I don't see why (9/8 x 28/27) should be superior to (9/8 x 25/24). I
don't think 76/64 is a crude interval or an approximation. It is a
legitimate, nicely resonating augmented second/minor third. It's just
the right flavour I need in my formulations for maqam scales. 7/6 is
rather inappropriate for my purposes in fact.

Oz.

✩ ✩ ✩
www.ozanyarman.com

On Nov 16, 2009, at 6:20 PM, a_sparschuh wrote:

> --- In tuning@yahoogroups.com, "monz" <joemonz@...> wrote:
>
>> to tune a particular "minor-3rd" to 75/64.
>
>>> I don't think 75/64 resonates superior to 7/6 by itself.....
>
>>> 7/6 does occur directly from the tonic in harmonic 7-limit...
>
> in deed, because 75/64 can be considered as crude
> 5-limit approximation of the "septimal-minor-3rd" 7/6
>
> (75/64) :=  (7/6)*(225/224) or in logarithmic Cent units
> ~274.6 C :=  ~266.9 C + ~7.7 C
>
> with the ingredients
>
> 7/6 http://en.wikipedia.org/wiki/Septimal_minor_third
> ~266.9 Cents
>
> * or +
>
> 225/224 http://en.wikipedia.org/wiki/Septimal_kleisma
> ~7.7 Cents
> =
> 75/64  classic augmented second := (9/8)*(25/24)
> http://www.huygens-fokker.org/docs/intervals.html
> ~274.6 Cents
>
> instead of
>
> 7/6 := (9/8)*(28/27) diatonic
>
> with 'Archytas's 1/3 tone (28/27) ~63 Cents
> that appears at first in all his 3 septimal tetrachords
>
> http://de.wikipedia.org/wiki/Archytas_von_Tarent
> "
> enharmonisches Tetrachord:  (28:27)(36:35)(5:4)
> chromatisches Tetrachord:  (28:27)(15:14)(6:5)
> diatonisches Tetrachord:  (28:27)(8:7)(9:8)
> "
>
> bye
> A.S.
>
>
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
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>

--- In tuning@yahoogroups.com, "freq_divider" <dubshot@...> wrote:
>
> Hi Carl,
>
> Thanx for the compliment. I'm not sure what effect you are
> referring to but that tune called 'drink milk' is basically
> derived from a classic jamaican riddim called 'hot milk'. It
> borrows the bassline + theme but it's re-tuned (so to speak)
> to 7-tet.

Ah, 7-tet, that's what I was looking for.

> By the way i personally don't think of 5-tet and 7-tet as
> 'microtonal' tunings, i'd say they'r macrotonal ;-)

Fair enough!

-Carl

Hi Carl,

Thanx for the compliment. I'm not sure what effect you are referring to but that
tune called 'drink milk' is basically derived from a classic jamaican riddim
called 'hot milk'. It borrows the bassline + theme but it's re-tuned (so to
speak) to 7-tet.

By the way i personally don't think of 5-tet and 7-tet as 'microtonal' tunings,
i'd say they'r macrotonal ;-)

Greetings, Anton

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Hi Anton- pretty cool, thanks for sharing.  I didn't notice
> anything overtly microtonal in the first track, but "drink milk"
> has something going on.  How did you get this effect?
>
> -Carl
>
> --- In tuning@yahoogroups.com, "freq_divider" <dubshot@> wrote:
> >
> > hi everybody,
> >
> > i've been working on a dub album. it has mostly classic reggae
> > basslines and melodies 'transposed' so to speak to gamelan-like
> > harmonies. it's electronic stuff with lots of dub fx
> >
> > the album is not out yet but there are already some tunes
> > available for free in either mp3/128 format over here
> >
> > http://www.xs4all.nl/~dubshot/ (the tunes marked with an asterisk)
> >
> > or in 16 bit wav format over here
> >
> > http://soundcloud.com/tony-dubshot
> >
> > the album, titled 'dub experryments' will be released early 2010
> > both as free mp3s and as a limited edition numbered cd (250
> > copies) that will be available via e-bay.
> >
> > if you want the full album please check back on my blog, which
> > is here
> >
> > http://dubshot.blogspot.com/
> >
> > in januari or februari 2010
> >
> > greetings, anton
> >
>

Hi Anton- pretty cool, thanks for sharing.  I didn't notice
anything overtly microtonal in the first track, but "drink milk"
has something going on.  How did you get this effect?

-Carl

--- In tuning@yahoogroups.com, "freq_divider" <dubshot@...> wrote:
>
> hi everybody,
>
> i've been working on a dub album. it has mostly classic reggae
> basslines and melodies 'transposed' so to speak to gamelan-like
> harmonies. it's electronic stuff with lots of dub fx
>
> the album is not out yet but there are already some tunes
> available for free in either mp3/128 format over here
>
> http://www.xs4all.nl/~dubshot/ (the tunes marked with an asterisk)
>
> or in 16 bit wav format over here
>
> http://soundcloud.com/tony-dubshot
>
> the album, titled 'dub experryments' will be released early 2010
> both as free mp3s and as a limited edition numbered cd (250
> copies) that will be available via e-bay.
>
> if you want the full album please check back on my blog, which
> is here
>
> http://dubshot.blogspot.com/
>
> in januari or februari 2010
>
> greetings, anton
>

hi everybody,

i've been working on a dub album. it has mostly classic reggae basslines and
melodies 'transposed' so to speak to gamelan-like harmonies. it's electronic
stuff with lots of dub fx

the album is not out yet but there are already some tunes available for free in
either mp3/128 format over here

http://www.xs4all.nl/~dubshot/ (the tunes marked with an asterisk)

or in 16 bit wav format over here

http://soundcloud.com/tony-dubshot

the album, titled 'dub experryments' will be released early 2010 both as free
mp3s and as a limited edition numbered cd (250 copies) that will be available
via e-bay.

if you want the full album please check back on my blog, which is here

http://dubshot.blogspot.com/

in januari or februari 2010

greetings, anton

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

> to tune a particular "minor-3rd" to 75/64.

> > I don't think 75/64 resonates superior to 7/6 by itself.....

> > 7/6 does occur directly from the tonic in harmonic 7-limit...

in deed, because 75/64 can be considered as crude
5-limit approximation of the "septimal-minor-3rd" 7/6

  (75/64) :=  (7/6)*(225/224) or in logarithmic Cent units
~274.6 C :=  ~266.9 C + ~7.7 C

with the ingredients

7/6 http://en.wikipedia.org/wiki/Septimal_minor_third
~266.9 Cents

* or +

225/224 http://en.wikipedia.org/wiki/Septimal_kleisma
~7.7 Cents
=
75/64  classic augmented second := (9/8)*(25/24)
http://www.huygens-fokker.org/docs/intervals.html
~274.6 Cents

instead of

7/6 := (9/8)*(28/27) diatonic

with 'Archytas's 1/3 tone (28/27) ~63 Cents
that appears at first in all his 3 septimal tetrachords

http://de.wikipedia.org/wiki/Archytas_von_Tarent
"
enharmonisches Tetrachord:  (28:27)(36:35)(5:4)
chromatisches Tetrachord:  (28:27)(15:14)(6:5)
diatonisches Tetrachord:  (28:27)(8:7)(9:8)
"

bye
A.S.

that's a good point.  Thanks.  I don't know much about microtonal music or
tuning.  (Curiously, I believe it is, to some extent, irrelant in tonal music,
which is more interested in the gross interval category, for purposed of
counterpoint and chord construction.  I notice there are different musical
psychology paradigms between tuning theorists and psychoacoustic researchers who
try to integrate acoustics with tonality.  Peace!

--- In tuning@yahoogroups.com, "cameron" <misterbobro@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "octatonic10" <octatonic10@> wrote:
> >
> > but in a chord progression, does it really matter?  The average >tonal ear
won't notice the tuning differences you describe.  But of >course for microtonal
music it is interesting!
>
> The "average tonal ear" won't notice the difference between a flat seven and a
blue flat seven?
>
> Not only is your statement wrong, it is interestingly "maximally" wrong in my
experience. In introducing the theoretical concepts of JI and microtonality to
people, I find that it is a blued b7 that is the instant audible eye-opener. A
5/4 often gets a puzzled, well, it's more "church" sounding..., without the
comprehension that the intervals, and not just the timbre, have been changed.
>
>
>
>
>
>
> >
> > --- In tuning@yahoogroups.com, Ozan Yarman <ozanyarman@> wrote:
> > >
> > > This is an interesting and wholesome diminished seventh chord that I
> > > couldn't find in the Chords database of SCALA:
> > >
> > > 135:160:192:225
> > >
> > > When the chord is unfolded, it yields:
> > >
> > > 5/3 x 128/75 x 5/3.
> > >
> > > The ratios are:
> > >
> > > 1/1
> > > 32/27
> > > 6/5
> > > 75/64
> > >
> > > I find 75/64 to be a much more agreeable septimal minor third compared
> > > to 7/6.
> > >
> > > In Yarman-36 (a,b,c) the steps are (over the regular 12-tone layer):
> > >
> > > 18 8 18.
> > >
> > > The notation is:
> > >
> > > C E/b F# Ad
> > >
> > > Cordially,
> > > Oz.
> > >
> > > â&#65533;© â&#65533;© â&#65533;©
> > > www.ozanyarman.com
> > >
> >
>

Back around 1999, when i "justified" my piece
_3 Plus 4_, i wrote some posts here about my
empirical experiments where i ended up deciding
to tune a particular "minor-3rd" to 75/64.
I summarized them a couple of years ago here:

http://launch.groups.yahoo.com/group/tuning/message/72769


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


--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
>
> Hi Oz,
>
> Very neat, since we are in the 5-limit. And already, the 75/64 minor
> > third resonates superior to 7/6.
> >
> I don't think 75/64 resonates superior to 7/6 by itself.
>
> I personally don't see 75/64 as a basic "harmonic 6-limit building block",
> but as an interval forming between 2 very simple intervals from the tonic,
> namely 8/5 and 15/8.
> As an interval directly from the tonic 75/64 does not occur (atleast not
> untill very high harmonic interval permutations).
> 7/6 does occur directly from the tonic in harmonic 7-limit though, and I
> personally see 7/6 as much more consonant than 75/64 by itself.
> Only the structure 9/8 4/3 8/5 15/8 I see as more simple than 7-limit. It is
> a 6-limit structure even though it has a 75/64 interval between 8/5 and
> 15/8.
>
> Marcel
>

Hello Graham, a late reply:

On Nov 2, 2009, at 8:05 AM, Graham Breed wrote:

> Ozan Yarman wrote:
>> ✩ ✩ ✩
>> www.ozanyarman.com
>>
>> On Oct 31, 2009, at 7:38 AM, Graham Breed wrote:
>>
>>> Ozan Yarman wrote:
>>>
>>>> So, if I eliminate the pitchbend lookup tables in Timidity
>>>> entirely,
>>>> do I arrive at MTS with 16384 increments per interval (semitone,
>>>> wholetone, etc...)?
>>> Yes.  But it's only as good as the sample set you're using.
>>> If the samples aren't tuned that accurately, the results
>>> won't be anyway.  That's why you should go for a purely
>>> algorithmic approach for high-precision tuning.
>>
>> So you mean that it is safer to keep the PB lookup tables and
>> implement linear interpolation?
>
> No, I mean it may not be worth bothering.  If your samples
> aren't tuned to MTS precision it doesn't matter how
> precisely Timidity retunes them -- unless it does something
> clever with pitch recognition, which I doubt.



I have experienced firsthand that the same soundfont contains patches
that respond differently to pitch bends. One patch was a Reed Organ
that only accepted cent increments, and the other was a Fantasia Pad
that at least accepted 0.39 cent increments (due to the restriction of
Timidity++ maybe?).



> But
> ZynAddSubFX or VAZ Plus or Csound don't require real-world
> samples and so you can get much better control over the
> pitch.  So if you really care about this level of precision
> you may be better off without a sampler.
>


I concur.


> If you want to work with SoundFonts you may have to stomach
> this level of imprecision.  I have a vague idea that the
> SoundFont standard doesn't specify the pitch of samples any
> more precisely than Timidity's tuning tables anyway ...


Yes, there is always the danger of that happening.


> which would be a good reason why Timdity uses that level of
> precision.


Possibly.


>
>> Send me both a version of tables.c with no lookup tables and maximum
>> precision and another version with 256 divisions of the equal
>> semitone
>> improved with linear interpolation. I'll test both versions if I can
>> ever successfully compile Timidity for Windows.
>
> I can do that if you're ready to compile it.


I found this document on the internet for the compiling of Timidity++:

http://www.csee.umbc.edu/help/sound/TiMidity++-2.13.2/doc/C/README.w32

It seems a lot of work, but I already set up Mingw and Msys (am not
sure what additional libraries and components are needed), Got the
pexports, pdcurses... I downloaded Oggvorbis, Gogo nocoder, Flac,
Portaudio and Portmidi, but the instructions require me to compile
them seperately, at which I was not successful.


> I can also
> send you ZynAddSubFX instruments because I'm playing with it
> now.  Maybe other people can help you there as well.
>


Yes, I would very much like to have your ZASFX instruments.


>
>                   Graham
>
>


Cordially,
Oz.

This kind of diminished chord is on VIIth step of the major/minor
scale, so your chords except the last one are not in their root
position. Have you written it intentionally just for a better
comparison how spelling is changed?

BTW the same chord can have more enharmonic versions, for example:
H# - D# - F# - A (resolves into C# maj/min)
Eb - Gb - Bbb - Dbb (into Fb)
Gx - H# - D# - F# (into A#)

Daniel Forro



On 13 Nov 2009, at 7:33 AM, Marcel de Velde wrote:

>
>
> Hello Charles,
>
> It seems to me that the diminished seventh is three steps of bIII (L
> +s) ; producing I, bIII, bV, and bbVII e.g. C Eb Gb Bbb
> I don't understand what bIII (L+s) etc means.


Minor third (as a combination from L-arge second + s-mall second). I
don't like this confusing way of writing, because not always the
higher note of this minor third has "b" accidental (like for example
C# - E, or D# - F#).
And concerning Ls system, that's maybe useful for scales, but not for
description of intervals. If we want to count somehow size of bigger
intervals, then using small second as a measure is enough good (minor
third = 3, fifth = 7 etc.).


> But as far as spelling the diminished 7th chord C Eb Gb Bbb yes you
> can!
>
> The 4 different way to spell the diminished 7th and all it's
> inversion are:
>
> In the tonic of Bb (16/9): C (1/1) - Eb (32/27) - Gb (64/45) - A (5/3)
>
> In the tonic of G (3/2): C (1/1) - Eb (6/5) - F# (45/32) - A (27/16)
> And may I add I agree with Oz that this is the nicest sounding one
> (due to 9/4 beeing higher from tonic than 9/8).
>
> In the tonic of E (5/4): C (1/1) - D# (75/64) - F# (45/32) - A (5/3)
>
> In the tonic of Db (16/15): C (1/1) - Eb (6/5) - Gb (64/45) - Bbb
> (128/75)
> C Eb Gb Bbb indeed :)
>
> Kind regards,
> Marcel
>
>
>
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--- In tuning@yahoogroups.com, Ozan Yarman <ozanyarman@...> wrote:
>
> This is an interesting and wholesome diminished seventh chord that I
> couldn't find in the Chords database of SCALA:
>
> 135:160:192:225
>
> When the chord is unfolded, it yields:
>
> 5/3 x 128/75 x 5/3.
>
> The ratios are:
>
> 1/1
> 32/27
> 6/5
> 75/64
>

Looking at those ratios, it turns out that this is the tuning you should get
with the dim 7th chord in 1st inversion. In C harmonic minor that would be a D,
F, Ab, B. Remember that the D to F in the 5-limit just intonation is a 32:27.

> I find 75/64 to be a much more agreeable septimal minor third compared
> to 7/6.
>

The 75/64 is actually a 5-limit augmented second (Ab B). Notice that it is a
25:24 sharper than a 9:8 second.

The 75:64 is, however, present in the 5-limit German 6th chord and is, as
observed by Marcel, very near to the 7:6 interval.

Much as the ancient deer hunter cut his ancient deer along the lines of its soft
tissue and bone-structure (rather than anything resembling fractions or ratios),
it's also a known archeological fact that the ancient flute maker was just as
apt to cut the holes on their flutes according to the specific, conginital
physical space between their own fingers rather any great cosmic overture or
physiological blind obedience of the ear.....

That said, i was amused to notice today while absent-mindedly half-Christmas
shopping, that this particular store's Guitar Hero action figures all had
guitars with no frets or fret markers..........maybe someday, in some great
Darwinesque inertia that's spiraling towards some for-better-or-worse
contemporary evolutionary path of least resistance, frets and fret lines will
simply be more trouble than they're worth, or an archaic, half-forgotten oddity
from an odd and long bygone day.

Well,who knows........but reality is what it is, and with that in mind I salute
thee, Lars Umlaut, Axel Steel, and Johnny Napalm......so you yon little plastic
selfs and little inflexibly girded fretless guitar
attachments-------------------------Let it Begin !

Dear brother Danny,

While 7-limit has a cool flavour all its own, I would like to obtain a
5-limit diminished seventh for my own selfish purposes.

Cordially,
Oz.

✩ ✩ ✩
www.ozanyarman.com

On Nov 12, 2009, at 10:05 PM, Danny Wier wrote:

> Turns out that chord is listed in Scala as a third inversion... ~D.
>
> ----- Original Message -----
> From: "Danny Wier"
>
>
>> I have a 7-limit chord similar to yours (it maps to the same
>> degrees in
>> 41, 53 and 72-edo):
>>
>> * 21:25:30:35
>> * cumulative: 25/21 10/7 5/3
>> * consecutive: 25/21 6/5 7/6
>>
>> Actually, I'd consider this a first inversion diminished seventh,
>> since a root-position chord would be A-C-Eb-Gb, or 35:42:50:60 the
>> same 7-limit system, where 6/5, 25/21 and 32/27 are the three sizes
>> of
>> minor third (7/6 normally is an augmented second).
>>
>> ~D.
>
>
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
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>
>
>

Now that I think of it, the first inversion of the chord, which is
160:192:225:270 or 316 + 275 + 316 cents is more pleasing to my ears
actually:

    0:          1/1           C    Dbb   unison, perfect prime
    1:          6/5                      minor third
    2:         45/32          F#   Gb    diatonic tritone
    3:         27/16          A    Bbb   Pythagorean major sixth

1st inversion of this chord unfolded yields:

27/16 x 5/3 x 128/75

Very neat, since we are in the 5-limit. And already, the 75/64 minor
third resonates superior to 7/6.

In Yarman-36 notation, this would be:

Cd Eb F|<| A

Correction on the steps!

10 + 8 + 10 (~320 + ~280 + ~320 cents).

Cordially,
Oz.


✩ ✩ ✩
www.ozanyarman.com

On Nov 12, 2009, at 6:02 PM, Marcel de Velde wrote:

>
>
> Hi Oz,
>
> This is an interesting and wholesome diminished seventh chord that I
> couldn't find in the Chords database of SCALA:
>
> 135:160:192:225
>
> When the chord is unfolded, it yields:
>
> 5/3 x 128/75 x 5/3.
>
> The ratios are:
>
> 1/1
> 32/27
> 6/5
> 75/64
>
> I find 75/64 to be a much more agreeable septimal minor third compared
> to 7/6.
>
> In Yarman-36 (a,b,c) the steps are (over the regular 12-tone layer):
>
> 18 8 18.
>
> The notation is:
>
> C E/b F# Ad
>
> Cordially,
> Oz.
>
>
> Yes this is the diminished 7th chord that I used in Beethoven's Drei
> Equali No1 :)
> As far as I'm personally concerned it's the only correct Just
> Intonation diminished 7th.
>
> In Tonal-JI this chord occurs as D (9/8) - F (4/3) - Ab (8/5) - B
> (15/8) where the tonic is C (1/1).
> I recently discussed this chord extensively on the JustIntonation
> Yahoo group and gave several examples of it's use.
>
> In the Beethoven piece it's used like this:
> C (4/3) - F# (15/8) - Eb (16/5) - A (9/2)
> Bb (6/5) - G (2/1) - D (3/1) - Bb (24/5)
> Where the tonic is G (1/1).
>
> Another way to use it is for instance:
> F (4/3) - Ab (8/5) - B (15/8) - D (9/4)  <diminished 7th>
> F (4/3) - G (3/2) - B (15/8) - D (9/4)  <dominant 7th>
> C (1/1) - G (3/2) - C (2/1) - E (5/4)  <tonic major>
> In the tonic of C (1/1)
>
> King regards,
> Marcel
>
>

...and the B in Marcel's example there is a major diesis flat, so I don't know
what to call it. :-)

--- In tuning@yahoogroups.com, "cameron" <misterbobro@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > If 1/1 is C, why would 15/8 be A##?
>
> Oops, the "wrong note" is the Ab being a G#: D, F, G#, B. The doubly augmented
sixth occurs in the Beethoven example I think, have to check again.
>
>
> >
> > -Mike
> >
> >
> > On Thu, Nov 12, 2009 at 2:19 PM, cameron <misterbobro@> wrote:
> > >
> > >
> > >
> > > --- In tuning@yahoogroups.com, Marcel de Velde <m.develde@> wrote:
> > > >
> > >
> > > > Yes this is the diminished 7th chord that I used in Beethoven's Drei
>Equali
> > > > No1 :)
> > > > As far as I'm personally concerned it's the only correct Just
>Intonation
> > > > diminished 7th.
> > > >
> > > > In Tonal-JI this chord occurs as D (9/8) - F (4/3) - Ab (8/5) - B (15/8)
> > > > where the tonic is C (1/1).
> > >
> > > You're using D, F, Ab, A##. You might want to study the term "diesis" a
bit.
> > >
> > > You must understand that in doing what you doing, are not actually working
with Beethoven; rather, you are doing a kind of science-fiction tuning. Groovy,
go to it. If it sounds good it is good. History doesn't just go away, though.
> > >
> > > (Ozan has taken on a heavier burden, something that has been attempted
since the 19th century without complete success, though
> > > a lot of great music has been made in the try: maqam/modal music with
polyphony and functional harmony. This is a vast uncharted area, especially in
the area of notation and determining what pitches actually work in real life.)
> > >
> > >
> >
>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> If 1/1 is C, why would 15/8 be A##?

Oops, the "wrong note" is the Ab being a G#: D, F, G#, B. The doubly augmented
sixth occurs in the Beethoven example I think, have to check again.


>
> -Mike
>
>
> On Thu, Nov 12, 2009 at 2:19 PM, cameron <misterbobro@...> wrote:
> >
> >
> >
> > --- In tuning@yahoogroups.com, Marcel de Velde <m.develde@> wrote:
> > >
> >
> > > Yes this is the diminished 7th chord that I used in Beethoven's Drei
>Equali
> > > No1 :)
> > > As far as I'm personally concerned it's the only correct Just >Intonation
> > > diminished 7th.
> > >
> > > In Tonal-JI this chord occurs as D (9/8) - F (4/3) - Ab (8/5) - B (15/8)
> > > where the tonic is C (1/1).
> >
> > You're using D, F, Ab, A##. You might want to study the term "diesis" a bit.
> >
> > You must understand that in doing what you doing, are not actually working
with Beethoven; rather, you are doing a kind of science-fiction tuning. Groovy,
go to it. If it sounds good it is good. History doesn't just go away, though.
> >
> > (Ozan has taken on a heavier burden, something that has been attempted since
the 19th century without complete success, though
> > a lot of great music has been made in the try: maqam/modal music with
polyphony and functional harmony. This is a vast uncharted area, especially in
the area of notation and determining what pitches actually work in real life.)
> >
> >
>

Turns out that chord is listed in Scala as a third inversion... ~D.

----- Original Message -----
From: "Danny Wier"


>I have a 7-limit chord similar to yours (it maps to the same degrees in
>41, 53 and 72-edo):
>
> * 21:25:30:35
> * cumulative: 25/21 10/7 5/3
> * consecutive: 25/21 6/5 7/6
>
> Actually, I'd consider this a first inversion diminished seventh,
> since a root-position chord would be A-C-Eb-Gb, or 35:42:50:60 the
> same 7-limit system, where 6/5, 25/21 and 32/27 are the three sizes of
> minor third (7/6 normally is an augmented second).
>
> ~D.

I have a 7-limit chord similar to yours (it maps to the same degrees in
41, 53 and 72-edo):

* 21:25:30:35
* cumulative: 25/21 10/7 5/3
* consecutive: 25/21 6/5 7/6

Actually, I'd consider this a first inversion diminished seventh, since
a root-position chord would be A-C-Eb-Gb, or 35:42:50:60 the same
7-limit system, where 6/5, 25/21 and 32/27 are the three sizes of minor
third (7/6 normally is an augmented second).

~D.

----- Original Message -----
From: "Ozan Yarman":

This is an interesting and wholesome diminished seventh chord that I
couldn't find in the Chords database of SCALA:

135:160:192:225

When the chord is unfolded, it yields:

5/3 x 128/75 x 5/3.

The ratios are:

1/1
32/27
6/5
75/64

I find 75/64 to be a much more agreeable septimal minor third compared
to 7/6.

In Yarman-36 (a,b,c) the steps are (over the regular 12-tone layer):

18 8 18.

The notation is:

C E/b F# Ad

Cordially,
Oz.

If 1/1 is C, why would 15/8 be A##?

-Mike


On Thu, Nov 12, 2009 at 2:19 PM, cameron <misterbobro@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
> >
>
> > Yes this is the diminished 7th chord that I used in Beethoven's Drei >Equali
> > No1 :)
> > As far as I'm personally concerned it's the only correct Just >Intonation
> > diminished 7th.
> >
> > In Tonal-JI this chord occurs as D (9/8) - F (4/3) - Ab (8/5) - B (15/8)
> > where the tonic is C (1/1).
>
> You're using D, F, Ab, A##. You might want to study the term "diesis" a bit.
>
> You must understand that in doing what you doing, are not actually working
with Beethoven; rather, you are doing a kind of science-fiction tuning. Groovy,
go to it. If it sounds good it is good. History doesn't just go away, though.
>
> (Ozan has taken on a heavier burden, something that has been attempted since
the 19th century without complete success, though
> a lot of great music has been made in the try: maqam/modal music with
polyphony and functional harmony. This is a vast uncharted area, especially in
the area of notation and determining what pitches actually work in real life.)
>
>

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
>

> Yes this is the diminished 7th chord that I used in Beethoven's Drei >Equali
> No1 :)
> As far as I'm personally concerned it's the only correct Just >Intonation
> diminished 7th.
>
> In Tonal-JI this chord occurs as D (9/8) - F (4/3) - Ab (8/5) - B (15/8)
> where the tonic is C (1/1).

You're using D, F, Ab, A##. You might want to study the term "diesis" a bit.

You must understand that in doing what you doing, are not actually working with
Beethoven; rather, you are doing a kind of science-fiction tuning. Groovy, go to
it. If it sounds good it is good. History doesn't just go away, though.

(Ozan has taken on a heavier burden, something that has been attempted since the
19th century without complete success, though
a lot of great music has been made in the try: maqam/modal music with polyphony
and functional harmony. This is a vast uncharted area, especially in the area of
notation and determining what pitches actually work in real life.)

--- In tuning@yahoogroups.com, "octatonic10" <octatonic10@...> wrote:
>
> but in a chord progression, does it really matter?  The average >tonal ear
won't notice the tuning differences you describe.  But of >course for microtonal
music it is interesting!

The "average tonal ear" won't notice the difference between a flat seven and a
blue flat seven?

Not only is your statement wrong, it is interestingly "maximally" wrong in my
experience. In introducing the theoretical concepts of JI and microtonality to
people, I find that it is a blued b7 that is the instant audible eye-opener. A
5/4 often gets a puzzled, well, it's more "church" sounding..., without the
comprehension that the intervals, and not just the timbre, have been changed.






>
> --- In tuning@yahoogroups.com, Ozan Yarman <ozanyarman@> wrote:
> >
> > This is an interesting and wholesome diminished seventh chord that I
> > couldn't find in the Chords database of SCALA:
> >
> > 135:160:192:225
> >
> > When the chord is unfolded, it yields:
> >
> > 5/3 x 128/75 x 5/3.
> >
> > The ratios are:
> >
> > 1/1
> > 32/27
> > 6/5
> > 75/64
> >
> > I find 75/64 to be a much more agreeable septimal minor third compared
> > to 7/6.
> >
> > In Yarman-36 (a,b,c) the steps are (over the regular 12-tone layer):
> >
> > 18 8 18.
> >
> > The notation is:
> >
> > C E/b F# Ad
> >
> > Cordially,
> > Oz.
> >
> > â&#65533;© â&#65533;© â&#65533;©
> > www.ozanyarman.com
> >
>