimer.html

http://www.mreclipse.com/TSE99reports/TSE99Espenak.html

for an explanation and pictures of the event.

As for the other fallacious argument you made, a temperature of zero degrees
lacks qualification. Is it Kelvin degrees, Celcius degrees or Fahrenheit
degrees? If it is Kelvin degrees, 0 denotes the absence of molecular motion
in ideal conditions. If one is talking about Celsius degrees, 0 denotes the
absence of liquid water in ideal conditions.

However, 0 degrees Fahrenheit is a little problematic:

http://en.wikipedia.org/wiki/Fahrenheit

And I think one should throw it out the window altogether, for there is no
clarity as to what 0 degrees Fahrenheit means.

Still, even as it is now, one could establish 0 degrees Fahrenheit to denote
a state for the absence of some quality or another. So my argument stands.

> >
> > Your definition of inversion is likewise lacking. An interval can only
be
> > inverted if the base pitch is flipped over to its octave. Likewise,
chords
> > are inverted in this fashion. Since unison is two same pitches at the
base,
>
> You are already assuming to much. Intervals have no inherent direction,
> there is no base. Flip one or the other, the outcome will be the same.
> In order to prevent you form bringing up that "flip" is not defined for
> isolated primes, please think of two melodies in double counterpoint and
> flip one of these over. Watch what happens to primes and octaves.
>

You are talking about an inversion and you think you are at a liberty to
invert and transpose an interval just like that... without establishing a
proper point of reference? My good fellow, tell me please, what are the
inversions of a C major chord? Can you claim that a second inversion of F
major is related to any inversion of C major?

My German is horrible but here goes:

`Jaa, u flipz zee pitsch oaf zee baz tonne un octaf haier und schnell!`

That ought to show you the importance of a base tone for any chord or
interval you may wish to invert.

Achtung! You are not allowed to say that you don't need a base tone for
inversion operations. It is this very tone that you transpose an octave
above for inversion to take place.

How else can chord inversions be realized anyhow?

And why should unison be an exception to the rule when it is resting on the
base tone for an inversion operation?

Inverting the unison carries both pitches an octave above. Never mind the
centuries of error committed in the name of scholastic tradition. Just admit
that octave equivalance resolves the problem, and that's that!

> >
> > Do you need someone else to come to the rescue?
>
> When I'm making up words to translate concepts I only learned in German,
> yes.
>

Then why don't I see anyone coming to my aid to help with the concepts I
learned in and translate from Turkish? Wait a minute... what am I saying? I
learned nothing in Turkish. Hahahaha.

So much for being an anglophone.

> I don't see anyone making
> > relevant statements powerful enough to defeat my valid arguments.
>
> So many drivers, all on the wrong lane.
>

Yea, we all know what it feels like to drive around the London Times Square.
Charles!

> >>
> >
> > Unison. They will resolve to a state of zero interval, hence the absence
> > thereof.
>
> They were in an interval relationship before, but aren't any more?
> Shedding samsara to go to interval nirwana?
>

They formed an interval before, and do not anymore. Open and close. Is it so
difficult to conceive of it? If it bothers you, never play a unison again.
LOL

> klaus
>

Oz.

Absence of a quantity expressed in terms of a unit of measurement is not the
absence of a number. Everyone knows that 0 is a whole number and still,
denotes a void/null point for measurements.

Lord! Send me a mathematician that doth seeth the light!

----- Original Message -----
From: "klaus schmirler" <KSchmir@online.de>
To: <tuning@yahoogroups.com>
Sent: 02 Mart 2006 Per�embe 21:46
Subject: Re: [tuning] Re: unison as an interval

> Ozan Yarman wrote:
>
> > Goodness gracious monz! I did not deny at all the need for negative
numbers
> > in a continuum of integers. I merely pointed out the significance of
zero in
> > that continuum... that it is a point denoting the absence of a quality
or
> > quantity, as in 0 degrees Celcius, denoting (ideally) the absence of
liquid
> > water, or Absolute Zero temperature, denoting (ideally) the absence of
> > molecular motion, or 0 Watts, denoting (ideally) the absence of power.
>
> No, you are (in this analogy) defining it as the absence of a number.
>
> klaus
>

Hi Ozan.

You wrote:

> Have you not read http://home.ubalt.edu/ntsbarsh/zero/ZERO.HTM

I have. And I'm getting a feeling like if it was written 100 years ago.
Don't try to persuade me to find a source which shares my view. You don't
know how lucky you are that I have lots of other things to do for the
academy at which I study. If I had more time, I surely would.

> You can define both infinetesimal and infinitely large in mathematics as
> long as you remain faithful to the terminology. Infinitely small does not
> equal 0. You are decreasing in size perpetually, but you never reach zero.
> In contrast, you can increase in size perpetually, and never reach an end.

I see you've not got my idea. OK, so another example.
Take the number 1, add 1/2 to this, and you get 1.5. Add 1/4, and you get
1.75. Add 1/8, and you get 1.875. Add 1/16, and you get 1.9375. ... If you
go on doing this for an infinite number of times, you eventually reach 2. If
you do this for a finite number of times, you'll never get there.

> What? Zero is not something too small to be called a value, it is the
> absence of value proper, or rather, the absence of whatever it is you want
> to count.

Never! This is just the same as if you said that negative numbers are
nonsense (or don't exist) and trying to proove it stating that you can't
hold "minus two apples" in your hand or that noone can take two apples away
from you if you don't have even one of them.

> According to John Wallis, "Infinitely means more than any Finite number
> assignable". It is the impossibility of assigning a substantial quantity.

This proves MY point. Even the number of existing finite numbers is
infinite. That means if you stack finite numbers in whatever way (even some
extremely huge ones), you would have to do this for an infinite number of
times in order to get to infinity.

> infinity is not the largest value, it is the impossibility of descerning a
> finite value.

Can you tell me who was the author of this statement? Probably not someone
who has a passion for examining the internal structure of values and their
properties/relations. If this was true, then you could say, for example,
that the number of 100 trillion was infinity some millenia ago (at the times
when even highly aware people were unwilling or unable to accept its large
quantity) and is not anymore as we have already developped skills for
describing and using numbers this large. But this is not the case. The
calculators which call a large number "infinity" are calling it like that
not for any "infinityness" but for its value which is too large for them to
accept. If there was a calculator which could work with numbers as large as
there exist in the world, infinity would never appear as a result because
calculators are not designed for operating with infinity.

I wrote:

> > That means zero times infinity
> > is actually an uncertain value denoting the range between these two
rather
> > than a single position in that range.
>
>
> It is not only uncertain, but also indeterminable.

That's what I meant. It's indeterminable to be given a single position in
the range between 0 and infinity, but it's the range. Maybe this example
will help you understand better what I mean. Everyone knows that "X^0 = 1"
whatever value you assign to X. Taking this result from the other end, I can
actually say that the 0th root of 1 can result in any number existing. Do
you want to tell me its impossible to describe the result of the 0th root of
1, or, for that matter, the 0th root of any number?

Petr

> > What? Zero is not something too small to be called a value, it is the
> > absence of value proper, or rather, the absence of whatever it is you want
> > to count.
>
> Never! This is just the same as if you said that negative numbers are
> nonsense (or don't exist) and trying to proove it stating that you can't
> hold "minus two apples" in your hand or that noone can take two apples away
> from you if you don't have even one of them.
>

Getting in this discussion is itself off topic, but my goal is to bring people back to
pragmatic musical discussion...

Negative numbers don't exist outside of the world of ideas. But neither do positive
numbers. Numbers are ideas. They exist. As ideas. Not otherwise. I don't care to
discuss the nature of existence. BUT, we may as well remember that since ideas
necessarily exist inside our heads, we should stop ANY attempt to "prove" or "disprove"
the nature of ideas. That implies using external or at least logical rules to deal with these
ideas. It won't go anywhere.
To say that 1.9999 (repeat nines for infinity) = 2 is not right or wrong. It's a bunch of
SYMBOLS. In other words, we have a notation system for categorizing our ideas. And for
COMMUNICATION'S sake we have to agree whether or not we allow this equalization of two
different symbols. These ideas do not otherwise externally exist. Any debate that thinks
that 2 or 1.99999... is something more tangible than a symbol for communication is
kidding themselves. So quit it. Go back and figure out if there was something that was
worth communicating, and figure out how to get the message across and work together to
understand, instead of debating the wording! I didn't catch if there was a message to start
with or just wordplay.

-Aaron

Hi Oz,

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:

> I'm saying that neither the Julian nor the Gregorian
> calendars acknowledge the existance of a 0 point in
> the integer continuum of negative and positive
> numbers, whereas they ordinarily should have.

But this is wrong. The Julian and Gregorian calendars
don't recognize a *year* zero, but they do both recognize
a zero *point*: the singularity between the end of BC
and the beginning of AD.

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
>
> Hi Oz,
>
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
>
> > I'm saying that neither the Julian nor the Gregorian
> > calendars acknowledge the existance of a 0 point in
> > the integer continuum of negative and positive
> > numbers, whereas they ordinarily should have.
>
>
>
> But this is wrong. The Julian and Gregorian calendars
> don't recognize a *year* zero, but they do both recognize
> a zero *point*: the singularity between the end of BC
> and the beginning of AD.

Actually, this is wrong too -- Ozan's whole point is
that by his type of reckoning, there *isn't* any "between":
there is simply the zero moment which exists beyond any
type of measurement system, because it represents
nothingness.

I'd say that this discussion is going off-topic now,
because it's becoming about metaphysics, and thus should
go on metatuning ... but Ozan no longer subscribes there,
so the only place to engage him in discussion on it is
the hypertuning list.

/hypertuning/

Great photo, Oz, BTW ... it blows away the monochrome
Andromeda Galaxy photo that i use on celestial-tuning.

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In tuning@yahoogroups.com, "Aaron Wolf" <backfromthesilo@...> wrote:

> Negative numbers don't exist outside of the world of ideas.
> But neither do positive numbers. Numbers are ideas.
> They exist. As ideas. Not otherwise. I don't care to
> discuss the nature of existence. BUT, we may as well
> remember that since ideas necessarily exist inside our
> heads, we should stop ANY attempt to "prove" or "disprove"
> the nature of ideas.

Numbers are simply a means to quantify our perception
of the natural world. They can mean anything we want
them to -- the important thing about them is that they
follow certain predictable rules. 2+2=4, always, so
no matter to what use we decide to employ these numbers,
we know that that operation will always work.

There's no reason why the concept of zero cannot
embrace both the idea of an absence of any measureable
quantity in a finite sense, and also as a balancing point
at the center of a continuum of values both positive
and negative. Zero works very well for both concepts.

IOW, i see no argument except that Ozan seems to want
to win one (so i'm agreeing with Gene too). We can have
two definitions of "unison": one where it is not an
interval, but instead a separate concept where there
is a total lack of interval; and another, where it is
an interval like all others, whose value in pitch-space
is zero.

My goodness ... my Encyclopedia entry for "diesis" has
no less than 7 separate definitions -- what's the big
deal with giving unison 2?

-monz
http://tonalsoft.com
Tonescape microtonal music software

Joe,

To throw in my 5 cents worth *monkey wrench* into this never-ending discussion, 2+2=4 does not always hold.

The outcome depends on the *module* one is working under, as in *clock arithmetic*.

If there are 4 hours in one day, then 2 hours + 2 hours = 0 (zero) hours.

Can Akkoc

monz <monz@tonalsoft.com> wrote:
--- In tuning@yahoogroups.com, "Aaron Wolf" <backfromthesilo@...> wrote:

> Negative numbers don't exist outside of the world of ideas.
> But neither do positive numbers. Numbers are ideas.
> They exist. As ideas. Not otherwise. I don't care to
> discuss the nature of existence. BUT, we may as well
> remember that since ideas necessarily exist inside our
> heads, we should stop ANY attempt to "prove" or "disprove"
> the nature of ideas.

Numbers are simply a means to quantify our perception
of the natural world. They can mean anything we want
them to -- the important thing about them is that they
follow certain predictable rules. 2+2=4, always, so
no matter to what use we decide to employ these numbers,
we know that that operation will always work.

There's no reason why the concept of zero cannot
embrace both the idea of an absence of any measureable
quantity in a finite sense, and also as a balancing point
at the center of a continuum of values both positive
and negative. Zero works very well for both concepts.

IOW, i see no argument except that Ozan seems to want
to win one (so i'm agreeing with Gene too). We can have
two definitions of "unison": one where it is not an
interval, but instead a separate concept where there
is a total lack of interval; and another, where it is
an interval like all others, whose value in pitch-space
is zero.

My goodness ... my Encyclopedia entry for "diesis" has
no less than 7 separate definitions -- what's the big
deal with giving unison 2?

-monz
http://tonalsoft.com
Tonescape microtonal music software

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Hi Can,

--- In tuning@yahoogroups.com, Can Akkoc <can193849@...> wrote:
>
> Joe,
>
> To throw in my 5 cents worth *monkey wrench* into
> this never-ending discussion, 2+2=4 does not always hold.
>
> The outcome depends on the *module* one is working under,
> as in *clock arithmetic*.
>
> If there are 4 hours in one day, then
> 2 hours + 2 hours = 0 (zero) hours.

Yes, of course, you're absolutely right ... and this is
in fact an important point to bring up here, because modolo
arithmetic is important in any tuning which recognizes
an equivalence-interval.

But still, in mod-4 math, in a sense 4 = 0, so 2+2=4
is still true, sort of ...

-monz
http://tonalsoft.com
Tonescape microtonal music software

Petr,

----- Original Message -----
From: "Petr Par�zek" <p.parizek@chello.cz>
To: <tuning@yahoogroups.com>
Sent: 03 Mart 2006 Cuma 0:54
Subject: Re: [tuning] Re: unison as an interval

> Hi Ozan.
>
> You wrote:
>
> > Have you not read http://home.ubalt.edu/ntsbarsh/zero/ZERO.HTM
>
> I have. And I'm getting a feeling like if it was written 100 years ago.
> Don't try to persuade me to find a source which shares my view. You don't
> know how lucky you are that I have lots of other things to do for the
> academy at which I study. If I had more time, I surely would.
>

We all have things to attend to, and I'm no expert in mathematics. However,
I will staunchly defend my point of view until I'm proven wrong.

> > You can define both infinetesimal and infinitely large in mathematics as
> > long as you remain faithful to the terminology. Infinitely small does
not
> > equal 0. You are decreasing in size perpetually, but you never reach
zero.
> > In contrast, you can increase in size perpetually, and never reach an
end.
>
> I see you've not got my idea. OK, so another example.
> Take the number 1, add 1/2 to this, and you get 1.5. Add 1/4, and you get
> 1.75. Add 1/8, and you get 1.875. Add 1/16, and you get 1.9375. ... If you
> go on doing this for an infinite number of times, you eventually reach 2.
If
> you do this for a finite number of times, you'll never get there.
>

I do not think at all that you will ever reach 2, you will simply get closer
and closer to it. The difference will diminish constantly, but never vanish
altogether.

> > What? Zero is not something too small to be called a value, it is the
> > absence of value proper, or rather, the absence of whatever it is you
want
> > to count.
>
> Never! This is just the same as if you said that negative numbers are
> nonsense (or don't exist) and trying to proove it stating that you can't
> hold "minus two apples" in your hand or that noone can take two apples
away
> from you if you don't have even one of them.
>

If I owe you 5 dollars and I have no money in my possession to pay you, my
assets are -5 dollars. Never did I claim anywhere that negative numbers do
not exist. I see that you appreciate neither zero nor negativity in their
proper context in the integer continuum.

> > According to John Wallis, "Infinitely means more than any Finite number
> > assignable". It is the impossibility of assigning a substantial
quantity.
>
> This proves MY point. Even the number of existing finite numbers is
> infinite. That means if you stack finite numbers in whatever way (even
some
> extremely huge ones), you would have to do this for an infinite number of
> times in order to get to infinity.
>

The number of existing finite numbers are not infinite. You cannot reach
infinity by stacking finite numbers, unless you do this indefinitely, and
this does not render finite numbers the status of infinity. You will only
reach insurmountable numbers by doing so a definite number of times.
Infinity is an endlessly indefinite process in either the positive, or the
negative direction.

> > infinity is not the largest value, it is the impossibility of descerning
a
> > finite value.
>
> Can you tell me who was the author of this statement? Probably not someone
> who has a passion for examining the internal structure of values and their
> properties/relations.

I am the author of that statement in all my ignorance and daring.

If this was true, then you could say, for example,
> that the number of 100 trillion was infinity some millenia ago (at the
times
> when even highly aware people were unwilling or unable to accept its large
> quantity)

What do people who lived thousands of years ago have anything to do with the
mathematical concept of infinity? I'm referring to the impossibility not
depending on the limitations of the human mind, but the actual workings of
the cosmos.

and is not anymore as we have already developped skills for
> describing and using numbers this large. But this is not the case. The
> calculators which call a large number "infinity" are calling it like that
> not for any "infinityness" but for its value which is too large for them
to
> accept.

Take for instance Pi. If it is a trancendental number as it is said to be,
then we can safely claim that the integers after the dot will go on
indefinitely without reaching an end. Thus we can say that Pi is infinitely
complex, meaning that you cannot exhaust the numerical detail of Pi. If it
was possible to exhaust decimal places, you cannot say any longer that the
chain of numbers is infinitely long.

http://en.wikipedia.org/wiki/Pi

Forgive me for saying so, but I do not think you grasp infinity at all.

> > It is not only uncertain, but also indeterminable.
>
> That's what I meant. It's indeterminable to be given a single position in
> the range between 0 and infinity, but it's the range. Maybe this example
> will help you understand better what I mean. Everyone knows that "X^0 = 1"
> whatever value you assign to X. Taking this result from the other end, I
can
> actually say that the 0th root of 1 can result in any number existing. Do
> you want to tell me its impossible to describe the result of the 0th root
of
> 1, or, for that matter, the 0th root of any number?
>

It is impossible to pinpoint what the zeroth root of 1 may be. Thus the
result is indefinite.

> Petr
>
>

Oz.

Rounding off decimal places to whole numbers for the sake of convenience
does not equal an argument propounded in defense of the unison being an
interval... which is not.

----- Original Message -----
From: "Aaron Wolf" <backfromthesilo@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 03 Mart 2006 Cuma 1:36
Subject: [tuning] Re: unison as an interval

>
> > > What? Zero is not something too small to be called a value, it is the
> > > absence of value proper, or rather, the absence of whatever it is you
want
> > > to count.
> >
> > Never! This is just the same as if you said that negative numbers are
> > nonsense (or don't exist) and trying to proove it stating that you can't
> > hold "minus two apples" in your hand or that noone can take two apples
away
> > from you if you don't have even one of them.
> >
>
> Getting in this discussion is itself off topic, but my goal is to bring
people back to
> pragmatic musical discussion...
>
> Negative numbers don't exist outside of the world of ideas. But neither
do positive
> numbers. Numbers are ideas. They exist. As ideas. Not otherwise. I
don't care to
> discuss the nature of existence. BUT, we may as well remember that since
ideas
> necessarily exist inside our heads, we should stop ANY attempt to "prove"
or "disprove"
> the nature of ideas. That implies using external or at least logical
rules to deal with these
> ideas. It won't go anywhere.
> To say that 1.9999 (repeat nines for infinity) = 2 is not right or wrong.
It's a bunch of
> SYMBOLS. In other words, we have a notation system for categorizing our
ideas. And for
> COMMUNICATION'S sake we have to agree whether or not we allow this
equalization of two
> different symbols. These ideas do not otherwise externally exist. Any
debate that thinks
> that 2 or 1.99999... is something more tangible than a symbol for
communication is
> kidding themselves. So quit it. Go back and figure out if there was
something that was
> worth communicating, and figure out how to get the message across and work
together to
> understand, instead of debating the wording! I didn't catch if there was
a message to start
> with or just wordplay.
>
> -Aaron
>

Please include my point too with any entry on unison in your encyclopedia
then.

----- Original Message -----
From: "monz" <monz@tonalsoft.com>
To: <tuning@yahoogroups.com>
Sent: 03 Mart 2006 Cuma 6:25
Subject: [tuning] Re: unison as an interval

> --- In tuning@yahoogroups.com, "Aaron Wolf" <backfromthesilo@...> wrote:
>
>
> > Negative numbers don't exist outside of the world of ideas.
> > But neither do positive numbers. Numbers are ideas.
> > They exist. As ideas. Not otherwise. I don't care to
> > discuss the nature of existence. BUT, we may as well
> > remember that since ideas necessarily exist inside our
> > heads, we should stop ANY attempt to "prove" or "disprove"
> > the nature of ideas.
>
>
>
> Numbers are simply a means to quantify our perception
> of the natural world. They can mean anything we want
> them to -- the important thing about them is that they
> follow certain predictable rules. 2+2=4, always, so
> no matter to what use we decide to employ these numbers,
> we know that that operation will always work.
>
> There's no reason why the concept of zero cannot
> embrace both the idea of an absence of any measureable
> quantity in a finite sense, and also as a balancing point
> at the center of a continuum of values both positive
> and negative. Zero works very well for both concepts.
>
> IOW, i see no argument except that Ozan seems to want
> to win one (so i'm agreeing with Gene too). We can have
> two definitions of "unison": one where it is not an
> interval, but instead a separate concept where there
> is a total lack of interval; and another, where it is
> an interval like all others, whose value in pitch-space
> is zero.
>
> My goodness ... my Encyclopedia entry for "diesis" has
> no less than 7 separate definitions -- what's the big
> deal with giving unison 2?
>
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>
>
>
>

I meant to say, they consider 0 as 1, and 1 as 0, which complicates our
communication even in music theory.

----- Original Message -----
From: "monz" <monz@tonalsoft.com>
To: <tuning@yahoogroups.com>
Sent: 03 Mart 2006 Cuma 6:06
Subject: [tuning] Re: unison as an interval

> Hi Oz,
>
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> > I'm saying that neither the Julian nor the Gregorian
> > calendars acknowledge the existance of a 0 point in
> > the integer continuum of negative and positive
> > numbers, whereas they ordinarily should have.
>
>
>
> But this is wrong. The Julian and Gregorian calendars
> don't recognize a *year* zero, but they do both recognize
> a zero *point*: the singularity between the end of BC
> and the beginning of AD.
>
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>
>
>

Thanks. What is celestial tuning?

>
> I'd say that this discussion is going off-topic now,
> because it's becoming about metaphysics, and thus should
> go on metatuning ... but Ozan no longer subscribes there,
> so the only place to engage him in discussion on it is
> the hypertuning list.
>
> /hypertuning/
>
>
> Great photo, Oz, BTW ... it blows away the monochrome
> Andromeda Galaxy photo that i use on celestial-tuning.
>
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>
>
>

Hi Ozan.

You wrote:

> I do not think at all that you will ever reach 2, you will simply get
closer
> and closer to it. The difference will diminish constantly, but never
vanish
> altogether.

You have actually said the same as I have, only from a different point of
view. People's lives last for a finite number of days and that's why noone
can witness an operation repeating for an infinite number of times, let
alone do it themselves.

> If I owe you 5 dollars and I have no money in my possession to pay you, my
> assets are -5 dollars.

Okay, so the value is -5 (i.e. a negative value). Then, if you get $5, you
have a positive amount. After you give that to me, your assets are 0 (i.e. a
neutral value). I don't see any radical change.

> The number of existing finite numbers are not infinite. You cannot reach
> infinity by stacking finite numbers, unless you do this indefinitely, and
> this does not render finite numbers the status of infinity. You will only
> reach insurmountable numbers by doing so a definite number of times.
> Infinity is an endlessly indefinite process in either the positive, or the
> negative direction.

Almost, but I said "infinite number of times" and you're saying
"indefinite", which is probably why you've understood my words in a
different way than I meant them. But basically I think you're proving both
your and my point here now.

> What do people who lived thousands of years ago have anything to do with
the
> mathematical concept of infinity? I'm referring to the impossibility not
> depending on the limitations of the human mind, but the actual workings of
> the cosmos.

Then, I admit, I'm totally unaware what you mean.

> Take for instance Pi. If it is a trancendental number as it is said to be,
> then we can safely claim that the integers after the dot will go on
> indefinitely without reaching an end. Thus we can say that Pi is
infinitely
> complex, meaning that you cannot exhaust the numerical detail of Pi. If it
> was possible to exhaust decimal places, you cannot say any longer that the
> chain of numbers is infinitely long.
>
> http://en.wikipedia.org/wiki/Pi

Again, you're proving both your and my point at the same time now.

> Forgive me for saying so, but I do not think you grasp infinity at all.

I'm confused. Right now, I've got such a feeling like that infinity seems to
be something more or less similar to both of us, only each of us views it
from a different angle.

> It is impossible to pinpoint what the zeroth root of 1 may be. Thus the
> result is indefinite.

Again, that's just what I meant.

Petr

Petr Parízek wrote:

>> If I owe you 5 dollars and I have no money in my possession to pay you, my
>> assets are -5 dollars.
>
> Okay, so the value is -5 (i.e. a negative value). Then, if you get $5, you
> have a positive amount. After you give that to me, your assets are 0 (i.e. a
> neutral value). I don't see any radical change.

Petr, don't fall for the arguments about infinity and 1 versus 0. The
first has nothing to do with intervals, the second are two arbitrary
starting points for counting which in both cases progresses with the
same cardinal numbers. Ozan didn't acknowledge that there is a way to
invert intervals in a counterpoint by transposing the upper voice down,
so I doubt negative numbers will help his understanding.

More to the point, if an analogy is needed, would be an argument whether
addition by 0 or multiplication by 1 exist. Addition of zero is
first-grade math, just before going higher than 10.

klaus

Then we are at par with each other!

----- Original Message -----
From: "Petr Par�zek" <p.parizek@chello.cz>
To: <tuning@yahoogroups.com>
Sent: 06 Mart 2006 Pazartesi 22:43
Subject: Re: [tuning] Re: unison as an interval

> Hi Ozan.
>
> You wrote:
>
> > I do not think at all that you will ever reach 2, you will simply get
> closer
> > and closer to it. The difference will diminish constantly, but never
> vanish
> > altogether.
>
> You have actually said the same as I have, only from a different point of
> view. People's lives last for a finite number of days and that's why noone
> can witness an operation repeating for an infinite number of times, let
> alone do it themselves.
>
> > If I owe you 5 dollars and I have no money in my possession to pay you,
my
> > assets are -5 dollars.
>
> Okay, so the value is -5 (i.e. a negative value). Then, if you get $5, you
> have a positive amount. After you give that to me, your assets are 0 (i.e.
a
> neutral value). I don't see any radical change.
>
> > The number of existing finite numbers are not infinite. You cannot reach
> > infinity by stacking finite numbers, unless you do this indefinitely,
and
> > this does not render finite numbers the status of infinity. You will
only
> > reach insurmountable numbers by doing so a definite number of times.
> > Infinity is an endlessly indefinite process in either the positive, or
the
> > negative direction.
>
> Almost, but I said "infinite number of times" and you're saying
> "indefinite", which is probably why you've understood my words in a
> different way than I meant them. But basically I think you're proving both
> your and my point here now.
>
> > What do people who lived thousands of years ago have anything to do with
> the
> > mathematical concept of infinity? I'm referring to the impossibility not
> > depending on the limitations of the human mind, but the actual workings
of
> > the cosmos.
>
> Then, I admit, I'm totally unaware what you mean.
>
> > Take for instance Pi. If it is a trancendental number as it is said to
be,
> > then we can safely claim that the integers after the dot will go on
> > indefinitely without reaching an end. Thus we can say that Pi is
> infinitely
> > complex, meaning that you cannot exhaust the numerical detail of Pi. If
it
> > was possible to exhaust decimal places, you cannot say any longer that
the
> > chain of numbers is infinitely long.
> >
> > http://en.wikipedia.org/wiki/Pi
>
> Again, you're proving both your and my point at the same time now.
>
> > Forgive me for saying so, but I do not think you grasp infinity at all.
>
> I'm confused. Right now, I've got such a feeling like that infinity seems
to
> be something more or less similar to both of us, only each of us views it
> from a different angle.
>
> > It is impossible to pinpoint what the zeroth root of 1 may be. Thus the
> > result is indefinite.
>
> Again, that's just what I meant.
>
> Petr
>

Apparently you did not get my drift at all Kraig. You can transpose, invert,
mutilate any interval you want, except the unison (+2 tones, 1 pitch, 0
interval), which gets treated IMNSHO in context of octave equivalances...
that is, you can only transform unison (by non-linear mapping) if you want
it to suddenly sound the interval of an octave. Otherwise, all operations
can be in both directions.

----- Original Message -----
From: "klaus schmirler" <KSchmir@online.de>
To: <tuning@yahoogroups.com>
Sent: 07 Mart 2006 Sal� 2:30
Subject: Re: [tuning] Re: unison as an interval

Petr Par�zek wrote:

>> If I owe you 5 dollars and I have no money in my possession to pay you,
my
>> assets are -5 dollars.
>
> Okay, so the value is -5 (i.e. a negative value). Then, if you get $5, you
> have a positive amount. After you give that to me, your assets are 0 (i.e.
a
> neutral value). I don't see any radical change.

Petr, don't fall for the arguments about infinity and 1 versus 0. The
first has nothing to do with intervals, the second are two arbitrary
starting points for counting which in both cases progresses with the
same cardinal numbers. Ozan didn't acknowledge that there is a way to
invert intervals in a counterpoint by transposing the upper voice down,
so I doubt negative numbers will help his understanding.

More to the point, if an analogy is needed, would be an argument whether
addition by 0 or multiplication by 1 exist. Addition of zero is
first-grade math, just before going higher than 10.

klaus

Ozan Yarman wrote:
> Apparently you did not get my drift at all Kraig.

Klaus.

You can transpose, invert,
> mutilate any interval you want, except the unison (+2 tones, 1 pitch, 0
> interval), which gets treated IMNSHO in context of octave equivalances...
> that is, you can only transform unison (by non-linear mapping) if you want
> it to suddenly

Did you understand that this is not about intervals in isolation? Primes and octaves may happen in passing, but they are typical cadence intervals, prepared by a leading tone and whatever other note your idiom provides for the other part. Take this:

d c
b c

Start at the 6th and at the 3rd. The 6th resolves to an octave, the 3rd to a prime. Most people would assume, and so far it so hasn't created any problems that a different view of the prime would solve, that

a) an interval resolves to another interval
b) octaves and primes are inversions of each other.

This is all I see as pertinent to the topic.

klaus

sound the interval of an octave. Otherwise, all operations
> can be in both directions.

> Ozan Yarman wrote:
> > Apparently you did not get my drift at all Kraig.
>
> Klaus.
>

A thousand thousand pardons effendi!

>
> Did you understand that this is not about intervals in isolation? Primes
> and octaves may happen in passing, but they are typical cadence
> intervals, prepared by a leading tone and whatever other note your idiom
> provides for the other part. Take this:
>
> d c
> b c
>
> Start at the 6th and at the 3rd. The 6th resolves to an octave, the 3rd
> to a prime. Most people would assume, and so far it so hasn't created
> any problems that a different view of the prime would solve, that
>
> a) an interval resolves to another interval
> b) octaves and primes are inversions of each other.
>
> This is all I see as pertinent to the topic.
>
> klaus
>

I have no objection for a minor third resolving to a unison or a major sixth
resolving to an octave. I just object to the `inversion` of unison to the
octave. Exchanging unison with the octave, or transforming the unison to one
or more octaves is much more congruent in the context that unison has an
intervallic value of 0 and that primes and octaves are equivalent.

Oz.

Ozan Yarman wrote:
> >> Ozan Yarman wrote:
>>> Apparently you did not get my drift at all Kraig.
>> Klaus.
>>
> > > A thousand thousand pardons effendi!

Effendiler, please. After all this concerns Kraig too.

> > >> Did you understand that this is not about intervals in isolation? Primes
>> and octaves may happen in passing, but they are typical cadence
>> intervals, prepared by a leading tone and whatever other note your idiom
>> provides for the other part. Take this:
>>
>> d c
>> b c
>>
>> Start at the 6th and at the 3rd. The 6th resolves to an octave, the 3rd
>> to a prime. Most people would assume, and so far it so hasn't created
>> any problems that a different view of the prime would solve, that
>>
>> a) an interval resolves to another interval
>> b) octaves and primes are inversions of each other.
>>
>> This is all I see as pertinent to the topic.
>>
>> klaus
>>
> > > I have no objection for a minor third resolving to a unison or a major sixth
> resolving to an octave. I just object to the `inversion` of unison to the
> octave. Exchanging unison with the octave, or transforming the unison to one
> or more octaves is much more congruent in the context that unison has an
> intervallic value of 0 and that primes and octaves are equivalent.

The operation - exchange of lower and higher parts - is the same as for fifths and fourths, and both prime and octave are regarded as identity intervals. For intervals in context, this makes a lot of sense.

The starting-on-one matter is not relevant as long as you do nothing more but count. Adding intervals, however, is a different matter; two 8ves are a 15th; I don't like that either. But at least the error is consistent: 5+4, 3+6, 7+2 and, yes, 1+8 all add up to 9, which in musical terms should be an octave.

If it isn't clear now, I'll give in. I really can't do any more.

klaus

Hi Oz,

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Please include my point too with any entry on unison
> in your encyclopedia then.

I know you've already written a *lot* about it, but i got
involved in other things over the last week and now can't
be bothered to hunt for what i need.

Please, be so kind as to post what you would like me to
include in the Encyclopedia entry as a wholly new and
separate definition #2 of "unison", and i'll simply copy
and paste it into the webpage. Thanks in advance.

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Thanks. What is celestial tuning?

An offshoot tuning list:

/celestial-tuning/

I created it about 5 years ago, when this "big list"
suddenly began spawning a number of offspring lists.

Folks here periodically complained that the discussion
was digressing too far away from music, to which i
had to keep retorting that in my research, the ancient
concepts of tuning which i frequently encountered
dealt with harmony not only in relation to music, but
also as a way to explain the mechanics of the whole cosmos.
And i was as interested in studying the astronomical
implications of these tuning theories as i was the
musical ones.

-monz
http://tonalsoft.com
Tonescape microtonal music software

> >
> > A thousand thousand pardons effendi!
>
> Effendiler, please. After all this concerns Kraig too.
>

But he hardly gets it I'm unashamed to say. LOL

> >
> > I have no objection for a minor third resolving to a unison or a major
sixth
> > resolving to an octave. I just object to the `inversion` of unison to
the
> > octave. Exchanging unison with the octave, or transforming the unison to
one
> > or more octaves is much more congruent in the context that unison has an
> > intervallic value of 0 and that primes and octaves are equivalent.
>
> The operation - exchange of lower and higher parts - is the same as for
> fifths and fourths, and both prime and octave are regarded as identity
> intervals. For intervals in context, this makes a lot of sense.
>
> The starting-on-one matter is not relevant as long as you do nothing
> more but count. Adding intervals, however, is a different matter; two
> 8ves are a 15th; I don't like that either. But at least the error is
> consistent: 5+4, 3+6, 7+2 and, yes, 1+8 all add up to 9, which in
> musical terms should be an octave.
>
> If it isn't clear now, I'll give in. I really can't do any more.
>
> klaus
>
>

Show me then, how you invert unison in Western contrapunctus.

Oz.

Thanks monz. That's very interesting!

SNIP

> An offshoot tuning list:
>
> /celestial-tuning/
>
>
> I created it about 5 years ago, when this "big list"
> suddenly began spawning a number of offspring lists.
>
> Folks here periodically complained that the discussion
> was digressing too far away from music, to which i
> had to keep retorting that in my research, the ancient
> concepts of tuning which i frequently encountered
> dealt with harmony not only in relation to music, but
> also as a way to explain the mechanics of the whole cosmos.
> And i was as interested in studying the astronomical
> implications of these tuning theories as i was the
> musical ones.
>
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>
>

Well, my arguments can be summed up as follows:

In the domain of integers, zero is a neuter number denoting the absence of
whatever is being counted.

In context of calculating the distance between an upper and a lower pitch
(see *interval, The Harvard Dictionary of Music 4th ed.), an intervallic
value of 0 denotes the absence of an interval. Hence, `unison` (one sound)
is the zeroth step, the absence of a `between`, the lack of a frequency
difference between two or more tones that occupy the same pitch. Thus, it is
redundant to speak of an `interval of a unison` as if such a measurably
quantity seperating tones from each other existed, as long as it is agreed
that an error by musicians sounding a unison is not the fault of the unison.

In a world not cognizant of zero, the zeroth position has been designated as
the `perfect prime`, and remains hence in our music vocabulary. This greatly
adds to the confusion regarding interval inversions:

0 1 2 3 4 5 6 7 (what should have been)
1 2 3 4 5 6 7 8 (as is)
c d e f g a b c'
c----------------
c B A G F E D C

Invertible counterpoint does indeed allow the tonic of melody A and the
tonic of melody B seperated by an octave to meet at the unison when
transposed:

at the interval of an octave:

7 8 7 6 7 (what should have been)
8 9 8 7 8 (as is)
c b c d c
C D C B C

at unison:

0 1 0 1 0 (what should have been)
1 2 1 2 1 (as is)
C D C B C
c b c d c

In this special case, octave equivalances come into play, and hence unison
is made to equal one or more octaves:

1/8 = 1/4 = 1/2 = 1 = 2 = 4 = 8
ad infinitum.

This is the reason why a music is said to play in unison while seperated by
one or more octaves.

Cordially,
Oz.

----- Original Message -----
From: "monz" <monz@tonalsoft.com>
To: <tuning@yahoogroups.com>
Sent: 08 Mart 2006 �ar�amba 2:04
Subject: [tuning] Encyclopedia addition - unison as an interval

> Hi Oz,
>
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > Please include my point too with any entry on unison
> > in your encyclopedia then.
>
>
>
> I know you've already written a *lot* about it, but i got
> involved in other things over the last week and now can't
> be bothered to hunt for what i need.
>
> Please, be so kind as to post what you would like me to
> include in the Encyclopedia entry as a wholly new and
> separate definition #2 of "unison", and i'll simply copy
> and paste it into the webpage. Thanks in advance.
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>
>

Ozan Yarman wrote:
>>> A thousand thousand pardons effendi!
>> Effendiler, please. After all this concerns Kraig too.
>>
> > > But he hardly gets it I'm unashamed to say. LOL

Turkish grammar is so simple and logical and has the nice touch of adding a little complexity just for sound's sake, it's a pity not everyone learns it. My own ability begins and ends with plural formation.

> > > Show me then, how you invert unison in Western contrapunctus.

I showed you before: by looking at intervals in their context, in a musical line. No cadence this time, just some aimless noodling with an unprepared dissonance:

a g a g a g a g
d f e g f d e c

Play it a fifth apart, and the g's in the middle meet at the prime. Turn the parts around (and imagine a bassline to take care of the fourths if you want to), and the g's are an octave apart.

klaus

> >
> > Show me then, how you invert unison in Western contrapunctus.
>
> I showed you before: by looking at intervals in their context, in a
> musical line. No cadence this time, just some aimless noodling with an
> unprepared dissonance:
>
> a g a g a g a g
> d f e g f d e c
>
> Play it a fifth apart, and the g's in the middle meet at the prime. Turn
> the parts around (and imagine a bassline to take care of the fourths if
> you want to), and the g's are an octave apart.
>
> klaus
>

I think the term "inversion" isn't very helpful to actually understand
this example. I would teach this as "octave transposition" and noting
the effect of whether a part were in the octave above or below the
other. That, to me, is a far more clear way to talk about this.

>
> Turkish grammar is so simple and logical and has the nice touch of
> adding a little complexity just for sound's sake, it's a pity not
> everyone learns it. My own ability begins and ends with plural formation.
>

Free lessons shall be given this weekend at my mansion during noon hours for
those interested. Prayer rugs are free of charge too. LOL

> >
>
> >
> > Show me then, how you invert unison in Western contrapunctus.
>
> I showed you before: by looking at intervals in their context, in a
> musical line. No cadence this time, just some aimless noodling with an
> unprepared dissonance:
>
> a g a g a g a g
> d f e g f d e c
>
> Play it a fifth apart, and the g's in the middle meet at the prime. Turn
> the parts around (and imagine a bassline to take care of the fourths if
> you want to), and the g's are an octave apart.
>

This is invertible counterpoint, nothing more. It's only a matter of
transposing voices. No where does it require to consider unison an interval.

> klaus
>
>

Oz.

Ozan Yarman wrote:

>>> Show me then, how you invert unison in Western contrapunctus.
>> I showed you before: by looking at intervals in their context, in a
>> musical line. No cadence this time, just some aimless noodling with an
>> unprepared dissonance:
>>
>> a g a g a g a g
>> d f e g f d e c
>>
>> Play it a fifth apart, and the g's in the middle meet at the prime. Turn
>> the parts around (and imagine a bassline to take care of the fourths if
>> you want to), and the g's are an octave apart.
>>
> > > This is invertible counterpoint, nothing more. It's only a matter of
> transposing voices. No where does it require to consider unison an interval.
>

It's bad invertible counterpoint because it has a lot of fifths which turn into fourths which are a no-no. Sixths, thirds, octaves and primes would be fine; seconds and sevenths, fourths and fifths need to be treated as dissonances. This was an explanation of the principles of inverted counterpoint in terms of its admissible and forbidden ... intervals. There is still a relationship between two parts that wants to be described, even if they momentarily hit the same note.

Aaron, most musical terms have acquired multiple meanings in the course of history. However, in most cases the context gives useful hints. The problem around here is that terms are likely to be lifted from context to context (the original one here was "interval") until they turn to putty. If my memory doesn't deceive me very much, even the twelve toners whose prime is 0 and who count 9, t, e speak of inversions (at axis x, where the inversion is the complement for x). I have suggested "octave complement" for inverse intervals, swiped 82% from the grammarian's "object complement". I'd actually prefer "do the flip-o-roony".

klaus

> Aaron, most musical terms have acquired multiple meanings in the course
> of history. However, in most cases the context gives useful hints. The
> problem around here is that terms are likely to be lifted from context
> to context (the original one here was "interval") until they turn to
> putty. If my memory doesn't deceive me very much, even the twelve toners
> whose prime is 0 and who count 9, t, e speak of inversions (at axis x,
> where the inversion is the complement for x). I have suggested "octave
> complement" for inverse intervals, swiped 82% from the grammarian's
> "object complement". I'd actually prefer "do the flip-o-roony".
>
> klaus
>

I agree that we need to be aware of existing definitions, but language isn't
prescribed as much as evolves to wherever it is at by a mix of factors.
I think my term "octave transposition" is so clear that it is pretty obvious
what I mean. And it would seem that "inversion" needs clarification and
specification in order to mean much, so therefore that therm seems to me
a less direct, less effective way to communicate. And since my use of
"octave transposition" doesn't require changing any accepted definitions,
I think it is a better way to go, though admittedly not the only way.

-Aaron

And as one more plug for the celestial-tuning list,
i'd like to mention that i try to be very vigilant about
deleting the posts which come in about "finding the
love of your life" or "finding a great sex partner",
and banning their authors.

I wish that the owners and moderators of other lists
to which i subscribe would do the same. It's exasperating
to have to wade thru all that junk to read the good posts,
especially on the lists that don't have much traffic.

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Thanks monz. That's very interesting!
>
> SNIP
>
> > An offshoot tuning list:
> >
> > /celestial-tuning/
> >
> >
> > I created it about 5 years ago, when this "big list"
> > suddenly began spawning a number of offspring lists.
> >
> > Folks here periodically complained that the discussion
> > was digressing too far away from music, to which i
> > had to keep retorting that in my research, the ancient
> > concepts of tuning which i frequently encountered
> > dealt with harmony not only in relation to music, but
> > also as a way to explain the mechanics of the whole cosmos.
> > And i was as interested in studying the astronomical
> > implications of these tuning theories as i was the
> > musical ones.