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about naming tritave and ......

🔗Mohajeri Shahin <shahinm@kayson-ir.com>

2/2/2006 12:50:48 AM

Hi all

We know that 2/1 + 3/2 is tritave ......

Is there any reference and method about naming other interval like 2/1
+4/3 or 2/1+9/8 and other in the same way as tritave? (my proposal : can
we name 2/1+4/3 fourtave ... 2/1+5/4 as pentave .. and so on?)

thanks

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

🔗Hudson Lacerda <hfmlacerda@yahoo.com.br>

2/2/2006 5:40:22 AM

Mohajeri Shahin escreveu:
> Hi all
> > We know that 2/1 + 3/2 is tritave ......
> > Is there any reference and method about naming other interval like 2/1
> +4/3 or 2/1+9/8 and other in the same way as tritave? (my proposal : can
> we name 2/1+4/3 fourtave ... 2/1+5/4 as pentave .. and so on?)

I don't know, and I don't like the idea.

Why not just use, if you are talking about *equivalence*, "modulo 3/1", "modulo 8/3", or then "3/1 equivalence", "8/3 equivalence", and so on?

Regards,
Hudson

--
Hudson Lacerda <http://geocities.yahoo.com.br/hfmlacerda/>
*Nï¿½o deixe seu voto sumir! http://www.votoseguro.org/
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🔗Keenan Pepper <keenanpepper@gmail.com>

2/2/2006 10:05:55 AM

On 2/2/06, Hudson Lacerda <hfmlacerda@yahoo.com.br> wrote:
> Mohajeri Shahin escreveu:
> > Hi all
> >
> > We know that 2/1 + 3/2 is tritave ......
> >
> > Is there any reference and method about naming other interval like 2/1
> > +4/3 or 2/1+9/8 and other in the same way as tritave? (my proposal : can
> > we name 2/1+4/3 fourtave ... 2/1+5/4 as pentave .. and so on?)
>
> I don't know, and I don't like the idea.
>
> Why not just use, if you are talking about *equivalence*, "modulo 3/1",
> "modulo 8/3", or then "3/1 equivalence", "8/3 equivalence", and so on?
>
> Regards,
> Hudson

I agree. BTW, there are some interesting systems with 4/1 equivalence
which only contain even powers of two. That is, 4, 16, 64... are okay
but 2, 8, 32... are thrown out. Meantone still works, because 81/80
contains only even powers of two, and it makes a pretty interesting
scale. Dividing the 4/1 into 5, 13, 25, or 49 parts is also
interesting.

Keenan

🔗Rich Holmes <rsholmes@mailbox.syr.edu>

2/2/2006 11:32:15 AM

"Mohajeri Shahin" <shahinm@kayson-ir.com> writes:

> Hi all
>
> We know that 2/1 + 3/2 is tritave ......
>
> Is there any reference and method about naming other interval like 2/1
> +4/3 or 2/1+9/8 and other in the same way as tritave? (my proposal : can
> we name 2/1+4/3 fourtave ... 2/1+5/4 as pentave .. and so on?)

And what would you name 2/1+8/4? "Octave"?

"Tritave" was a stupid, stupid choice of terminology; let's not
compound it.

- Rich Holmes

🔗Mohajeri Shahin <shahinm@kayson-ir.com>

2/4/2006 6:32:00 AM

Hi rich holmes , dear freind

As if you are very allergic to this word , Sorry i made you angry ,
although this word is being used :
http://tonalsoft.com/enc/e/equivalence-interval.aspx ,
http://en.wikipedia.org/wiki/Bohlen-Pierce_scale

I thought may be there is a refrence for naming intervals greater than
octave . any how, I am over with it !!!!

So if we have 3/1 then i think bohlen-pierce scale as an EDI system
(EQUAL DIVISION OF INTERVAL) with I=3/1or ED(3/1).

Now Here is ED(5/2) system with steps of 226.6 cent:

0:-- 1/1 C Dbb unison, perfect prime

1:-- 226.616 cents

2:-- 453.232 cents

3:-- 679.849 cents

4:-- 906.465 cents

5:-- 1133.081 cents

6:-- 1359.697 cents

7: -- 1586.314 cents

And so on

It is approximately in 7-limit rational system as scala reported :

0: -- 1/1 -- C -- Dbb unison, perfect prime

1: -- 8/7 -- D-- Ebb septimal whole tone

2: -- 35/27 -- 9/4-tone, septimal
semi-diminished fourth

3: -- 40/27 -- G -- Abb grave fifth

4: -- 27/16-- A -- Bbb Pythagorean major sixth

5: -- 48/25-- B -- Cb classic diminished octave

6: -- 35/16-- septimal neutral second + 1
octave

7: -- 5/2 -- E-- Fb major 10th

You can test it , sounding good to me !

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 Rich Holmes
Sent: Thursday, February 02, 2006 11:02 PM
To: tuning@yahoogroups.com
Subject: Re: [tuning] about naming tritave and ......

"Mohajeri Shahin" <shahinm@kayson-ir.com> writes:

> Hi all
>
> We know that 2/1 + 3/2 is tritave ......
>
> Is there any reference and method about naming other interval like 2/1
> +4/3 or 2/1+9/8 and other in the same way as tritave? (my proposal :
can
> we name 2/1+4/3 fourtave ... 2/1+5/4 as pentave .. and so on?)

And what would you name 2/1+8/4? "Octave"?

"Tritave" was a stupid, stupid choice of terminology; let's not
compound it.

- Rich Holmes

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🔗Gene Ward Smith <genewardsmith@coolgoose.com>

2/4/2006 1:39:25 PM

--- In tuning@yahoogroups.com, "Mohajeri Shahin" <shahinm@...> wrote:

> Now Here is ED(5/2) system with steps of 226.6 cent:

Why do you want to avoid octaves? What harm do they do?

🔗Hudson Lacerda <hfmlacerda@yahoo.com.br>

2/4/2006 4:08:33 PM

Gene Ward Smith escreveu:
> --- In tuning@yahoogroups.com, "Mohajeri Shahin" <shahinm@...> wrote:
> > >>Now Here is ED(5/2) system with steps of 226.6 cent:
> > > Why do you want to avoid octaves? What harm do they do?

Why not? :-)

Regards,
Hudson

P.S.
Gene, I liked your 46ET music so much. Have you got all the sax fingerings need?

--
Hudson Lacerda <http://geocities.yahoo.com.br/hfmlacerda/>
*Nï¿½o deixe seu voto sumir! http://www.votoseguro.org/
*Apï¿½ie o Manifesto: http://www.votoseguro.com/alertaprofessores/

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🔗Gene Ward Smith <genewardsmith@coolgoose.com>

2/4/2006 4:11:22 PM

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

> P.S.
> Gene, I liked your 46ET music so much. Have you got all the sax
> fingerings need?

Thanks. Unfortunately, I haven't a single clue about how to finger a
sax. How well do saxophones do in mictrointonational terms?

🔗Hudson Lacerda <hfmlacerda@yahoo.com.br>

2/4/2006 4:36:11 PM

Gene Ward Smith escreveu:
> --- In tuning@yahoogroups.com, Hudson Lacerda <hfmlacerda@...> wrote:
> > >>P.S.
>>Gene, I liked your 46ET music so much. Have you got all the sax >>fingerings need?
> > > Thanks. Unfortunately, I haven't a single clue about how to finger a
> sax. How well do saxophones do in mictrointonational terms?

I just know that quartertones became already part of "standard" sax technique. I have no info about getting more subdivisions.

For oboe, there is at least one book on new techniques, containing fingerings in eighthtone quantisation.

BTW, maby some people missed I put my recorder quartertone fingering online, still in .jpg scanned pages <http://geocities.yahoo.com.br/hfmlacerda/abc/recorder-fng.tgz>. I plan make a PostScript + text edition (data in text file, to be read by a PostScript program).

Cheers,
Hudson

--
Hudson Lacerda <http://geocities.yahoo.com.br/hfmlacerda/>
*Nï¿½o deixe seu voto sumir! http://www.votoseguro.org/
*Apï¿½ie o Manifesto: http://www.votoseguro.com/alertaprofessores/

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🔗Hudson Lacerda <hfmlacerda@yahoo.com.br>

2/4/2006 5:54:22 PM

Mohajeri Shahin escreveu:
> Hi rich holmes , dear freind
> > As if you are very allergic to this word , Sorry i made you angry ,
> although this word is being used :
> http://tonalsoft.com/enc/e/equivalence-interval.aspx ,
> http://en.wikipedia.org/wiki/Bohlen-Pierce_scale

Sure, but "used" is not the same than "properly used".

(It seems that Pierce or Mathews coined the word "tritave", it that correct?)

> I thought may be there is a refrence for naming intervals greater than
> octave . any how, I am over with it !!!!

At least in Portuguese (other languages too, I think), we have expressions that correspond to "compound third" (10th), "compound fifth" (12th) and so on. Not optimal however, because all these: 9th, 16th and 23th are "compound seconds".

Yet: when a scale has no 8 notes for octave (inclusive), it does not make *really* sense to use the word "octave" for 2/1!

The precise meaning of intervals is catch by frequency ratios. Why avoid them? If we shall create new words, "tritave" is not a model to follow.

> So if we have 3/1 then i think bohlen-pierce scale as an EDI system
> (EQUAL DIVISION OF INTERVAL) with I=3/1or ED(3/1).
> > Now Here is ED(5/2) system with steps of 226.6 cent:
[...]
> It is approximately in 7-limit rational system as scala reported :
[...]
> You can test it , sounding good to me ! Interesting, but, honest, 226.6 cents is an analysis unit too big for me. I will try 14 steps in 5/2.

Gene asked about avoiding octaves (concerning to the choice to do not the octave as equivalence interval). I like the idea to tinkering with other modulos; BP is a good example of a non-octave scale.

I have a related question: BP works well for odd-harmonics, and sounds somewhat hard if one uses also even-harmonics. Which partials are you using for modulo 5/2? Are using (or planning to use) inharmonic tones? Please note that a 2/1 ratio is implied in 5/2, if you want to use harmonic timbres, then octaves will be there...

For non-octave equivalence, I think this is an important question: how to make understandable by ear the intended equivalence interval? Octave intervals inside the scale can be distracting (a potencial problem for BP music: there are distracting "mistuned-octave" intervals), so the timbre is decisive.

BTW, the 1133.081 cents interval in your scale sounds very interesting in homogeneous superpositions (I tried it with an organ-like timbre).

[R.Holmes wrote:]
> And what would you name 2/1+8/4? "Octave"?

lol :-D

Regards,
Hudson

--
Hudson Lacerda <http://geocities.yahoo.com.br/hfmlacerda/>
*Nï¿½o deixe seu voto sumir! http://www.votoseguro.org/
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🔗Gene Ward Smith <genewardsmith@coolgoose.com>

2/4/2006 7:18:20 PM

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

> Gene asked about avoiding octaves (concerning to the choice to do not
> the octave as equivalence interval). I like the idea to tinkering with
> other modulos; BP is a good example of a non-octave scale.

On the other hand it's closely related to bohpier temperament, for
which you can use 5 out of 41 or 16 out of 131 as a generator, and
treat as you would any 7-limit linear temperament.

My inclination with nonoctave temperaments is to subvert them by
adding back octaves. For instance, with 88 cents steps, which is by
definition definable in 150-edo, why not treat it that way? Or instead
of 11 steps of 150, 5 steps of 68 will work. I've considered trying to
write something in five parts, each part of which was confined to the
88.235 step scale of 68 notes equal to a certain number modulo five.
Each *part* is in the Morrison scale, but the whole thing is another
story.

🔗Hudson Lacerda <hfmlacerda@yahoo.com.br>

2/5/2006 2:27:02 PM

Gene Ward Smith escreveu:
> --- In tuning@yahoogroups.com, Hudson Lacerda <hfmlacerda@...> wrote:
> > >>Gene asked about avoiding octaves (concerning to the choice to do not >>the octave as equivalence interval). I like the idea to tinkering with >>other modulos; BP is a good example of a non-octave scale.
> > > On the other hand it's closely related to bohpier temperament, for
> which you can use 5 out of 41 or 16 out of 131 as a generator, and
> treat as you would any 7-limit linear temperament.

My only music piece BP-based is written in quarter-tones (well, 8EDO), so that the false-relations typical of BP scale are "rounded" to more "stable" intervals.

> > My inclination with nonoctave temperaments is to subvert them by
> adding back octaves.

Nothing against use octaves, but: are you sure the listeners will *perceive* the pitch equivalence? The octaves are never a problem itself, but when the octaves "catch back" the equivalence, cancelling the intended modulo, there is an harmonic (compositional) problem.

By other hand (as Gene suggested), one can explore, in a composition, ambiguities between coincident scales.

Regards,
Hudson

--
Hudson Lacerda <http://geocities.yahoo.com.br/hfmlacerda/>
*Nï¿½o deixe seu voto sumir! http://www.votoseguro.org/
*Apï¿½ie o Manifesto: http://www.votoseguro.com/alertaprofessores/

== THE WAR IN IRAQ COSTS ==
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_______________________________________________________
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🔗Keenan Pepper <keenanpepper@gmail.com>

2/5/2006 2:47:40 PM

On 2/5/06, Hudson Lacerda <hfmlacerda@yahoo.com.br> wrote:
[snip]
> My only music piece BP-based is written in quarter-tones (well, 8EDO),
> so that the false-relations typical of BP scale are "rounded" to more
> "stable" intervals.

Well, 3/1 (the most consonant BP interval) goes to 1950 cents, which
is hardly "stable"...

> >
> > My inclination with nonoctave temperaments is to subvert them by
> > adding back octaves.
>
> Nothing against use octaves, but: are you sure the listeners will
> *perceive* the pitch equivalence? The octaves are never a problem
> itself, but when the octaves "catch back" the equivalence, cancelling
> the intended modulo, there is an harmonic (compositional) problem.

Exactly. If you use any interval more consonant than your interval of
equivalence, it tends to usurp that role.

> By other hand (as Gene suggested), one can explore, in a composition,
> ambiguities between coincident scales.
>
> Regards,
> Hudson

Keenan

🔗Hudson Lacerda <hfmlacerda@yahoo.com.br>

2/5/2006 3:12:33 PM

Keenan Pepper escreveu:
> On 2/5/06, Hudson Lacerda <hfmlacerda@yahoo.com.br> wrote:
> [snip]
> >>My only music piece BP-based is written in quarter-tones (well, 8EDO),
>>so that the false-relations typical of BP scale are "rounded" to more
>>"stable" intervals.
> > > Well, 3/1 (the most consonant BP interval) goes to 1950 cents, which
> is hardly "stable"...

Ooops. I was wrong! Not 8EDO, which was used in another (related) piece of mine...

I didn't remember more, but I am sure the harmony was based on the "BP-triad" 3:5:7, using 1900 cents equivalence etc., but the music all the pitches were rounded to quarter-tones. It is a piece for clarinet and guitar (an unfinished edition --PS and MIDI-- is used as an example for microabc package).

Cheers,
Hudson

--
Hudson Lacerda <http://geocities.yahoo.com.br/hfmlacerda/>
*Não deixe seu voto sumir! http://www.votoseguro.org/
*Apóie o Manifesto: http://www.votoseguro.com/alertaprofessores/

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🔗Carl Lumma <clumma@yahoo.com>

2/6/2006 12:58:47 PM

> My inclination with nonoctave temperaments is to subvert them by
> adding back octaves. For instance, with 88 cents steps, which is by
> definition definable in 150-edo, why not treat it that way?

That's a nice way, but the complexity certainly goes up. That
is, it might make some temperaments look not as good. Especially,
as I believe Mohajeri pointed out, when the octave isn't the
equivalence interval.

-Carl

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

2/6/2006 3:25:24 PM

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > My inclination with nonoctave temperaments is to subvert them by
> > adding back octaves. For instance, with 88 cents steps, which is by
> > definition definable in 150-edo, why not treat it that way?
>
> That's a nice way, but the complexity certainly goes up. That
> is, it might make some temperaments look not as good. Especially,
> as I believe Mohajeri pointed out, when the octave isn't the
> equivalence interval.

In this case, 88/1200 = 11/150 gives octacot temperament, which is
pretty good. Mohajeri's example was instructive, but making music with
harmony in mind is another matter.

🔗Carl Lumma <clumma@yahoo.com>

2/6/2006 6:36:14 PM

> > > My inclination with nonoctave temperaments is to subvert them by
> > > adding back octaves. For instance, with 88 cents steps, which is
> > > by definition definable in 150-edo, why not treat it that way?
> >
> > That's a nice way, but the complexity certainly goes up. That
> > is, it might make some temperaments look not as good. Especially,
> > as I believe Mohajeri pointed out, when the octave isn't the
> > equivalence interval.
>
> In this case, 88/1200 = 11/150 gives octacot temperament, which is
> pretty good.

In what "limit"? But composers might not want complete limits.
And if they intended to avoid octaves, 88CET would certainly
trump 150.

-Carl

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

2/6/2006 6:44:18 PM

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:

> > In this case, 88/1200 = 11/150 gives octacot temperament, which is
> > pretty good.
>
> In what "limit"?

7 or 11.

> But composers might not want complete limits.

MOS are a good way of getting incomplete chords in abundence, actually.

> And if they intended to avoid octaves, 88CET would certainly
> trump 150.

But it's very, very limited.

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

2/17/2006 4:35:33 PM

Since the tritave is 3/1, your names would apply most logically to
4/1 and 5/1, not to 8/3 and 5/2 as you seem to imply . . .

--- In tuning@yahoogroups.com, "Mohajeri Shahin" <shahinm@...> wrote:
>
> Hi all
>
> We know that 2/1 + 3/2 is tritave ......
>
> Is there any reference and method about naming other interval like
2/1
> +4/3 or 2/1+9/8 and other in the same way as tritave? (my
proposal : can
> we name 2/1+4/3 fourtave ... 2/1+5/4 as pentave .. and so on?)
>
>
>
> thanks
>
>
>
> 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
>

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

2/17/2006 5:23:00 PM

--- In tuning@yahoogroups.com, Keenan Pepper <keenanpepper@...> wrote:
>
> On 2/2/06, Hudson Lacerda <hfmlacerda@...> wrote:
> > Mohajeri Shahin escreveu:
> > > Hi all
> > >
> > > We know that 2/1 + 3/2 is tritave ......
> > >
> > > Is there any reference and method about naming other interval
like 2/1
> > > +4/3 or 2/1+9/8 and other in the same way as tritave? (my
proposal : can
> > > we name 2/1+4/3 fourtave ... 2/1+5/4 as pentave .. and so on?)
> >
> > I don't know, and I don't like the idea.
> >
> > Why not just use, if you are talking about *equivalence*, "modulo
3/1",
> > "modulo 8/3", or then "3/1 equivalence", "8/3 equivalence", and
so on?
> >
> > Regards,
> > Hudson
>
> I agree. BTW, there are some interesting systems with 4/1
equivalence
> which only contain even powers of two. That is, 4, 16, 64... are
okay
> but 2, 8, 32... are thrown out. Meantone still works, because 81/80
> contains only even powers of two, and it makes a pretty interesting
> scale.

I don't get this. When I look at meantone with a 4:1 interval of
equivalence, I get that the period is half the interval of
equivalence (i.e., ~2:1), and that all the scales end up looking
exactly the same as the conventional meantone ones. So what did you
mean by "a pretty interesting scale"?

🔗Keenan Pepper <keenanpepper@gmail.com>

2/18/2006 12:42:47 PM

On 2/17/06, wallyesterpaulrus <wallyesterpaulrus@yahoo.com> wrote:
[...]
> I don't get this. When I look at meantone with a 4:1 interval of
> equivalence, I get that the period is half the interval of
> equivalence (i.e., ~2:1), and that all the scales end up looking
> exactly the same as the conventional meantone ones. So what did you
> mean by "a pretty interesting scale"?

Here's the 9-note MOS (ratios which differ by 81/80 are joined by a tilde):

1/1 5/4 4/3 5/3 16/9~9/5 20/9~9/4 16/5 3/1 15/4 4/1

Keenan

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

2/20/2006 10:53:51 AM

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
> On 2/17/06, wallyesterpaulrus <wallyesterpaulrus@...> wrote:
> [...]
> > I don't get this. When I look at meantone with a 4:1 interval of
> > equivalence, I get that the period is half the interval of
> > equivalence (i.e., ~2:1), and that all the scales end up looking
> > exactly the same as the conventional meantone ones. So what did you
> > mean by "a pretty interesting scale"?
>
> Here's the 9-note MOS (ratios which differ by 81/80 are joined by a tilde):
>
> 1/1 5/4 4/3 5/3 16/9~9/5 20/9~9/4 16/5 3/1 15/4 4/1
>
> Keenan

Surely this construction is going to forever miss out on half the ratios in the 5-limit, right? What's the generator of this MOS you're referring to? How does one reach 6/5 and 3/2 with it? I think this must be an incomplete, "half-meantone" tuning you're referring to. Is Pajara still Pajara when you only use 1 MOS? No; it's then a Superpyth tuning based on primes {2,3,7} instead.

🔗Keenan Pepper <keenanpepper@gmail.com>

2/20/2006 3:25:09 PM

[...]
> > Here's the 9-note MOS (ratios which differ by 81/80 are joined by a tilde):
> >
> > 1/1 5/4 4/3 5/3 16/9~9/5 20/9~9/4 16/5 3/1 15/4 4/1
> >
> > Keenan
>
> Surely this construction is going to forever miss out on half the ratios in the 5-limit, right? What's the generator of this MOS you're referring to? How does one reach 6/5 and 3/2 with it? I think this must be an incomplete, "half-meantone" tuning you're referring to. Is Pajara still Pajara when you only use 1 MOS? No; it's then a Superpyth tuning based on primes {2,3,7} instead.

Exactly: it's half-meantone. It's based on the "primes" {3,4,5}. The
generator is 4/3. Maybe I should write something in it to prove it's
not just a novelty.

Keenan