Meantone sharp can be lower than the flat, but Arel-Ezgi notation?

Monz,

Do you approve of the fact that the Arel-Ezgi notation utilizes F# as 4 commas higher than F within the G Major Rast scale (whose third degree B is lowered by a ditonic comma to achieve a perfect fifth) in a tuning which is practically 53tET?

I was entertaining the idea that the apotome sharp, as George Secor tought me, equals 7 fifths minus 4 octaves. It is clear that Turkish Music notation is fundamentally flawed in this respect.

Also, do you approve of the practice which allows the standart diapason (A4=440Hz) to be altered in Turkish Music regardless of the inclusion of voices or strings in unison monody? The above-mentioned G-Major Rast is then rendered as D Major Rast in `Bolahenk Key` (Transposes ~260 Hz C4=Rast a whole tone above to D) with the note names preserved as they are.

This is a practice which I find absurd and wrong. Any music expressed on the 5-line staff today (with only historical or contemporary works as exceptions) should not have the liberty of assigning any frequency to the sol-fa (Such as D5=440Hz) when there is a plethora of established standarts out there that adhere to international conventions.

Cordially,
Ozan

----- Original Message -----
From: monz
To: tuning@yahoogroups.com
Sent: 24 Nisan 2005 Pazar 2:05
Subject: [tuning] Re: Mozart -Haydn in 55-edo

hi Ozan,

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

> Monz, the fact that Leopold
> Mozart assumed that the
> whole tone consists of 9
> commas, the diatonic semitone,
> 5, and the chromatic semitone,
> 4, is exactly the kind of
> numerology one finds in the
> Yekta-Arel-Ezgi school, where
> a cycle of 24 fifths are taken
> as the perfect Turkish Music
> system of tuning and where
> the comma steps defining the
> two distinct semitones above
> are reversed.

yes, in many of my posts on this subject over the last
few days, i've pointed out that when the comma steps
for the semitones are reversed, the result is 53-edo,
which has been a theoretical standard for Turkish music
for a long time.

i'll repeat in case you missed it:

where the octave = 5 tones + 2 diatonic semitones,

me, monz,
/tuning/topicId_58099.html#58141

> assuming a closed tuning, this division into 9 commas
> produces either 53-edo or 55-edo, depending on which
> of the two different semitones (chromatic and diatonic)
> is the larger one. making the chromatic semitone larger
> (thus, a pythagorean system) gives 53-edo, and making
> the diatonic larger (thus, a meantone) gives 55:
>
> .......................... 53-edo ........... 55-edo
>
> t = tone .................... 9 ................ 9
> s = diatonic semitone ....... 4 ................ 5
> octave = 5t + 2s ..... (5*9)+(2*4)=53 ... (5*9)+(2*5)=55

> I would be much happier if it was said that the major
> whole tone is the 9/8th of an open string, but could
> be tempered depending on the tuning.

i'm sure that would be fine for Turkish music ... but
not for either of the Mozarts. European common-practice
music always tempered out the syntonic-comma, which means
that there has to be a mean-tone, not a major and minor
whole-tone. it's important to this repertoire that there
is no distinction between different whole-tones -- there
is only one size of whole-tone, and thus it is a meantone.

-monz

Ozan Yarman wrote:

> Do you approve of the fact that the Arel-Ezgi notation utilizes F# as 4 > commas
> higher than F within the G Major Rast scale (whose third degree B is > lowered by
> a ditonic comma to achieve a perfect fifth) in a tuning which is > practically 53tET?

> I was entertaining the idea that the apotome sharp, as George Secor tought > me,
> equals 7 fifths minus 4 octaves. It is clear that Turkish Music notation > is
> fundamentally flawed in this respect.

I'm not Monz, obviously, but I need to comment myself. I've always wondered this. In Arel-Ezgi notation, B-F# is a wolf. Maybe he wanted a limma alteration for sharps to make F#/Gb and other enharmonic pairs the same pitch. And usually sharps tend to be lowered a comma anyway because they're found in makamlar with Hicaz tetrachords. It's still confusing, and I have to agree with you - F# should be 5 commas higher than F, not 4.

And if enharmonic pairs only map to the same pitch in 12, 24, 36 etc. tone and not in 17, 19, 22, 29, 31, 41, 43 and so on, why should they be the same in 53-tone?

How standard is Arel-Ezgi in Turkish practice anyway? And how often is Yekta Bey or Karadeniz used in comparison?

> Also, do you approve of the practice which allows the standart diapason
> (A4=440Hz) to be altered in Turkish Music regardless of the inclusion of > voices
> or strings in unison monody? The above-mentioned G-Major Rast is then > rendered
> as D Major Rast in `Bolahenk Key` (Transposes ~260 Hz C4=Rast a whole tone
> above to D) with the note names preserved as they are.
>
> This is a practice which I find absurd and wrong. Any music expressed on > the
> 5-line staff today (with only historical or contemporary works as > exceptions)
> should not have the liberty of assigning any frequency to the sol-fa (Such > as
> D5=440Hz) when there is a plethora of established standarts out there that
> adhere to international conventions.

You mean how Rast, which is written and sounded as middle C in Arabic tuning, is written G a fifth higher but sounded D a fourth lower in Turkish? I have to agree with you there too, as I'm a fan of international standards (on a similar note, I have a major beef with the fact that most my fellow Americans avoid using SI/Metric so much and stick to English measurements). Now I know a Turkish or Armenian oud is usually tuned a major second higher than an Arabic oud, so Rast on the former is higher than Rast on the latter, but that's hardly different than how clarinets can be in A, B-flat, C, D and E-flat (and there's also the metal "Turkish clarinet" in G).

[As an afterthought, when I got my Egyptian oud, I didn't think about how the tuning would match up with guitar, which is tuned to roughly E minor, so I probably should've gotten a Turkish instrument, or have the guitar tuned a whole step down, nu-metal-like.]

~Danny~

hi Ozan and Danny,

--- In tuning@yahoogroups.com, "Danny Wier" <dawiertx@s...> wrote:

> Ozan Yarman wrote:
>
> > Do you approve of the fact that the Arel-Ezgi notation
> > utilizes F# as 4 commas higher than F within the G Major
> > Rast scale (whose third degree B is lowered by a ditonic
> > comma to achieve a perfect fifth) in a tuning which is
> > practically 53tET?
>
> > I was entertaining the idea that the apotome sharp, as
> > George Secor tought me, equals 7 fifths minus 4 octaves.

the standard way of notating that is with
the 2,3-monzo |-11 7, > .

the -11 exponent of 2 could be expressed (-7-4), because:

. a "5th" with ratio 3/2 has the 2,3-monzo |-1 1, > , so

. seven 5ths = |-1 1, > * 7 = |-7 7, > = ratio 2187/128.

then, subtracting 4 octaves is |1 0, > * -4 = |-4 0, > .

so |-7 7, >
+ |-4 0, >
------------
= |-11 7, > = ratio 2187/2048 = the pythagorean apotome.

a lattice of the pythagorean chain with F = n^0 :

|----- apotome ------|

0 1 2 3 4 5 6 7 = exponents of 3
+--+--+--+--+--+--+--+-
F C G D A E B F#

> > It is clear that Turkish Music notation is fundamentally
> > flawed in this respect.

how so? an explanation might make an interesting
Encyclopedia entry.

> I'm not Monz, obviously,

it's OK, i am. ;-)

> but I need to comment myself. I've always wondered
> this. In Arel-Ezgi notation, B-F# is a wolf. Maybe he
> wanted a limma alteration for sharps to make F#/Gb and
> other enharmonic pairs the same pitch. And usually sharps
> tend to be lowered a comma anyway because they're found
> in makamlar with Hicaz tetrachords. It's still confusing,
> and I have to agree with you - F# should be 5 commas higher
> than F, not 4.
>
> And if enharmonic pairs only map to the same pitch in
> 12, 24, 36 etc. tone and not in 17, 19, 22, 29, 31, 41, 43
> and so on, why should they be the same in 53-tone?

hmm ... i'm wondering if there are other tunings besides
12n-edo (i.e., the aristoxenean family) which have similar
enharmonically equivalent pairs based on the familiar
letter-name nominals with sharps and flats. anyone care
to post a list? ... that would be a great addition to
the Encyclopedia "enharmonic equivalence" page.

anyway, in 53-edo,

. 4 commas make a diatonic semitone ("limma",
if emulating pythagorean tuning), and

. 5 commas make a chromatic semitone ("apotome"
in pythagorean).

so according to a 53-edo notation, F# should
be 5 commas higher than F.

i don't know of a way for enharmonic pairs to be equal
in 53-edo, unless some totally different notation
(i.e, not based on the pythagorean/meantone letters)
is used.

every equal temperament will exhibit
enharmonic equivalence, because they all
temper out certain commas. whatever the notation
is, enharmonic equivalence will occur somewhere.

i'm wondering if the phenomenon of enharmonic equivalence
has anything to do with whether or not the cardinality size
of the set of nominals, is the same as the number
of notes inside the periodicity-block. ...?

> > Also, do you approve of the practice which allows
> > the standart diapason (A4=440Hz) to be altered in
> > Turkish Music regardless of the inclusion of voices
> > or strings in unison monody? The above-mentioned
> > G-Major Rast is then rendered as D Major Rast in
> > `Bolahenk Key` (Transposes ~260 Hz C4=Rast a whole tone
> > above to D) with the note names preserved as they are.
> >
> > This is a practice which I find absurd and wrong.

this, and Danny's follow-up comments, sound to me just
like the nonsense of transposition on so many European
instruments. i don't know enough about Turkish music
to comment further than that, but basically, i also
agree that this is silly.

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

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

> hmm ... i'm wondering if there are other tunings besides
> 12n-edo (i.e., the aristoxenean family) which have similar
> enharmonically equivalent pairs based on the familiar
> letter-name nominals with sharps and flats. anyone care
> to post a list? ... that would be a great addition to
> the Encyclopedia "enharmonic equivalence" page.

I'm not too sure what the question is, but any et with fifths as a
generator will have enharmonic pairs, and that occurs whenever the
gcd of the number of steps in the fifth and in the octave is one; that
is, they are relatively prime.

> i don't know of a way for enharmonic pairs to be equal
> in 53-edo, unless some totally different notation
> (i.e, not based on the pythagorean/meantone letters)
> is used.

What do you mean by "equal"? In 53, Fbbb = A####, for instance.

> i'm wondering if the phenomenon of enharmonic equivalence
> has anything to do with whether or not the cardinality size
> of the set of nominals, is the same as the number
> of notes inside the periodicity-block. ...?

Again, I'm not sure what you are asking. The 3-limit "block" for
2187/2048 is just the nominals F-B, however.

Sorry for the late reply Danny, I'm having difficulty following the barrage
of e-mails and have neglected your message.

However, let me point out that your entry into this conversation is most
fortunate, as I value your opinions no less.

>
> I'm not Monz, obviously, but I need to comment myself. I've always
wondered
> this. In Arel-Ezgi notation, B-F# is a wolf. Maybe he wanted a limma
> alteration for sharps to make F#/Gb and other enharmonic pairs the same
> pitch. And usually sharps tend to be lowered a comma anyway because
they're
> found in makamlar with Hicaz tetrachords. It's still confusing, and I have
> to agree with you - F# should be 5 commas higher than F, not 4.
>

Thank you! You cannot imagine how hard it is to convince people around here
that the sharp in 53tET or any pythagorean system closely resembling it must
be 5 steps, not 4.

> And if enharmonic pairs only map to the same pitch in 12, 24, 36 etc. tone
> and not in 17, 19, 22, 29, 31, 41, 43 and so on, why should they be the
same
> in 53-tone?
>

The correct application of enharmonic pair should depend on a selected set
out of the whole scale, such as 7 out of 53 for Rast.

> How standard is Arel-Ezgi in Turkish practice anyway? And how often is
Yekta
> Bey or Karadeniz used in comparison?
>

Scarcely, or not all. Arel-Ezgi diumvirate has monopoly over Turkish Maqam
Music notation I'm afraid, a theory fraught with perils.

>
> You mean how Rast, which is written and sounded as middle C in Arabic
> tuning, is written G a fifth higher but sounded D a fourth lower in
Turkish?

Exactly!

> I have to agree with you there too, as I'm a fan of international
standards
> (on a similar note, I have a major beef with the fact that most my fellow
> Americans avoid using SI/Metric so much and stick to English
measurements).

Right. I am 115 kgs and that makes me look flabbier when you convert that
into pounds.

> Now I know a Turkish or Armenian oud is usually tuned a major second
higher
> than an Arabic oud, so Rast on the former is higher than Rast on the
latter,
> but that's hardly different than how clarinets can be in A, B-flat, C, D
and
> E-flat (and there's also the metal "Turkish clarinet" in G).
>

Which, I find wrong in regards to key transposition. Transposing instruments
should not be those whose strings can be retuned according to whim
regardless of the change of size. The violin family is a valid example to
this. Such is not the case for wind instruments whose key system remains the
same despite their diversity in size. Accordinly, the cousin clarinets A,
Bb, E and G are good examples.

> [As an afterthought, when I got my Egyptian oud, I didn't think about how
> the tuning would match up with guitar, which is tuned to roughly E minor,
so
> I probably should've gotten a Turkish instrument, or have the guitar tuned
a
> whole step down, nu-metal-like.]
>
> ~Danny~
>
>

I personally like them both.

Cordially,
Ozan

Hi Monz,

I've become a fan of the exponent notation and your HEWM usage. However, as Danny pointed out, the B-F# in Arel-Ezgi notation is a wolf, wheras F# is properly read by `law-abiding musicians` as 5 steps out of 53tET.

An exhaustive report on the shortcomings and flaws of the Yekta-Arel-Ezgi theory will have to wait my doctorate thesis I'm afraid.

So we are in "accord" regarding the application of the apotome sharp, yes?

As for the enharmonic equivalance of alphabetically ordered letter pairs in 53tET or other pythagorean tunings, might I suggest extracting an independent transposable set out of 53tET depending on the maqam or mode whereby only one instance of every letter pair will correspond to enharmonically equivalent tones (such as E# = F)?

I'm glad to recieve your support regarding the Ahenk nonsense which cost me an entire evening of explanations as I was trying to outline the intricate details of the proposed notational revolution to my colleague and Qanun virtuoso Ruhi Ayangil.

Cordially,
Ozan

----- Original Message -----
From: monz
To: tuning@yahoogroups.com
Sent: 27 Nisan 2005 Çarşamba 13:46
Subject: [tuning] Re: Meantone sharp can be lower than the flat, but Arel-Ezgi notation?

hi Ozan and Danny,

--- In tuning@yahoogroups.com, "Danny Wier" <dawiertx@s...> wrote:

> Ozan Yarman wrote:
>
> > Do you approve of the fact that the Arel-Ezgi notation
> > utilizes F# as 4 commas higher than F within the G Major
> > Rast scale (whose third degree B is lowered by a ditonic
> > comma to achieve a perfect fifth) in a tuning which is
> > practically 53tET?
>
> > I was entertaining the idea that the apotome sharp, as
> > George Secor tought me, equals 7 fifths minus 4 octaves.

the standard way of notating that is with
the 2,3-monzo |-11 7, > .

the -11 exponent of 2 could be expressed (-7-4), because:

. a "5th" with ratio 3/2 has the 2,3-monzo |-1 1, > , so

. seven 5ths = |-1 1, > * 7 = |-7 7, > = ratio 2187/128.

then, subtracting 4 octaves is |1 0, > * -4 = |-4 0, > .

so |-7 7, >
+ |-4 0, >
------------
= |-11 7, > = ratio 2187/2048 = the pythagorean apotome.

a lattice of the pythagorean chain with F = n^0 :

|----- apotome ------|

0 1 2 3 4 5 6 7 = exponents of 3
+--+--+--+--+--+--+--+-
F C G D A E B F#

> > It is clear that Turkish Music notation is fundamentally
> > flawed in this respect.

how so? an explanation might make an interesting
Encyclopedia entry.

> I'm not Monz, obviously,

it's OK, i am. ;-)

> but I need to comment myself. I've always wondered
> this. In Arel-Ezgi notation, B-F# is a wolf. Maybe he
> wanted a limma alteration for sharps to make F#/Gb and
> other enharmonic pairs the same pitch. And usually sharps
> tend to be lowered a comma anyway because they're found
> in makamlar with Hicaz tetrachords. It's still confusing,
> and I have to agree with you - F# should be 5 commas higher
> than F, not 4.
>
> And if enharmonic pairs only map to the same pitch in
> 12, 24, 36 etc. tone and not in 17, 19, 22, 29, 31, 41, 43
> and so on, why should they be the same in 53-tone?

hmm ... i'm wondering if there are other tunings besides
12n-edo (i.e., the aristoxenean family) which have similar
enharmonically equivalent pairs based on the familiar
letter-name nominals with sharps and flats. anyone care
to post a list? ... that would be a great addition to
the Encyclopedia "enharmonic equivalence" page.

anyway, in 53-edo,

. 4 commas make a diatonic semitone ("limma",
if emulating pythagorean tuning), and

. 5 commas make a chromatic semitone ("apotome"
in pythagorean).

so according to a 53-edo notation, F# should
be 5 commas higher than F.

i don't know of a way for enharmonic pairs to be equal
in 53-edo, unless some totally different notation
(i.e, not based on the pythagorean/meantone letters)
is used.

every equal temperament will exhibit
enharmonic equivalence, because they all
temper out certain commas. whatever the notation
is, enharmonic equivalence will occur somewhere.

i'm wondering if the phenomenon of enharmonic equivalence
has anything to do with whether or not the cardinality size
of the set of nominals, is the same as the number
of notes inside the periodicity-block. ...?

> > Also, do you approve of the practice which allows
> > the standart diapason (A4=440Hz) to be altered in
> > Turkish Music regardless of the inclusion of voices
> > or strings in unison monody? The above-mentioned
> > G-Major Rast is then rendered as D Major Rast in
> > `Bolahenk Key` (Transposes ~260 Hz C4=Rast a whole tone
> > above to D) with the note names preserved as they are.
> >
> > This is a practice which I find absurd and wrong.

this, and Danny's follow-up comments, sound to me just
like the nonsense of transposition on so many European
instruments. i don't know enough about Turkish music
to comment further than that, but basically, i also
agree that this is silly.

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