Yahoo Tuning Groups Ultimate Backup tuning Arabian comma dispute

On Wed, 7 Dec 2005, Ozan Yarman wrote:
>
> There is a lot of controversy concerning the theory of Maqamat in which I
> represent but a minority opposition to general 24-tone trends. In my
> proposal (79 MOS 159-tET) there are two commas of importance:
>
> 1. 15.092273 cents which can be approximated by 5182/5137 (11 limit) or
> 115/114 (23 limit).
>
> 2. 22.80273 cents which can be approximated by 917/905 (7 limit), 382/377
> (29 limit), or 153/151 (151 limit).
>
> ----- Original Message -----
> From: "Gene Ward Smith" <gwsmith@svpal.org>
> To: <tuning@yahoogroups.com>
> Sent: 07 Aralï¿½k 2005 ï¿½arï¿½amba 2:42
> Subject: [tuning] Arabian comma dispute
>
>
> > There is a dispute over the accuracy of the following article:
> >
> > http://en.wikipedia.org/wiki/Arabian_comma
> >
> > which is discussed on the corresponding talk page:
> >
> > http://en.wikipedia.org/wiki/Talk:Arabian_comma
> >
> > Any comments on all of this?

Hi Ozan,

I had hoped you would have more to say on this ...

IIRC, it's only a few months back you were saying how the
classical tuning, with 53 steps per octave, gave wholetones
of 9 steps and semitones of 4 or 5. What's the history of
this division; was it 53-EDO; and who introduced it and when?
(Surely not al-Farabi, who Shahin tells us went for 144-EDO.)

Regards,
Yahya

--
No virus found in this outgoing message.
Checked by AVG Free Edition.
Version: 7.1.371 / Virus Database: 267.13.12/194 - Release Date: 7/12/05

🔗oyarman@ozanyarman.com

Brother Yahya, welcome back!

I do have more to say on this matter, but not all at once I'm sure. For one
thing, to my knowledge, the earliest reference to 53 commas per octave
hereabouts is that propounded by Kemal Ilerici (innovator of sesquitertian
harmony) ca.1950s, which seems to be based on the Western practice of 9
commas per whole-tone. Though this is an arbitrary definition leading one to
think of 55-eq (hence the Mozartian scheme according to monz) as well as
53-eq, Turkish musicians seem to have taken it to mean the latter. Mildan
Niyazi Ayomak, composer and theorist, 1888-1947, certainly gives that
impression. No wonder, since Turkish Maqam Music is purportedly Pythagorean!

I am therefore appalled by the fact that the Holdrian comma is presented as
the Arabic comma, notwithstanding the fact that some Maqam theorists had
Arabic names and wrote their works in Arabic (heck, they were Islamic
scholars of diverse origins, which is hardly surprising). Seeing as the
majority of Arabs today learn music theory WITHOUT any commas, it is a
dichotomy how any comma could be Arabic!

On the contrary, Erol Sayan, composer extraordinaire of Turkish `Art` Music
claims that the comma is the basis of National Turkish Music. He even
goes to the ends of the earth to re-discover America and calculate the
Holdrian comma, while failing to recognize it as such. Who is this Holder
fellow anyway?

Here is a letter by Darius Milhaud to Kemal Ilerici himself:

`J'ai ï¿½tï¿½ trï¿½s interessï¿½ par les recherches de Monsieur Kemal Ilerici pour
retrouver les sources de la tradition nationale ou la musique turque et les
exprimer dans ses oeuvres. (my father tells me that that's bad French!)

`Il serait souhaitable pour son ouvrage didactique sur la musique turque
soit traduit (father say it should have been "d'ï¿½tre traduite"), en
plusieurs langues ï¿½trangï¿½res. Cela ne manqauerait pas d'intï¿½resser les
musicologues, les professeurs et les compositeurs occidentaux...`

Paris, Dec. 53

It is suspect whether Milhaud did write this `grade C letter` at all. Here
is an English translation loyal to the text:

`I was very interested by the research of Mister Kemal Ilerici to find the
sources of the national tradition or the turkish music and to express them
in his work.

`It is desirable for his didactic work on the turkish music, that it's
translated in various foreign languages. This will not escape to interest
the occidental musicologists, the professors and the composers.`

Paris, Dec. 53

Cordially,
Oz.

----- Original Message -----
From: "Yahya Abdal-Aziz" <yahya@melbpc.org.au>
To: <tuning@yahoogroups.com>
Sent: 08 Aralï¿½k 2005 Perï¿½embe 16:40
Subject: [tuning] Re: Arabian comma dispute

>
> On Wed, 7 Dec 2005, Ozan Yarman wrote:
> >
> > There is a lot of controversy concerning the theory of Maqamat in which
I
> > represent but a minority opposition to general 24-tone trends. In my
> > proposal (79 MOS 159-tET) there are two commas of importance:
> >
> > 1. 15.092273 cents which can be approximated by 5182/5137 (11 limit) or
> > 115/114 (23 limit).
> >
> > 2. 22.80273 cents which can be approximated by 917/905 (7 limit),
382/377
> > (29 limit), or 153/151 (151 limit).
> >
> > ----- Original Message -----
> > From: "Gene Ward Smith" <gwsmith@svpal.org>
> > To: <tuning@yahoogroups.com>
> > Sent: 07 Aralï¿½k 2005 ï¿½arï¿½amba 2:42
> > Subject: [tuning] Arabian comma dispute
> >
> >
> > > There is a dispute over the accuracy of the following article:
> > >
> > > http://en.wikipedia.org/wiki/Arabian_comma
> > >
> > > which is discussed on the corresponding talk page:
> > >
> > > http://en.wikipedia.org/wiki/Talk:Arabian_comma
> > >
> > > Any comments on all of this?
>
>
> Hi Ozan,
>
> I had hoped you would have more to say on this ...
>
> IIRC, it's only a few months back you were saying how the
> classical tuning, with 53 steps per octave, gave wholetones
> of 9 steps and semitones of 4 or 5. What's the history of
> this division; was it 53-EDO; and who introduced it and when?
> (Surely not al-Farabi, who Shahin tells us went for 144-EDO.)
>
> Regards,
> Yahya
>
> --
> No virus found in this outgoing message.
> Checked by AVG Free Edition.
> Version: 7.1.371 / Virus Database: 267.13.12/194 - Release Date: 7/12/05
>
>
>
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
>
> Yahoo! Groups Links
>
>
>
>
>
>
>
>
>

🔗Yahya Abdal-Aziz <yahya@melbpc.org.au>

Le 8 Dec 2005, mon frï¿½re Ozan Yarman a ï¿½crit:
>
> Brother Yahya, welcome back!

Thank you, Ozan, nice to hear from you!

> I do have more to say on this matter, but not all at once I'm sure. For
one
> thing, to my knowledge, the earliest reference to 53 commas per octave
> hereabouts is that propounded by Kemal Ilerici (innovator of sesquitertian
> harmony) ...

sesqui- = one and a half (lit. six fourths), so harmony using 1.5 thirds,
intervals approximating 1.5 times 300, 350 and 400 cents, therefore
450, 525 and 600 cents? Two kinds of bad fourth and a tritone?
Ouch! Sounds painful ... but perhaps you will enlighten me on what
this term (sesquitertian harmony) really means?

> ... ca.1950s, ...

Very much later than I thought.

> ... which seems to be based on the Western practice of 9
> commas per whole-tone. Though this is an arbitrary definition leading one
to
> think of 55-eq (hence the Mozartian scheme according to monz) as well as
> 53-eq, Turkish musicians seem to have taken it to mean the latter. Mildan
> Niyazi Ayomak, composer and theorist, 1888-1947, ...

Hang on, that's _before_ the circa 1950s you mentioned above!
Was he still writing _posthumously_? 8~0 <-- (that's a wide-eyed,
wrinkled-nose and open-mouthed smiley.)

> ... certainly gives that
> impression. No wonder, since Turkish Maqam Music is purportedly
Pythagorean!
>
> I am therefore appalled by the fact that the Holdrian comma is presented
as
> the Arabic comma, notwithstanding the fact that some Maqam theorists had
> Arabic names and wrote their works in Arabic (heck, they were Islamic
> scholars of diverse origins, which is hardly surprising). Seeing as the
> majority of Arabs today learn music theory WITHOUT any commas, it is a
> dichotomy how any comma could be Arabic!

It's puzzling.

> On the contrary, Erol Sayan, composer extraordinaire of Turkish `Art`
Music
> claims that the comma is the basis of National Turkish Music. He even
> goes to the ends of the earth to re-discover America and calculate the
> Holdrian comma, while failing to recognize it as such. Who is this Holder
> fellow anyway?

I thought you knew ...

> Here is a letter by Darius Milhaud to Kemal Ilerici himself:
>
> `J'ai ï¿½tï¿½ trï¿½s interessï¿½ par les recherches de Monsieur Kemal Ilerici pour
> retrouver les sources de la tradition nationale ou la musique turque et
les
> exprimer dans ses oeuvres. (my father tells me that that's bad French!)

Scans and parses OK to my ears.

> `Il serait souhaitable pour son ouvrage didactique sur la musique turque
> soit traduit (father say it should have been "d'ï¿½tre traduite"), ...

That's better, but I would prefer it had read:
> `Il serait souhaitable _si_ son ouvrage didactique sur la musique turque
> soit traduit, ...

But even a fluent French speaker may make the occasional
grammatical mistake! He may have started with your father's
form of the sentence in mind, but switched to mine part-way
thru ... We all do that from time to time, you know.

> ... en
> plusieurs langues ï¿½trangï¿½res. Cela ne manqauerait pas d'intï¿½resser les ...

Should be 'manquerait'

> ... musicologues, les professeurs et les compositeurs occidentaux...`
>
> Paris, Dec. 53
>
> It is suspect whether Milhaud did write this `grade C letter` at all. Here
> is an English translation loyal to the text:
>
> `I was very interested by the research of Mister Kemal Ilerici to find the

Should be '... by Mister Kemal Ilerici's researches ...'

> sources of the national tradition or the turkish music and to express them
> in his work.
>
> `It is desirable for his didactic work on the turkish music, that it's
> translated in various foreign languages. This will not escape to interest
> the occidental musicologists, the professors and the composers.`

Or, perhaps,

`It is desirable that his didactic work on the turkish music be
translated into various foreign languages. This will not fail to interest
occidental musicologists, teachers and composers.`

> Paris, Dec. 53

> Cordially,
> Oz.

> ----- Original Message -----
> From: "Yahya Abdal-Aziz" <yahya@...>
> To: <tuning@yahoogroups.com>
> Sent: 08 Aralï¿½k 2005 Perï¿½embe 16:40
> Subject: [tuning] Re: Arabian comma dispute
>
>
> >
> > On Wed, 7 Dec 2005, Ozan Yarman wrote:
> > >
> > > There is a lot of controversy concerning the theory of Maqamat in
which
> I
> > > represent but a minority opposition to general 24-tone trends. In my
> > > proposal (79 MOS 159-tET) there are two commas of importance:
> > >
> > > 1. 15.092273 cents which can be approximated by 5182/5137 (11 limit)
or
> > > 115/114 (23 limit).
> > >
> > > 2. 22.80273 cents which can be approximated by 917/905 (7 limit),
> 382/377
> > > (29 limit), or 153/151 (151 limit).
> > >
> > > ----- Original Message -----
> > > From: "Gene Ward Smith" <gwsmith@...>
> > > To: <tuning@yahoogroups.com>
> > > Sent: 07 Aralï¿½k 2005 ï¿½arï¿½amba 2:42
> > > Subject: [tuning] Arabian comma dispute
> > >
> > >
> > > > There is a dispute over the accuracy of the following article:
> > > >
> > > > http://en.wikipedia.org/wiki/Arabian_comma
> > > >
> > > > which is discussed on the corresponding talk page:
> > > >
> > > > http://en.wikipedia.org/wiki/Talk:Arabian_comma
> > > >
> > > > Any comments on all of this?
> >
> >
> > Hi Ozan,
> >
> > I had hoped you would have more to say on this ...
> >
> > IIRC, it's only a few months back you were saying how the
> > classical tuning, with 53 steps per octave, gave wholetones
> > of 9 steps and semitones of 4 or 5. What's the history of
> > this division; was it 53-EDO; and who introduced it and when?
> > (Surely not al-Farabi, who Shahin tells us went for 144-EDO.)
> >
> > Regards,
> > Yahya

--
No virus found in this outgoing message.
Checked by AVG Free Edition.
Version: 7.1.371 / Virus Database: 267.13.13/195 - Release Date: 8/12/05

🔗oyarman@ozanyarman.com

----- Original Message -----
From: "Yahya Abdal-Aziz" <yahya@melbpc.org.au>
To: <tuning@yahoogroups.com>
Sent: 09 Aralï¿½k 2005 Cuma 14:25
Subject: [tuning] Re: Arabian comma dispute

>
> Le 8 Dec 2005, mon frï¿½re Ozan Yarman a ï¿½crit:
> >
> > Brother Yahya, welcome back!
>
> Thank you, Ozan, nice to hear from you!
>
>
> > I do have more to say on this matter, but not all at once I'm sure. For
> one
> > thing, to my knowledge, the earliest reference to 53 commas per octave
> > hereabouts is that propounded by Kemal Ilerici (innovator of
sesquitertian
> > harmony) ...
>
> sesqui- = one and a half (lit. six fourths), so harmony using 1.5 thirds,
> intervals approximating 1.5 times 300, 350 and 400 cents, therefore
> 450, 525 and 600 cents? Two kinds of bad fourth and a tritone?
> Ouch! Sounds painful ... but perhaps you will enlighten me on what
> this term (sesquitertian harmony) really means?
>
>

Sesquitertia is a perfect fourth in musical lingo. Sesquitertian harmony is
a kind of weird counterpoint using stacked perfect fourths such as C F Bb
and its inversions as consonances.

> > ... ca.1950s, ...
>
> Very much later than I thought.
>
>

That's what I have been trying to say on this matter since the beginning.
It's fairly recent that people began to think of commas in terms of 53-tET
in Turkey.

> > ... which seems to be based on the Western practice of 9
> > commas per whole-tone. Though this is an arbitrary definition leading
one
> to
> > think of 55-eq (hence the Mozartian scheme according to monz) as well as
> > 53-eq, Turkish musicians seem to have taken it to mean the latter.
Mildan
> > Niyazi Ayomak, composer and theorist, 1888-1947, ...
>
> Hang on, that's _before_ the circa 1950s you mentioned above!
> Was he still writing _posthumously_? 8~0 <-- (that's a wide-eyed,
> wrinkled-nose and open-mouthed smiley.)
>

The concept of 9 commas per whole tone is, not the concept of 53 commas per
octave specifically. As I mentioned, 55-tET can also be inferred.

>
> > ... certainly gives that
> > impression. No wonder, since Turkish Maqam Music is purportedly
> Pythagorean!
> >
> > I am therefore appalled by the fact that the Holdrian comma is presented
> as
> > the Arabic comma, notwithstanding the fact that some Maqam theorists had
> > Arabic names and wrote their works in Arabic (heck, they were Islamic
> > scholars of diverse origins, which is hardly surprising). Seeing as the
> > majority of Arabs today learn music theory WITHOUT any commas, it is a
> > dichotomy how any comma could be Arabic!
>
> It's puzzling.
>
>

The bottom line is, there is no such thing as the Arabian comma, unless one
considers 3088/3011 which is a 44 cent diesis given by Mikhail Mushaqa
between the 4th and 5th degrees of his quarter-tone system.

> > On the contrary, Erol Sayan, composer extraordinaire of Turkish `Art`
> Music
> > claims that the comma is the basis of National Turkish Music. He even
> > goes to the ends of the earth to re-discover America and calculate the
> > Holdrian comma, while failing to recognize it as such. Who is this
Holder
> > fellow anyway?
>
> I thought you knew ...
>
>

The William Holder of the 18th century?

Cordially,
Oz.

🔗monz <monz@tonalsoft.com>

Hi Yahya,

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:
>
>
> Le 8 Dec 2005, mon frère Ozan Yarman a écrit:
>
> > I do have more to say on this matter, but not all at
> > once I'm sure. For one thing, to my knowledge, the
> > earliest reference to 53 commas per octave hereabouts
> > is that propounded by Kemal Ilerici (innovator of
> > sesquitertian harmony) ...
>
> sesqui- = one and a half (lit. six fourths), so harmony
> using 1.5 thirds, intervals approximating 1.5 times 300,
> 350 and 400 cents, therefore 450, 525 and 600 cents?
> Two kinds of bad fourth and a tritone? Ouch! Sounds
> painful ... but perhaps you will enlighten me on what
> this term (sesquitertian harmony) really means?

I'll jump in here. I haven't been following this thread,
and so don't really know what you guys are talking about,
but i *can* clarify some terminology here.

"Sesquitertian" is an old Latin term, probably used first
by Boethius c.505 AD. "Sesqui" is a prefix meaning "one more",
so "sesquitertian" literally means "one more than 3",
which indicates the ratio 4/3.

Presumably the "sesquitertian harmony" Ozan is referring
to is one that is based on perfect-4ths.

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

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

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

Dear yahya

I didn't want to say he invent it , I told, as documented in his book and works of others , he is the first to introduce usage of 144-edo . Is it possible for me to know some reasons of your claim about 144-edo and farabi?

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 <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 Yahya Abdal-Aziz
Sent: Thursday, December 08, 2005 6:11 PM
To: tuning@yahoogroups.com
Subject: [tuning] Re: Arabian comma dispute

On Wed, 7 Dec 2005, Ozan Yarman wrote:
>
> There is a lot of controversy concerning the theory of Maqamat in which I
> represent but a minority opposition to general 24-tone trends. In my
> proposal (79 MOS 159-tET) there are two commas of importance:
>
> 1. 15.092273 cents which can be approximated by 5182/5137 (11 limit) or
> 115/114 (23 limit).
>
> 2. 22.80273 cents which can be approximated by 917/905 (7 limit), 382/377
> (29 limit), or 153/151 (151 limit).
>
> ----- Original Message -----
> From: "Gene Ward Smith" <gwsmith@svpal.org>
> To: <tuning@yahoogroups.com>
> Sent: 07 Aralýk 2005 Çarþamba 2:42
> Subject: [tuning] Arabian comma dispute
>
>
> > There is a dispute over the accuracy of the following article:
> >
> > http://en.wikipedia.org/wiki/Arabian_comma
> >
> > which is discussed on the corresponding talk page:
> >
> > http://en.wikipedia.org/wiki/Talk:Arabian_comma
> >
> > Any comments on all of this?

Hi Ozan,

I had hoped you would have more to say on this ...

Regards,
Yahya

--
No virus found in this outgoing message.
Checked by AVG Free Edition.
Version: 7.1.371 / Virus Database: 267.13.12/194 - Release Date: 7/12/05

You can configure your subscription by sending an empty email to one
of these addresses (from the address at which you receive the list):
tuning-subscribe@yahoogroups.com - join the tuning group.
tuning-unsubscribe@yahoogroups.com - leave the group.
tuning-nomail@yahoogroups.com - turn off mail from the group.
tuning-digest@yahoogroups.com - set group to send daily digests.
tuning-normal@yahoogroups.com - set group to send individual emails.
tuning-help@yahoogroups.com - receive general help information.

SPONSORED LINKS

Music education
<http://groups.yahoo.com/gads?t=ms&k=Music+education&w1=Music+education&
w2=Music+production+education&w3=Music+education+degree&w4=Degree+educat
ion+music+online&w5=Music+business+education&w6=Music+education+online&c
=6&s=174&.sig=zMNRfOOOdo7nVqxhYS_0Yg>

Music production education
<http://groups.yahoo.com/gads?t=ms&k=Music+production+education&w1=Music
+education&w2=Music+production+education&w3=Music+education+degree&w4=De
gree+education+music+online&w5=Music+business+education&w6=Music+educati
on+online&c=6&s=174&.sig=xvNPUlceIGAdVcjAsHH8JA>

Music education degree
<http://groups.yahoo.com/gads?t=ms&k=Music+education+degree&w1=Music+edu
cation&w2=Music+production+education&w3=Music+education+degree&w4=Degree
+education+music+online&w5=Music+business+education&w6=Music+education+o
nline&c=6&s=174&.sig=lrDYh_-yrdu524mpql-csg>

Degree education music online
<http://groups.yahoo.com/gads?t=ms&k=Degree+education+music+online&w1=Mu
sic+education&w2=Music+production+education&w3=Music+education+degree&w4
=Degree+education+music+online&w5=Music+business+education&w6=Music+educ
ation+online&c=6&s=174&.sig=SVm8lC0-Q2tryy6Hv14ihQ>

Music business education
<http://groups.yahoo.com/gads?t=ms&k=Music+business+education&w1=Music+e
ducation&w2=Music+production+education&w3=Music+education+degree&w4=Degr
ee+education+music+online&w5=Music+business+education&w6=Music+education
+online&c=6&s=174&.sig=pCxzd_uR0dRaYO3MB1Fpvw>

Music education online
<http://groups.yahoo.com/gads?t=ms&k=Music+education+online&w1=Music+edu
cation&w2=Music+production+education&w3=Music+education+degree&w4=Degree
+education+music+online&w5=Music+business+education&w6=Music+education+o
nline&c=6&s=174&.sig=DaqBb8P8ErSmB8MxxA-ePw>

________________________________

YAHOO! GROUPS LINKS

* Visit your group "tuning </tuning>
" on the web.

* To unsubscribe from this group, send an email to:
tuning-unsubscribe@yahoogroups.com
<mailto:tuning-unsubscribe@yahoogroups.com?subject=Unsubscribe>

* Your use of Yahoo! Groups is subject to the Yahoo! Terms of
Service <http://docs.yahoo.com/info/terms/> .

________________________________

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

As great a philosopher as he may be, he is also the first to import Greek genera of tetrachords to the Islamic middle-east. How compatible these were to the practice of the day is a mystery.

----- Original Message -----
From: Mohajeri Shahin
To: tuning@yahoogroups.com
Sent: 11 Aralık 2005 Pazar 6:08
Subject: RE: [tuning] Re: Arabian comma dispute

Hi , dear monz

Thanks for reply

Farabi,as mentioned in his great book ,had studied The theories of Aristoxenos and the others . his book " moosighi-al-kabir " was wrote as his student wanted him for gathering musical knowledge. farabi in the preface of the book writes that this book includes works of the past and himself…….." so he was the first who introduced theoretical basis of 144-edo in islamic middle east .

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

🔗Yahya Abdal-Aziz <yahya@melbpc.org.au>

Hi monz,

On Fri, 09 Dec 2005, you wrote:
>
> Hi Yahya,
>
>
> --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz"
> <yahya@m...> wrote:
>
...
> > > sesquitertian harmony) ...
> >
> > sesqui- = one and a half (lit. six fourths), so harmony
> > using 1.5 thirds, intervals approximating 1.5 times 300,
> > 350 and 400 cents, therefore 450, 525 and 600 cents?
> > Two kinds of bad fourth and a tritone? Ouch! Sounds
> > painful ... but perhaps you will enlighten me on what
> > this term (sesquitertian harmony) really means?
>
> I'll jump in here. I haven't been following this thread,
> and so don't really know what you guys are talking about,
> but i *can* clarify some terminology here.
>
> "Sesquitertian" is an old Latin term, probably used first
> by Boethius c.505 AD. "Sesqui" is a prefix meaning "one more",
> so "sesquitertian" literally means "one more than 3",
> which indicates the ratio 4/3.
>
> Presumably the "sesquitertian harmony" Ozan is referring
> to is one that is based on perfect-4ths.

Thanks for the correction! I should have said
that I _think_ that sesqui means one and a half.
Obviously a failure of generalisation from the only
other example I knew of, namely "sesquicentenary",
as used on an Australian stamp of 1953 that
commemorated 150 years of European settlement
of Tasmania.

Though how they would obtain the meaning 150 years
from morphemes meaning "one more than a century"
entirely defeats my understanding ...

Ozan has confirmed that he meant harmonies based
on stacked fourths, rather than stacked thirds. It's
my guess that many of us have played with stacking
fourths, seconds, even fifths - I have some examples
in my manuscript notes dated in the late sixties - and
like many interesting ideas, will probably be
independently rediscovered many times over.

With alternative tunings such as 53-EDO, considered
as a scale in its own right (as Gene for one is happy to
do, not needing to consider it as a gamut from which
to draw only a handful or two of notes per octave to
form a scale), it may make perfectly good sense to
build harmonies by stacking, say, "eighteenths".

Regards,
Yahya

--
No virus found in this outgoing message.
Checked by AVG Free Edition.
Version: 7.1.371 / Virus Database: 267.13.13/197 - Release Date: 9/12/05

🔗Yahya Abdal-Aziz <yahya@melbpc.org.au>

Hi monz,

On Sat, 10 Dec 2005 you wrote:

> --- In tuning@yahoogroups.com, "Mohajeri Shahin"
> <shahinm@k...> wrote:
> >
> > Dear yahya
> >
> >
> >
> > I didn't want to say he invent it , I told, as documented
> > in his book and works of others , he is the first to
> > introduce usage of 144-edo . Is it possible for me to
> > know some reasons of your claim about 144-edo and farabi?
>
>
> The theories of Aristoxenos (c.330 BC), which are open
> to a wide variety of interpretations, clearly suggest
> 144-edo.
>
> I suggest several different interpretations on my webpage
> about Aristoxenos, finally deciding that 144-edo is the
> both the simplest and most likely:
>
> http://sonic-arts.org/monzo/aristoxenus/318tet.htm#144edo

-----------

Fascinating stuff! But does this really make
sense? On the same page, and immediately
above this statement, you wrote:

-----------

"APPENDICES - other mathematical possibilities for measuring Aristoxenus's
genera

1. Cleonides's (4/3)^(1/30)

2. 144-tET - a useful approximation to Aristoxenus's system, much less
sophisticated than 318-tET

3. very extended Pythagorean - I was speculating that this was a possibility
for Aristoxenus,
but Macran 1902 [p 247] gives Plutarch [33.1145] quoting Aristoxenus:

>> the magnitude of this interval (i.e., the quarter-tone) cannot be
determined by concord,
>> as can the semitone, the tone, and the like.

This passage clearly indicates that Aristoxenus did not carry the
Pythagorean tuning out far
enough to derive the quarter-tones from it; it just as clearly indicates,
however, that
Aristoxenus expected to be able to derive his Pythagorean semitones from the
method of
Tuning by Concords.

<< give extent of system: to 12 tones as described in A's Tuning by Concords
>>

4. Rational - Ptolemy, me"

-----------

So, if "Aristoxenus did not carry the Pythagorean
tuning out far enough to derive the quarter-tones
from it", is it reasonable to assume that he ever
contemplated 144-EDO? It seems to me that the
most likely reasons for anyone's choosing 144-EDO
would be to allow further rational division of 12
equal semitones into halves, quarters, sixths and
twelfths - the simplest of these being the quarter-
tone. Had he contemplated 144-EDO, it can hardly
have escaped his notice that it supports quarter-
tones.

In perplexity,
Yahya

--
No virus found in this outgoing message.
Checked by AVG Free Edition.
Version: 7.1.371 / Virus Database: 267.13.13/197 - Release Date: 9/12/05

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

I would have someone tell me, rather, howcome 1200/53 cents is ascribed the
saucy definition: `Arabian comma`, when Arabs are not known to use commas -
much less 53-tET - at all in their interpretation of Maqam Music theory. A
comma named after a nation who doesn't use or need it?? Hilarious.

Oz.

----- Original Message -----
From: "Yahya Abdal-Aziz" <yahya@melbpc.org.au>
To: <tuning@yahoogroups.com>
Sent: 13 Aralï¿½k 2005 Salï¿½ 11:42
Subject: [tuning] Re: Arabian comma dispute

>
> Hi Ozan and Mohajeri,
>
> On Sun, 11 Dec 2005 Ozan wrote:
> > As great a philosopher as he may be, he is
> > also the first to import Greek genera of
> > tetrachords to the Islamic middle-east.
> > How compatible these were to the practice
> > of the day is a mystery.
> >
> > ----- Original Message -----
> > From: Mohajeri Shahin
> ...
> > Farabi,as mentioned in his great book ,had
> > studied The theories of Aristoxenos and the
> > others . his book " moosighi-al-kabir " was
> > wrote as his student wanted him for gathering
> > musical knowledge. farabi in the preface of
> > the book writes that this book includes works
> > of the past and himselfï¿½ï¿½.." so he was the
> > first who introduced theoretical basis of
> > 144-edo in islamic middle east .
>
> Was that in the same book, "moosighi-al-kabir"
> ("The Great Music")? Is there an accessible
> English translation of Farabi's book?
>
> Regards,
> Yahya
>
> --

🔗monz <monz@tonalsoft.com>

Hi Yahya,

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:

> So, if "Aristoxenus did not carry the Pythagorean
> tuning out far enough to derive the quarter-tones
> from it", is it reasonable to assume that he ever
> contemplated 144-EDO? It seems to me that the
> most likely reasons for anyone's choosing 144-EDO
> would be to allow further rational division of 12
> equal semitones into halves, quarters, sixths and
> twelfths - the simplest of these being the quarter-
> tone. Had he contemplated 144-EDO, it can hardly
> have escaped his notice that it supports quarter-
> tones.
>
> In perplexity,
> Yahya

At least part of the reason for your perplexity is
the fact that my Aristoxenus page is very sloppy and
badly in need of editing ... something which i've needed
to do for years but just can't get to until i have a
serious block of time to devote to it.

For starters, i used the Latinized spelling of his name,
but when i finally edit the page i'll probably stick to
the Greek spelling Aristoxenos.

The most important thing to point out about his theories
is that, at the end of his process of "tuning by concords",
that is, upon reaching the 12th note, the last concord
derived is supposed to sound similar to all the other ones.

This is impossible in true pythagorean tuning, because
the last "concord" will be smaller by a pythagorean comma,
i.e., a type of "wolf-5th" of ~678 cents.

The last section of my page, "Amendment from 2003.07.20",
represents my latest thoughts on the subject -- so while
everything before it is interesting, and worth reading from
a historical point of view, what i propose in this last
section is what i think most likely represents Aristoxenos's
theories.

Aristoxenos used divisions as small as 1/12-tone and 1/8-tone
in his actual descriptions, and so the smallest division
needed to encompass all the possibilities in his various
generic shades is 1/24-tone. Obviously, this implies 144-edo.

I describe a mathematical procedure which exactly follows
his descriptions, wherein a "ditone" (major-3rd) is tuned
by concords but then is assumed to be a logarithmic 4/5 of
a "perfect-4th". Assuming the perfect-4th to be a pythagorean
4/3 ratio, this leads to a smallest division of (4/3)^(1/60),
and was the division described by Cleonides, whose work is
a main source for Aristoxenos.

But one cannot assume Aristoxenos's "perfect-4th" to be
a 4/3 ratio, because of the discrepancy of the size of
"concords" in his "tuning by concords" method, as mentioned
above.

So ultimately, 144-edo seems to be the best tuning to assume
for the fitting together of all the disparate and seemingly
contradictory statements made by Aristoxenos. That's why
i used 144-edo for the tuning of the notated illustrations
and audio examples at the end of my webpage.

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

🔗Yahya Abdal-Aziz <yahya@melbpc.org.au>

Hi Ozan,

On Tue, 13 Dec 2005 you wrote:
>
> I would have someone tell me, rather, howcome 1200/53 cents is ascribed
the
> saucy definition: `Arabian comma`, when Arabs are not known to use
commas -
> much less 53-tET - at all in their interpretation of Maqam Music theory. A
> comma named after a nation who doesn't use or need it?? Hilarious.

I take your point. Still, I wish you might answer
my question more directly!

> > On Sun, 11 Dec 2005 Ozan wrote:
> > > As great a philosopher as he may be, he is
> > > also the first to import Greek genera of
> > > tetrachords to the Islamic middle-east.
> > > How compatible these were to the practice
> > > of the day is a mystery.
> > >
> > > ----- Original Message -----
> > > From: Mohajeri Shahin
> > ...
> > > Farabi,as mentioned in his great book ,had
> > > studied The theories of Aristoxenos and the
> > > others . his book " moosighi-al-kabir " was
> > > wrote as his student wanted him for gathering
> > > musical knowledge. farabi in the preface of
> > > the book writes that this book includes works
> > > of the past and himselfï¿½ï¿½.." so he was the
> > > first who introduced theoretical basis of
> > > 144-edo in islamic middle east .
>
And Yahya replied:
> > Was that in the same book, "moosighi-al-kabir"
> > ("The Great Music")? Is there an accessible
> > English translation of Farabi's book?

Regards,
Yahya

--
No virus found in this outgoing message.
Checked by AVG Free Edition.
Version: 7.1.371 / Virus Database: 267.13.13/197 - Release Date: 9/12/05

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:
>
>
> Hi monz,
>
> On Sat, 10 Dec 2005 you wrote:
>
> > --- In tuning@yahoogroups.com, "Mohajeri Shahin"
> > <shahinm@k...> wrote:
> > >
> > > Dear yahya
> > >
> > >
> > >
> > > I didn't want to say he invent it , I told, as documented
> > > in his book and works of others , he is the first to
> > > introduce usage of 144-edo . Is it possible for me to
> > > know some reasons of your claim about 144-edo and farabi?
> >
> >
> > The theories of Aristoxenos (c.330 BC), which are open
> > to a wide variety of interpretations, clearly suggest
> > 144-edo.
> >
> > I suggest several different interpretations on my webpage
> > about Aristoxenos, finally deciding that 144-edo is the
> > both the simplest and most likely:
> >
> > http://sonic-arts.org/monzo/aristoxenus/318tet.htm#144edo
>
> -----------
>
> Fascinating stuff! But does this really make
> sense? On the same page, and immediately
> above this statement, you wrote:
>
> -----------
>
> "APPENDICES - other mathematical possibilities for measuring
Aristoxenus's
> genera
>
> 1. Cleonides's (4/3)^(1/30)
>
> 2. 144-tET - a useful approximation to Aristoxenus's system, much
less
> sophisticated than 318-tET
>
> 3. very extended Pythagorean - I was speculating that this was a
possibility
> for Aristoxenus,
> but Macran 1902 [p 247] gives Plutarch [33.1145] quoting
Aristoxenus:
>
> >> the magnitude of this interval (i.e., the quarter-tone) cannot be
> determined by concord,
> >> as can the semitone, the tone, and the like.
>
> This passage clearly indicates that Aristoxenus did not carry the
> Pythagorean tuning out far
> enough to derive the quarter-tones from it; it just as clearly
indicates,
> however, that
> Aristoxenus expected to be able to derive his Pythagorean semitones
from the
> method of
> Tuning by Concords.
>
> << give extent of system: to 12 tones as described in A's Tuning by
Concords
> >>
>
> 4. Rational - Ptolemy, me"
>
> -----------
>
> So, if "Aristoxenus did not carry the Pythagorean
> tuning out far enough to derive the quarter-tones
> from it", is it reasonable to assume that he ever
> contemplated 144-EDO?

Sure!

> It seems to me that the
> most likely reasons for anyone's choosing 144-EDO
> would be to allow further rational division of 12
> equal semitones into halves, quarters, sixths and
> twelfths - the simplest of these being the quarter-
> tone. Had he contemplated 144-EDO, it can hardly
> have escaped his notice that it supports quarter-
> tones.

Of course they didn't! He mentions quarter-tones explicitly. But the
point here is that these additional notes are *not* obtained by
carrying out Pythagorean tuning (which is a chain of pure
fifths/fourths, aka 3-limit JI) far enough to obtain anything like a
quarter-tone. Instead, the quarter-tones are obtained by *equal
division* (or something quite similar).

> In perplexity,
> Yahya

I tried replying because it didn't seem to me that Monz addressed
your perplexity here, but maybe he did . . .

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

That would make it more Islamic than Arabic (rather than Arabian, which
denotes a land mass). Then of course, we would need a Jewish schisma and a
Jesuit diesis too...

But the unidecimal neutral third is 11/9, not 27/22. But I see what you
mean, they are both 11-limit. Scala names the difference in between the ~7
cent `neutral third comma`. Tempering this out would indeed have some
significance. Is this tempered in 24-tET? It appears so to me. Paul, what
was the formula for checking out if a ratio was tempered in a scale? Was it
something like:

243=3*3*3*3*3 (3^5)
242=2*11*11 (2*11^2)

24-edo prime 3 is 38 steps,
prime 11 is 83 steps,
prime 2 is 24 steps.

to make 243 equal to 242,

5*38=2*83+24

The result is 190=190 steps for both, and 243/242 vanishes in 24-tET?

Still, I find no logic behind re-naming the Holdrian comma as Arabian.

Cordially,
Ozan

----- Original Message -----
From: "Gene Ward Smith" <gwsmith@svpal.org>
To: <tuning@yahoogroups.com>
Sent: 14 Aralï¿½k 2005 ï¿½arï¿½amba 3:11
Subject: [tuning] Re: Arabian comma dispute

> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@y...> wrote:
>
> > I believe that an Arabian or Arabic comma *has* been proposed/defined,
> > probably by Gene Ward Smith. Was it 243:242?
>
> I asked if it would be reasonable to call that "Arabic". It is the
> difference between the two unidecimal neutral thirds of 27/22 and
> 11/9, just as 2401/2400 is the difference between the two septimal
> minor thirds of 49/40 and 60/49.
>
>
>

🔗Yahya Abdal-Aziz <yahya@melbpc.org.au>

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

Hi Yahya,

----- Original Message -----
From: "Yahya Abdal-Aziz" <yahya@melbpc.org.au>
To: <tuning@yahoogroups.com>
Sent: 14 Aralï¿½k 2005 ï¿½arï¿½amba 8:08
Subject: [tuning] Re: Arabian comma dispute

>
> Hi Ozan,
>
> You wrote, of al-Farabi:
> > > > As great a philosopher as he may be, he is
> > > > also the first to import Greek genera of
> > > > tetrachords to the Islamic middle-east.
>
> I asked for clarification:
> > > Was that in the same book, "moosighi-al-kabir"
> > > ("The Great Music")? Is there an accessible
> > > English translation of Farabi's book?
>

I thought the question was directed at brother Mohajeri.

> I had hoped that you, or Shahin, or some other
> savant, would answer these questions. Your reply
> concerned the illogic of there ever being an
> "Arabian comma", but did not answer either of
> my questions. Do please answer if you can!
>

Brother Mohajeri posted the references. Having never seen a Turkish or
English copy of Farabi's work, I can only speak from indirect references. As
far as I am informed, Farabi used only tetrachordal divisions in his theory,
including perhaps the 27/22 interval known as the neutral third. Maybe monz
can tell if this interval is specified in Greek and Latin treatises before
him.

> Regards,
> Yahya
>
>

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

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

> That would make it more Islamic than Arabic (rather than Arabian,
which
> denotes a land mass). Then of course, we would need a Jewish
schisma and a
> Jesuit diesis too...
>
> But the unidecimal neutral third is 11/9, not 27/22.

Doesnt't a stack of two neutral thirds yield a consonant perfect
fifth in Arabic music? (I don't say Islamic since the music of
Pakistan, for instance, doesn't seem to use these intervals).

> But I see what you
> mean, they are both 11-limit. Scala names the difference in between
the ~7
> cent `neutral third comma`. Tempering this out would indeed have
some
> significance. Is this tempered in 24-tET? It appears so to me.

243:242 vanishes in 24-equal, yes.

> Paul, what
> was the formula for checking out if a ratio was tempered in a
scale? Was it
> something like:
>
> 243=3*3*3*3*3 (3^5)
> 242=2*11*11 (2*11^2)
>
> 24-edo prime 3 is 38 steps,
> prime 11 is 83 steps,
> prime 2 is 24 steps.
>
> to make 243 equal to 242,
>
> 5*38=2*83+24
>
> The result is 190=190 steps for both, and 243/242 vanishes in 24-
>tET?

Yup! Therefore, stacking two approximate 11:9s yields an approximate
3:2.

> Still, I find no logic behind re-naming the Holdrian comma as
Arabian.

Never heard of the Holdrian comma. Is that the same as the Mercator
comma?

> Cordially,
> Ozan
>
> ----- Original Message -----
> From: "Gene Ward Smith" <gwsmith@s...>
> To: <tuning@yahoogroups.com>
> Sent: 14 Aralýk 2005 Çarþamba 3:11
> Subject: [tuning] Re: Arabian comma dispute
>
>
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> > <wallyesterpaulrus@y...> wrote:
> >
> > > I believe that an Arabian or Arabic comma *has* been
proposed/defined,
> > > probably by Gene Ward Smith. Was it 243:242?
> >
> > I asked if it would be reasonable to call that "Arabic". It is the
> > difference between the two unidecimal neutral thirds of 27/22 and
> > 11/9, just as 2401/2400 is the difference between the two septimal
> > minor thirds of 49/40 and 60/49.
> >
> >
> >
>

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

Hi Paul,

----- Original Message -----
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 15 Aralï¿½k 2005 Perï¿½embe 22:58
Subject: [tuning] Re: Arabian comma dispute

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

[PA]
Doesnt't a stack of two neutral thirds yield a consonant perfect
fifth in Arabic music? (I don't say Islamic since the music of
Pakistan, for instance, doesn't seem to use these intervals).

[OZ]
You mean the 694.8 cent (121:81) fifth? I have observed this with nearly all
Maqam genres contrary to what diverse theories say. It's one of the reasons
why I promote 79 MOS 159-tET, since it contains enough of these fifths at
several degrees, 33 of them in fact.

[PA]
243:242 vanishes in 24-equal, yes.

[OZ]
As well as a million other commas, you told me. So it's not any more special
than, say, the syntonic comma. So 24-tET is not best explained as a tuning
which tempers out that particular interval, but as a tuning which tempers
out 243:242 along with syntonic, pythagorean, archytas's commas, nearly all
types of dieses, kleismas, schismas, etc... This hardly makes it Arabian,
don't you think?

[PA]
Yup! Therefore, stacking two approximate 11:9s yields an approximate
3:2.

[OZ]
Namely, the 700 cent perfect fifth, which is 350+350 cents in 24-edo. With
79 MOS 159-tET, you get 347+347 cents.

> Still, I find no logic behind re-naming the Holdrian comma as
Arabian.

Never heard of the Holdrian comma. Is that the same as the Mercator
comma?

[OZ]
Mercator's comma is what remains after you cycle 53 fifths, no? Holdrian
comma, conversely, is the tiniest portion resulting from the 53 equal
divisions of the octave. We say `Holder kommasi` in Turkish. It is the
favourite system by which Maqams are explained (after designating 1, 4, 5,
8, 9 commas per whole tone, which I find awfully erroneous). I wonder,
still, if it really was proposed by William Holder of the late 17th, early
18th centuries.

> Cordially,
> Ozan
>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

🔗Yahya Abdal-Aziz <yahya@melbpc.org.au>

Hi Paul,

On Wed, 14 Dec 2005, "wallyesterpaulrus" wrote:
>
> --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz"
> <yahya@m...> wrote:
> >
> >
> > Hi monz,
> >
> > On Sat, 10 Dec 2005 you wrote:
> >
> > > --- In tuning@yahoogroups.com, "Mohajeri Shahin"
> > > <shahinm@k...> wrote:
> > > >
> > > > Dear yahya
> > > >
> > > >
> > > >
> > > > I didn't want to say he invent it , I told, as documented
> > > > in his book and works of others , he is the first to
> > > > introduce usage of 144-edo . Is it possible for me to
> > > > know some reasons of your claim about 144-edo and farabi?
> > >
> > >
> > > The theories of Aristoxenos (c.330 BC), which are open
> > > to a wide variety of interpretations, clearly suggest
> > > 144-edo.
> > >
> > > I suggest several different interpretations on my webpage
> > > about Aristoxenos, finally deciding that 144-edo is the
> > > both the simplest and most likely:
> > >
> > > http://sonic-arts.org/monzo/aristoxenus/318tet.htm#144edo
> >
> > -----------
> >
> > Fascinating stuff! But does this really make
> > sense? On the same page, and immediately
> > above this statement, you wrote:
> >
> > -----------
> >
> > "APPENDICES - other mathematical possibilities for measuring
> Aristoxenus's
> > genera
> >
> > 1. Cleonides's (4/3)^(1/30)
> >
> > 2. 144-tET - a useful approximation to Aristoxenus's system, much
> > less sophisticated than 318-tET
> >
> > 3. very extended Pythagorean - I was speculating that this was a
> > possibility for Aristoxenus, but Macran 1902 [p 247] gives Plutarch
> > [33.1145] quoting Aristoxenus:
> >
> > >> the magnitude of this interval (i.e., the quarter-tone) cannot be
> > >> determined by concord, as can the semitone, the tone, and the
> > >> like.
> >
> > This passage clearly indicates that Aristoxenus did not carry the
> > Pythagorean tuning out far enough to derive the quarter-tones
> > from it; it just as clearly indicates, however, that Aristoxenus
> > expected to be able to derive his Pythagorean semitones from the
> > method of Tuning by Concords.
> >
> > << give extent of system: to 12 tones as described in A's Tuning by
> > Concords>>
> >
> > 4. Rational - Ptolemy, me"
> >
> > -----------
> >
> > So, if "Aristoxenus did not carry the Pythagorean
> > tuning out far enough to derive the quarter-tones
> > from it", is it reasonable to assume that he ever
> > contemplated 144-EDO?
>
> Sure!
>
> > It seems to me that the
> > most likely reasons for anyone's choosing 144-EDO
> > would be to allow further rational division of 12
> > equal semitones into halves, quarters, sixths and
> > twelfths - the simplest of these being the quarter-
> > tone. Had he contemplated 144-EDO, it can hardly
> > have escaped his notice that it supports quarter-
> > tones.
>
> Of course they didn't! He mentions quarter-tones explicitly. But the
> point here is that these additional notes are *not* obtained by
> carrying out Pythagorean tuning (which is a chain of pure
> fifths/fourths, aka 3-limit JI) far enough to obtain anything like a
> quarter-tone. Instead, the quarter-tones are obtained by *equal
> division* (or something quite similar).
>
> > In perplexity,
> > Yahya
>
> I tried replying because it didn't seem to me that Monz addressed
> your perplexity here, but maybe he did . . .

You both did! :-) - by emphasising the fact (previously
unknown to me) that Aristoxenos did actually discuss
quartertones and further divisions of them. All I had
to go on before that was the statement on monz' page
that Aristoxenos did not carry Pythagorean tuning out
far enough to derive quartertones from it, leaving it
uncertain whether he had discussed them at all.

Thanks for your clarification.

Regards,
Yahya

--
No virus found in this outgoing message.
Checked by AVG Free Edition.
Version: 7.1.371 / Virus Database: 267.14.1/204 - Release Date: 15/12/05

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@o...> wrote:
>
> Hi Paul,
>
> ----- Original Message -----
> From: "wallyesterpaulrus" <wallyesterpaulrus@y...>
> To: <tuning@yahoogroups.com>
> Sent: 15 Aralýk 2005 Perþembe 22:58
> Subject: [tuning] Re: Arabian comma dispute
>
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@o...>
wrote:
>
> > That would make it more Islamic than Arabic (rather than Arabian,
> which
> > denotes a land mass). Then of course, we would need a Jewish
> schisma and a
> > Jesuit diesis too...
> >
> > But the unidecimal neutral third is 11/9, not 27/22.
>
> [PA]
> Doesnt't a stack of two neutral thirds yield a consonant perfect
> fifth in Arabic music? (I don't say Islamic since the music of
> Pakistan, for instance, doesn't seem to use these intervals).
>
> [OZ]
> You mean the 694.8 cent (121:81) fifth?

Not necessarily. The neutral thirds may be widened somewhat.

> I have observed this with nearly all
> Maqam genres contrary to what diverse theories say.

Excellent.

> It's one of the reasons
> why I promote 79 MOS 159-tET, since it contains enough of these
fifths at
> several degrees, 33 of them in fact.

Try as I might, I still can't make sense out of this.

> > But I see what you
> > mean, they are both 11-limit. Scala names the difference in
between
> the ~7
> > cent `neutral third comma`. Tempering this out would indeed have
> some
> > significance. Is this tempered in 24-tET? It appears so to me.
>
>
> [PA]
> 243:242 vanishes in 24-equal, yes.
>
> [OZ]
> As well as a million other commas, you told me. So it's not any
more special
> than, say, the syntonic comma. So 24-tET is not best explained as a
tuning
> which tempers out that particular interval, but as a tuning which
tempers
> out 243:242 along with syntonic, pythagorean, archytas's commas,
nearly all
> types of dieses, kleismas, schismas, etc...

You don't need all that many to explain/define/justify 24-equal, if
explain/define/justifying 24-equal interests you for some
reason . . .

> This hardly makes it Arabian,
> don't you think?

Whoa. You just changed the subject, I believe. I'd like to address
the above but I'm afraid I'd get whiplash. Could you slow down? At
least, I'm not the one who brought up 24-equal in this thread, so I'd
rather not be forced to defend such statements about it (if it is
indeed what they are about).

> > Still, I find no logic behind re-naming the Holdrian comma as
> Arabian.
>
> Never heard of the Holdrian comma. Is that the same as the Mercator
> comma?
>
> [OZ]
> Mercator's comma is what remains after you cycle 53 fifths, no?
Holdrian
> comma, conversely, is the tiniest portion resulting from the 53
equal
> divisions of the octave.

Oh, 1/53 octave?

> We say `Holder kommasi` in Turkish. It is the
> favourite system by which Maqams are explained (after designating
1, 4, 5,
> 8, 9 commas per whole tone, which I find awfully erroneous). I
wonder,
> still, if it really was proposed by William Holder of the late
17th, early
> 18th centuries.

If he proposed 53-equal (and he wouldn't have been the first to do
so), then I guess in a sense he did "propose" it . . .

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

----- Original Message -----
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 19 Aralï¿½k 2005 Pazartesi 23:12
Subject: [tuning] Re: Arabian comma dispute

Hi Paul,

> You mean the 694.8 cent (121:81) fifth?

[PA]
Not necessarily. The neutral thirds may be widened somewhat.

[OZ]
Of course, or narrowed as the occasion demands it.

> It's one of the reasons
> why I promote 79 MOS 159-tET, since it contains enough of these
fifths at
> several degrees, 33 of them in fact.

[PA]
Try as I might, I still can't make sense out of this.

[OZ]
Try as I might, I still can't make you see the sense in this.

> This hardly makes it Arabian,
> don't you think?

[PA]
Whoa. You just changed the subject, I believe. I'd like to address
the above but I'm afraid I'd get whiplash. Could you slow down? At
least, I'm not the one who brought up 24-equal in this thread, so I'd
rather not be forced to defend such statements about it (if it is
indeed what they are about).

[OZ]
I haven't changed the subject, it says there on top: `Arabian comma
dispute`. I'm trying to understand why any comma would have to be Arabic in
the first place, whether it is the 22.64 cent Holdrian/Mercator comma (as
Gene put forth), or the 7.13 cent 243:242.

> Mercator's comma is what remains after you cycle 53 fifths, no?
Holdrian
> comma, conversely, is the tiniest portion resulting from the 53
equal
> divisions of the octave.

[PA]
Oh, 1/53 octave?

[OZ]
Yep. Gene has provided the necessary reference.

Cordially,
Ozan