Ozan's 159-edo-based tuning

Hi Oz,

Please post either the details of your subset-of-159-edo tuning,
or links to previous posts containing them. Thanks.

I want to make some Tonescape files of it.

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

Dear monz, my tuning scheme involves 33 equal divisions of the pure fourth.

1. [log (4/3) * 1200]/(log 2) divided by 33 =
15.092272701048866128954947492807 cents.

2. Carry the comma to the 79th step and you reach
1192.2895433828604241874408519317 cents.

3. Complete the octave to 1200 cents and move the
22.802729318188441941514095561079 cent comma between steps 45-46. You do
this by key transposing the tuning to the -46th step.

Voila! You now have a circulating temperament which is practically a subset
of 159-tET. There are three sizes of fifths by which one can formulate
diatonical scales:

0: 1/1 C RAST
1: 15.092 cents C/
2: 30.185 cents C//
3: 45.277 cents C^ Db(
4: 60.369 cents C) Dbv
5: 75.461 cents C#\ Db\\
6: 90.554 cents C# Db\
7: 105.646 cents C#/ Db
8: 120.738 cents C#// Db/
9: 135.830 cents C#^ D(
10: 150.923 cents C#) Dv
11: 166.015 cents D\\
12: 181.107 cents D\
13: 196.200 cents D DUGAH
14: 211.292 cents D/ Dugah again
15: 226.384 cents D//
16: 241.476 cents D^ Eb(
17: 256.569 cents D) Ebv
18: 271.661 cents D#\ Eb\\
19: 286.753 cents D# Eb\
20: 301.845 cents D#/ Eb
21: 316.938 cents D#// Eb/
22: 332.030 cents D#^ E(
23: 347.122 cents D#) Ev
24: 362.215 cents E\\
25: 377.307 cents E\ lower segah
26: 392.399 cents E SEGAH
27: 407.491 cents E/ Fb Buselik
28: 422.584 cents E// Fb/ Nishabur
29: 437.676 cents E^ F(
30: 452.768 cents E) Fv
31: 467.860 cents E#\ F\\
32: 482.953 cents E# F\
33: 498.045 cents F CHARGAH
34: 513.137 cents F/
35: 528.230 cents F//
36: 543.322 cents F^ Gb(
37: 558.414 cents F) Gbv
38: 573.506 cents F#\ Gb\\
39: 588.599 cents F# Gb\
40: 603.691 cents F#/ Gb
41: 618.783 cents F#// Gb/
42: 633.875 cents F#^ G(
43: 648.968 cents F#) Gv
44: 664.060 cents G\\
45: 679.152 cents G\
46: 701.955 cents G NEVA
47: 717.047 cents G/
48: 732.140 cents G//
49: 747.232 cents G^ Ab(
50: 762.324 cents G) Abv
51: 777.416 cents G#\ Ab\\
52: 792.509 cents G# Ab\
53: 807.601 cents G#/ Ab
54: 822.693 cents G#// Ab/
55: 837.785 cents G#^ A(
56: 852.878 cents G#) Av
57: 867.970 cents A\\
58: 883.062 cents A\ Hisar
59: 898.155 cents A HUSEYNI/Hisarek
60: 913.247 cents A/ Huseyni again
61: 928.339 cents A//
62: 943.431 cents A^ Bb(
63: 958.524 cents A) Bbv
64: 973.616 cents A#\ Bb\\
65: 988.708 cents A# Bb\
66: 1003.800 cents A#/ Bb
67: 1018.893 cents A#// Bb/
68: 1033.985 cents A#^ B(
69: 1049.077 cents A#) Bv
70: 1064.170 cents B\\
71: 1079.262 cents B\
72: 1094.354 cents B EVDJ
73: 1109.446 cents B/ Cb Mahur
74: 1124.539 cents B// Cb/ Mahurek (my proposal)
75: 1139.631 cents B^ C(
76: 1154.723 cents B) Cv
77: 1169.815 cents B#\ C\\
78: 1184.908 cents B# C\
79: 1200.000 cents C GERDANIYE

Some degrees yield excellent 11 limit results, while others produce adorable
5 limit and sufficiently close 7 limit intervals. I had implemented this
tuning on my special Qanun, and also installed Wittner fine-tuners to the
strings for accuracy of pitch. Although my hands are still numb from all
that tuning, I am very pleased, and so are Qanun performers who were
"unfortunate" enough to have met me.

Cordially
Oz.

----- Original Message -----
From: "monz" <monz@tonalsoft.com>
To: <tuning@yahoogroups.com>
Sent: 16 �ubat 2006 Per�embe 11:19
Subject: [tuning] Ozan's 159-edo-based tuning

> Hi Oz,
>
>
> Please post either the details of your subset-of-159-edo tuning,
> or links to previous posts containing them. Thanks.
>
> I want to make some Tonescape files of it.
>
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>
>
>

Hi Oz,

Thanks for posting those details.
I still have some questions:

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Dear monz, my tuning scheme involves 33 equal divisions
> of the pure fourth.
>
> 1. [log (4/3) * 1200]/(log 2) divided by 33 =
> 15.092272701048866128954947492807 cents.
>
> 2. Carry the comma to the 79th step and you reach
> 1192.2895433828604241874408519317 cents.
>
> 3. Complete the octave to 1200 cents and move the
> 22.802729318188441941514095561079 cent comma between
> steps 45-46.

This isn't clear to me. I see that the final step,
between ~1192 cents and the octave, is ~7.710456617 cents,
and that that plus one step of ~15.0922727 cents is the
~22.8027293-cent "comma". But doesn't "completing the octave"
eliminate that and leave you only with the smaller ~7.7-cent
step?

> You do this by key transposing the tuning to the -46th step.

You started from zero and went upwards to the 79th step.
So what's the "-46th step"?

I tried constructing steps of ~15.092 cents backwards
into the negative numbers, then transposed, but i didn't
get the same results you did. There's no ~3/2 ratio in mine.

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

monz,

----- Original Message -----
From: "monz" <monz@tonalsoft.com>
To: <tuning@yahoogroups.com>
Sent: 16 �ubat 2006 Per�embe 19:56
Subject: [tuning] Re: Ozan's 159-edo-based tuning

> Hi Oz,
>
>
> Thanks for posting those details.
> I still have some questions:
>
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > Dear monz, my tuning scheme involves 33 equal divisions
> > of the pure fourth.
> >
> > 1. [log (4/3) * 1200]/(log 2) divided by 33 =
> > 15.092272701048866128954947492807 cents.
> >
> > 2. Carry the comma to the 79th step and you reach
> > 1192.2895433828604241874408519317 cents.
> >
> > 3. Complete the octave to 1200 cents and move the
> > 22.802729318188441941514095561079 cent comma between
> > steps 45-46.
>
>
> This isn't clear to me. I see that the final step,
> between ~1192 cents and the octave, is ~7.710456617 cents,
> and that that plus one step of ~15.0922727 cents is the
> ~22.8027293-cent "comma". But doesn't "completing the octave"
> eliminate that and leave you only with the smaller ~7.7-cent
> step?
>

Aie. What I meant is that you replace 1192 cents with 1200 cents. You know,
move it up a notch so that the octave is pure.

> > You do this by key transposing the tuning to the -46th step.
>
>
> You started from zero and went upwards to the 79th step.
> So what's the "-46th step"?
>

Given the octave equivalance of 0 cents = 1200 cents, key transposing the
scale over to the -46th step is equivalent to transposing it to the 33rd
step. You are, in effect moving the larger `comma` between the 45.-46.
steps.

> I tried constructing steps of ~15.092 cents backwards
> into the negative numbers, then transposed, but i didn't
> get the same results you did. There's no ~3/2 ratio in mine.
>
>
>

If you are using scala do this:

1. File>New>Equal temperament, division 33, formal octave 4/3, number of
tones 79.

2. Edit the 79th degree pitch and type 1200.0 from the Edit Window

3. Modify>Key>To degree 33, or else, -46.

2. Set nota E79

Voila!

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

Oz.

Ozan,

Have you ever tried recording your Qanun? It sounds like a
marvelous instrument!

-Carl

> Dear monz, my tuning scheme involves 33 equal divisions of the
> pure fourth.
>
> 1. [log (4/3) * 1200]/(log 2) divided by 33 =
> 15.092272701048866128954947492807 cents.
>
> 2. Carry the comma to the 79th step and you reach
> 1192.2895433828604241874408519317 cents.
>
> 3. Complete the octave to 1200 cents and move the
> 22.802729318188441941514095561079 cent comma between steps 45-46.
> You do this by key transposing the tuning to the -46th step.
>
> Voila! You now have a circulating temperament which is practically
> a subset of 159-tET. There are three sizes of fifths by which one
> can formulate diatonical scales:
>
> 0: 1/1 C RAST
> 1: 15.092 cents C/
> 2: 30.185 cents C//
> 3: 45.277 cents C^ Db(
> 4: 60.369 cents C) Dbv
> 5: 75.461 cents C#\ Db\\
> 6: 90.554 cents C# Db\
> 7: 105.646 cents C#/ Db
> 8: 120.738 cents C#// Db/
> 9: 135.830 cents C#^ D(
> 10: 150.923 cents C#) Dv
> 11: 166.015 cents D\\
> 12: 181.107 cents D\
> 13: 196.200 cents D DUGAH
> 14: 211.292 cents D/ Dugah again
> 15: 226.384 cents D//
> 16: 241.476 cents D^ Eb(
> 17: 256.569 cents D) Ebv
> 18: 271.661 cents D#\ Eb\\
> 19: 286.753 cents D# Eb\
> 20: 301.845 cents D#/ Eb
> 21: 316.938 cents D#// Eb/
> 22: 332.030 cents D#^ E(
> 23: 347.122 cents D#) Ev
> 24: 362.215 cents E\\
> 25: 377.307 cents E\ lower segah
> 26: 392.399 cents E SEGAH
> 27: 407.491 cents E/ Fb Buselik
> 28: 422.584 cents E// Fb/ Nishabur
> 29: 437.676 cents E^ F(
> 30: 452.768 cents E) Fv
> 31: 467.860 cents E#\ F\\
> 32: 482.953 cents E# F\
> 33: 498.045 cents F CHARGAH
> 34: 513.137 cents F/
> 35: 528.230 cents F//
> 36: 543.322 cents F^ Gb(
> 37: 558.414 cents F) Gbv
> 38: 573.506 cents F#\ Gb\\
> 39: 588.599 cents F# Gb\
> 40: 603.691 cents F#/ Gb
> 41: 618.783 cents F#// Gb/
> 42: 633.875 cents F#^ G(
> 43: 648.968 cents F#) Gv
> 44: 664.060 cents G\\
> 45: 679.152 cents G\
> 46: 701.955 cents G NEVA
> 47: 717.047 cents G/
> 48: 732.140 cents G//
> 49: 747.232 cents G^ Ab(
> 50: 762.324 cents G) Abv
> 51: 777.416 cents G#\ Ab\\
> 52: 792.509 cents G# Ab\
> 53: 807.601 cents G#/ Ab
> 54: 822.693 cents G#// Ab/
> 55: 837.785 cents G#^ A(
> 56: 852.878 cents G#) Av
> 57: 867.970 cents A\\
> 58: 883.062 cents A\ Hisar
> 59: 898.155 cents A HUSEYNI/Hisarek
> 60: 913.247 cents A/ Huseyni again
> 61: 928.339 cents A//
> 62: 943.431 cents A^ Bb(
> 63: 958.524 cents A) Bbv
> 64: 973.616 cents A#\ Bb\\
> 65: 988.708 cents A# Bb\
> 66: 1003.800 cents A#/ Bb
> 67: 1018.893 cents A#// Bb/
> 68: 1033.985 cents A#^ B(
> 69: 1049.077 cents A#) Bv
> 70: 1064.170 cents B\\
> 71: 1079.262 cents B\
> 72: 1094.354 cents B EVDJ
> 73: 1109.446 cents B/ Cb Mahur
> 74: 1124.539 cents B// Cb/ Mahurek (my proposal)
> 75: 1139.631 cents B^ C(
> 76: 1154.723 cents B) Cv
> 77: 1169.815 cents B#\ C\\
> 78: 1184.908 cents B# C\
> 79: 1200.000 cents C GERDANIYE
>
> Some degrees yield excellent 11 limit results, while others
> produce adorable 5 limit and sufficiently close 7 limit
> intervals. I had implemented this tuning on my special Qanun,
> and also installed Wittner fine-tuners to the strings for
> accuracy of pitch. Although my hands are still numb from all
> that tuning, I am very pleased, and so are Qanun performers
> who were "unfortunate" enough to have met me.
>
> Cordially
> Oz.

I would like to hear it as well, oh Ambassador of the Qanun.

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> Ozan,
>
> Have you ever tried recording your Qanun? It sounds like a
> marvelous instrument!
>
> -Carl
>
> > Dear monz, my tuning scheme involves 33 equal divisions of the
> > pure fourth.
> >
> > 1. [log (4/3) * 1200]/(log 2) divided by 33 =
> > 15.092272701048866128954947492807 cents.
> >
> > 2. Carry the comma to the 79th step and you reach
> > 1192.2895433828604241874408519317 cents.
> >
> > 3. Complete the octave to 1200 cents and move the
> > 22.802729318188441941514095561079 cent comma between steps 45-46.
> > You do this by key transposing the tuning to the -46th step.
> >
> > Voila! You now have a circulating temperament which is practically
> > a subset of 159-tET. There are three sizes of fifths by which one
> > can formulate diatonical scales:
> >
> > 0: 1/1 C RAST
> > 1: 15.092 cents C/
> > 2: 30.185 cents C//
> > 3: 45.277 cents C^ Db(
> > 4: 60.369 cents C) Dbv
> > 5: 75.461 cents C#\ Db\\
> > 6: 90.554 cents C# Db\
> > 7: 105.646 cents C#/ Db
> > 8: 120.738 cents C#// Db/
> > 9: 135.830 cents C#^ D(
> > 10: 150.923 cents C#) Dv
> > 11: 166.015 cents D\\
> > 12: 181.107 cents D\
> > 13: 196.200 cents D DUGAH
> > 14: 211.292 cents D/ Dugah again
> > 15: 226.384 cents D//
> > 16: 241.476 cents D^ Eb(
> > 17: 256.569 cents D) Ebv
> > 18: 271.661 cents D#\ Eb\\
> > 19: 286.753 cents D# Eb\
> > 20: 301.845 cents D#/ Eb
> > 21: 316.938 cents D#// Eb/
> > 22: 332.030 cents D#^ E(
> > 23: 347.122 cents D#) Ev
> > 24: 362.215 cents E\\
> > 25: 377.307 cents E\ lower segah
> > 26: 392.399 cents E SEGAH
> > 27: 407.491 cents E/ Fb Buselik
> > 28: 422.584 cents E// Fb/ Nishabur
> > 29: 437.676 cents E^ F(
> > 30: 452.768 cents E) Fv
> > 31: 467.860 cents E#\ F\\
> > 32: 482.953 cents E# F\
> > 33: 498.045 cents F CHARGAH
> > 34: 513.137 cents F/
> > 35: 528.230 cents F//
> > 36: 543.322 cents F^ Gb(
> > 37: 558.414 cents F) Gbv
> > 38: 573.506 cents F#\ Gb\\
> > 39: 588.599 cents F# Gb\
> > 40: 603.691 cents F#/ Gb
> > 41: 618.783 cents F#// Gb/
> > 42: 633.875 cents F#^ G(
> > 43: 648.968 cents F#) Gv
> > 44: 664.060 cents G\\
> > 45: 679.152 cents G\
> > 46: 701.955 cents G NEVA
> > 47: 717.047 cents G/
> > 48: 732.140 cents G//
> > 49: 747.232 cents G^ Ab(
> > 50: 762.324 cents G) Abv
> > 51: 777.416 cents G#\ Ab\\
> > 52: 792.509 cents G# Ab\
> > 53: 807.601 cents G#/ Ab
> > 54: 822.693 cents G#// Ab/
> > 55: 837.785 cents G#^ A(
> > 56: 852.878 cents G#) Av
> > 57: 867.970 cents A\\
> > 58: 883.062 cents A\ Hisar
> > 59: 898.155 cents A HUSEYNI/Hisarek
> > 60: 913.247 cents A/ Huseyni again
> > 61: 928.339 cents A//
> > 62: 943.431 cents A^ Bb(
> > 63: 958.524 cents A) Bbv
> > 64: 973.616 cents A#\ Bb\\
> > 65: 988.708 cents A# Bb\
> > 66: 1003.800 cents A#/ Bb
> > 67: 1018.893 cents A#// Bb/
> > 68: 1033.985 cents A#^ B(
> > 69: 1049.077 cents A#) Bv
> > 70: 1064.170 cents B\\
> > 71: 1079.262 cents B\
> > 72: 1094.354 cents B EVDJ
> > 73: 1109.446 cents B/ Cb Mahur
> > 74: 1124.539 cents B// Cb/ Mahurek (my proposal)
> > 75: 1139.631 cents B^ C(
> > 76: 1154.723 cents B) Cv
> > 77: 1169.815 cents B#\ C\\
> > 78: 1184.908 cents B# C\
> > 79: 1200.000 cents C GERDANIYE
> >
> > Some degrees yield excellent 11 limit results, while others
> > produce adorable 5 limit and sufficiently close 7 limit
> > intervals. I had implemented this tuning on my special Qanun,
> > and also installed Wittner fine-tuners to the strings for
> > accuracy of pitch. Although my hands are still numb from all
> > that tuning, I am very pleased, and so are Qanun performers
> > who were "unfortunate" enough to have met me.
> >
> > Cordially
> > Oz.
>

Hello Carl and Joe,

Well, since you insist, I made an amateurish recording here:

http://www.ozanyarman.com/anonymous/79-ton-Qanun1.mp3
(This is not for the faint of heart!)

Fumbling as I am, I tried to show some basic modulations that are desirable
through the Seyir of a Taqsim. This pitiable attempt of mine makes use of
Maqam Buselik with a Hijaz tetrachord attached to the dominant tone and some
Nikriz flavours even higher up.

Cordially,
Oz.

----- Original Message -----
From: "Carl Lumma" <clumma@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 16 �ubat 2006 Per�embe 22:30
Subject: [tuning] Re: Ozan's 159-edo-based tuning

> Ozan,
>
> Have you ever tried recording your Qanun? It sounds like a
> marvelous instrument!
>
> -Carl
>

-----------

I would like to hear it as well, oh Ambassador of the Qanun.

On 2/16/06, Ozan Yarman <ozanyarman@ozanyarman.com> wrote:
> Hello Carl and Joe,
>
> Well, since you insist, I made an amateurish recording here:
>
> http://www.ozanyarman.com/anonymous/79-ton-Qanun1.mp3
> (This is not for the faint of heart!)
>
> Fumbling as I am, I tried to show some basic modulations that are desirable
> through the Seyir of a Taqsim. This pitiable attempt of mine makes use of
> Maqam Buselik with a Hijaz tetrachord attached to the dominant tone and some
> Nikriz flavours even higher up.
>
> Cordially,
> Oz.

I thought it sounded awesome! Is the qanun similar to Harry Partch's
Harmonic Canon? Same root word?

Keenan

Thank you Keenan! Qanun is surely synonymous with the Latin word Canon. It
may further be associated with Canaan, which reminds me, your name seems to
be derived from a similar root. We could be talking about biblical history
here.

As for Harry Partch's harmonic canon, I do believe he was trying to invent
something else.

Cordially,
Ozan

----- Original Message -----
From: "Keenan Pepper" <keenanpepper@gmail.com>
To: <tuning@yahoogroups.com>
Sent: 17 �ubat 2006 Cuma 4:35
Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning

> On 2/16/06, Ozan Yarman <ozanyarman@ozanyarman.com> wrote:
> > Hello Carl and Joe,
> >
> > Well, since you insist, I made an amateurish recording here:
> >
> > http://www.ozanyarman.com/anonymous/79-ton-Qanun1.mp3
> > (This is not for the faint of heart!)
> >
> > Fumbling as I am, I tried to show some basic modulations that are
desirable
> > through the Seyir of a Taqsim. This pitiable attempt of mine makes use
of
> > Maqam Buselik with a Hijaz tetrachord attached to the dominant tone and
some
> > Nikriz flavours even higher up.
> >
> > Cordially,
> > Oz.
>
> I thought it sounded awesome! Is the qanun similar to Harry Partch's
> Harmonic Canon? Same root word?
>
> Keenan
>

Ozan, that's simply wonderful! Wow!
You must take it upon yourself to refine your techniques until
you are satisfied with them. Then share more!

-Carl

> Hello Carl and Joe,
>
> Well, since you insist, I made an amateurish recording here:
>
> http://www.ozanyarman.com/anonymous/79-ton-Qanun1.mp3
> (This is not for the faint of heart!)
>
> Fumbling as I am, I tried to show some basic modulations that
> are desirable through the Seyir of a Taqsim. This pitiable
> attempt of mine makes use of Maqam Buselik with a Hijaz
> tetrachord attached to the dominant tone and some Nikriz
> flavours even higher up.
>
> Cordially,
> Oz.
>
> ----- Original Message -----
> From: "Carl Lumma" <clumma@...>
> To: <tuning@yahoogroups.com>
> Sent: 16 Þubat 2006 Perþembe 22:30
> Subject: [tuning] Re: Ozan's 159-edo-based tuning
>
> > Ozan,
> >
> > Have you ever tried recording your Qanun? It sounds like a
> > marvelous instrument!
> >
> > -Carl

Thank you for the encouragement Carl! I'll see what I can do.

Cordially,
Ozan

----- Original Message -----
From: "Carl Lumma" <clumma@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 17 �ubat 2006 Cuma 15:49
Subject: [tuning] Re: Ozan's 159-edo-based tuning

Ozan, that's simply wonderful! Wow!
You must take it upon yourself to refine your techniques until
you are satisfied with them. Then share more!

-Carl

I agree with Carl: very nice, Ozan!

- Dave

Ozan Yarman wrote:
> Thank you for the encouragement Carl! I'll see what I can do.
> > Cordially,
> Ozan
> > ----- Original Message -----
> From: "Carl Lumma" <clumma@yahoo.com>
> To: <tuning@yahoogroups.com>
> Sent: 17 �ubat 2006 Cuma 15:49
> Subject: [tuning] Re: Ozan's 159-edo-based tuning
> > > Ozan, that's simply wonderful! Wow!
> You must take it upon yourself to refine your techniques until
> you are satisfied with them. Then share more!
> > -Carl
> > > > 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
> > > > > > >

Ben de _ me too.

Can Akkoc

Dave Seidel <dave@superluminal.com> wrote:
I agree with Carl: very nice, Ozan!

- Dave

Ozan Yarman wrote:
> Thank you for the encouragement Carl! I'll see what I can do.
>
> Cordially,
> Ozan
>
> ----- Original Message -----
> From: "Carl Lumma"
> To:
> Sent: 17 �ubat 2006 Cuma 15:49
> Subject: [tuning] Re: Ozan's 159-edo-based tuning
>
>
> Ozan, that's simply wonderful! Wow!
> You must take it upon yourself to refine your techniques until
> you are satisfied with them. Then share more!
>
> -Carl
>
>
>
> 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
>
>
>
>
>
>
>

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Hi Oz,

I agree with the others: this sounds great!

Can you post any photos of your Qanun?

How about a score of what you played on this mp3?
(Doesn't have to be in regular notation, any format is fine,
even ASCII. I'd love to make a Tonescape file of it.)

BTW, thanks for clarifying how you constructed the tuning.
Now i've got it.

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

--- In tuning@yahoogroups.com, Dave Seidel <dave@...> wrote:
>
> I agree with Carl: very nice, Ozan!
>
> - Dave
>
> Ozan Yarman wrote:
> > Thank you for the encouragement Carl! I'll see what I can do.
> >
> > Cordially,
> > Ozan
> >
> > ----- Original Message -----
> > From: "Carl Lumma" <clumma@...>
> > To: <tuning@yahoogroups.com>
> > Sent: 17 Þubat 2006 Cuma 15:49
> > Subject: [tuning] Re: Ozan's 159-edo-based tuning
> >
> >
> > Ozan, that's simply wonderful! Wow!
> > You must take it upon yourself to refine your techniques until
> > you are satisfied with them. Then share more!
> >
> > -Carl

Hi Oz,

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

> Some degrees yield excellent 11 limit results, while
> others produce adorable 5 limit and sufficiently close
> 7 limit intervals.

Other than the one perfect 3/2 ratio, do you consider
this tuning to represent 3 as a prime-factor?

Can you please post a table showing how you associate these
prime-factors with their respective scale degrees? It would
help me put together a Tonescape Tonespace of your tuning.

Has Gene or anyone else investigated any possible
unison-vectors, or whether this tuning represents a
TM-reduced-basis, etc.?

My point is that to create a Tonespace of it, i need to
know what to use as generators. There are already several
possibilities:

* a chain created by (4/3)^(1/33)

* a chain created by 2^(1/159), with ~half the notes missing

* a 4-dimensional "block" created by tempered approximations
of prime-factors 2, 5, 7, 11

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

I definitely agree with Carl.

On Fri, 17 Feb 2006, Carl Lumma wrote:

> Ozan, that's simply wonderful! Wow!
> You must take it upon yourself to refine your techniques until
> you are satisfied with them. Then share more!
>
> -Carl
>
>> Hello Carl and Joe,
>>
>> Well, since you insist, I made an amateurish recording here:
>>
>> http://www.ozanyarman.com/anonymous/79-ton-Qanun1.mp3
>> (This is not for the faint of heart!)
>>
>> Fumbling as I am, I tried to show some basic modulations that
>> are desirable through the Seyir of a Taqsim. This pitiable
>> attempt of mine makes use of Maqam Buselik with a Hijaz
>> tetrachord attached to the dominant tone and some Nikriz
>> flavours even higher up.
>>
>> Cordially,
>> Oz.
>>
>> ----- Original Message -----
>> From: "Carl Lumma" <clumma@...>
>> To: <tuning@yahoogroups.com>
>> Sent: 16 Þubat 2006 Perþembe 22:30
>> Subject: [tuning] Re: Ozan's 159-edo-based tuning
>>
>>> Ozan,
>>>
>>> Have you ever tried recording your Qanun? It sounds like a
>>> marvelous instrument!
>>>
>>> -Carl
>
>
>
>
>
>
>
> 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
>
>
>
>
>
>
>

Ozan,

On Fri, 17 Feb 2006, Ozan Yarman wrote:
>
> Hello Carl and Joe,
>
> Well, since you insist, I made an amateurish recording here:
>
> http://www.ozanyarman.com/anonymous/79-ton-Qanun1.mp3
> (This is not for the faint of heart!)
>
> Fumbling as I am, I tried to show some basic modulations that are
desirable
> through the Seyir of a Taqsim. This pitiable attempt of mine makes use of
> Maqam Buselik with a Hijaz tetrachord attached to the dominant tone and
some
> Nikriz flavours even higher up.

Very enjoyable! Thank you.

Could you point out the times at which you use
the Hijaz tetrachord, and also the Nikriz?

Regards,
Yahya

--
No virus found in this outgoing message.
Checked by AVG Free Edition.
Version: 7.1.375 / Virus Database: 267.15.11/264 - Release Date: 17/2/06

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
>
> Hi Oz,
>
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
>
> > Some degrees yield excellent 11 limit results, while
> > others produce adorable 5 limit and sufficiently close
> > 7 limit intervals.
>
>
> Other than the one perfect 3/2 ratio, do you consider
> this tuning to represent 3 as a prime-factor?
>
> Can you please post a table showing how you associate these
> prime-factors with their respective scale degrees? It would
> help me put together a Tonescape Tonespace of your tuning.
>
> Has Gene or anyone else investigated any possible
> unison-vectors,

We have been trying very hard to do so, since so many useful MOS
(and, more generally, DE) scales arise so naturally from delimiting
the lattice by a set of unison vectors, all but one of which is
tempered out. So far, though, Ozan's answers to our queries have been
inconsistent, seemingly, both with one another and with such an
approach. I'm reserving any judgment until there's a lot more clarity
in our mutual understanding.

> or whether this tuning represents a
> TM-reduced-basis, etc.?

What would that mean, exactly? You can TM-reduce the set of unison
vectors that are tempered out, but of course this has no effect on
the resulting tuning system. Meanwhile, a tuning representing or
having a basis of vanishing unison vectors would seem to consist of
only one note, so I'm not sure what use that would be.

>
>
> My point is that to create a Tonespace of it, i need to
> know what to use as generators. There are already several
> possibilities:
>
> * a chain created by (4/3)^(1/33)
>
> * a chain created by 2^(1/159), with ~half the notes missing
>
> * a 4-dimensional "block" created by tempered approximations
> of prime-factors 2, 5, 7, 11

Why isn't prime 3 in there too?

--- In tuning@yahoogroups.com, Dave Seidel <dave@...> wrote:
>
> I agree with Carl: very nice, Ozan!

Some striking modulations. Is that what the system is for?

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

> Has Gene or anyone else investigated any possible
> unison-vectors, or whether this tuning represents a
> TM-reduced-basis, etc.?

It's a MOS, 79 steps per octave with generator 2 steps of 159.
Correspondng linear temperaments do not seem distinguished. In the
7-limit we have <<33 55 95 9 58 69||, with commas 10976/10935 and the
5-limit comma |3 -18 11>
>
> My point is that to create a Tonespace of it, i need to
> know what to use as generators. There are already several
> possibilities:

I'd recommend a chain created by 2^(2/159), which is very little
different than (4/3)^(1/33); it has pure octaves rather than pure fourths.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "monz" <monz@> wrote:
>
> > Has Gene or anyone else investigated any possible
> > unison-vectors, or whether this tuning represents a
> > TM-reduced-basis, etc.?
>
> It's a MOS, 79 steps per octave with generator 2 steps of 159.
> Correspondng linear temperaments do not seem distinguished. In the
> 7-limit we have <<33 55 95 9 58 69||, with commas 10976/10935 and the
> 5-limit comma |3 -18 11>

I should note, however, that 159 is interesting as a high or very high
limit system, and the 80&159 temperament looks better in higher
limits. Of course in something like the 29 limit you may as well just
use all 159 notes, and I really don't see why Ozan doesn't do that
always, and simply adopt 159edo as a way of notating maqam music.
Anyway, 159 is consistent through the 17 limit, but the patent (ie
"standard") val is strong up to 29 at least.

Aside from being nice for higher limits, it has a nearly pure fifth,
inherited from 53, a flat meantone fifth in the vicinity of 19 equal,
and a 709.4 cent fifth of the kind Paul has been pointing out can be
useful. With its best tuning, it tempers out 15625/15552 and
32805/32768 (inherited from 53) as well as 1029/1024 and 10976/10935,
which are not 53-et commas. Tempering out both 1029/1024 and
32805/32768, leading to "guiron", gives a generator of 31 steps of
159, which is an example of the sort of thing one might do by way of
an alternative to the 79-note MOS (a 77-note MOS, perhaps).

> I should note, however, that 159 is interesting as a high or very
> high limit system, and the 80&159 temperament looks better in
> higher limits. Of course in something like the 29 limit you may
> as well just use all 159 notes, and I really don't see why Ozan
> doesn't do that always,

He's answered that. 'Too many notes.'

-Carl

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@...> wrote:
>
>
> Ozan,
>
> On Fri, 17 Feb 2006, Ozan Yarman wrote:
> >
> > Hello Carl and Joe,
> >
> > Well, since you insist, I made an amateurish recording here:
> >
> > http://www.ozanyarman.com/anonymous/79-ton-Qanun1.mp3
> > (This is not for the faint of heart!)
> >
> > Fumbling as I am, I tried to show some basic modulations
> > that are desirable through the Seyir of a Taqsim. This
> > pitiable attempt of mine makes use of Maqam Buselik with
> > a Hijaz tetrachord attached to the dominant tone and
> > some Nikriz flavours even higher up.
>
>
> Very enjoyable! Thank you.
>
> Could you point out the times at which you use
> the Hijaz tetrachord, and also the Nikriz?

And also, could you provide ratios and cents values
to illustrate these Turkish terms?

I've followed very little of the discussion of Turkish
music that's been going on here for about the last year,
but am very interested in it. At some future point,
when i have the time to learn about it, i'd like to
explore its historical connections -- i'd guess that
part of it follows a line like: Sumerian -> Babylonian ->
Persian -> Greek -> (Roman) -> Turkish.

I've made a Tonescape file of your 79-MOS as a subset
of 159-edo in (2,)5,7,11-space, with 2 as the identity
interval, and using TM-basis for the 159-edo periodicity-block.
I'll post the 79-MOS-degree_to_ratio correspondence as soon
as i get a chance.

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

Hi Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@>
> wrote:
> >
> > --- In tuning@yahoogroups.com, "monz" <monz@> wrote:
> >
> > > Has Gene or anyone else investigated any possible
> > > unison-vectors, or whether this tuning represents a
> > > TM-reduced-basis, etc.?
> >
> > It's a MOS, 79 steps per octave with generator 2 steps
> > of 159. Correspondng linear temperaments do not seem
> > distinguished. In the 7-limit we have <<33 55 95 9 58 69||,
> > with commas 10976/10935 and the 5-limit comma |3 -18 11>
>
> I should note, however, that 159 is interesting as a high
> or very high limit system, and the 80&159 temperament looks
> better in higher limits. Of course in something like the
> 29 limit you may as well just use all 159 notes, and I
> really don't see why Ozan doesn't do that always, and
> simply adopt 159edo as a way of notating maqam music.

Yes, that makes a lot of sense to me too.

> Anyway, 159 is consistent through the 17 limit, but the
> patent (ie "standard") val is strong up to 29 at least.
>
> Aside from being nice for higher limits, it has a nearly
> pure fifth, inherited from 53, a flat meantone fifth in
> the vicinity of 19 equal, and a 709.4 cent fifth of the
> kind Paul has been pointing out can be useful. With its
> best tuning, it tempers out 15625/15552 and 32805/32768
> (inherited from 53) as well as 1029/1024 and 10976/10935,
> which are not 53-et commas. Tempering out both 1029/1024
> and 32805/32768, leading to "guiron", gives a generator
> of 31 steps of 159, which is an example of the sort of
> thing one might do by way of an alternative to the 79-note
> MOS (a 77-note MOS, perhaps).

Gene, since you have a working copy of Tonescape, could
you make some Tuning files representing Ozan's tuning?
I'd appreciate that.

I've just attempted to upload my Tonescape file of it
to our website, but am having a server problem. Should
be up there later today.

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

Hi Ozan, Yahya, et al,

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

> I've made a Tonescape file of your 79-MOS as a subset
> of 159-edo in (2,)5,7,11-space, with 2 as the identity
> interval, and using TM-basis for the 159-edo periodicity-block.
> I'll post the 79-MOS-degree_to_ratio correspondence as soon
> as i get a chance.

And here it is ... Ozan, see how well it agrees/disagrees
with your perceptions.

Ozan Yarman's Qanun tuning
as 79-MOS out of 159-edo, in 5-7-11-space
identity interval = 2/1 ratio

degree ... ~cents .. ------ monzo ------- ....... ratio
...................... 2 .. 5 .. 7 .. 11

... 0 ..... 0.000 .. [ 0 .. 0 .. 0 .. 0 > ....... 1 / 1
... 1 .... 15.094 .. [ 4 ..-2 ..-1 .. 1 > ..... 176 / 175
... 2 .... 30.189 .. [ 3 ..-1 .. 1 ..-1 > ...... 56 / 55
... 3 .... 45.283 .. [ 7 ..-3 .. 0 .. 0 > ..... 128 / 125
... 4 .... 60.377 .. [ 6 ..-2 .. 2 ..-2 > .... 3136 / 3025
... 5 .... 75.472 .. [10 ..-4 .. 1 ..-1 > .... 7168 / 6875
... 6 .... 90.566 .. [ 1 .. 5 ..-2 ..-2 > .... 6250 / 5929
... 7 ... 105.660 .. [-7 .. 1 ..-2 .. 3 > .... 6655 / 6272
... 8 ... 120.755 .. [-8 .. 2 .. 0 .. 1 > ..... 275 / 256
... 9 ... 135.849 .. [-4 .. 0 ..-1 .. 2 > ..... 121 / 112
.. 10 ... 150.943 .. [-5 .. 1 .. 1 .. 0 > ...... 35 / 32
.. 11 ... 166.038 .. [-1 ..-1 .. 0 .. 1 > ...... 11 / 10
.. 12 ... 181.132 .. [-2 .. 0 .. 2 ..-1 > ...... 49 / 44
.. 13 ... 196.226 .. [ 2 ..-2 .. 1 .. 0 > ...... 28 / 25
.. 14 ... 211.321 .. [ 1 ..-1 .. 3 ..-2 > ..... 686 / 605
.. 15 ... 226.415 .. [ 5 ..-3 .. 2 ..-1 > .... 1568 / 1375
.. 16 ... 241.509 .. [ 1 .. 3 ..-4 .. 1 > .... 2750 / 2401
.. 17 ... 256.604 .. [ 0 .. 4 ..-2 ..-1 > ..... 625 / 539
.. 18 ... 271.698 .. [ 4 .. 2 ..-3 .. 0 > ..... 400 / 343
.. 19 ... 286.792 .. [ 3 .. 3 ..-1 ..-2 > .... 1000 / 847
.. 20 ... 301.887 .. [ 7 .. 1 ..-2 ..-1 > ..... 640 / 539
.. 21 ... 316.981 .. [-6 .. 0 .. 1 .. 1 > ...... 77 / 64
.. 22 ... 332.075 .. [-2 ..-2 .. 0 .. 2 > ..... 121 / 100
.. 23 ... 347.170 .. [-3 ..-1 .. 2 .. 0 > ...... 49 / 40
.. 24 ... 362.264 .. [ 1 ..-3 .. 1 .. 1 > ..... 154 / 125
.. 25 ... 377.358 .. [ 0 ..-2 .. 3 ..-1 > ..... 343 / 275
.. 26 ... 392.453 .. [ 4 ..-4 .. 2 .. 0 > ..... 784 / 625
.. 27 ... 407.547 .. [-5 .. 5 ..-1 ..-1 > .... 3125 / 2464
.. 28 ... 422.642 .. [-1 .. 3 ..-2 .. 0 > ..... 125 / 98
.. 29 ... 437.736 .. [ 3 .. 1 ..-3 .. 1 > ..... 440 / 343
.. 30 ... 452.830 .. [ 2 .. 2 ..-1 ..-1 > ..... 100 / 77
.. 31 ... 467.925 .. [ 6 .. 0 ..-2 .. 0 > ...... 64 / 49
.. 32 ... 483.019 .. [ 5 .. 1 .. 0 ..-2 > ..... 160 / 121
.. 33 ... 498.113 .. [ 9 ..-1 ..-1 ..-1 > ..... 512 / 385
.. 34 ... 513.208 .. [-4 ..-2 .. 2 .. 1 > ..... 539 / 400
.. 35 ... 528.302 .. [ 0 ..-4 .. 1 .. 2 > ..... 847 / 625
.. 36 ... 543.396 .. [-1 ..-3 .. 3 .. 0 > ..... 343 / 250
.. 37 ... 558.491 .. [-5 .. 3 ..-3 .. 2 > ... 15125 / 10976
.. 38 ... 573.585 .. [-6 .. 4 ..-1 .. 0 > ..... 625 / 448
.. 39 ... 588.679 .. [-2 .. 2 ..-2 .. 1 > ..... 275 / 196
.. 40 ... 603.774 .. [-3 .. 3 .. 0 ..-1 > ..... 125 / 88
.. 41 ... 618.868 .. [ 1 .. 1 ..-1 .. 0 > ...... 10 / 7
.. 42 ... 633.962 .. [ 0 .. 2 .. 1 ..-2 > ..... 175 / 121
.. 43 ... 649.057 .. [ 4 .. 0 .. 0 ..-1 > ...... 16 / 11
.. 44 ... 664.151 .. [ 8 ..-2 ..-1 .. 0 > ..... 256 / 175
.. 45 ... 679.245 .. [ 7 ..-1 .. 1 ..-2 > ..... 896 / 605
.. 46 ... 701.887 .. [ 4 .. 3 .. 0 ..-3 > .... 2000 / 1331
.. 47 ... 716.981 .. [-4 ..-1 .. 0 .. 2 > ..... 121 / 80
.. 48 ... 732.075 .. [-5 .. 0 .. 2 .. 0 > ...... 49 / 32
.. 49 ... 747.170 .. [-1 ..-2 .. 1 .. 1 > ...... 77 / 50
.. 50 ... 762.264 .. [ 3 ..-4 .. 0 .. 2 > ..... 968 / 625
.. 51 ... 777.358 .. [ 2 ..-3 .. 2 .. 0 > ..... 196 / 125
.. 52 ... 792.453 .. [ 6 ..-5 .. 1 .. 1 > .... 4928 / 3125
.. 53 ... 807.547 .. [-3 .. 4 ..-2 .. 0 > ..... 625 / 392
.. 54 ... 822.642 .. [ 1 .. 2 ..-3 .. 1 > ..... 550 / 343
.. 55 ... 837.736 .. [ 0 .. 3 ..-1 ..-1 > ..... 125 / 77
.. 56 ... 852.830 .. [ 4 .. 1 ..-2 .. 0 > ...... 80 / 49
.. 57 ... 867.925 .. [ 3 .. 2 .. 0 ..-2 > ..... 200 / 121
.. 58 ... 883.019 .. [ 7 .. 0 ..-1 ..-1 > ..... 128 / 77
.. 59 ... 898.113 .. [ 6 .. 1 .. 1 ..-3 > .... 2240 / 1331
.. 60 ... 913.208 .. [-2 ..-3 .. 1 .. 2 > ..... 847 / 500
.. 61 ... 928.302 .. [-3 ..-2 .. 3 .. 0 > ..... 343 / 200
.. 62 ... 943.396 .. [ 1 ..-4 .. 2 .. 1 > .... 1078 / 625
.. 63 ... 958.491 .. [-8 .. 5 ..-1 .. 0 > .... 3125 / 1792
.. 64 ... 973.585 .. [-4 .. 3 ..-2 .. 1 > .... 1375 / 784
.. 65 ... 988.679 .. [ 0 .. 1 ..-3 .. 2 > ..... 605 / 343
.. 66 .. 1003.774 .. [-1 .. 2 ..-1 .. 0 > ...... 25 / 14
.. 67 .. 1018.868 .. [ 3 .. 0 ..-2 .. 1 > ...... 88 / 49
.. 68 .. 1033.962 .. [ 2 .. 1 .. 0 ..-1 > ...... 20 / 11
.. 69 .. 1049.057 .. [ 6 ..-1 ..-1 .. 0 > ...... 64 / 35
.. 70 .. 1064.151 .. [ 5 .. 0 .. 1 ..-2 > ..... 224 / 121
.. 71 .. 1079.245 .. [ 9 ..-2 .. 0 ..-1 > ..... 512 / 275
.. 72 .. 1094.340 .. [ 8 ..-1 .. 2 ..-3 > ... 12544 / 6655
.. 73 .. 1109.434 .. [ 0 ..-5 .. 2 .. 2 > .... 5929 / 3125
.. 74 .. 1124.528 .. [-9 .. 4 ..-1 .. 1 > .... 6875 / 3584
.. 75 .. 1139.623 .. [-5 .. 2 ..-2 .. 2 > .... 3025 / 1568
.. 76 .. 1154.717 .. [-6 .. 3 .. 0 .. 0 > ..... 125 / 64
.. 77 .. 1169.811 .. [-2 .. 1 ..-1 .. 1 > ...... 55 / 28
.. 78 .. 1184.906 .. [-3 .. 2 .. 1 ..-1 > ..... 175 / 88
(. 79 .. 1200.000 .. [ 1 .. 0 .. 0 .. 0 > ....... 2 / 1)

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

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
>
> Hi Ozan, Yahya, et al,
>
>
> --- In tuning@yahoogroups.com, "monz" <monz@> wrote:
>
> > I've made a Tonescape file of your 79-MOS as a subset
> > of 159-edo in (2,)5,7,11-space, with 2 as the identity
> > interval, and using TM-basis for the 159-edo periodicity-block.
> > I'll post the 79-MOS-degree_to_ratio correspondence as soon
> > as i get a chance.
>
>
> And here it is ... Ozan, see how well it agrees/disagrees
> with your perceptions.

And here's an alternate version of my table, for those
who want the monzo without the interpolated spacer periods:

Ozan Yarman's Qanun tuning
as 79-MOS out of 159-edo, in 5-7-11-space
identity interval = 2/1 ratio

degree ... ~cents .. 2,5,7,11-monzo ...... ratio

... 0 ..... 0.000 .. [ 0 0 0 0 > ......... 1 / 1
... 1 .... 15.094 .. [ 4 -2 -1 1 > ..... 176 / 175
... 2 .... 30.189 .. [ 3 -1 1 -1 > ...... 56 / 55
... 3 .... 45.283 .. [ 7 -3 0 0 > ...... 128 / 125
... 4 .... 60.377 .. [ 6 -2 2 -2 > .... 3136 / 3025
... 5 .... 75.472 .. [10 -4 1 -1 > .... 7168 / 6875
... 6 .... 90.566 .. [ 1 5 -2 -2 > .... 6250 / 5929
... 7 ... 105.660 .. [-7 1 -2 3 > ..... 6655 / 6272
... 8 ... 120.755 .. [-8 2 0 1 > ....... 275 / 256
... 9 ... 135.849 .. [-4 0 -1 2 > ...... 121 / 112
.. 10 ... 150.943 .. [-5 1 1 0 > ........ 35 / 32
.. 11 ... 166.038 .. [-1 -1 0 1 > ....... 11 / 10
.. 12 ... 181.132 .. [-2 0 2 -1 > ....... 49 / 44
.. 13 ... 196.226 .. [ 2 -2 1 0 > ....... 28 / 25
.. 14 ... 211.321 .. [ 1 -1 3 -2 > ..... 686 / 605
.. 15 ... 226.415 .. [ 5 -3 2 -1 > .... 1568 / 1375
.. 16 ... 241.509 .. [ 1 3 -4 1 > ..... 2750 / 2401
.. 17 ... 256.604 .. [ 0 4 -2 -1 > ..... 625 / 539
.. 18 ... 271.698 .. [ 4 2 -3 0 > ...... 400 / 343
.. 19 ... 286.792 .. [ 3 3 -1 -2 > .... 1000 / 847
.. 20 ... 301.887 .. [ 7 1 -2 -1 > ..... 640 / 539
.. 21 ... 316.981 .. [-6 0 1 1 > ........ 77 / 64
.. 22 ... 332.075 .. [-2 -2 0 2 > ...... 121 / 100
.. 23 ... 347.170 .. [-3 -1 2 0 > ....... 49 / 40
.. 24 ... 362.264 .. [ 1 -3 1 1 > ...... 154 / 125
.. 25 ... 377.358 .. [ 0 -2 3 -1 > ..... 343 / 275
.. 26 ... 392.453 .. [ 4 -4 2 0 > ...... 784 / 625
.. 27 ... 407.547 .. [-5 5 -1 -1 > .... 3125 / 2464
.. 28 ... 422.642 .. [-1 3 -2 0 > ...... 125 / 98
.. 29 ... 437.736 .. [ 3 1 -3 1 > ...... 440 / 343
.. 30 ... 452.830 .. [ 2 2 -1 -1 > ..... 100 / 77
.. 31 ... 467.925 .. [ 6 0 -2 0 > ....... 64 / 49
.. 32 ... 483.019 .. [ 5 1 0 -2 > ...... 160 / 121
.. 33 ... 498.113 .. [ 9 -1 -1 -1 > .... 512 / 385
.. 34 ... 513.208 .. [-4 -2 2 1 > ...... 539 / 400
.. 35 ... 528.302 .. [ 0 -4 1 2 > ...... 847 / 625
.. 36 ... 543.396 .. [-1 -3 3 0 > ...... 343 / 250
.. 37 ... 558.491 .. [-5 3 -3 2 > .... 15125 / 10976
.. 38 ... 573.585 .. [-6 4 -1 0 > ...... 625 / 448
.. 39 ... 588.679 .. [-2 2 -2 1 > ...... 275 / 196
.. 40 ... 603.774 .. [-3 3 0 -1 > ...... 125 / 88
.. 41 ... 618.868 .. [ 1 1 -1 0 > ....... 10 / 7
.. 42 ... 633.962 .. [ 0 2 1 -2 > ...... 175 / 121
.. 43 ... 649.057 .. [ 4 0 0 -1 > ....... 16 / 11
.. 44 ... 664.151 .. [ 8 -2 -1 0 > ..... 256 / 175
.. 45 ... 679.245 .. [ 7 -1 1 -2 > ..... 896 / 605
.. 46 ... 701.887 .. [ 4 3 0 -3 > ..... 2000 / 1331
.. 47 ... 716.981 .. [-4 -1 0 2 > ...... 121 / 80
.. 48 ... 732.075 .. [-5 0 2 0 > ........ 49 / 32
.. 49 ... 747.170 .. [-1 -2 1 1 > ....... 77 / 50
.. 50 ... 762.264 .. [ 3 -4 0 2 > ...... 968 / 625
.. 51 ... 777.358 .. [ 2 -3 2 0 > ...... 196 / 125
.. 52 ... 792.453 .. [ 6 -5 1 1 > ..... 4928 / 3125
.. 53 ... 807.547 .. [-3 4 -2 0 > ...... 625 / 392
.. 54 ... 822.642 .. [ 1 2 -3 1 > ...... 550 / 343
.. 55 ... 837.736 .. [ 0 3 -1 -1 > ..... 125 / 77
.. 56 ... 852.830 .. [ 4 1 -2 0 > ....... 80 / 49
.. 57 ... 867.925 .. [ 3 2 0 -2 > ...... 200 / 121
.. 58 ... 883.019 .. [ 7 0 -1 -1 > ..... 128 / 77
.. 59 ... 898.113 .. [ 6 1 1 -3 > ..... 2240 / 1331
.. 60 ... 913.208 .. [-2 -3 1 2 > ...... 847 / 500
.. 61 ... 928.302 .. [-3 -2 3 0 > ...... 343 / 200
.. 62 ... 943.396 .. [ 1 -4 2 1 > ..... 1078 / 625
.. 63 ... 958.491 .. [-8 5 -1 0 > ..... 3125 / 1792
.. 64 ... 973.585 .. [-4 3 -2 1 > ..... 1375 / 784
.. 65 ... 988.679 .. [ 0 1 -3 2 > ...... 605 / 343
.. 66 .. 1003.774 .. [-1 2 -1 0 > ....... 25 / 14
.. 67 .. 1018.868 .. [ 3 0 -2 1 > ....... 88 / 49
.. 68 .. 1033.962 .. [ 2 1 0 -1 > ....... 20 / 11
.. 69 .. 1049.057 .. [ 6 -1 -1 0 > ...... 64 / 35
.. 70 .. 1064.151 .. [ 5 0 1 -2 > ...... 224 / 121
.. 71 .. 1079.245 .. [ 9 -2 0 -1 > ..... 512 / 275
.. 72 .. 1094.340 .. [ 8 -1 2 -3 > ... 12544 / 6655
.. 73 .. 1109.434 .. [ 0 -5 2 2 > ..... 5929 / 3125
.. 74 .. 1124.528 .. [-9 4 -1 1 > ..... 6875 / 3584
.. 75 .. 1139.623 .. [-5 2 -2 2 > ..... 3025 / 1568
.. 76 .. 1154.717 .. [-6 3 0 0 > ....... 125 / 64
.. 77 .. 1169.811 .. [-2 1 -1 1 > ....... 55 / 28
.. 78 .. 1184.906 .. [-3 2 1 -1 > ...... 175 / 88
(. 79 .. 1200.000 .. [ 1 0 0 0 > ......... 2 / 1)

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

> --- In tuning@yahoogroups.com, "monz" <monz@> wrote:
> >
> > Hi Ozan, Yahya, et al,
> >
> >
> > --- In tuning@yahoogroups.com, "monz" <monz@> wrote:
> >
> > > I've made a Tonescape file of your 79-MOS as a subset
> > > of 159-edo in (2,)5,7,11-space, with 2 as the identity
> > > interval, and using TM-basis for the 159-edo periodicity-block.
> > > I'll post the 79-MOS-degree_to_ratio correspondence as soon
> > > as i get a chance.
> >
> >
> > And here it is ... Ozan, see how well it agrees/disagrees
> > with your perceptions.

I've uploaded a screenshot of a Tonescape Lattice of Ozan's
tuning to the tuning_files group:

/tuning/files/monz/ozan_79-mos_159-edo_5-7-11-space_lattice.gif

The Lattice points are labeled with the degree numbers.

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

Hi Gene,

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

> Gene, since you have a working copy of Tonescape, could
> you make some Tuning files representing Ozan's tuning?
> I'd appreciate that.
>
> I've just attempted to upload my Tonescape file of it
> to our website, but am having a server problem. Should
> be up there later today.

I emailed it to you as an attachment, to two different
addresses i have for you. The svpal one bounced back.
The other was your gmail.

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

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

> I emailed it to you as an attachment, to two different
> addresses i have for you. The svpal one bounced back.
> The other was your gmail.

OK, but I'm unclear what you want done; I had thought you'd taken care
of the problem judging by your recent posts.

Joe,

You might have to join the *notayaz* group in cyberspace if you are truly interested in getting to the bottom of some *mysterious* structures embedded in Turkish makam music.

That means you have to start learning Turkish soon.

Can Akkoc

monz <monz@tonalsoft.com> wrote:
--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@...> wrote:
>
>
> Ozan,
>
> On Fri, 17 Feb 2006, Ozan Yarman wrote:
> >
> > Hello Carl and Joe,
> >
> > Well, since you insist, I made an amateurish recording here:
> >
> > http://www.ozanyarman.com/anonymous/79-ton-Qanun1.mp3
> > (This is not for the faint of heart!)
> >
> > Fumbling as I am, I tried to show some basic modulations that are desirable through the Seyir of a Taqsim. This pitiable attempt of mine makes use of Maqam Buselik with a Hijaz tetrachord attached to the dominant tone and some Nikriz flavours even higher up.

> Very enjoyable! Thank you.
>
> Could you point out the times at which you use
> the Hijaz tetrachord, and also the Nikriz?

And also, could you provide ratios and cents values
to illustrate these Turkish terms?

I've followed very little of the discussion of Turkish
music that's been going on here for about the last year, but am very interested in it. At some future point, when i have the time to learn about it, i'd like to explore its historical connections -- i'd guess that
part of it follows a line like: Sumerian -> Babylonian ->
Persian -> Greek -> (Roman) -> Turkish.

I've made a Tonescape file of your 79-MOS as a subset
of 159-edo in (2,)5,7,11-space, with 2 as the identity
interval, and using TM-basis for the 159-edo periodicity-block.
I'll post the 79-MOS-degree_to_ratio correspondence as soon as i get a chance.

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

Hi Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:

> --- In tuning@yahoogroups.com, "monz" <monz@> wrote:
>
> > I emailed it to you as an attachment, to two different
> > addresses i have for you. The svpal one bounced back.
> > The other was your gmail.
>
> OK, but I'm unclear what you want done; I had thought
> you'd taken care of the problem judging by your recent posts.

It wasn't really that i saw a problem ... just many different
ways of modeling Ozan's Qanun tuning, and i was interested to
see what you might come up with.

The "solution" i used here doesn't totally satisfy me,
because it's a subset of 159-edo which only has ~half
of the notes of 159-edo: thus, there are holes all over
the Lattice. I'd prefer:

1) to use the actual tuning which Ozan apparently prefers,
(4/3)^(1/33), which is very close to but not exactly the
same as 159-edo;

2) to set it up in a 5,7,11-space rather than just as
a "linear" chain of generators;

3) to use consecutive powers of the generators, so that
it doesn't have all the "holes".

Besides, i just would like to see you playing around
with Tonescape again ... it's been a long time since
you showed me anything you did with it.

Note that (for the handful of testers we're working with)
the "Mustang" version is available from our website now,
when you login. You should download and install that,
so that you have the latest version running.

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

Hi Can,

--- In tuning@yahoogroups.com, Can Akkoc <can193849@...> wrote:
>
> Joe,
>
> You might have to join the *notayaz* group in cyberspace
> if you are truly interested in getting to the bottom of
> some *mysterious* structures embedded in Turkish makam music.
>
> That means you have to start learning Turkish soon.

Yes, i'm already aware of notayaz from Ozan. I've avoided
it so far precisely because i don't have time right now to
learn any more Turkish than the miniscule amount i already
know.

I've been planning (more like wishing for) a trip to Istanbul
for a couple of decades now ... someday ...

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

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

> Besides, i just would like to see you playing around
> with Tonescape again ... it's been a long time since
> you showed me anything you did with it.

I've been waiting for a new version to come out to see if I could use
it for composing.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@>
> wrote:
> >
> >
> I should note, however, that 159 is interesting as a high or very high
> limit system, and the 80&159 temperament looks better in higher
> limits.

So this implies an 80-note MOS rather than a 79-note one should be interesting?

Tempering out both 1029/1024 and
> 32805/32768, leading to "guiron", gives a generator of 31 steps of
> 159, which is an example of the sort of thing one might do by way of
> an alternative to the 79-note MOS (a 77-note MOS, perhaps).
>
Fascinating.

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > I should note, however, that 159 is interesting as a high or very
> > high limit system, and the 80&159 temperament looks better in
> > higher limits. Of course in something like the 29 limit you may
> > as well just use all 159 notes, and I really don't see why Ozan
> > doesn't do that always,
>
> He's answered that. 'Too many notes.'
>
> -Carl

But one would think that if one chooses a subset, it would be one where the consonant intervals can be transposed once or twice by the usual intervals of modulation (fourths and fifths), wouldn't one?

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
>
> Hi Ozan, Yahya, et al,
>
>
> --- In tuning@yahoogroups.com, "monz" <monz@> wrote:
>
> > I've made a Tonescape file of your 79-MOS as a subset
> > of 159-edo in (2,)5,7,11-space, with 2 as the identity
> > interval, and using TM-basis for the 159-edo periodicity-block.

Can you state this with more precision and detail, please, for those of us attempting to follow along?

> > I'll post the 79-MOS-degree_to_ratio correspondence as soon
> > as i get a chance.
>
>
> And here it is ... Ozan, see how well it agrees/disagrees
> with your perceptions.
>
>
>
> Ozan Yarman's Qanun tuning
> as 79-MOS out of 159-edo, in 5-7-11-space
> identity interval = 2/1 ratio
>
>
> degree ... ~cents .. ------ monzo ------- ....... ratio
> ...................... 2 .. 5 .. 7 .. 11
>
> ... 0 ..... 0.000 .. [ 0 .. 0 .. 0 .. 0 > ....... 1 / 1
> ... 1 .... 15.094 .. [ 4 ..-2 ..-1 .. 1 > ..... 176 / 175
> ... 2 .... 30.189 .. [ 3 ..-1 .. 1 ..-1 > ...... 56 / 55
> ... 3 .... 45.283 .. [ 7 ..-3 .. 0 .. 0 > ..... 128 / 125
> ... 4 .... 60.377 .. [ 6 ..-2 .. 2 ..-2 > .... 3136 / 3025
> ... 5 .... 75.472 .. [10 ..-4 .. 1 ..-1 > .... 7168 / 6875
> ... 6 .... 90.566 .. [ 1 .. 5 ..-2 ..-2 > .... 6250 / 5929
> ... 7 ... 105.660 .. [-7 .. 1 ..-2 .. 3 > .... 6655 / 6272
> ... 8 ... 120.755 .. [-8 .. 2 .. 0 .. 1 > ..... 275 / 256
> ... 9 ... 135.849 .. [-4 .. 0 ..-1 .. 2 > ..... 121 / 112
> .. 10 ... 150.943 .. [-5 .. 1 .. 1 .. 0 > ...... 35 / 32
> .. 11 ... 166.038 .. [-1 ..-1 .. 0 .. 1 > ...... 11 / 10
> .. 12 ... 181.132 .. [-2 .. 0 .. 2 ..-1 > ...... 49 / 44
> .. 13 ... 196.226 .. [ 2 ..-2 .. 1 .. 0 > ...... 28 / 25
> .. 14 ... 211.321 .. [ 1 ..-1 .. 3 ..-2 > ..... 686 / 605
> .. 15 ... 226.415 .. [ 5 ..-3 .. 2 ..-1 > .... 1568 / 1375
> .. 16 ... 241.509 .. [ 1 .. 3 ..-4 .. 1 > .... 2750 / 2401
> .. 17 ... 256.604 .. [ 0 .. 4 ..-2 ..-1 > ..... 625 / 539
> .. 18 ... 271.698 .. [ 4 .. 2 ..-3 .. 0 > ..... 400 / 343
> .. 19 ... 286.792 .. [ 3 .. 3 ..-1 ..-2 > .... 1000 / 847
> .. 20 ... 301.887 .. [ 7 .. 1 ..-2 ..-1 > ..... 640 / 539
> .. 21 ... 316.981 .. [-6 .. 0 .. 1 .. 1 > ...... 77 / 64
> .. 22 ... 332.075 .. [-2 ..-2 .. 0 .. 2 > ..... 121 / 100
> .. 23 ... 347.170 .. [-3 ..-1 .. 2 .. 0 > ...... 49 / 40
> .. 24 ... 362.264 .. [ 1 ..-3 .. 1 .. 1 > ..... 154 / 125
> .. 25 ... 377.358 .. [ 0 ..-2 .. 3 ..-1 > ..... 343 / 275
> .. 26 ... 392.453 .. [ 4 ..-4 .. 2 .. 0 > ..... 784 / 625
> .. 27 ... 407.547 .. [-5 .. 5 ..-1 ..-1 > .... 3125 / 2464
> .. 28 ... 422.642 .. [-1 .. 3 ..-2 .. 0 > ..... 125 / 98
> .. 29 ... 437.736 .. [ 3 .. 1 ..-3 .. 1 > ..... 440 / 343
> .. 30 ... 452.830 .. [ 2 .. 2 ..-1 ..-1 > ..... 100 / 77
> .. 31 ... 467.925 .. [ 6 .. 0 ..-2 .. 0 > ...... 64 / 49
> .. 32 ... 483.019 .. [ 5 .. 1 .. 0 ..-2 > ..... 160 / 121
> .. 33 ... 498.113 .. [ 9 ..-1 ..-17 ..-1 > ..... 512 / 385

I find it pretty humorous that you didn't even get 4/3 for 33 steps, one of the few clues Ozan has explicitly given us . . .

> .. 34 ... 513.208 .. [-4 ..-2 .. 2 .. 1 > ..... 539 / 400
> .. 35 ... 528.302 .. [ 0 ..-4 .. 1 .. 2 > ..... 847 / 625
> .. 36 ... 543.396 .. [-1 ..-3 .. 3 .. 0 > ..... 343 / 250
> .. 37 ... 558.491 .. [-5 .. 3 ..-3 .. 2 > ... 15125 / 10976
> .. 38 ... 573.585 .. [-6 .. 4 ..-1 .. 0 > ..... 625 / 448
> .. 39 ... 588.679 .. [-2 .. 2 ..-2 .. 1 > ..... 275 / 196
> .. 40 ... 603.774 .. [-3 .. 3 .. 0 ..-1 > ..... 125 / 88
> .. 41 ... 618.868 .. [ 1 .. 1 ..-1 .. 0 > ...... 10 / 7
> .. 42 ... 633.962 .. [ 0 .. 2 .. 1 ..-2 > ..... 175 / 121
> .. 43 ... 649.057 .. [ 4 .. 0 .. 0 ..-1 > ...... 16 / 11
> .. 44 ... 664.151 .. [ 8 ..-2 ..-1 .. 0 > ..... 256 / 175
> .. 45 ... 679.245 .. [ 7 ..-1 .. 1 ..-2 > ..... 896 / 605
> .. 46 ... 701.887 .. [ 4 .. 3 .. 0 ..-3 > .... 2000 / 1331
> .. 47 ... 716.981 .. [-4 ..-1 .. 0 .. 2 > ..... 121 / 80
> .. 48 ... 732.075 .. [-5 .. 0 .. 2 .. 0 > ...... 49 / 32
> .. 49 ... 747.170 .. [-1 ..-2 .. 1 .. 1 > ...... 77 / 50
> .. 50 ... 762.264 .. [ 3 ..-4 .. 0 .. 2 > ..... 968 / 625
> .. 51 ... 777.358 .. [ 2 ..-3 .. 2 .. 0 > ..... 196 / 125
> .. 52 ... 792.453 .. [ 6 ..-5 .. 1 .. 1 > .... 4928 / 3125
> .. 53 ... 807.547 .. [-3 .. 4 ..-2 .. 0 > ..... 625 / 392
> .. 54 ... 822.642 .. [ 1 .. 2 ..-3 .. 1 > ..... 550 / 343
> .. 55 ... 837.736 .. [ 0 .. 3 ..-1 ..-1 > ..... 125 / 77
> .. 56 ... 852.830 .. [ 4 .. 1 ..-2 .. 0 > ...... 80 / 49
> .. 57 ... 867.925 .. [ 3 .. 2 .. 0 ..-2 > ..... 200 / 121
> .. 58 ... 883.019 .. [ 7 .. 0 ..-1 ..-1 > ..... 128 / 77
> .. 59 ... 898.113 .. [ 6 .. 1 .. 1 ..-3 > .... 2240 / 1331
> .. 60 ... 913.208 .. [-2 ..-3 .. 1 .. 2 > ..... 847 / 500
> .. 61 ... 928.302 .. [-3 ..-2 .. 3 .. 0 > ..... 343 / 200
> .. 62 ... 943.396 .. [ 1 ..-4 .. 2 .. 1 > .... 1078 / 625
> .. 63 ... 958.491 .. [-8 .. 5 ..-1 .. 0 > .... 3125 / 1792
> .. 64 ... 973.585 .. [-4 .. 3 ..-2 .. 1 > .... 1375 / 784
> .. 65 ... 988.679 .. [ 0 .. 1 ..-3 .. 2 > ..... 605 / 343
> .. 66 .. 1003.774 .. [-1 .. 2 ..-1 .. 0 > ...... 25 / 14
> .. 67 .. 1018.868 .. [ 3 .. 0 ..-2 .. 1 > ...... 88 / 49
> .. 68 .. 1033.962 .. [ 2 .. 1 .. 0 ..-1 > ...... 20 / 11
> .. 69 .. 1049.057 .. [ 6 ..-1 ..-1 .. 0 > ...... 64 / 35
> .. 70 .. 1064.151 .. [ 5 .. 0 .. 1 ..-2 > ..... 224 / 121
> .. 71 .. 1079.245 .. [ 9 ..-2 .. 0 ..-1 > ..... 512 / 275
> .. 72 .. 1094.340 .. [ 8 ..-1 .. 2 ..-3 > ... 12544 / 6655
> .. 73 .. 1109.434 .. [ 0 ..-5 .. 2 .. 2 > .... 5929 / 3125
> .. 74 .. 1124.528 .. [-9 .. 4 ..-1 .. 1 > .... 6875 / 3584
> .. 75 .. 1139.623 .. [-5 .. 2 ..-2 .. 2 > .... 3025 / 1568
> .. 76 .. 1154.717 .. [-6 .. 3 .. 0 .. 0 > ..... 125 / 64
> .. 77 .. 1169.811 .. [-2 .. 1 ..-1 .. 1 > ...... 55 / 28
> .. 78 .. 1184.906 .. [-3 .. 2 .. 1 ..-1 > ..... 175 / 88
> (. 79 .. 1200.000 .. [ 1 .. 0 .. 0 .. 0 > ....... 2 / 1)
>
>
>
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>

Gene,

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
To: <tuning@yahoogroups.com>
Sent: 18 �ubat 2006 Cumartesi 8:43
Subject: [tuning] Re: Ozan's 159-edo-based tuning

> --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
> wrote:
> >
> > --- In tuning@yahoogroups.com, "monz" <monz@> wrote:
> >
> > > Has Gene or anyone else investigated any possible
> > > unison-vectors, or whether this tuning represents a
> > > TM-reduced-basis, etc.?
> >
> > It's a MOS, 79 steps per octave with generator 2 steps of 159.
> > Correspondng linear temperaments do not seem distinguished. In the
> > 7-limit we have <<33 55 95 9 58 69||, with commas 10976/10935 and the
> > 5-limit comma |3 -18 11>
>
> I should note, however, that 159 is interesting as a high or very high
> limit system, and the 80&159 temperament looks better in higher
> limits. Of course in something like the 29 limit you may as well just
> use all 159 notes, and I really don't see why Ozan doesn't do that
> always, and simply adopt 159edo as a way of notating maqam music.
> Anyway, 159 is consistent through the 17 limit, but the patent (ie
> "standard") val is strong up to 29 at least.
>

Can you give the step numbers for 80?

I cannot use all the 159 notes, because there is no space on the Qanun to
fix that many mandals!

> Aside from being nice for higher limits, it has a nearly pure fifth,
> inherited from 53, a flat meantone fifth in the vicinity of 19 equal,
> and a 709.4 cent fifth of the kind Paul has been pointing out can be
> useful. With its best tuning, it tempers out 15625/15552 and
> 32805/32768 (inherited from 53) as well as 1029/1024 and 10976/10935,
> which are not 53-et commas. Tempering out both 1029/1024 and
> 32805/32768, leading to "guiron", gives a generator of 31 steps of
> 159, which is an example of the sort of thing one might do by way of
> an alternative to the 79-note MOS (a 77-note MOS, perhaps).
>
>

Can you also give the step numbers for 77?

To be precise, `too many notes for any instrument of Maqam Music`.

----- Original Message -----
From: "Carl Lumma" <clumma@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 18 �ubat 2006 Cumartesi 9:05
Subject: [tuning] Re: Ozan's 159-edo-based tuning

> > I should note, however, that 159 is interesting as a high or very
> > high limit system, and the 80&159 temperament looks better in
> > higher limits. Of course in something like the 29 limit you may
> > as well just use all 159 notes, and I really don't see why Ozan
> > doesn't do that always,
>
> He's answered that. 'Too many notes.'
>
> -Carl
>
>

Is this lattice based on 159-eq? Or my 33 equal division of 4/3?

----- Original Message -----
From: "monz" <monz@tonalsoft.com>
To: <tuning@yahoogroups.com>
Sent: 19 �ubat 2006 Pazar 0:13
Subject: [tuning] Re: Ozan's 159-edo-based tuning

> > --- In tuning@yahoogroups.com, "monz" <monz@> wrote:
> > >
> > > Hi Ozan, Yahya, et al,
> > >
> > >
> > > --- In tuning@yahoogroups.com, "monz" <monz@> wrote:
> > >
> > > > I've made a Tonescape file of your 79-MOS as a subset
> > > > of 159-edo in (2,)5,7,11-space, with 2 as the identity
> > > > interval, and using TM-basis for the 159-edo periodicity-block.
> > > > I'll post the 79-MOS-degree_to_ratio correspondence as soon
> > > > as i get a chance.
> > >
> > >
> > > And here it is ... Ozan, see how well it agrees/disagrees
> > > with your perceptions.
>
>
>
> I've uploaded a screenshot of a Tonescape Lattice of Ozan's
> tuning to the tuning_files group:
>
>
/tuning/files/monz/ozan_79-mos_159
-edo_5-7-11-space_lattice.gif
>
>
> The Lattice points are labeled with the degree numbers.
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>
>

monz,

----- Original Message -----
From: "monz" <monz@tonalsoft.com>
To: <tuning@yahoogroups.com>
Sent: 18 �ubat 2006 Cumartesi 22:42
Subject: [tuning] Re: Ozan's 159-edo-based tuning

SNIP

> >
> > Could you point out the times at which you use
> > the Hijaz tetrachord, and also the Nikriz?
>
>
>
> And also, could you provide ratios and cents values
> to illustrate these Turkish terms?

Ok. The scales are these according to SCALA E79 with step numbers:

D Fb F G A B( C# D
13 27 33 46 59 68 85 92
(Buselik principal scale)

D E( F# G A B( C# D
13 22 39 46 59 68 85 92
(Zirguleli Hijaz, meaning Hijaz using perde zirgule at C#, effectively
doubling the Hijaz tetrachord over the dominant tone.)

A B( C# D Fb F-F# G A
-20 -11 6 13 27 33-39 46 59
(Hijaz principal scale)
3/4 away from its designated tonic

G A B( C# D E( F# G
46 59 68 85 92 101 118 125
(Nikriz principal scale - supplementary uses E and F)
3/2 away from its designated tonic

Compressed to one octave, the cent values are these:

0: 1/1 D
1: 135.830 cents Eb
2: 211.292 cents E
3: 301.845 cents F
4: 392.399 cents F#
5: 505.755 cents G
6: 701.955 cents A
7: 837.785 cents Bb
8: 1094.354 cents C#
9: 1200.000 cents D

>
> I've followed very little of the discussion of Turkish
> music that's been going on here for about the last year,
> but am very interested in it.

Glad to hear it.

At some future point,
> when i have the time to learn about it, i'd like to
> explore its historical connections -- i'd guess that
> part of it follows a line like: Sumerian -> Babylonian ->
> Persian -> Greek -> (Roman) -> Turkish.
>

That would be much anticipated.

>
> I've made a Tonescape file of your 79-MOS as a subset
> of 159-edo in (2,)5,7,11-space, with 2 as the identity
> interval, and using TM-basis for the 159-edo periodicity-block.
> I'll post the 79-MOS-degree_to_ratio correspondence as soon
> as i get a chance.
>
>

I'll look into it.

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

Oz.

monz,

----- Original Message -----
From: "monz" <monz@tonalsoft.com>
To: <tuning@yahoogroups.com>
Sent: 18 �ubat 2006 Cumartesi 23:43
Subject: [tuning] Re: Ozan's 159-edo-based tuning

> Hi Ozan, Yahya, et al,
>
>
> --- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
>
> > I've made a Tonescape file of your 79-MOS as a subset
> > of 159-edo in (2,)5,7,11-space, with 2 as the identity
> > interval, and using TM-basis for the 159-edo periodicity-block.
> > I'll post the 79-MOS-degree_to_ratio correspondence as soon
> > as i get a chance.
>
>
> And here it is ... Ozan, see how well it agrees/disagrees
> with your perceptions.
>

Let me see.

>
>
> Ozan Yarman's Qanun tuning
> as 79-MOS out of 159-edo, in 5-7-11-space
> identity interval = 2/1 ratio
>
>
> degree ... ~cents .. ------ monzo ------- ....... ratio
> ...................... 2 .. 5 .. 7 .. 11
>
> ... 0 ..... 0.000 .. [ 0 .. 0 .. 0 .. 0 > ....... 1 / 1
> ... 1 .... 15.094 .. [ 4 ..-2 ..-1 .. 1 > ..... 176 / 175
> ... 2 .... 30.189 .. [ 3 ..-1 .. 1 ..-1 > ...... 56 / 55
> ... 3 .... 45.283 .. [ 7 ..-3 .. 0 .. 0 > ..... 128 / 125
> ... 4 .... 60.377 .. [ 6 ..-2 .. 2 ..-2 > .... 3136 / 3025
> ... 5 .... 75.472 .. [10 ..-4 .. 1 ..-1 > .... 7168 / 6875
> ... 6 .... 90.566 .. [ 1 .. 5 ..-2 ..-2 > .... 6250 / 5929
> ... 7 ... 105.660 .. [-7 .. 1 ..-2 .. 3 > .... 6655 / 6272
> ... 8 ... 120.755 .. [-8 .. 2 .. 0 .. 1 > ..... 275 / 256
> ... 9 ... 135.849 .. [-4 .. 0 ..-1 .. 2 > ..... 121 / 112
> .. 10 ... 150.943 .. [-5 .. 1 .. 1 .. 0 > ...... 35 / 32
> .. 11 ... 166.038 .. [-1 ..-1 .. 0 .. 1 > ...... 11 / 10
> .. 12 ... 181.132 .. [-2 .. 0 .. 2 ..-1 > ...... 49 / 44
> .. 13 ... 196.226 .. [ 2 ..-2 .. 1 .. 0 > ...... 28 / 25
> .. 14 ... 211.321 .. [ 1 ..-1 .. 3 ..-2 > ..... 686 / 605
> .. 15 ... 226.415 .. [ 5 ..-3 .. 2 ..-1 > .... 1568 / 1375
> .. 16 ... 241.509 .. [ 1 .. 3 ..-4 .. 1 > .... 2750 / 2401
> .. 17 ... 256.604 .. [ 0 .. 4 ..-2 ..-1 > ..... 625 / 539
> .. 18 ... 271.698 .. [ 4 .. 2 ..-3 .. 0 > ..... 400 / 343
> .. 19 ... 286.792 .. [ 3 .. 3 ..-1 ..-2 > .... 1000 / 847
> .. 20 ... 301.887 .. [ 7 .. 1 ..-2 ..-1 > ..... 640 / 539
> .. 21 ... 316.981 .. [-6 .. 0 .. 1 .. 1 > ...... 77 / 64
> .. 22 ... 332.075 .. [-2 ..-2 .. 0 .. 2 > ..... 121 / 100
> .. 23 ... 347.170 .. [-3 ..-1 .. 2 .. 0 > ...... 49 / 40
> .. 24 ... 362.264 .. [ 1 ..-3 .. 1 .. 1 > ..... 154 / 125
> .. 25 ... 377.358 .. [ 0 ..-2 .. 3 ..-1 > ..... 343 / 275
> .. 26 ... 392.453 .. [ 4 ..-4 .. 2 .. 0 > ..... 784 / 625
> .. 27 ... 407.547 .. [-5 .. 5 ..-1 ..-1 > .... 3125 / 2464
> .. 28 ... 422.642 .. [-1 .. 3 ..-2 .. 0 > ..... 125 / 98
> .. 29 ... 437.736 .. [ 3 .. 1 ..-3 .. 1 > ..... 440 / 343
> .. 30 ... 452.830 .. [ 2 .. 2 ..-1 ..-1 > ..... 100 / 77
> .. 31 ... 467.925 .. [ 6 .. 0 ..-2 .. 0 > ...... 64 / 49
> .. 32 ... 483.019 .. [ 5 .. 1 .. 0 ..-2 > ..... 160 / 121
> .. 33 ... 498.113 .. [ 9 ..-1 ..-1 ..-1 > ..... 512 / 385

This is the reason why I prefer a pure fourth to the 53-edo fourth, although
they differ by 0.068 cents.

> .. 34 ... 513.208 .. [-4 ..-2 .. 2 .. 1 > ..... 539 / 400
> .. 35 ... 528.302 .. [ 0 ..-4 .. 1 .. 2 > ..... 847 / 625
> .. 36 ... 543.396 .. [-1 ..-3 .. 3 .. 0 > ..... 343 / 250
> .. 37 ... 558.491 .. [-5 .. 3 ..-3 .. 2 > ... 15125 / 10976
> .. 38 ... 573.585 .. [-6 .. 4 ..-1 .. 0 > ..... 625 / 448
> .. 39 ... 588.679 .. [-2 .. 2 ..-2 .. 1 > ..... 275 / 196
> .. 40 ... 603.774 .. [-3 .. 3 .. 0 ..-1 > ..... 125 / 88
> .. 41 ... 618.868 .. [ 1 .. 1 ..-1 .. 0 > ...... 10 / 7
> .. 42 ... 633.962 .. [ 0 .. 2 .. 1 ..-2 > ..... 175 / 121
> .. 43 ... 649.057 .. [ 4 .. 0 .. 0 ..-1 > ...... 16 / 11
> .. 44 ... 664.151 .. [ 8 ..-2 ..-1 .. 0 > ..... 256 / 175
> .. 45 ... 679.245 .. [ 7 ..-1 .. 1 ..-2 > ..... 896 / 605
> .. 46 ... 701.887 .. [ 4 .. 3 .. 0 ..-3 > .... 2000 / 1331

The fifth should have been 3/2. The complication arises from your preference
of 159 equal divisions of the octave, which is a very close approximation to
my proposal.

> .. 47 ... 716.981 .. [-4 ..-1 .. 0 .. 2 > ..... 121 / 80
> .. 48 ... 732.075 .. [-5 .. 0 .. 2 .. 0 > ...... 49 / 32
> .. 49 ... 747.170 .. [-1 ..-2 .. 1 .. 1 > ...... 77 / 50
> .. 50 ... 762.264 .. [ 3 ..-4 .. 0 .. 2 > ..... 968 / 625
> .. 51 ... 777.358 .. [ 2 ..-3 .. 2 .. 0 > ..... 196 / 125
> .. 52 ... 792.453 .. [ 6 ..-5 .. 1 .. 1 > .... 4928 / 3125
> .. 53 ... 807.547 .. [-3 .. 4 ..-2 .. 0 > ..... 625 / 392
> .. 54 ... 822.642 .. [ 1 .. 2 ..-3 .. 1 > ..... 550 / 343
> .. 55 ... 837.736 .. [ 0 .. 3 ..-1 ..-1 > ..... 125 / 77
> .. 56 ... 852.830 .. [ 4 .. 1 ..-2 .. 0 > ...... 80 / 49
> .. 57 ... 867.925 .. [ 3 .. 2 .. 0 ..-2 > ..... 200 / 121
> .. 58 ... 883.019 .. [ 7 .. 0 ..-1 ..-1 > ..... 128 / 77
> .. 59 ... 898.113 .. [ 6 .. 1 .. 1 ..-3 > .... 2240 / 1331
> .. 60 ... 913.208 .. [-2 ..-3 .. 1 .. 2 > ..... 847 / 500
> .. 61 ... 928.302 .. [-3 ..-2 .. 3 .. 0 > ..... 343 / 200
> .. 62 ... 943.396 .. [ 1 ..-4 .. 2 .. 1 > .... 1078 / 625
> .. 63 ... 958.491 .. [-8 .. 5 ..-1 .. 0 > .... 3125 / 1792
> .. 64 ... 973.585 .. [-4 .. 3 ..-2 .. 1 > .... 1375 / 784
> .. 65 ... 988.679 .. [ 0 .. 1 ..-3 .. 2 > ..... 605 / 343
> .. 66 .. 1003.774 .. [-1 .. 2 ..-1 .. 0 > ...... 25 / 14
> .. 67 .. 1018.868 .. [ 3 .. 0 ..-2 .. 1 > ...... 88 / 49
> .. 68 .. 1033.962 .. [ 2 .. 1 .. 0 ..-1 > ...... 20 / 11
> .. 69 .. 1049.057 .. [ 6 ..-1 ..-1 .. 0 > ...... 64 / 35
> .. 70 .. 1064.151 .. [ 5 .. 0 .. 1 ..-2 > ..... 224 / 121
> .. 71 .. 1079.245 .. [ 9 ..-2 .. 0 ..-1 > ..... 512 / 275
> .. 72 .. 1094.340 .. [ 8 ..-1 .. 2 ..-3 > ... 12544 / 6655
> .. 73 .. 1109.434 .. [ 0 ..-5 .. 2 .. 2 > .... 5929 / 3125
> .. 74 .. 1124.528 .. [-9 .. 4 ..-1 .. 1 > .... 6875 / 3584
> .. 75 .. 1139.623 .. [-5 .. 2 ..-2 .. 2 > .... 3025 / 1568
> .. 76 .. 1154.717 .. [-6 .. 3 .. 0 .. 0 > ..... 125 / 64
> .. 77 .. 1169.811 .. [-2 .. 1 ..-1 .. 1 > ...... 55 / 28
> .. 78 .. 1184.906 .. [-3 .. 2 .. 1 ..-1 > ..... 175 / 88
> (. 79 .. 1200.000 .. [ 1 .. 0 .. 0 .. 0 > ....... 2 / 1)
>
>

Some famous intervals made their way in, but would you not prefer my version
instead?

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

Dear monz,

Thanks very much for the praises. I have uploaded to pictures of my Qanun
to:

http://www.ozanyarman.com/anonymous/

Sorry for the bad quality. My webcam can do no better and the Qanun just
won't fit in my flatbed scanner!

A score is very easy to prepare with a frequency analyzer program.
Unfortunately Solo Explorer by Gailius Raskinis detected polyphony and could
not transcribe the piece.

The unalterated notes used are these according to SCALA e79:

A B( C# D Fb F G A B( C# D E( F# G A B( C# D

Fb equates to E buselik, not E segah, hence the characteristic of the
Buselik Maqam, whose tonic is lower D. However, I finished on lower A
Ashiran with a Hijaz flavor.

Cordially,
Oz.

----- Original Message -----
From: "monz" <monz@tonalsoft.com>
To: <tuning@yahoogroups.com>
Sent: 18 Şubat 2006 Cumartesi 1:23
Subject: [tuning] Re: Ozan's 159-edo-based tuning

Hi Oz,

I agree with the others: this sounds great!

Can you post any photos of your Qanun?

How about a score of what you played on this mp3?
(Doesn't have to be in regular notation, any format is fine,
even ASCII. I'd love to make a Tonescape file of it.)

BTW, thanks for clarifying how you constructed the tuning.
Now i've got it.

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

Hi monz,

----- Original Message -----
From: "monz" <monz@tonalsoft.com>
To: <tuning@yahoogroups.com>
Sent: 18 Şubat 2006 Cumartesi 1:38
Subject: [tuning] Re: Ozan's 159-edo-based tuning

> Hi Oz,
>
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> > Some degrees yield excellent 11 limit results, while
> > others produce adorable 5 limit and sufficiently close
> > 7 limit intervals.
>
>
> Other than the one perfect 3/2 ratio, do you consider
> this tuning to represent 3 as a prime-factor?
>

Surely, one may look at it that way also.

> Can you please post a table showing how you associate these
> prime-factors with their respective scale degrees? It would
> help me put together a Tonescape Tonespace of your tuning.
>

I can give you the whole-tone zone right here:

0: 1/1 C
1: 15.092 cents C/ comma
2: 30.185 cents C// minor diesis
3: 45.277 cents C^ Db( quarter-tone
4: 60.369 cents C) Dbv 1/3 tone/major diesis
5: 75.461 cents C#\ Db\\ minor chroma
6: 90.554 cents C# Db\ limma 3 & 5-limit
7: 105.646 cents C#/ Db apotome 3-limit
8: 120.738 cents C#// Db/ apotome 5-limit
9: 135.830 cents C#^ D( tridecimal 2/3 tone
10: 150.923 cents C#) Dv unidecimal neutral second
11: 166.015 cents D\\ Ptolemy's second
12: 181.107 cents D\ minor whole tone
13: 196.200 cents D major whole tone 1
14: 211.292 cents D/ major whole tone 2
(super-Pyth.)

SNIP

Oz.

To a great extent, yes. I have not even begun to scratch the surface of all the possibilities.

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
To: <tuning@yahoogroups.com>
Sent: 18 Şubat 2006 Cumartesi 6:52
Subject: [tuning] Re: Ozan's 159-edo-based tuning

> --- In tuning@yahoogroups.com, Dave Seidel <dave@...> wrote:
> >
> > I agree with Carl: very nice, Ozan!
>
> Some striking modulations. Is that what the system is for?
>
>

Paul, you are not helping in the least. I am not a tuning expert nor do I
claim to possess superior knowledge in matters of consonances. For gosh
sakes, I'm still new here and English is not my mother tongue. I have
pointed out to the best of my ability all the criteria that Maqam Music
requires and am very much satisfied with the results of my proposal at this
moment. But since you are hard to please, oblige me... what inconsistencies
have you discovered that I and the others are unaware of?

----- Original Message -----
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 18 Şubat 2006 Cumartesi 6:47
Subject: [tuning] Re: Ozan's 159-edo-based tuning

> --- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
> >
> > Hi Oz,
> >
> >
> > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> >
> > > Some degrees yield excellent 11 limit results, while
> > > others produce adorable 5 limit and sufficiently close
> > > 7 limit intervals.
> >
> >
> > Other than the one perfect 3/2 ratio, do you consider
> > this tuning to represent 3 as a prime-factor?
> >
> > Can you please post a table showing how you associate these
> > prime-factors with their respective scale degrees? It would
> > help me put together a Tonescape Tonespace of your tuning.
> >
> > Has Gene or anyone else investigated any possible
> > unison-vectors,
>
> We have been trying very hard to do so, since so many useful MOS
> (and, more generally, DE) scales arise so naturally from delimiting
> the lattice by a set of unison vectors, all but one of which is
> tempered out. So far, though, Ozan's answers to our queries have been
> inconsistent, seemingly, both with one another and with such an
> approach. I'm reserving any judgment until there's a lot more clarity
> in our mutual understanding.
>
> > or whether this tuning represents a
> > TM-reduced-basis, etc.?
>
> What would that mean, exactly? You can TM-reduce the set of unison
> vectors that are tempered out, but of course this has no effect on
> the resulting tuning system. Meanwhile, a tuning representing or
> having a basis of vanishing unison vectors would seem to consist of
> only one note, so I'm not sure what use that would be.
>
> >
> >
> > My point is that to create a Tonespace of it, i need to
> > know what to use as generators. There are already several
> > possibilities:
> >
> > * a chain created by (4/3)^(1/33)
> >
> > * a chain created by 2^(1/159), with ~half the notes missing
> >
> > * a 4-dimensional "block" created by tempered approximations
> > of prime-factors 2, 5, 7, 11
>
> Why isn't prime 3 in there too?
>
>
>

Can you please explain the first paragraph in layman terms Gene?

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
To: <tuning@yahoogroups.com>
Sent: 18 Şubat 2006 Cumartesi 7:17
Subject: [tuning] Re: Ozan's 159-edo-based tuning

> --- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
>
> > Has Gene or anyone else investigated any possible
> > unison-vectors, or whether this tuning represents a
> > TM-reduced-basis, etc.?
>
> It's a MOS, 79 steps per octave with generator 2 steps of 159.
> Correspondng linear temperaments do not seem distinguished. In the
> 7-limit we have <<33 55 95 9 58 69||, with commas 10976/10935 and the
> 5-limit comma |3 -18 11>
> >
> > My point is that to create a Tonespace of it, i need to
> > know what to use as generators. There are already several
> > possibilities:
>
> I'd recommend a chain created by 2^(2/159), which is very little
> different than (4/3)^(1/33); it has pure octaves rather than pure fourths.
>
>

Hello brother in Islam,

I'm happy you enjoyed the piece:

1. For the first 15 seconds I flirt on the Hijaz tetrachord starting on A.
2. From hereon to 20 seconds I descend to D to pronounce the Buselik
flavour.
3. From 20 seconds onward, I make a modulation from Hijaz on A to Buselik on
high D.
4. The modulations continue and come to a stop on D with a Buselik
repetition of the same motif.
5. From 33 seconds onward one hears a D minor arpeggio and I perform the
same motif on high D.
6. At about 40 seconds, I make a transition to a Nikriz flavor, which
requires an alteration of two notes of Buselik on high D, making another
Hijaz tetrachord.
7. From 50 seconds onward, I return to Buselik on high D and rest on A
Hijaz.
8. From 1:06 you hear the same motif and a transition to the Hijaz Maqam on
high D instead of D.
9. By 1:25, I begin to return to Buselik on D and sound the arpeggio of D
minor once more.
10. By 1:30 you hear Nikriz again.
11. By 1:40 Buselik again and a famous melody I borrowed.
12. At 1:57 minutes, I try to alterate F to F# but the mandals get stuck.
Fortunately, I recover and carry on.
13. Around 2 minutes, I come to rest at low A with a Hijaz tetrachord.
14. By 2:07, Nikriz one last time.
15. By 2:15 a G minor scale with a sesquitonal Bb, in fact a requirement of
Nikriz.
16. At 2:20 I have descended to low A Hijaz.

Cordially,
Oz.

----- Original Message -----
From: "Yahya Abdal-Aziz" <yahya@melbpc.org.au>
To: <tuning@yahoogroups.com>
Sent: 18 Şubat 2006 Cumartesi 6:01
Subject: [tuning] Re: Ozan's 159-edo-based tuning

>
> Ozan,
>
> On Fri, 17 Feb 2006, Ozan Yarman wrote:
> >
> > Hello Carl and Joe,
> >
> > Well, since you insist, I made an amateurish recording here:
> >
> > http://www.ozanyarman.com/anonymous/79-ton-Qanun1.mp3
> > (This is not for the faint of heart!)
> >
> > Fumbling as I am, I tried to show some basic modulations that are
> desirable
> > through the Seyir of a Taqsim. This pitiable attempt of mine makes use
of
> > Maqam Buselik with a Hijaz tetrachord attached to the dominant tone and
> some
> > Nikriz flavours even higher up.
>
>
> Very enjoyable! Thank you.
>
> Could you point out the times at which you use
> the Hijaz tetrachord, and also the Nikriz?
>
> Regards,
> Yahya
>

And how does 79 notes from 33 equal divisions of the pure fourth with octave
equivalances preclude the possibility of modulations Paul? Or better yet,
how does 77 or 80 do not?

----- Original Message -----
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 20 �ubat 2006 Pazartesi 12:56
Subject: [tuning] Re: Ozan's 159-edo-based tuning

> --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
> >
> > > I should note, however, that 159 is interesting as a high or very
> > > high limit system, and the 80&159 temperament looks better in
> > > higher limits. Of course in something like the 29 limit you may
> > > as well just use all 159 notes, and I really don't see why Ozan
> > > doesn't do that always,
> >
> > He's answered that. 'Too many notes.'
> >
> > -Carl
>
> But one would think that if one chooses a subset, it would be one where
the consonant intervals can be transposed once or twice by the usual
intervals of modulation (fourths and fifths), wouldn't one?
>
>
>

Paul,

> > >
> > I should note, however, that 159 is interesting as a high or very high
> > limit system, and the 80&159 temperament looks better in higher
> > limits.
>
> So this implies an 80-note MOS rather than a 79-note one should be
interesting?
>

I don't understand what you have against 79 anyway.

>
> Tempering out both 1029/1024 and
> > 32805/32768, leading to "guiron", gives a generator of 31 steps of
> > 159, which is an example of the sort of thing one might do by way of
> > an alternative to the 79-note MOS (a 77-note MOS, perhaps).
> >
> Fascinating.
>
>

It would be fascinating if we were given the chance to analyze it first.

Hi Ozan.

You wrote:

> The fifth should have been 3/2. The complication arises from your
preference
> of 159 equal divisions of the octave, which is a very close approximation
to
> my proposal.

Am I right in assuming that the fifth is closer to 3/2 in your tuning than
in 159-equal?

Petr

Petr, the default fifth is exactly 3/2 in my tuning:

0: 0.000 cents 0.000 0 0 commas C
46: 701.955 cents -0.000 0 0 commas G
13: 694.245 cents -7.710 -237 D
59: 701.955 cents -7.710 -237 A
26: 694.245 cents -15.421 -473 E
72: 701.955 cents -15.421 -473 B
39: 694.245 cents -23.131 -710 F#
6: 701.955 cents -23.131 -710 C#
52: 701.955 cents -23.131 -710 G#
19: 694.245 cents -30.842 -947 D#
65: 701.955 cents -30.842 -947 A#
32: 694.245 cents -38.552 -1183 E#
78: 701.955 cents -38.552 -1183 B#
45: 694.245 cents -46.263 -1420 G\
12: 701.955 cents -46.263 -1420 D\
58: 701.955 cents -46.263 -1420 A\
25: 694.245 cents -53.973 -1656 E\
71: 701.955 cents -53.973 -1656 B\
38: 694.245 cents -61.684 -1893 F#\
5: 701.955 cents -61.684 -1893 C#\
51: 701.955 cents -61.684 -1893 G#\
18: 694.245 cents -69.394 -2130 D#\
64: 701.955 cents -69.394 -2130 A#\
31: 694.245 cents -77.105 -2366 F\\
77: 701.955 cents -77.105 -2366 C\\
44: 694.245 cents -84.815 -2603 G\\
11: 701.955 cents -84.815 -2603 D\\
57: 701.955 cents -84.815 -2603 A\\
24: 694.245 cents -92.525 -2840 E\\
70: 701.955 cents -92.525 -2840 B\\
37: 694.245 cents -100.236 -3076 F)
4: 701.955 cents -100.236 -3076 C)
50: 701.955 cents -100.236 -3076 G)
17: 694.245 cents -107.946 -3313 D)
63: 701.955 cents -107.946 -3313 A)
30: 694.245 cents -115.657 -3550 Fv
76: 701.955 cents -115.657 -3550 Cv
43: 694.245 cents -123.367 -3786 Gv
10: 701.955 cents -123.367 -3786 Dv
56: 701.955 cents -123.367 -3786 Av
23: 694.245 cents -131.078 -4023 Ev
69: 701.955 cents -131.078 -4023 Bv
36: 694.245 cents -138.788 -4259 F^
3: 701.955 cents -138.788 -4259 C^
49: 701.955 cents -138.788 -4259 G^
16: 694.245 cents -146.499 -4496 D^
62: 701.955 cents -146.499 -4496 A^
29: 694.245 cents -154.209 -4733 F(
75: 701.955 cents -154.209 -4733 C(
42: 694.245 cents -161.920 -4969 G(
9: 701.955 cents -161.920 -4969 D(
55: 701.955 cents -161.920 -4969 A(
22: 694.245 cents -169.630 -5206 E(
68: 701.955 cents -169.630 -5206 B(
35: 694.245 cents -177.340 -5443 F//
2: 701.955 cents -177.340 -5443 C//
48: 701.955 cents -177.340 -5443 G//
15: 694.245 cents -185.051 -5679 D//
61: 701.955 cents -185.051 -5679 A//
28: 694.245 cents -192.761 -5916 E//
74: 701.955 cents -192.761 -5916 B//
41: 694.245 cents -200.472 -6153 Gb/
8: 701.955 cents -200.472 -6153 Db/
54: 701.955 cents -200.472 -6153 Ab/
21: 694.245 cents -208.182 -6389 Eb/
67: 701.955 cents -208.182 -6389 Bb/
34: 694.245 cents -215.893 -6626 F/
1: 701.955 cents -215.893 -6626 C/
47: 701.955 cents -215.893 -6626 G/
14: 694.245 cents -223.603 -6863 D/
60: 701.955 cents -223.603 -6863 A/
27: 694.245 cents -231.314 -7099 Fb
73: 701.955 cents -231.314 -7099 Cb
40: 694.245 cents -239.024 -7336 Gb
7: 701.955 cents -239.024 -7336 Db
53: 701.955 cents -239.024 -7336 Ab
20: 694.245 cents -246.735 -7572 Eb
66: 701.955 cents -246.735 -7572 Bb
33: 694.245 cents -254.445 -7809 F
79: 701.955 cents -254.445 -7809 C
Average absolute difference: 129.4185 cents
Root mean square difference: 149.7660 cents
Maximum absolute difference: 254.4451 cents
Maximum formal fifth difference: 7.7105 cents

----- Original Message -----
From: "Petr Par�zek" <p.parizek@chello.cz>
To: <tuning@yahoogroups.com>
Sent: 21 �ubat 2006 Sal� 18:45
Subject: [tuning] Re: Ozan's 159-edo-based tuning

> Hi Ozan.
>
> You wrote:
>
> > The fifth should have been 3/2. The complication arises from your
> preference
> > of 159 equal divisions of the octave, which is a very close
approximation
> to
> > my proposal.
>
> Am I right in assuming that the fifth is closer to 3/2 in your tuning than
> in 159-equal?
>
> Petr
>
>

Hi Oz,

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

> Is this lattice based on 159-eq? Or my 33 equal division of 4/3?
>
>
> > > > --- In tuning@yahoogroups.com, "monz" <monz@> wrote:
> > > >
> >
> > I've uploaded a screenshot of a Tonescape Lattice of Ozan's
> > tuning to the tuning_files group:
> >
> >
>
/tuning/files/monz/ozan_79-mos_159-edo_5-7-11-space_lattice.gif
> >
> >
> > The Lattice points are labeled with the degree numbers.

159-edo.

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

Hi Ozan.

Thanks a lot for the cycle. I must admit I haven't followed the discussion
very carefully. As far as I can see it, the places where there are two pure
fifths in a row repeat sometimes after 5 fifths and sometimes after 7
fifths. What is the rule for that? And where does the narrow fifth come
from?

Petr

Petr, the structure of the tuning comes from 33 equal divisions of the pure
fourth carried to 79 tones the 79th of which is completed to the octave and
the larger comma thus derived is then carried between steps 45-46 to yield a
voluminous well-temperament whereby you can adequately approximate 3, 5, 7,
11 and 13 limit consonant intervals.

----- Original Message -----
From: "Petr Par�zek" <p.parizek@chello.cz>
To: <tuning@yahoogroups.com>
Sent: 21 �ubat 2006 Sal� 19:13
Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning

> Hi Ozan.
>
> Thanks a lot for the cycle. I must admit I haven't followed the discussion
> very carefully. As far as I can see it, the places where there are two
pure
> fifths in a row repeat sometimes after 5 fifths and sometimes after 7
> fifths. What is the rule for that? And where does the narrow fifth come
> from?
>
> Petr
>
>
>
>
> 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
>
>
>
>
>
>
>
>
>
>

Hi Ozan.

You wrote:

> Petr, the structure of the tuning comes from 33 equal divisions of the
pure
> fourth carried to 79 tones the 79th of which is completed to the octave
and
> the larger comma thus derived is then carried between steps 45-46 to yield
a
> voluminous well-temperament whereby you can adequately approximate 3, 5,
7,
> 11 and 13 limit consonant intervals.

And if I rounded it off to 200-EDO instead of 159, would that work as well?

Petr

Probably so Petr, in fact 200-edo is one of my favorites nowadays.

Oz.

----- Original Message -----
From: "Petr Par�zek" <p.parizek@chello.cz>
To: <tuning@yahoogroups.com>
Sent: 21 �ubat 2006 Sal� 21:11
Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning

> Hi Ozan.
>
> You wrote:
>
> > Petr, the structure of the tuning comes from 33 equal divisions of the
> pure
> > fourth carried to 79 tones the 79th of which is completed to the octave
> and
> > the larger comma thus derived is then carried between steps 45-46 to
yield
> a
> > voluminous well-temperament whereby you can adequately approximate 3, 5,
> 7,
> > 11 and 13 limit consonant intervals.
>
> And if I rounded it off to 200-EDO instead of 159, would that work as
well?
>
> Petr
>
>

Hi Paul (and Oz),

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

> --- In tuning@yahoogroups.com, "monz" <monz@> wrote:
> >
> > Hi Ozan, Yahya, et al,
> >
> >
> > --- In tuning@yahoogroups.com, "monz" <monz@> wrote:
> >
> > > I've made a Tonescape file of your 79-MOS as a subset
> > > of 159-edo in (2,)5,7,11-space, with 2 as the identity
> > > interval, and using TM-basis for the 159-edo periodicity-block.
>
> Can you state this with more precision and detail, please,
> for those of us attempting to follow along?

TM-basis for 159-edo in 2,5,7,11-space:

.. 2,5,7,11-monzo ...... ratio ........ ~cents
---------------------------------------------------

.. [-12 -2 1 4 > .. 102487 / 102400 ... 1.470248198
.. [8 -8 5 -1 > .. 4302592 / 4296875 .. 2.301879062
.. [-5 3 3 -3 > .... 42875 / 42592 ... 11.46503391

> > degree ... ~cents .. ------ monzo ------- ....... ratio
> > ...................... 2 .. 5 .. 7 .. 11
> >
> > <snip>
> > .. 33 ... 498.113 .. [ 9 ..-1 ..-17 ..-1 > ..... 512 / 385
>
> I find it pretty humorous that you didn't even get 4/3
> for 33 steps, one of the few clues Ozan has explicitly
> given us . . .

Well, considering that 3 is *not* one of the prime-factors
in the Tonespace which i used, it's pretty obvious *why*
i didn't get 4/3.

But OK, yes, you're right ... since Ozan's tuning explicitly
has a "pure" 3/2 5th, and since i know that his preferred
version of the tuning uses (4/3)^(1/33) as the generator,
i guess i should have included prime-factor 3 in the Tonespace.
I'll do another one for 159-edo which includes 3, and post it.

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

Hi Ozan.

> Probably so Petr, in fact 200-edo is one of my favorites nowadays.

OK, I think I'm beginning to understand. Does this have something to do with
the discussion on 152-EDO you were leading with Paul? I think the two fifths
which that tuning has (i.e. one of 88 steps and the other of 89) could also
do an acceptable approximation (though somewhat poorer, I admit) to your
system.
Still, I'm getting such a feeling that 200-EDO could work extremely well as
the nearest fifth is amazingly close to 3/2.

Petr

Indeed, the topics revolve around a possible universal tuning that also
satisfy my requirements for Maqam Music. In this regard, voluminous equal
divisions of the octave are desirable such as 152, 159, 171, 193, 200,
etc... But as the number increases, so do the possibilities of ever
implementing such a tuning on an instrument diminish. My Qanun maker, an
aging veteran in the field, exceeded his own limits by constructing the
device I currently possess. Still, I'm always open to improvements. This
does not in anyway imply, however, that 79 tones practically out of 159-tET
are useless. On the contrary, Ruhi Ayangil, a famous Qanun virtuoso
colleague of mine certified himself the revolutionary aspects of my
endeavour and was mighty pleased when he performed on my Qanun. I had other
Qanunists look at it as well, and heard from them little criticism, if any.

As for 200-edo. I am very pleased with it since it has an excellent 1/4
Pyth-comma tempered fifth next to a just fifth. But is it good enough to be
called universal?

Cordially,
Ozan

----- Original Message -----
From: "Petr Par�zek" <p.parizek@chello.cz>
To: <tuning@yahoogroups.com>
Sent: 21 �ubat 2006 Sal� 21:46
Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning

> Hi Ozan.
>
> > Probably so Petr, in fact 200-edo is one of my favorites nowadays.
>
> OK, I think I'm beginning to understand. Does this have something to do
with
> the discussion on 152-EDO you were leading with Paul? I think the two
fifths
> which that tuning has (i.e. one of 88 steps and the other of 89) could
also
> do an acceptable approximation (though somewhat poorer, I admit) to your
> system.
> Still, I'm getting such a feeling that 200-EDO could work extremely well
as
> the nearest fifth is amazingly close to 3/2.
>
> Petr
>
>
>

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

> Can you give the step numbers for 80?

> Can you also give the step numbers for 77?

Some 159-et MOS:

Ozan[79]

222222222222222222222222222222222222222222222
2222222222222222222222222222222223

Ozan[80]

2222222222222222222222222222222222222222222222222
2222222222222222222222222222221

Guiron[77]

331313131313131331313131313131331313131313131331
31313131313133131313131313131

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

> Can you please explain the first paragraph in layman terms Gene?

> > It's a MOS, 79 steps per octave with generator 2 steps of 159.

It's a scale formed by means of a single generator within the octave,
where the number of steps is chosen so that only two step sizes
result. In this case no octave reduction is required, but it still can
be classified in this way.

http://tonalsoft.com/enc/m/mos.aspx

> > Correspondng linear temperaments do not seem distinguished. In the
> > 7-limit we have <<33 54 95 9 58 69||, with commas 10976/10935 and the
> > 5-limit comma |3 -18 11>

The mapping is such that 33 generators gives a fourth, 54 generators a
minor sixth, and 95 generators an approximate 16/7 interval, which
defines everything else in the 7-limit. It sends the small (six and a
half cent) interval, or comma, 10976/10935 to the unison. That is,
such an interval is "tempered out". Also tempered out is
2^3 5^11/3^18, of size 14.26 cents.

The "ozan" temperament, 80&159, gets more interesting in higher prime
limits. In the 11-limit, we get 4000/3993 and 3025/3024 as commas; in
the 13-limit 325/324 and 364/363; and so forth.

Hi Ozan.

> As for 200-edo. I am very pleased with it since it has an excellent 1/4
> Pyth-comma tempered fifth next to a just fifth. But is it good enough to
be
> called universal?

Well, speaking for myself at least, what more could I wish? The only case
where I might blame 200-EDO may be perhaps if I found a 3 cent detuning to
be too much (I mean when approximating 7/4). Indeed, I confess, in some
situations, I really do.

Petr

You mean this:

80 MOS 159tET
|
0: 1/1 C unison, perfect prime
1: 15.092 cents C/
2: 30.185 cents C//
3: 45.277 cents C^ Db(
4: 60.369 cents C) Dbv
5: 75.461 cents C#\ Db\\
6: 90.554 cents C# Db\
7: 105.646 cents C#/ Db
8: 120.738 cents C#// Db/
9: 135.830 cents C#^ D(
10: 150.923 cents C#) Dv
11: 166.015 cents D\\
12: 181.107 cents D\
13: 196.200 cents D
14: 211.292 cents D/
15: 226.384 cents D//
16: 241.476 cents D^ Eb(
17: 256.569 cents D) Ebv
18: 271.661 cents D#\ Eb\\
19: 286.753 cents D# Eb\
20: 301.845 cents D#/ Eb
21: 316.938 cents D#// Eb/
22: 332.030 cents D#^ E(
23: 347.122 cents D#) Ev
24: 362.215 cents E\\
25: 377.307 cents E\
26: 392.399 cents E
27: 407.491 cents E/ Fb
28: 422.584 cents E// Fb/
29: 437.676 cents E^ F(
30: 452.768 cents E) Fv
31: 467.860 cents E#\ F\\
32: 482.953 cents E# F\
33: 4/3 F perfect fourth
34: 513.137 cents F/
35: 528.230 cents F//
36: 543.322 cents F^ Gb(
37: 558.414 cents F) Gbv
38: 573.506 cents F#\ Gb\\
39: 588.599 cents F# Gb\
40: 603.691 cents F#/ Gb
41: 618.783 cents F#// Gb/
42: 633.875 cents F#^ G(
43: 648.968 cents F#) Gv
44: 664.060 cents G\\
45: 679.152 cents G\
46: 694.245 cents G
47: 701.955 cents G
48: 717.047 cents G/
49: 732.140 cents G//
50: 747.232 cents G^ Ab(
51: 762.324 cents G) Abv
52: 777.416 cents G#\ Ab\\
53: 792.509 cents G# Ab\
54: 807.601 cents G#/ Ab
55: 822.693 cents G#// Ab/
56: 837.785 cents G#^ A(
57: 852.878 cents G#) Av
58: 867.970 cents A\\
59: 883.062 cents A\
60: 898.155 cents A
61: 913.247 cents A/
62: 928.339 cents A//
63: 943.431 cents A^ Bb(
64: 958.524 cents A) Bbv
65: 973.616 cents A#\ Bb\\
66: 988.708 cents A# Bb\
67: 1003.800 cents A#/ Bb
68: 1018.893 cents A#// Bb/
69: 1033.985 cents A#^ B(
70: 1049.077 cents A#) Bv
71: 1064.170 cents B\\
72: 1079.262 cents B\
73: 1094.354 cents B
74: 1109.446 cents B/ Cb
75: 1124.539 cents B// Cb/
76: 1139.631 cents B^ C(
77: 1154.723 cents B) Cv
78: 1169.815 cents B#\ C\\
79: 1184.908 cents B# C\
80: 1200.000 cents C

If this is all there is to it, one only requires to affix an additional
mandal per octave ~8 cents just before every G. If you deem that I shall
benefit from doing so, please tell me, so that I may modify my Qanun
accordingly.

Also, SCALA cannot extract modes from such voluminous temperaments. I get an
error message saying that scale and mode sizes are unequal. Manuel, what do
you make out of this?

Until then, can you give me the cent values for Guiron[77] Gene?

Cordially,
Oz.

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
To: <tuning@yahoogroups.com>
Sent: 21 �ubat 2006 Sal� 22:07
Subject: [tuning] Re: Ozan's 159-edo-based tuning

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> > Can you give the step numbers for 80?
>
> > Can you also give the step numbers for 77?
>
> Some 159-et MOS:
>
> Ozan[79]
>
> 222222222222222222222222222222222222222222222
> 2222222222222222222222222222222223
>
> Ozan[80]
>
> 2222222222222222222222222222222222222222222222222
> 2222222222222222222222222222221
>
> Guiron[77]
>
> 331313131313131331313131313131331313131313131331
> 31313131313133131313131313131
>
>
>

Such is the problem I encountered myself with 7-limit consonances in
200-edo. If one chooses to deal with such high numbers, surely better
options exist within that nominal region. Gene suggested 313 as a universal
tuning if I'm not mistaken. The problem is, you cannot go much higher than
80 or so tones with a Qanun, or for any other practical instrument of Maqam
Music for that matter.

Cordially,
Ozan

----- Original Message -----
From: "Petr Par�zek" <p.parizek@chello.cz>
To: <tuning@yahoogroups.com>
Sent: 21 �ubat 2006 Sal� 22:34
Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning

> Hi Ozan.
>
> > As for 200-edo. I am very pleased with it since it has an excellent 1/4
> > Pyth-comma tempered fifth next to a just fifth. But is it good enough to
> be
> > called universal?
>
> Well, speaking for myself at least, what more could I wish? The only case
> where I might blame 200-EDO may be perhaps if I found a 3 cent detuning to
> be too much (I mean when approximating 7/4). Indeed, I confess, in some
> situations, I really do.
>
> Petr
>

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:

> Am I right in assuming that the fifth is closer to 3/2 in your
tuning than
> in 159-equal?

No it isn't. In 159 equal, the fifth is flat by the same amount as in
53 equal, which is 0.068 cents. In Ozan's tuning, both the fifth and
the octave are flat by the same amount, 0.164 cents. Neither figure is
at all large, of course.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Petr, the default fifth is exactly 3/2 in my tuning:

OK, I misstated; but then your tuning is not based on an equal
division of the fourth into 33 parts.

Gene, you got it all wrong. The octave and the fifth are just in my tuning.

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
To: <tuning@yahoogroups.com>
Sent: 21 �ubat 2006 Sal� 23:07
Subject: [tuning] Re: Ozan's 159-edo-based tuning

--- In tuning@yahoogroups.com, Petr Par�zek <p.parizek@...> wrote:

> Am I right in assuming that the fifth is closer to 3/2 in your
tuning than
> in 159-equal?

No it isn't. In 159 equal, the fifth is flat by the same amount as in
53 equal, which is 0.068 cents. In Ozan's tuning, both the fifth and
the octave are flat by the same amount, 0.164 cents. Neither figure is
at all large, of course.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Probably so Petr, in fact 200-edo is one of my favorites nowadays.

Based on the numbers you gave, your scale is badly approximated by 200
edo, whereas 159 edo is pretty much perfect, and is audibly
indistinguishable. The numbers below should make it clear why I think
there is no point in fussing about the difference between your scale
and your scale tuned to 159 edo; it's really a 159-et, 79-note MOS.

Yarman scale in cents

yar := [15.092000, 30.185000, 45.277000, 60.369000, 75.461000,
90.554000, 105.646000, 120.738000, 135.830000, 150.923000, 166.015000,
181.107000, 196.200000, 211.292000, 226.384000, 241.476000,
256.569000, 271.661000, 286.753000, 301.845000, 316.938000,
332.030000, 347.122000, 362.215000, 377.307000, 392.399000,
407.491000, 422.584000, 437.676000, 452.768000, 467.860000,
482.953000, 498.045000, 513.137000, 528.230000, 543.322000,
558.414000, 573.506000, 588.599000, 603.691000, 618.783000,
633.875000, 648.968000, 664.060000, 679.152000, 694.245000,
709.337000, 724.429000, 739.521000, 754.614000, 769.706000,
784.798000, 799.890000, 814.983000, 830.075000, 845.167000,
860.260000, 875.352000, 890.444000, 905.536000, 920.629000,
935.721000, 950.813000, 965.905000, 980.998000, 996.090000,
1011.182000, 1026.275000, 1041.367000, 1056.459000, 1071.551000,
1086.644000, 1101.736000, 1116.828000, 1131.920000, 1147.013000,
1162.105000, 1177.197000, 1200.000000]

Yarman scale in 159-edo steps

yar159 := [1.99969000, 3.99951250, 5.99920250, 7.99889250, 9.99858250,
11.9984050, 13.9980950, 15.9977850, 17.9974750, 19.9972975,
21.9969875, 23.9966775, 25.9965000, 27.9961900, 29.9958800,
31.9955700, 33.9953925, 35.9950825, 37.9947725, 39.9944625,
41.9942850, 43.9939750, 45.9936650, 47.9934875, 49.9931775,
51.9928675, 53.9925575, 55.9923800, 57.9920700, 59.9917600,
61.9914500, 63.9912725, 65.9909625, 67.9906525, 69.9904750,
71.9901650, 73.9898550, 75.9895450, 77.9893675, 79.9890575,
81.9887475, 83.9884375, 85.9882600, 87.9879500, 89.9876400,
91.9874625, 93.9871525, 95.9868425, 97.9865325, 99.9863550,
101.986045, 103.985735, 105.985425, 107.985248, 109.984938,
111.984628, 113.984450, 115.984140, 117.983830, 119.983520,
121.983342, 123.983032, 125.982722, 127.982412, 129.982235,
131.981925, 133.981615, 135.981438, 137.981128, 139.980818,
141.980508, 143.980330, 145.980020, 147.979710, 149.979400,
151.979222, 153.978912, 155.978602, 159.000000];

The Yarman scale in 200 edo

yar200 := [2.51533333, 5.03083333, 7.54616667, 10.0615000, 12.5768333,
15.0923333, 17.6076667, 20.1230000, 22.6383333, 25.1538333,
27.6691667, 30.1845000, 32.7000000, 35.2153333, 37.7306667,
40.2460000, 42.7615000, 45.2768333, 47.7921667, 50.3075000,
52.8230000, 55.3383333, 57.8536667, 60.3691667, 62.8845000,
65.3998333, 67.9151667, 70.4306667, 72.9460000, 75.4613333,
77.9766667, 80.4921667, 83.0075000, 85.5228334, 88.0383334,
90.5536667, 93.0690000, 95.5843334, 98.0998334, 100.615167,
103.130500, 105.645833, 108.161333, 110.676667, 113.192000,
115.707500, 118.222833, 120.738167, 123.253500, 125.769000,
128.284333, 130.799667, 133.315000, 135.830500, 138.345833,
140.861167, 143.376667, 145.892000, 148.407333, 150.922667,
153.438167, 155.953500, 158.468833, 160.984167, 163.499667,
166.015000, 168.530333, 171.045833, 173.561167, 176.076500,
178.591833, 181.107333, 183.622667, 186.138000, 188.653333,
191.168833, 193.684167, 196.199500, 200.000000];

It is. You carry the comma to the 79th tone, convert it to 1200 cents,
rotate the scale so that the larger comma comes between step numbers 45-46.
This procedure gives a pure fifth on the 46th step.

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
To: <tuning@yahoogroups.com>
Sent: 21 �ubat 2006 Sal� 23:08
Subject: [tuning] Re: Ozan's 159-edo-based tuning

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > Petr, the default fifth is exactly 3/2 in my tuning:
>
> OK, I misstated; but then your tuning is not based on an equal
> division of the fourth into 33 parts.
>
>

Hi Ozan.

> It is. You carry the comma to the 79th tone, convert it to 1200 cents,
> rotate the scale so that the larger comma comes between step numbers
45-46.
> This procedure gives a pure fifth on the 46th step.

OK, my final question on this, I hope. Where does the number 33 come from?

Petr

Hi Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
>
> > Can you please explain the first paragraph in layman terms Gene?
>
> > > It's a MOS, 79 steps per octave with generator 2 steps of 159.
>
> It's a scale formed by means of a single generator within
> the octave, where the number of steps is chosen so that only
> two step sizes result. In this case no octave reduction is
> required, but it still can be classified in this way.
>
> http://tonalsoft.com/enc/m/mos.aspx
>
> > > Correspondng linear temperaments do not seem distinguished.
> > > In the 7-limit we have <<33 54 95 9 58 69||, with commas
> > > 10976/10935 and the 5-limit comma |3 -18 11>
>
> The mapping is such that 33 generators gives a fourth,
> 54 generators a minor sixth, and 95 generators an
> approximate 16/7 interval, which defines everything else
> in the 7-limit. It sends the small (six and a half cent)
> interval, or comma, 10976/10935 to the unison. That is,
> such an interval is "tempered out". Also tempered out is
> 2^3 5^11/3^18, of size 14.26 cents.
>
> The "ozan" temperament, 80&159, gets more interesting in
> higher prime limits. In the 11-limit, we get 4000/3993 and
> 3025/3024 as commas; in the 13-limit 325/324 and 364/363;
> and so forth.

Thanks from me! This is exactly what i was looking for,
for constructing Tonescape Lattices of various versions
of Ozan's Qanun tuning.

Now if only i had the time to spend on it ...

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

I don't dispute that my scale is, just as you say, 79 MOS 159-tET Gene,
since the largest error is 0.093 cents compared to my method of achieving
it. However, I prefer the latter for clarity.

In comparison, 200-edo is off by as much as 3 cents, which is indeed
problematic:

Step size is 6.0000 cents
1: 15.092: 3: 18.0000 cents, diff. 0.484621 steps, 2.9077 cents
2: 30.185: 5: 30.0000 cents, diff. -0.030758 steps, -0.1846 cents
3: 45.277: 8: 48.0000 cents, diff. 0.453863 steps, 2.7232 cents
4: 60.369: 10: 60.0000 cents, diff. -0.061515 steps, -0.3691 cents
5: 75.461: 13: 78.0000 cents, diff. 0.423106 steps, 2.5386 cents
6: 90.554: 15: 90.0000 cents, diff. -0.092273 steps, -0.5536 cents
7: 105.646: 18: 108.0000 cents, diff. 0.392348 steps, 2.3541 cents
8: 120.738: 20: 120.0000 cents, diff. -0.123031 steps, -0.7382 cents
9: 135.830: 23: 138.0000 cents, diff. 0.361590 steps, 2.1695 cents
10: 150.923: 25: 150.0000 cents, diff. -0.153788 steps, -0.9227 cents
11: 166.015: 28: 168.0000 cents, diff. 0.330833 steps, 1.9850 cents
12: 181.107: 30: 180.0000 cents, diff. -0.184546 steps, -1.1073 cents
13: 196.200: 33: 198.0000 cents, diff. 0.300075 steps, 1.8005 cents
14: 211.292: 35: 210.0000 cents, diff. -0.215303 steps, -1.2918 cents
15: 226.384: 38: 228.0000 cents, diff. 0.269318 steps, 1.6159 cents
16: 241.476: 40: 240.0000 cents, diff. -0.246061 steps, -1.4764 cents
17: 256.569: 43: 258.0000 cents, diff. 0.238560 steps, 1.4314 cents
18: 271.661: 45: 270.0000 cents, diff. -0.276818 steps, -1.6609 cents
19: 286.753: 48: 288.0000 cents, diff. 0.207801 steps, 1.2468 cents
20: 301.845: 50: 300.0000 cents, diff. -0.307576 steps, -1.8455 cents
21: 316.938: 53: 318.0000 cents, diff. 0.177045 steps, 1.0623 cents
22: 332.030: 55: 330.0000 cents, diff. -0.338333 steps, -2.0300 cents
23: 347.122: 58: 348.0000 cents, diff. 0.146286 steps, 0.8777 cents
24: 362.215: 60: 360.0000 cents, diff. -0.369091 steps, -2.2146 cents
25: 377.307: 63: 378.0000 cents, diff. 0.115530 steps, 0.6932 cents
26: 392.399: 65: 390.0000 cents, diff. -0.399848 steps, -2.3991 cents
27: 407.491: 68: 408.0000 cents, diff. 0.084771 steps, 0.5086 cents
28: 422.584: 70: 420.0000 cents, diff. -0.430606 steps, -2.5836 cents
29: 437.676: 73: 438.0000 cents, diff. 0.054015 steps, 0.3241 cents
30: 452.768: 75: 450.0000 cents, diff. -0.461363 steps, -2.7682 cents
31: 467.860: 78: 468.0000 cents, diff. 0.023256 steps, 0.1395 cents
32: 482.953: 80: 480.0000 cents, diff. -0.492121 steps, -2.9527 cents
33: 498.045: 83: 498.0000 cents, diff. -0.007500 steps, -0.0450 cents
34: 513.137: 86: 516.0000 cents, diff. 0.477120 steps, 2.8627 cents
35: 528.230: 88: 528.0000 cents, diff. -0.038258 steps, -0.2295 cents
36: 543.322: 91: 546.0000 cents, diff. 0.446363 steps, 2.6782 cents
37: 558.414: 93: 558.0000 cents, diff. -0.069015 steps, -0.4141 cents
38: 573.506: 96: 576.0000 cents, diff. 0.415605 steps, 2.4936 cents
39: 588.599: 98: 588.0000 cents, diff. -0.099773 steps, -0.5986 cents
40: 603.691: 101: 606.0000 cents, diff. 0.384848 steps, 2.3091 cents
41: 618.783: 103: 618.0000 cents, diff. -0.130530 steps, -0.7832 cents
42: 633.875: 106: 636.0000 cents, diff. 0.354090 steps, 2.1245 cents
43: 648.968: 108: 648.0000 cents, diff. -0.161288 steps, -0.9677 cents
44: 664.060: 111: 666.0000 cents, diff. 0.323333 steps, 1.9400 cents
45: 679.152: 113: 678.0000 cents, diff. -0.192046 steps, -1.1523 cents
46: 701.955: 117: 702.0000 cents, diff. 0.007500 steps, 0.0450 cents
47: 717.047: 120: 720.0000 cents, diff. 0.492120 steps, 2.9527 cents
48: 732.140: 122: 732.0000 cents, diff. -0.023258 steps, -0.1396 cents
49: 747.232: 125: 750.0000 cents, diff. 0.461363 steps, 2.7682 cents
50: 762.324: 127: 762.0000 cents, diff. -0.054016 steps, -0.3241 cents
51: 777.416: 130: 780.0000 cents, diff. 0.430605 steps, 2.5836 cents
52: 792.509: 132: 792.0000 cents, diff. -0.084773 steps, -0.5086 cents
53: 807.601: 135: 810.0000 cents, diff. 0.399848 steps, 2.3991 cents
54: 822.693: 137: 822.0000 cents, diff. -0.115531 steps, -0.6932 cents
55: 837.785: 140: 840.0000 cents, diff. 0.369090 steps, 2.2145 cents
56: 852.878: 142: 852.0000 cents, diff. -0.146288 steps, -0.8777 cents
57: 867.970: 145: 870.0000 cents, diff. 0.338333 steps, 2.0300 cents
58: 883.062: 147: 882.0000 cents, diff. -0.177046 steps, -1.0623 cents
59: 898.155: 150: 900.0000 cents, diff. 0.307575 steps, 1.8454 cents
60: 913.247: 152: 912.0000 cents, diff. -0.207803 steps, -1.2468 cents
61: 928.339: 155: 930.0000 cents, diff. 0.276816 steps, 1.6609 cents
62: 943.431: 157: 942.0000 cents, diff. -0.238561 steps, -1.4314 cents
63: 958.524: 160: 960.0000 cents, diff. 0.246060 steps, 1.4764 cents
64: 973.616: 162: 972.0000 cents, diff. -0.269318 steps, -1.6159 cents
65: 988.708: 165: 990.0000 cents, diff. 0.215301 steps, 1.2918 cents
66: 1003.800: 167: 1002.0000 cents, diff. -0.300076 steps, -1.8005
cents
67: 1018.893: 170: 1020.0000 cents, diff. 0.184545 steps, 1.1073
cents
68: 1033.985: 172: 1032.0000 cents, diff. -0.330833 steps, -1.9850
cents
69: 1049.077: 175: 1050.0000 cents, diff. 0.153786 steps, 0.9227
cents
70: 1064.170: 177: 1062.0000 cents, diff. -0.361591 steps, -2.1696
cents
71: 1079.262: 180: 1080.0000 cents, diff. 0.123030 steps, 0.7382
cents
72: 1094.354: 182: 1092.0000 cents, diff. -0.392348 steps, -2.3541
cents
73: 1109.446: 185: 1110.0000 cents, diff. 0.092271 steps, 0.5536
cents
74: 1124.539: 187: 1122.0000 cents, diff. -0.423106 steps, -2.5386
cents
75: 1139.631: 190: 1140.0000 cents, diff. 0.061515 steps, 0.3691
cents
76: 1154.723: 192: 1152.0000 cents, diff. -0.453865 steps, -2.7232
cents
77: 1169.815: 195: 1170.0000 cents, diff. 0.030756 steps, 0.1845
cents
78: 1184.908: 197: 1182.0000 cents, diff. -0.484621 steps, -2.9077
cents
79: 1200.000: 200: 1200.0000 cents, diff. 0.000000 steps, 0.0000
cents
Total absolute difference : 19.59939 steps, 117.5964 cents
Average absolute difference: 0.248093 steps, 1.4886 cents
Root mean square difference: 0.289285 steps, 1.7357 cents
Highest absolute difference: 0.492121 steps, 2.9527 cents

Were it not for the fact that the narrower fifth is within the desirable
range of 3/11 comma meantone, I would dump it all together.

Cordially,
Oz.

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
To: <tuning@yahoogroups.com>
Sent: 21 �ubat 2006 Sal� 23:38
Subject: [tuning] Re: Ozan's 159-edo-based tuning

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > Probably so Petr, in fact 200-edo is one of my favorites nowadays.
>
> Based on the numbers you gave, your scale is badly approximated by 200
> edo, whereas 159 edo is pretty much perfect, and is audibly
> indistinguishable. The numbers below should make it clear why I think
> there is no point in fussing about the difference between your scale
> and your scale tuned to 159 edo; it's really a 159-et, 79-note MOS.
>
> Yarman scale in cents
>
> yar := [15.092000, 30.185000, 45.277000, 60.369000, 75.461000,
> 90.554000, 105.646000, 120.738000, 135.830000, 150.923000, 166.015000,
> 181.107000, 196.200000, 211.292000, 226.384000, 241.476000,
> 256.569000, 271.661000, 286.753000, 301.845000, 316.938000,
> 332.030000, 347.122000, 362.215000, 377.307000, 392.399000,
> 407.491000, 422.584000, 437.676000, 452.768000, 467.860000,
> 482.953000, 498.045000, 513.137000, 528.230000, 543.322000,
> 558.414000, 573.506000, 588.599000, 603.691000, 618.783000,
> 633.875000, 648.968000, 664.060000, 679.152000, 694.245000,
> 709.337000, 724.429000, 739.521000, 754.614000, 769.706000,
> 784.798000, 799.890000, 814.983000, 830.075000, 845.167000,
> 860.260000, 875.352000, 890.444000, 905.536000, 920.629000,
> 935.721000, 950.813000, 965.905000, 980.998000, 996.090000,
> 1011.182000, 1026.275000, 1041.367000, 1056.459000, 1071.551000,
> 1086.644000, 1101.736000, 1116.828000, 1131.920000, 1147.013000,
> 1162.105000, 1177.197000, 1200.000000]
>
> Yarman scale in 159-edo steps
>
> yar159 := [1.99969000, 3.99951250, 5.99920250, 7.99889250, 9.99858250,
> 11.9984050, 13.9980950, 15.9977850, 17.9974750, 19.9972975,
> 21.9969875, 23.9966775, 25.9965000, 27.9961900, 29.9958800,
> 31.9955700, 33.9953925, 35.9950825, 37.9947725, 39.9944625,
> 41.9942850, 43.9939750, 45.9936650, 47.9934875, 49.9931775,
> 51.9928675, 53.9925575, 55.9923800, 57.9920700, 59.9917600,
> 61.9914500, 63.9912725, 65.9909625, 67.9906525, 69.9904750,
> 71.9901650, 73.9898550, 75.9895450, 77.9893675, 79.9890575,
> 81.9887475, 83.9884375, 85.9882600, 87.9879500, 89.9876400,
> 91.9874625, 93.9871525, 95.9868425, 97.9865325, 99.9863550,
> 101.986045, 103.985735, 105.985425, 107.985248, 109.984938,
> 111.984628, 113.984450, 115.984140, 117.983830, 119.983520,
> 121.983342, 123.983032, 125.982722, 127.982412, 129.982235,
> 131.981925, 133.981615, 135.981438, 137.981128, 139.980818,
> 141.980508, 143.980330, 145.980020, 147.979710, 149.979400,
> 151.979222, 153.978912, 155.978602, 159.000000];
>
> The Yarman scale in 200 edo
>
> yar200 := [2.51533333, 5.03083333, 7.54616667, 10.0615000, 12.5768333,
> 15.0923333, 17.6076667, 20.1230000, 22.6383333, 25.1538333,
> 27.6691667, 30.1845000, 32.7000000, 35.2153333, 37.7306667,
> 40.2460000, 42.7615000, 45.2768333, 47.7921667, 50.3075000,
> 52.8230000, 55.3383333, 57.8536667, 60.3691667, 62.8845000,
> 65.3998333, 67.9151667, 70.4306667, 72.9460000, 75.4613333,
> 77.9766667, 80.4921667, 83.0075000, 85.5228334, 88.0383334,
> 90.5536667, 93.0690000, 95.5843334, 98.0998334, 100.615167,
> 103.130500, 105.645833, 108.161333, 110.676667, 113.192000,
> 115.707500, 118.222833, 120.738167, 123.253500, 125.769000,
> 128.284333, 130.799667, 133.315000, 135.830500, 138.345833,
> 140.861167, 143.376667, 145.892000, 148.407333, 150.922667,
> 153.438167, 155.953500, 158.468833, 160.984167, 163.499667,
> 166.015000, 168.530333, 171.045833, 173.561167, 176.076500,
> 178.591833, 181.107333, 183.622667, 186.138000, 188.653333,
> 191.168833, 193.684167, 196.199500, 200.000000];
>
>

Let me answer to that with a question of my own Petr: Where does the number
12 come from?

----- Original Message -----
From: "Petr Par�zek" <p.parizek@chello.cz>
To: <tuning@yahoogroups.com>
Sent: 21 �ubat 2006 Sal� 23:47
Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning

> Hi Ozan.
>
> > It is. You carry the comma to the 79th tone, convert it to 1200 cents,
> > rotate the scale so that the larger comma comes between step numbers
> 45-46.
> > This procedure gives a pure fifth on the 46th step.
>
> OK, my final question on this, I hope. Where does the number 33 come from?
>
> Petr
>
>

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
>
> Hi Ozan.
>
> > It is. You carry the comma to the 79th tone, convert
> > it to 1200 cents, rotate the scale so that the larger
> > comma comes between step numbers 45-46.
> > This procedure gives a pure fifth on the 46th step.
>
> OK, my final question on this, I hope. Where does the
> number 33 come from?

In Ozan's tuning, the 4/3 ratio "perfect 4th" is divided
into 33 equal steps. Thus (4/3)^(1/33) is the generator
of the scale. This is ~15.0922727 cents.

If you take 79 steps of that size, the 79th degree is
~1192.289543 cents. Instead of using this last pitch,
Ozan substitutes the octave 1200 cents. This last step
thus becomes ~22 cents, a bit larger than all the other
steps.

Then he rotates (transposes) the scale so that this
larger step comes between degrees 45 and 46. By doing
this, instead of having a pseudo-meantone "5th" at the
46th degree, he now has a 3/2 "perfect-5th".

Sorry if all this is obvious and i'm just repeating Ozan,
but it was hard for me to understand what he meant by
the way he described it, so i'm just offering my version
in case it helps anyone else.

It is possible to find a 79-tone subset of 159-edo which
is not exactly the same as this, but is very close.

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

Exactly! I apologize for wasting everyone's precious time with my horrible
English.

Oz.

----- Original Message -----
From: "monz" <monz@tonalsoft.com>
To: <tuning@yahoogroups.com>
Sent: 22 �ubat 2006 �ar�amba 0:04
Subject: [tuning] Re: Ozan's 159-edo-based tuning

--- In tuning@yahoogroups.com, Petr Par�zek <p.parizek@...> wrote:
>
> Hi Ozan.
>
> > It is. You carry the comma to the 79th tone, convert
> > it to 1200 cents, rotate the scale so that the larger
> > comma comes between step numbers 45-46.
> > This procedure gives a pure fifth on the 46th step.
>
> OK, my final question on this, I hope. Where does the
> number 33 come from?

In Ozan's tuning, the 4/3 ratio "perfect 4th" is divided
into 33 equal steps. Thus (4/3)^(1/33) is the generator
of the scale. This is ~15.0922727 cents.

If you take 79 steps of that size, the 79th degree is
~1192.289543 cents. Instead of using this last pitch,
Ozan substitutes the octave 1200 cents. This last step
thus becomes ~22 cents, a bit larger than all the other
steps.

Then he rotates (transposes) the scale so that this
larger step comes between degrees 45 and 46. By doing
this, instead of having a pseudo-meantone "5th" at the
46th degree, he now has a 3/2 "perfect-5th".

Sorry if all this is obvious and i'm just repeating Ozan,
but it was hard for me to understand what he meant by
the way he described it, so i'm just offering my version
in case it helps anyone else.

It is possible to find a 79-tone subset of 159-edo which
is not exactly the same as this, but is very close.

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

Hi Ozan.

> Let me answer to that with a question of my own Petr: Where does the
number
> 12 come from?

I'm not sure I understand. The idea of 12 tones in the octave (no matter if
spaced equally or unequally) is centuries old, maybe even millenia. I
thought the idea of 33 steps in a fourth was something like a result of your
own experience. That's why I was asking how you had found it.

Petr

Aha! So you don't question the validity of 12 tones simply because it has
historical precedence and my tuning does not? Surely you see the dichotomy.

33 equal divisions of the fourth is just a number that is convenient for my
purposes. Other than that, there is nothing terribly magical about it.

Oz.

----- Original Message -----
From: "Petr Par�zek" <p.parizek@chello.cz>
To: <tuning@yahoogroups.com>
Sent: 22 �ubat 2006 �ar�amba 0:09
Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning

> Hi Ozan.
>
> > Let me answer to that with a question of my own Petr: Where does the
> number
> > 12 come from?
>
> I'm not sure I understand. The idea of 12 tones in the octave (no matter
if
> spaced equally or unequally) is centuries old, maybe even millenia. I
> thought the idea of 33 steps in a fourth was something like a result of
your
> own experience. That's why I was asking how you had found it.
>
> Petr
>
>

Ozan wrote:

>Also, SCALA cannot extract modes from such voluminous temperaments. I get an
>error message saying that scale and mode sizes are unequal. Manuel, what do
>you make out of this?

You have to make sure that the steps add up to the number of notes in the
scale. Otherwise the program concludes that you made a typo. So you cannot
delete the last note this way. If you want to, you must do it separately.

Manuel

This probably means that Gene gave me numbers that don't add up.

----- Original Message -----
From: "Manuel Op de Coul" <coul@hccnet.nl>
To: <tuning@yahoogroups.com>
Sent: 22 �ubat 2006 �ar�amba 0:20
Subject: [tuning] Re: Re: Ozan's 159-edo-based tuning

> Ozan wrote:
>
> >Also, SCALA cannot extract modes from such voluminous temperaments. I
get an
> >error message saying that scale and mode sizes are unequal. Manuel, what
do
> >you make out of this?
>
> You have to make sure that the steps add up to the number of notes in the
> scale. Otherwise the program concludes that you made a typo. So you cannot
> delete the last note this way. If you want to, you must do it separately.
>
> Manuel
>
>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Indeed, the topics revolve around a possible universal tuning that also
> satisfy my requirements for Maqam Music. In this regard, voluminous
equal
> divisions of the octave are desirable such as 152, 159, 171, 193, 200,
> etc... But as the number increases, so do the possibilities of ever
> implementing such a tuning on an instrument diminish.

One tuning which has been much on my mind recently (because I'm
working with it) is 224-et. This has an extremely good meantone fifth,
the meantone fifth of 112-edo. It also has an excellent schismatic
fifth. It is an excellent division up to the 13 limit, and supports
the octoid temperament. This is relevant since Octoid[72], the octoid
temperament on 72 notes, seems to have a lot of the properties you
want, as well as other interesting properties involving harmony.
Octoid[72] can be described as six different well-temperaments stacked
next to each other, giving the kind of alternation of fifths you seem
to be looking for. It, of course, involves fewer notes than your
79-note scale, and gives much greater scope to harmony and nearly-just
intervals.

Anyway here is one mode of it:

! octoid72.scl
Octoid[72] in 224-et tuning
72
!
16.071429
32.142857
48.214286
64.285714
85.714286
101.785714
117.857143
133.928571
150.000000
166.071429
182.142857
198.214286
214.285714
235.714286
251.785714
267.857143
283.928571
300.000000
316.071429
332.142857
348.214286
364.285714
385.714286
401.785714
417.857143
433.928571
450.000000
466.071429
482.142857
498.214286
514.285714
535.714286
551.785714
567.857143
583.928571
600.000000
616.071429
632.142857
648.214286
664.285714
685.714286
701.785714
717.857143
733.928571
750.000000
766.071429
782.142857
798.214286
814.285714
835.714286
851.785714
867.857143
883.928571
900.000000
916.071429
932.142857
948.214286
964.285714
985.714286
1001.785714
1017.857143
1033.928571
1050.000000
1066.071429
1082.142857
1098.214286
1114.285714
1135.714286
1151.785714
1167.857143
1183.928571
1200.000000

Hi Ozan.

> Aha! So you don't question the validity of 12 tones simply because it has
> historical precedence and my tuning does not? Surely you see the
dichotomy.

I'm realizing I have to be pretty careful about how to say something to make
others understand my words in the way they were really meant. At this time,
either my statement was totally unclear or my questions made you
misunderstandd my view.
OK, I'll try to make things clearer.

1. The number 12 is easily explainable for me not for its historical
precedence but for the acoustical properties of the intervals, no matter if
pure or approximated. Since I've never examined 33 equal divisions of the
fourth, I was just unaware.
2. We all know that, for instance, 13-EDO or 11-EDO doesn't have the
properties wich are being so valued in 12-EDO. So I was interested if, for
example, dividing the fourth into 32 or 34 equal steps instead of 33 would
harm the system, and if so, how much. Or, in other words, if you found the
number 33 using some formulas while trying to meet some of your requirements
(like I could find 19-EDO, 22, 31, 50, or 53 while trying to find a good
tuning for common tonal music), or if it was just one of your free
decisions.
3. Neither I speak some great English, and ... Well, who cares? Is it worth
it?

Petr

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> monz,
>
> ----- Original Message -----
> From: "monz" <monz@...>
> To: <tuning@yahoogroups.com>
> Sent: 18 Þubat 2006 Cumartesi 23:43
> Subject: [tuning] Re: Ozan's 159-edo-based tuning
>
>
> > Hi Ozan, Yahya, et al,
> >
> >
> > --- In tuning@yahoogroups.com, "monz" <monz@> wrote:
> >
> > > I've made a Tonescape file of your 79-MOS as a subset
> > > of 159-edo in (2,)5,7,11-space, with 2 as the identity
> > > interval, and using TM-basis for the 159-edo periodicity-block.
> > > I'll post the 79-MOS-degree_to_ratio correspondence as soon
> > > as i get a chance.
> >
> >
> > And here it is ... Ozan, see how well it agrees/disagrees
> > with your perceptions.
> >
>
>
> Let me see.
>
>
> >
> >
> > Ozan Yarman's Qanun tuning
> > as 79-MOS out of 159-edo, in 5-7-11-space
> > identity interval = 2/1 ratio
> >
> >
> > degree ... ~cents .. ------ monzo ------- ....... ratio
> > ...................... 2 .. 5 .. 7 .. 11
> >
> > ... 0 ..... 0.000 .. [ 0 .. 0 .. 0 .. 0 > ....... 1 / 1
> > ... 1 .... 15.094 .. [ 4 ..-2 ..-1 .. 1 > ..... 176 / 175
> > ... 2 .... 30.189 .. [ 3 ..-1 .. 1 ..-1 > ...... 56 / 55
> > ... 3 .... 45.283 .. [ 7 ..-3 .. 0 .. 0 > ..... 128 / 125
> > ... 4 .... 60.377 .. [ 6 ..-2 .. 2 ..-2 > .... 3136 / 3025
> > ... 5 .... 75.472 .. [10 ..-4 .. 1 ..-1 > .... 7168 / 6875
> > ... 6 .... 90.566 .. [ 1 .. 5 ..-2 ..-2 > .... 6250 / 5929
> > ... 7 ... 105.660 .. [-7 .. 1 ..-2 .. 3 > .... 6655 / 6272
> > ... 8 ... 120.755 .. [-8 .. 2 .. 0 .. 1 > ..... 275 / 256
> > ... 9 ... 135.849 .. [-4 .. 0 ..-1 .. 2 > ..... 121 / 112
> > .. 10 ... 150.943 .. [-5 .. 1 .. 1 .. 0 > ...... 35 / 32
> > .. 11 ... 166.038 .. [-1 ..-1 .. 0 .. 1 > ...... 11 / 10
> > .. 12 ... 181.132 .. [-2 .. 0 .. 2 ..-1 > ...... 49 / 44
> > .. 13 ... 196.226 .. [ 2 ..-2 .. 1 .. 0 > ...... 28 / 25
> > .. 14 ... 211.321 .. [ 1 ..-1 .. 3 ..-2 > ..... 686 / 605
> > .. 15 ... 226.415 .. [ 5 ..-3 .. 2 ..-1 > .... 1568 / 1375
> > .. 16 ... 241.509 .. [ 1 .. 3 ..-4 .. 1 > .... 2750 / 2401
> > .. 17 ... 256.604 .. [ 0 .. 4 ..-2 ..-1 > ..... 625 / 539
> > .. 18 ... 271.698 .. [ 4 .. 2 ..-3 .. 0 > ..... 400 / 343
> > .. 19 ... 286.792 .. [ 3 .. 3 ..-1 ..-2 > .... 1000 / 847
> > .. 20 ... 301.887 .. [ 7 .. 1 ..-2 ..-1 > ..... 640 / 539
> > .. 21 ... 316.981 .. [-6 .. 0 .. 1 .. 1 > ...... 77 / 64
> > .. 22 ... 332.075 .. [-2 ..-2 .. 0 .. 2 > ..... 121 / 100
> > .. 23 ... 347.170 .. [-3 ..-1 .. 2 .. 0 > ...... 49 / 40
> > .. 24 ... 362.264 .. [ 1 ..-3 .. 1 .. 1 > ..... 154 / 125
> > .. 25 ... 377.358 .. [ 0 ..-2 .. 3 ..-1 > ..... 343 / 275
> > .. 26 ... 392.453 .. [ 4 ..-4 .. 2 .. 0 > ..... 784 / 625
> > .. 27 ... 407.547 .. [-5 .. 5 ..-1 ..-1 > .... 3125 / 2464
> > .. 28 ... 422.642 .. [-1 .. 3 ..-2 .. 0 > ..... 125 / 98
> > .. 29 ... 437.736 .. [ 3 .. 1 ..-3 .. 1 > ..... 440 / 343
> > .. 30 ... 452.830 .. [ 2 .. 2 ..-1 ..-1 > ..... 100 / 77
> > .. 31 ... 467.925 .. [ 6 .. 0 ..-2 .. 0 > ...... 64 / 49
> > .. 32 ... 483.019 .. [ 5 .. 1 .. 0 ..-2 > ..... 160 / 121
> > .. 33 ... 498.113 .. [ 9 ..-1 ..-1 ..-1 > ..... 512 / 385
>
> This is the reason why I prefer a pure fourth to the 53-edo fourth, although
> they differ by 0.068 cents.

I don't understand. Monz gave you a JI scale, not EDO intervals. It's true that Monz is trying to give you a 'rationalization' that derives circuitously from 159-tET, but it's simply his poor methodology that caused him to arrive at 512/385 rather than 4/3 here, not the fact that he started with an ET (not an EDO, BTW)

> > .. 34 ... 513.208 .. [-4 ..-2 .. 2 .. 1 > ..... 539 / 400
> > .. 35 ... 528.302 .. [ 0 ..-4 .. 1 .. 2 > ..... 847 / 625
> > .. 36 ... 543.396 .. [-1 ..-3 .. 3 .. 0 > ..... 343 / 250
> > .. 37 ... 558.491 .. [-5 .. 3 ..-3 .. 2 > ... 15125 / 10976
> > .. 38 ... 573.585 .. [-6 .. 4 ..-1 .. 0 > ..... 625 / 448
> > .. 39 ... 588.679 .. [-2 .. 2 ..-2 .. 1 > ..... 275 / 196
> > .. 40 ... 603.774 .. [-3 .. 3 .. 0 ..-1 > ..... 125 / 88
> > .. 41 ... 618.868 .. [ 1 .. 1 ..-1 .. 0 > ...... 10 / 7
> > .. 42 ... 633.962 .. [ 0 .. 2 .. 1 ..-2 > ..... 175 / 121
> > .. 43 ... 649.057 .. [ 4 .. 0 .. 0 ..-1 > ...... 16 / 11
> > .. 44 ... 664.151 .. [ 8 ..-2 ..-1 .. 0 > ..... 256 / 175
> > .. 45 ... 679.245 .. [ 7 ..-1 .. 1 ..-2 > ..... 896 / 605
> > .. 46 ... 701.887 .. [ 4 .. 3 .. 0 ..-3 > .... 2000 / 1331
>
> The fifth should have been 3/2. The complication arises from your preference
> of 159 equal divisions of the octave,

Not so. See my comments above, which apply here as well.

> which is a very close approximation to
> my proposal.
>
> > .. 47 ... 716.981 .. [-4 ..-1 .. 0 .. 2 > ..... 121 / 80
> > .. 48 ... 732.075 .. [-5 .. 0 .. 2 .. 0 > ...... 49 / 32
> > .. 49 ... 747.170 .. [-1 ..-2 .. 1 .. 1 > ...... 77 / 50
> > .. 50 ... 762.264 .. [ 3 ..-4 .. 0 .. 2 > ..... 968 / 625
> > .. 51 ... 777.358 .. [ 2 ..-3 .. 2 .. 0 > ..... 196 / 125
> > .. 52 ... 792.453 .. [ 6 ..-5 .. 1 .. 1 > .... 4928 / 3125
> > .. 53 ... 807.547 .. [-3 .. 4 ..-2 .. 0 > ..... 625 / 392
> > .. 54 ... 822.642 .. [ 1 .. 2 ..-3 .. 1 > ..... 550 / 343
> > .. 55 ... 837.736 .. [ 0 .. 3 ..-1 ..-1 > ..... 125 / 77
> > .. 56 ... 852.830 .. [ 4 .. 1 ..-2 .. 0 > ...... 80 / 49
> > .. 57 ... 867.925 .. [ 3 .. 2 .. 0 ..-2 > ..... 200 / 121
> > .. 58 ... 883.019 .. [ 7 .. 0 ..-1 ..-1 > ..... 128 / 77
> > .. 59 ... 898.113 .. [ 6 .. 1 .. 1 ..-3 > .... 2240 / 1331
> > .. 60 ... 913.208 .. [-2 ..-3 .. 1 .. 2 > ..... 847 / 500
> > .. 61 ... 928.302 .. [-3 ..-2 .. 3 .. 0 > ..... 343 / 200
> > .. 62 ... 943.396 .. [ 1 ..-4 .. 2 .. 1 > .... 1078 / 625
> > .. 63 ... 958.491 .. [-8 .. 5 ..-1 .. 0 > .... 3125 / 1792
> > .. 64 ... 973.585 .. [-4 .. 3 ..-2 .. 1 > .... 1375 / 784
> > .. 65 ... 988.679 .. [ 0 .. 1 ..-3 .. 2 > ..... 605 / 343
> > .. 66 .. 1003.774 .. [-1 .. 2 ..-1 .. 0 > ...... 25 / 14
> > .. 67 .. 1018.868 .. [ 3 .. 0 ..-2 .. 1 > ...... 88 / 49
> > .. 68 .. 1033.962 .. [ 2 .. 1 .. 0 ..-1 > ...... 20 / 11
> > .. 69 .. 1049.057 .. [ 6 ..-1 ..-1 .. 0 > ...... 64 / 35
> > .. 70 .. 1064.151 .. [ 5 .. 0 .. 1 ..-2 > ..... 224 / 121
> > .. 71 .. 1079.245 .. [ 9 ..-2 .. 0 ..-1 > ..... 512 / 275
> > .. 72 .. 1094.340 .. [ 8 ..-1 .. 2 ..-3 > ... 12544 / 6655
> > .. 73 .. 1109.434 .. [ 0 ..-5 .. 2 .. 2 > .... 5929 / 3125
> > .. 74 .. 1124.528 .. [-9 .. 4 ..-1 .. 1 > .... 6875 / 3584
> > .. 75 .. 1139.623 .. [-5 .. 2 ..-2 .. 2 > .... 3025 / 1568
> > .. 76 .. 1154.717 .. [-6 .. 3 .. 0 .. 0 > ..... 125 / 64
> > .. 77 .. 1169.811 .. [-2 .. 1 ..-1 .. 1 > ...... 55 / 28
> > .. 78 .. 1184.906 .. [-3 .. 2 .. 1 ..-1 > ..... 175 / 88
> > (. 79 .. 1200.000 .. [ 1 .. 0 .. 0 .. 0 > ....... 2 / 1)
> >
> >
>
>
> Some famous intervals made their way in, but would you not prefer my version
> instead?

I'm dying to see "your version", especially if it allows us more insight into your system than we could get before.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> This probably means that Gene gave me numbers that don't add up.

Which numbers were these?

It is interesting indeed! However, the octoid just doesn't do everything I
require from a voluminous temperament or MOS. Can you suggest something a
little higher at about 80 or so tones?

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
To: <tuning@yahoogroups.com>
Sent: 22 �ubat 2006 �ar�amba 0:33
Subject: [tuning] Re: Ozan's 159-edo-based tuning

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > Indeed, the topics revolve around a possible universal tuning that also
> > satisfy my requirements for Maqam Music. In this regard, voluminous
> equal
> > divisions of the octave are desirable such as 152, 159, 171, 193, 200,
> > etc... But as the number increases, so do the possibilities of ever
> > implementing such a tuning on an instrument diminish.
>
> One tuning which has been much on my mind recently (because I'm
> working with it) is 224-et. This has an extremely good meantone fifth,
> the meantone fifth of 112-edo. It also has an excellent schismatic
> fifth. It is an excellent division up to the 13 limit, and supports
> the octoid temperament. This is relevant since Octoid[72], the octoid
> temperament on 72 notes, seems to have a lot of the properties you
> want, as well as other interesting properties involving harmony.
> Octoid[72] can be described as six different well-temperaments stacked
> next to each other, giving the kind of alternation of fifths you seem
> to be looking for. It, of course, involves fewer notes than your
> 79-note scale, and gives much greater scope to harmony and nearly-just
> intervals.
>

SNIP

These:

Some 159-et MOS:

Ozan[79]

222222222222222222222222222222222222222222222
2222222222222222222222222222222223

Ozan[80]

2222222222222222222222222222222222222222222222222
2222222222222222222222222222221

Guiron[77]

331313131313131331313131313131331313131313131331
31313131313133131313131313131

Do they add up? Or did I do something wrong perhaps?

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
To: <tuning@yahoogroups.com>
Sent: 22 �ubat 2006 �ar�amba 0:50
Subject: [tuning] Re: Ozan's 159-edo-based tuning

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > This probably means that Gene gave me numbers that don't add up.
>
> Which numbers were these?
>
>

I agree with Gene that the current version of Scala does not produce sensible results when using e31 with 103-equal, e79 with 159-equal, etc. Of course you may have your own reasons for liking or disliking what it's doing, but one should not take the SCALA output for granted. For but one thing, the result will be sensitive to the choice of starting note, usually taken as C.

-- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Dear monz,
>
> Thanks very much for the praises. I have uploaded to pictures of my Qanun
> to:
>
> http://www.ozanyarman.com/anonymous/
>
> Sorry for the bad quality. My webcam can do no better and the Qanun just
> won't fit in my flatbed scanner!
>
> A score is very easy to prepare with a frequency analyzer program.
> Unfortunately Solo Explorer by Gailius Raskinis detected polyphony and could
> not transcribe the piece.
>
> The unalterated notes used are these according to SCALA e79:
>
> A B( C# D Fb F G A B( C# D E( F# G A B( C# D
>
> Fb equates to E buselik, not E segah, hence the characteristic of the
> Buselik Maqam, whose tonic is lower D. However, I finished on lower A
> Ashiran with a Hijaz flavor.
>
> Cordially,
> Oz.
>
> ----- Original Message -----
> From: "monz" <monz@...>
> To: <tuning@yahoogroups.com>
> Sent: 18 Þubat 2006 Cumartesi 1:23
> Subject: [tuning] Re: Ozan's 159-edo-based tuning
>
>
> Hi Oz,
>
>
> I agree with the others: this sounds great!
>
> Can you post any photos of your Qanun?
>
> How about a score of what you played on this mp3?
> (Doesn't have to be in regular notation, any format is fine,
> even ASCII. I'd love to make a Tonescape file of it.)
>
>
> BTW, thanks for clarifying how you constructed the tuning.
> Now i've got it.
>
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>

SNIP

>
> This is the reason why I prefer a pure fourth to the 53-edo fourth,
although
> they differ by 0.068 cents.

[PA]
I don't understand. Monz gave you a JI scale, not EDO intervals. It's true
that Monz is trying to give you a 'rationalization' that derives
circuitously from 159-tET, but it's simply his poor methodology that caused
him to arrive at 512/385 rather than 4/3 here, not the fact that he started
with an ET (not an EDO, BTW)

[OZ]
Sorry! I was just looking at the cent values before I calculated the ratios.
Moz omitted 3 limit intervals and messed up the entire scale as a result,
which I am sure he will correct at his earliest convenience.

SNIP

Cordially,
Ozan

I found no faults with SCALA e79 notation for 79 MOS 159-tET beforehand. Or
do you believe that I take everything for granted before putting them to
good use?

----- Original Message -----
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 22 �ubat 2006 �ar�amba 0:57
Subject: [tuning] Re: Ozan's 159-edo-based tuning

I agree with Gene that the current version of Scala does not produce
sensible results when using e31 with 103-equal, e79 with 159-equal, etc. Of
course you may have your own reasons for liking or disliking what it's
doing, but one should not take the SCALA output for granted. For but one
thing, the result will be sensitive to the choice of starting note, usually
taken as C.

-- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Dear monz,
>
> Thanks very much for the praises. I have uploaded to pictures of my Qanun
> to:
>
> http://www.ozanyarman.com/anonymous/
>
> Sorry for the bad quality. My webcam can do no better and the Qanun just
> won't fit in my flatbed scanner!
>
> A score is very easy to prepare with a frequency analyzer program.
> Unfortunately Solo Explorer by Gailius Raskinis detected polyphony and
could
> not transcribe the piece.
>
> The unalterated notes used are these according to SCALA e79:
>
> A B( C# D Fb F G A B( C# D E( F# G A B( C# D
>
> Fb equates to E buselik, not E segah, hence the characteristic of the
> Buselik Maqam, whose tonic is lower D. However, I finished on lower A
> Ashiran with a Hijaz flavor.
>
> Cordially,
> Oz.

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

> But OK, yes, you're right ... since Ozan's tuning explicitly
> has a "pure" 3/2 5th, and since i know that his preferred
> version of the tuning uses (4/3)^(1/33) as the generator,
> i guess i should have included prime-factor 3 in the Tonespace.
> I'll do another one for 159-edo which includes 3, and post it.

Lo and behold ...

Ozan Yarman - 79-MOS 159-edo, in (2,)3,5,7,11-space
===================================================

TM-basis unison-vectors:

. 2,3,5,7,11-monzo ..... ratio .........~cents
-------------------------------------------------

.. [-3 2 -1 2 -1 > ... 441 / 440 .... 3.930158439
.. [-7 -1 1 1 1 > .... 385 / 384 .... 4.502561833
.. [5 -7 -1 3 0 > .. 10976 / 10935 .. 6.478999485
.. [-2 -2 4 1 -2 > .. 4375 / 4356 ... 7.534875468

The 79-MOS 159-edo tuning in 2,3,5,7,11-space:

degree .. ~cents ... 2,3,5,7,11-monzo ..... ratio
----------------------------------------------------

... 0 ..... 0.000 .. [ 0 0, 0 0 0 > ....... 1 / 1
... 1 .... 15.094 .. [ 4 0, -2 -1 1 > ... 176 / 175
... 2 .... 30.189 .. [ 3 0, -1 1 -1 > .... 56 / 55
... 3 .... 45.283 .. [ 0 -1, -2 1 1 > .... 77 / 75
... 4 .... 60.377 .. [ 2 -3, 0 1 0 > ..... 28 / 27
... 5 .... 75.472 .. [ 6 -3, -2 0 1 > ... 704 / 675
... 6 .... 90.566 .. [ 0 4, 0 -1 -1 > .... 81 / 77
... 7 ... 105.660 .. [ -3 3, -1 -1 1 .... 297 / 280
... 8 ... 120.755 .. [ -1 1, 1 -1 0 > .... 15 / 14
... 9 ... 135.849 .. [ 3 1, -1 -2 1 > ... 264 / 245
.. 10 ... 150.943 .. [ 2 1, 0 0 -1 > ..... 12 / 11
.. 11 ... 166.038 .. [ -1 0, -1 0 1 > .... 11 / 10
.. 12 ... 181.132 .. [ 1 -2, 1 0 0 > ..... 10 / 9
.. 13 ... 196.226 .. [ 2 0, -2 1 0 > ..... 28 / 25
.. 14 ... 211.321 .. [ 4 -2, 0 1 -1 > ... 112 / 99
.. 15 ... 226.415 .. [ 1 -3, -1 1 1 > ... 154 / 135
.. 16 ... 241.509 .. [ -2 2, 2 -2 0 > ... 225 / 196
.. 17 ... 256.604 .. [ -1 4, -1 -1 0 ..... 81 / 70
.. 18 ... 271.698 .. [ 1 2, 1 -1 -1 > .... 90 / 77
.. 19 ... 286.792 .. [ -2 1, 0 -1 1 > .... 33 / 28
.. 20 ... 301.887 .. [ -3 1, 1 1 -1 > ... 105 / 88
.. 21 ... 316.981 .. [ 1 1, -1 0 0 > ...... 6 / 5
.. 22 ... 332.075 .. [ 3 -1, 1 0 -1 > .... 40 / 33
.. 23 ... 347.170 .. [ 0 -2, 0 0 1 > ..... 11 / 9
.. 24 ... 362.264 .. [ -1 -2, 1 2 -1 .... 245 / 198
.. 25 ... 377.358 .. [ 3 -2, -1 1 0 > .... 56 / 45
.. 26 ... 392.453 .. [ 5 -4, 1 1 -1 > .. 1120 / 891
.. 27 ... 407.547 .. [ -3 2, 1 -2 1 > ... 495 / 392
.. 28 ... 422.642 .. [ -4 2, 2 0 -1 > ... 225 / 176
.. 29 ... 437.736 .. [ 0 2, 0 -1 0 > ...... 9 / 7
.. 30 ... 452.830 .. [ 2 0, 2 -1 -1 > ... 100 / 77
.. 31 ... 467.925 .. [ -4 1, 0 1 0 > ..... 21 / 16
.. 32 ... 483.019 .. [ 0 1, -2 0 1 > ..... 33 / 25
.. 33 ... 498.113 .. [ 2 -1, 0 0 0 > ...... 4 / 3
.. 34 ... 513.208 .. [ 6 -1, -2 -1 1 .... 704 / 525
.. 35 ... 528.302 .. [ -2 -2, 0 2 0 > .... 49 / 36
.. 36 ... 543.396 .. [ 2 -2, -2 1 1 > ... 308 / 225
.. 37 ... 558.491 .. [ -1 3, 1 -2 0 > ... 135 / 98
.. 38 ... 573.585 .. [ 0 5, -2 -1 0 > ... 243 / 175
.. 39 ... 588.679 .. [ -5 2, 1 0 0 > ..... 45 / 32
.. 40 ... 603.774 .. [ -1 2, -1 -1 1 ..... 99 / 70
.. 41 ... 618.868 .. [ 1 0, 1 -1 0 > ..... 10 / 7
.. 42 ... 633.962 .. [ 2 2, -2 0 0 > ..... 36 / 25
.. 43 ... 649.057 .. [ -3 -1, 1 1 0 > .... 35 / 24
.. 44 ... 664.151 .. [ 1 -1, -1 0 1 > .... 22 / 15
.. 45 ... 679.245 .. [ 3 -3, 1 0 0 > ..... 40 / 27
.. 46 ... 701.887 .. [ -1 1, 0 0 0 > ...... 3 / 2
.. 47 ... 716.981 .. [ 3 1, -2 -1 1 > ... 264 / 175
.. 48 ... 732.075 .. [ 5 -1, 0 -1 0 > .... 32 / 21
.. 49 ... 747.170 .. [ -1 0, -2 1 1 > .... 77 / 50
.. 50 ... 762.264 .. [ 1 -2, 0 1 0 > ..... 14 / 9
.. 51 ... 777.358 .. [ 5 -2, -2 0 1 > ... 352 / 225
.. 52 ... 792.453 .. [ 4 -2, -1 2 -1 .... 784 / 495
.. 53 ... 807.547 .. [ -4 4, -1 -1 1 .... 891 / 560
.. 54 ... 822.642 .. [ -2 2, 1 -1 0 > .... 45 / 28
.. 55 ... 837.736 .. [ 2 2, -1 -2 1 > ... 396 / 245
.. 56 ... 852.830 .. [ 1 2, 0 0 -1 > ..... 18 / 11
.. 57 ... 867.925 .. [ -2 1, -1 0 1 > .... 33 / 20
.. 58 ... 883.019 .. [ 0 -1, 1 0 0 > ...... 5 / 3
.. 59 ... 898.113 .. [ 4 -1, -1 -1 1 .... 176 / 105
.. 60 ... 913.208 .. [ 3 -1, 0 1 -1 > .... 56 / 33
.. 61 ... 928.302 .. [ 0 -2, -1 1 1 > .... 77 / 45
.. 62 ... 943.396 .. [ 2 -4, 1 1 0 > .... 140 / 81
.. 63 ... 958.491 .. [ -2 5, -1 -1 0 .... 243 / 140
.. 64 ... 973.585 .. [ 0 3, 1 -1 -1 > ... 135 / 77
.. 65 ... 988.679 .. [ -3 2, 0 -1 1 > .... 99 / 56
.. 66 .. 1003.774 .. [ -1 0, 2 -1 0 > .... 25 / 14
.. 67 .. 1018.868 .. [ 0 2, -1 0 0 > ...... 9 / 5
.. 68 .. 1033.962 .. [ 2 0, 1 0 -1 > ..... 20 / 11
.. 69 .. 1049.057 .. [ -1 -1, 0 0 1 > .... 11 / 6
.. 70 .. 1064.151 .. [ 1 -3, 2 0 0 > ..... 50 / 27
.. 71 .. 1079.245 .. [ 2 -1, -1 1 0 > .... 28 / 15
.. 72 .. 1094.340 .. [ 4 -3, 1 1 -1 > ... 560 / 297
.. 73 .. 1109.434 .. [ 1 -4, 0 1 1 > .... 154 / 81
.. 74 .. 1124.528 .. [ -5 3, 2 0 -1 > ... 675 / 352
.. 75 .. 1139.623 .. [ -1 3, 0 -1 0 > .... 27 / 14
.. 76 .. 1154.717 .. [ 1 1, 2 -1 -1 > ... 150 / 77
.. 77 .. 1169.811 .. [ 5 1, 0 -2 0 > ..... 96 / 49
.. 78 .. 1184.906 .. [ -3 0, 2 1 -1 > ... 175 / 88
(. 79 .. 1200.000 .. [ 1 0, 0 0 0> ........ 2 / 1)

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

Ozan, I apologize again for my manner. I simply seek mutual edification. Our past discussions on the topic contained my preliminary reactions, which you seem to be asking me to rehash, but I prefer to move forward instead of backwards. The inconsistencies I was referring to were seeming incompatibilities between your way of thinking and the assumptions behind the technical machinery that Monz, Gene, and I are used to. Whether you choose to answer my present set of questions or not, you have my heartfelt support in every musical endeavor, particularly those which will allow your rich musical heritage to survive the wave of 12-equal hegemony.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Paul, you are not helping in the least. I am not a tuning expert nor do I
> claim to possess superior knowledge in matters of consonances. For gosh
> sakes, I'm still new here and English is not my mother tongue. I have
> pointed out to the best of my ability all the criteria that Maqam Music
> requires and am very much satisfied with the results of my proposal at this
> moment. But since you are hard to please, oblige me... what inconsistencies
> have you discovered that I and the others are unaware of?
>
>
> ----- Original Message -----
> From: "wallyesterpaulrus" <wallyesterpaulrus@...>
> To: <tuning@yahoogroups.com>
> Sent: 18 Þubat 2006 Cumartesi 6:47
> Subject: [tuning] Re: Ozan's 159-edo-based tuning
>
>
> > --- In tuning@yahoogroups.com, "monz" <monz@> wrote:
> > >
> > > Hi Oz,
> > >
> > >
> > > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> > >
> > > > Some degrees yield excellent 11 limit results, while
> > > > others produce adorable 5 limit and sufficiently close
> > > > 7 limit intervals.
> > >
> > >
> > > Other than the one perfect 3/2 ratio, do you consider
> > > this tuning to represent 3 as a prime-factor?
> > >
> > > Can you please post a table showing how you associate these
> > > prime-factors with their respective scale degrees? It would
> > > help me put together a Tonescape Tonespace of your tuning.
> > >
> > > Has Gene or anyone else investigated any possible
> > > unison-vectors,
> >
> > We have been trying very hard to do so, since so many useful MOS
> > (and, more generally, DE) scales arise so naturally from delimiting
> > the lattice by a set of unison vectors, all but one of which is
> > tempered out. So far, though, Ozan's answers to our queries have been
> > inconsistent, seemingly, both with one another and with such an
> > approach. I'm reserving any judgment until there's a lot more clarity
> > in our mutual understanding.
> >
> > > or whether this tuning represents a
> > > TM-reduced-basis, etc.?
> >
> > What would that mean, exactly? You can TM-reduce the set of unison
> > vectors that are tempered out, but of course this has no effect on
> > the resulting tuning system. Meanwhile, a tuning representing or
> > having a basis of vanishing unison vectors would seem to consist of
> > only one note, so I'm not sure what use that would be.
> >
> > >
> > >
> > > My point is that to create a Tonespace of it, i need to
> > > know what to use as generators. There are already several
> > > possibilities:
> > >
> > > * a chain created by (4/3)^(1/33)
> > >
> > > * a chain created by 2^(1/159), with ~half the notes missing
> > >
> > > * a 4-dimensional "block" created by tempered approximations
> > > of prime-factors 2, 5, 7, 11
> >
> > Why isn't prime 3 in there too?
> >
> >
> >
>

Hi Paul and Ozan,

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

> > > [monz]
> > > .. 33 ... 498.113 .. [ 9 ..-1 ..-1 ..-1 > ..... 512 / 385
> >
> >[Ozan]
> > This is the reason why I prefer a pure fourth to the
> > 53-edo fourth, although they differ by 0.068 cents.
>
> I don't understand. Monz gave you a JI scale, not EDO
> intervals.

Eh? The cents values are all from 159-edo.
The monzos and ratios are the approximate JI values.

> It's true that Monz is trying to give you a
> 'rationalization' that derives circuitously from 159-tET,
> but it's simply his poor methodology that caused him to
> arrive at 512/385 rather than 4/3 here, not the fact that
> he started with an ET (not an EDO, BTW)

Poor methodology? I deliberately left out prime-factor 3,
that's what caused me to arrive at 512-385 rather than 4/3.
Perhaps that was a poor judgment, but otherwise my
methodology is fine. Anyway, by now i've posted the
alternative which does include 3.

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

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

> Sorry! I was just looking at the cent values before I
> calculated the ratios. Moz [monz] omitted 3 limit intervals
> and messed up the entire scale as a result, which I am
> sure he will correct at his earliest convenience.

Done. See message 64456.

/tuning/topicId_64170.html#64456

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

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> It is interesting indeed! However, the octoid just doesn't do
everything I
> require from a voluminous temperament or MOS. Can you suggest
something a
> little higher at about 80 or so tones?

I could, but in order to make sensible suggestions it would be good to
hear why Octoid[72] won't work for you. For all I know, Octoid[80],
with 80 notes to the octave, would.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> And how does 79 notes from 33 equal divisions of the pure fourth with octave
> equivalances preclude the possibility of modulations Paul?

I didn't say that.

> Or better yet,
> how does 77 or 80 do not?

I have yet to look at the specific scales Gene was referring to. One possibility for 80-out-of-159 is simply the complement of your 79-out-of-159 scale, so that version would share most properties in common with your scale. Actually, if the 80&159 temperament that Gene referred to yields your scale exactly, then maybe Monz would want to switch to the TM-reduced kernel basis for this temperament rather than one for 159-tone (or any other) equal temperament.

> ----- Original Message -----
> From: "wallyesterpaulrus" <wallyesterpaulrus@...>
> To: <tuning@yahoogroups.com>
> Sent: 20 Þubat 2006 Pazartesi 12:56
> Subject: [tuning] Re: Ozan's 159-edo-based tuning
>
>
> > --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@> wrote:
> > >
> > > > I should note, however, that 159 is interesting as a high or very
> > > > high limit system, and the 80&159 temperament looks better in
> > > > higher limits. Of course in something like the 29 limit you may
> > > > as well just use all 159 notes, and I really don't see why Ozan
> > > > doesn't do that always,
> > >
> > > He's answered that. 'Too many notes.'
> > >
> > > -Carl
> >
> > But one would think that if one chooses a subset, it would be one where
> the consonant intervals can be transposed once or twice by the usual
> intervals of modulation (fourths and fifths), wouldn't one?
> >
> >
> >
>

Petr,

----- Original Message -----
From: "Petr Par�zek" <p.parizek@chello.cz>
To: <tuning@yahoogroups.com>
Sent: 22 �ubat 2006 �ar�amba 0:37
Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning

> Hi Ozan.
>
> > Aha! So you don't question the validity of 12 tones simply because it
has
> > historical precedence and my tuning does not? Surely you see the
> dichotomy.
>
> I'm realizing I have to be pretty careful about how to say something to
make
> others understand my words in the way they were really meant. At this
time,
> either my statement was totally unclear or my questions made you
> misunderstandd my view.

That happens to me a lot.

> OK, I'll try to make things clearer.
>
> 1. The number 12 is easily explainable for me not for its historical
> precedence but for the acoustical properties of the intervals, no matter
if
> pure or approximated. Since I've never examined 33 equal divisions of the
> fourth, I was just unaware.

Well, you said it. The acoustical properties of 33 equal divisions of the
pure fourth are remarkable from my point of view.

> 2. We all know that, for instance, 13-EDO or 11-EDO doesn't have the
> properties wich are being so valued in 12-EDO. So I was interested if, for
> example, dividing the fourth into 32 or 34 equal steps instead of 33 would
> harm the system, and if so, how much.

Pretty much, I assure you.

Or, in other words, if you found the
> number 33 using some formulas while trying to meet some of your
requirements
> (like I could find 19-EDO, 22, 31, 50, or 53 while trying to find a good
> tuning for common tonal music), or if it was just one of your free
> decisions.

I chanced upon this while I was trying to find temperaments that contained
adequately tempered fifths in range. Specifically, I was focused on 79-tET,
wanted to shift the two fifths so that they were equally distant from pure:

1. (log 3/2) x 1200 divided by (log 2) over 46+47/2 times 79 = 1192.56871
cents.

2. Completed the 79th tone to 1200 cents and moved the large comma between
steps 45-46.

Then I realized that it was possible to make the fifth pure only if one
divided the pure fourth into 33 equal parts which - when carried to the 79th
tone - resulted in 1192.28954 cents, practically the same as above.
Afterwards, one only needed to edit the value of the octave and rotate the
scale in the same manner.

Here are the differences between two approaches:

1: 1: -0.004 cents -0.003536 0.0005 Hertz, 0.0323 cycles/min.
2: 2: -0.007 cents -0.007062 0.0011 Hertz, 0.0652 cycles/min.
3: 3: -0.011 cents -0.010599 0.0016 Hertz, 0.0987 cycles/min.
4: 4: -0.014 cents -0.014135 0.0022 Hertz, 0.1327 cycles/min.
5: 5: -0.018 cents -0.017672 0.0028 Hertz, 0.1674 cycles/min.
6: 6: -0.021 cents -0.021198 0.0034 Hertz, 0.2025 cycles/min.
7: 7: -0.025 cents -0.024735 0.0040 Hertz, 0.2384 cycles/min.
8: 8: -0.028 cents -0.028261 0.0046 Hertz, 0.2748 cycles/min.
9: 9: -0.032 cents -0.031798 0.0052 Hertz, 0.3119 cycles/min.
10: 10: -0.035 cents -0.035334 0.0058 Hertz, 0.3496 cycles/min.
11: 11: -0.039 cents -0.038871 0.0065 Hertz, 0.3879 cycles/min.
12: 12: -0.042 cents -0.042397 0.0071 Hertz, 0.4268 cycles/min.
13: 13: -0.046 cents -0.045934 0.0078 Hertz, 0.4665 cycles/min.
14: 14: -0.049 cents -0.049470 0.0084 Hertz, 0.5068 cycles/min.
15: 15: -0.053 cents -0.053007 0.0091 Hertz, 0.5478 cycles/min.
16: 16: -0.057 cents -0.056533 0.0098 Hertz, 0.5893 cycles/min.
17: 17: -0.060 cents -0.060070 0.0105 Hertz, 0.6317 cycles/min.
18: 18: -0.064 cents -0.063606 0.0112 Hertz, 0.6747 cycles/min.
19: 19: -0.067 cents -0.067132 0.0120 Hertz, 0.7184 cycles/min.
20: 20: -0.071 cents -0.070669 0.0127 Hertz, 0.7628 cycles/min.
21: 21: -0.074 cents -0.074205 0.0135 Hertz, 0.8080 cycles/min.
22: 22: -0.078 cents -0.077742 0.0142 Hertz, 0.8540 cycles/min.
23: 23: -0.081 cents -0.081268 0.0150 Hertz, 0.9005 cycles/min.
24: 24: -0.085 cents -0.084805 0.0158 Hertz, 0.9479 cycles/min.
25: 25: -0.088 cents -0.088341 0.0166 Hertz, 0.9961 cycles/min.
26: 26: -0.092 cents -0.091878 0.0174 Hertz, 1.0450 cycles/min.
27: 27: -0.095 cents -0.095404 0.0182 Hertz, 1.0947 cycles/min.
28: 28: -0.099 cents -0.098941 0.0191 Hertz, 1.1452 cycles/min.
29: 29: -0.102 cents -0.102477 0.0199 Hertz, 1.1965 cycles/min.
30: 30: -0.106 cents -0.106014 0.0208 Hertz, 1.2486 cycles/min.
31: 31: -0.110 cents -0.109540 0.0217 Hertz, 1.3015 cycles/min.
32: 32: -0.113 cents -0.113077 0.0226 Hertz, 1.3552 cycles/min.
33: 33: -0.117 cents -0.116613 0.0235 Hertz, 1.4099 cycles/min.
34: 34: -0.120 cents -0.120140 0.0244 Hertz, 1.4652 cycles/min.
35: 35: -0.124 cents -0.123676 0.0254 Hertz, 1.5216 cycles/min.
36: 36: -0.127 cents -0.127212 0.0263 Hertz, 1.5788 cycles/min.
37: 37: -0.131 cents -0.130749 0.0273 Hertz, 1.6369 cycles/min.
38: 38: -0.134 cents -0.134275 0.0283 Hertz, 1.6957 cycles/min.
39: 39: -0.138 cents -0.137812 0.0293 Hertz, 1.7556 cycles/min.
40: 40: -0.141 cents -0.141348 0.0303 Hertz, 1.8165 cycles/min.
41: 41: -0.145 cents -0.144885 0.0313 Hertz, 1.8782 cycles/min.
42: 42: -0.148 cents -0.148411 0.0323 Hertz, 1.9408 cycles/min.
43: 43: -0.152 cents -0.151948 0.0334 Hertz, 2.0044 cycles/min.
44: 44: -0.155 cents -0.155484 0.0345 Hertz, 2.0690 cycles/min.
45: 45: -0.159 cents -0.159011 0.0356 Hertz, 2.1345 cycles/min.
46: 46: 0.117 cents 0.116613 0.0264 Hertz, 1.5860 cycles/min.
47: 47: 0.113 cents 0.113087 0.0259 Hertz, 1.5515 cycles/min.
48: 48: 0.110 cents 0.109550 0.0253 Hertz, 1.5161 cycles/min.
49: 49: 0.106 cents 0.106014 0.0247 Hertz, 1.4800 cycles/min.
50: 50: 0.102 cents 0.102487 0.0241 Hertz, 1.4433 cycles/min.
51: 51: 0.099 cents 0.098951 0.0234 Hertz, 1.4057 cycles/min.
52: 52: 0.095 cents 0.095414 0.0228 Hertz, 1.3674 cycles/min.
53: 53: 0.092 cents 0.091878 0.0221 Hertz, 1.3282 cycles/min.
54: 54: 0.088 cents 0.088351 0.0215 Hertz, 1.2884 cycles/min.
55: 55: 0.085 cents 0.084815 0.0208 Hertz, 1.2477 cycles/min.
56: 56: 0.081 cents 0.081278 0.0201 Hertz, 1.2061 cycles/min.
57: 57: 0.078 cents 0.077742 0.0194 Hertz, 1.1638 cycles/min.
58: 58: 0.074 cents 0.074215 0.0187 Hertz, 1.1207 cycles/min.
59: 59: 0.071 cents 0.070679 0.0179 Hertz, 1.0766 cycles/min.
60: 60: 0.067 cents 0.067142 0.0172 Hertz, 1.0317 cycles/min.
61: 61: 0.064 cents 0.063616 0.0164 Hertz, 0.9861 cycles/min.
62: 62: 0.060 cents 0.060080 0.0157 Hertz, 0.9394 cycles/min.
63: 63: 0.057 cents 0.056543 0.0149 Hertz, 0.8919 cycles/min.
64: 64: 0.053 cents 0.053007 0.0141 Hertz, 0.8434 cycles/min.
65: 65: 0.049 cents 0.049480 0.0132 Hertz, 0.7942 cycles/min.
66: 66: 0.046 cents 0.045944 0.0124 Hertz, 0.7439 cycles/min.
67: 67: 0.042 cents 0.042407 0.0115 Hertz, 0.6926 cycles/min.
68: 68: 0.039 cents 0.038871 0.0107 Hertz, 0.6404 cycles/min.
69: 69: 0.035 cents 0.035344 0.0098 Hertz, 0.5874 cycles/min.
70: 70: 0.032 cents 0.031808 0.0089 Hertz, 0.5333 cycles/min.
71: 71: 0.028 cents 0.028271 0.0080 Hertz, 0.4782 cycles/min.
72: 72: 0.025 cents 0.024735 0.0070 Hertz, 0.4220 cycles/min.
73: 73: 0.021 cents 0.021208 0.0061 Hertz, 0.3650 cycles/min.
74: 74: 0.018 cents 0.017672 0.0051 Hertz, 0.3068 cycles/min.
75: 75: 0.014 cents 0.014135 0.0041 Hertz, 0.2476 cycles/min.
76: 76: 0.011 cents 0.010609 0.0031 Hertz, 0.1874 cycles/min.
77: 77: 0.007 cents 0.007072 0.0021 Hertz, 0.1260 cycles/min.
78: 78: 0.004 cents 0.003536 0.0011 Hertz, 0.0636 cycles/min.
79: 79: 1/1 0.000000 0.0000 Hertz, 0.0000
cycles/min.
Total absolute difference : 5.6399 cents
Average absolute difference: 0.0714 cents
Root mean square difference: 0.0833 cents
Highest absolute difference: 0.1590 cents
Number of notes different: 78

When compared with 159-tET, `equally distant fifths from pure` approach
yields tones that are 0.0660 cents different at maximum.

Cordially,
Ozan

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Paul,
>
> > > >
> > > I should note, however, that 159 is interesting as a high or very high
> > > limit system, and the 80&159 temperament looks better in higher
> > > limits.
> >
> > So this implies an 80-note MOS rather than a 79-note one should be
> interesting?
> >
>
> I don't understand what you have against 79 anyway.

Absolutely nothing. In fact, if it implies an 80-note MOS, it implies a 79-note MOS too, since 159-80=79. I thought of that only after I wrote the above.

>
> >
> > Tempering out both 1029/1024 and
> > > 32805/32768, leading to "guiron", gives a generator of 31 steps of
> > > 159, which is an example of the sort of thing one might do by way of
> > > an alternative to the 79-note MOS (a 77-note MOS, perhaps).
> > >
> > Fascinating.
> >
> >
>
> It would be fascinating if we were given the chance to analyze it first.
>
Indeed.

Why, it looks pretty good monz! I'm mighty pleased with your effort.

----- Original Message -----
From: "monz" <monz@tonalsoft.com>
To: <tuning@yahoogroups.com>
Sent: 22 �ubat 2006 �ar�amba 1:26
Subject: [tuning] Ozan's 79-MOS 159-edo tuning in 2,3,5,7,11-space

> --- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
>
> > But OK, yes, you're right ... since Ozan's tuning explicitly
> > has a "pure" 3/2 5th, and since i know that his preferred
> > version of the tuning uses (4/3)^(1/33) as the generator,
> > i guess i should have included prime-factor 3 in the Tonespace.
> > I'll do another one for 159-edo which includes 3, and post it.
>
>
> Lo and behold ...
>
>
> Ozan Yarman - 79-MOS 159-edo, in (2,)3,5,7,11-space
> ===================================================
>
>
> TM-basis unison-vectors:
>
> . 2,3,5,7,11-monzo ..... ratio .........~cents
> -------------------------------------------------
>
> .. [-3 2 -1 2 -1 > ... 441 / 440 .... 3.930158439
> .. [-7 -1 1 1 1 > .... 385 / 384 .... 4.502561833
> .. [5 -7 -1 3 0 > .. 10976 / 10935 .. 6.478999485
> .. [-2 -2 4 1 -2 > .. 4375 / 4356 ... 7.534875468
>
>
>
> The 79-MOS 159-edo tuning in 2,3,5,7,11-space:
>
> degree .. ~cents ... 2,3,5,7,11-monzo ..... ratio
> ----------------------------------------------------
>
> ... 0 ..... 0.000 .. [ 0 0, 0 0 0 > ....... 1 / 1
> ... 1 .... 15.094 .. [ 4 0, -2 -1 1 > ... 176 / 175
> ... 2 .... 30.189 .. [ 3 0, -1 1 -1 > .... 56 / 55
> ... 3 .... 45.283 .. [ 0 -1, -2 1 1 > .... 77 / 75
> ... 4 .... 60.377 .. [ 2 -3, 0 1 0 > ..... 28 / 27
> ... 5 .... 75.472 .. [ 6 -3, -2 0 1 > ... 704 / 675
> ... 6 .... 90.566 .. [ 0 4, 0 -1 -1 > .... 81 / 77
> ... 7 ... 105.660 .. [ -3 3, -1 -1 1 .... 297 / 280
> ... 8 ... 120.755 .. [ -1 1, 1 -1 0 > .... 15 / 14
> ... 9 ... 135.849 .. [ 3 1, -1 -2 1 > ... 264 / 245
> .. 10 ... 150.943 .. [ 2 1, 0 0 -1 > ..... 12 / 11
> .. 11 ... 166.038 .. [ -1 0, -1 0 1 > .... 11 / 10
> .. 12 ... 181.132 .. [ 1 -2, 1 0 0 > ..... 10 / 9
> .. 13 ... 196.226 .. [ 2 0, -2 1 0 > ..... 28 / 25
> .. 14 ... 211.321 .. [ 4 -2, 0 1 -1 > ... 112 / 99
> .. 15 ... 226.415 .. [ 1 -3, -1 1 1 > ... 154 / 135
> .. 16 ... 241.509 .. [ -2 2, 2 -2 0 > ... 225 / 196
> .. 17 ... 256.604 .. [ -1 4, -1 -1 0 ..... 81 / 70
> .. 18 ... 271.698 .. [ 1 2, 1 -1 -1 > .... 90 / 77
> .. 19 ... 286.792 .. [ -2 1, 0 -1 1 > .... 33 / 28
> .. 20 ... 301.887 .. [ -3 1, 1 1 -1 > ... 105 / 88
> .. 21 ... 316.981 .. [ 1 1, -1 0 0 > ...... 6 / 5
> .. 22 ... 332.075 .. [ 3 -1, 1 0 -1 > .... 40 / 33
> .. 23 ... 347.170 .. [ 0 -2, 0 0 1 > ..... 11 / 9
> .. 24 ... 362.264 .. [ -1 -2, 1 2 -1 .... 245 / 198
> .. 25 ... 377.358 .. [ 3 -2, -1 1 0 > .... 56 / 45
> .. 26 ... 392.453 .. [ 5 -4, 1 1 -1 > .. 1120 / 891
> .. 27 ... 407.547 .. [ -3 2, 1 -2 1 > ... 495 / 392
> .. 28 ... 422.642 .. [ -4 2, 2 0 -1 > ... 225 / 176
> .. 29 ... 437.736 .. [ 0 2, 0 -1 0 > ...... 9 / 7
> .. 30 ... 452.830 .. [ 2 0, 2 -1 -1 > ... 100 / 77
> .. 31 ... 467.925 .. [ -4 1, 0 1 0 > ..... 21 / 16
> .. 32 ... 483.019 .. [ 0 1, -2 0 1 > ..... 33 / 25
> .. 33 ... 498.113 .. [ 2 -1, 0 0 0 > ...... 4 / 3
> .. 34 ... 513.208 .. [ 6 -1, -2 -1 1 .... 704 / 525
> .. 35 ... 528.302 .. [ -2 -2, 0 2 0 > .... 49 / 36
> .. 36 ... 543.396 .. [ 2 -2, -2 1 1 > ... 308 / 225
> .. 37 ... 558.491 .. [ -1 3, 1 -2 0 > ... 135 / 98
> .. 38 ... 573.585 .. [ 0 5, -2 -1 0 > ... 243 / 175
> .. 39 ... 588.679 .. [ -5 2, 1 0 0 > ..... 45 / 32
> .. 40 ... 603.774 .. [ -1 2, -1 -1 1 ..... 99 / 70
> .. 41 ... 618.868 .. [ 1 0, 1 -1 0 > ..... 10 / 7
> .. 42 ... 633.962 .. [ 2 2, -2 0 0 > ..... 36 / 25
> .. 43 ... 649.057 .. [ -3 -1, 1 1 0 > .... 35 / 24
> .. 44 ... 664.151 .. [ 1 -1, -1 0 1 > .... 22 / 15
> .. 45 ... 679.245 .. [ 3 -3, 1 0 0 > ..... 40 / 27
> .. 46 ... 701.887 .. [ -1 1, 0 0 0 > ...... 3 / 2
> .. 47 ... 716.981 .. [ 3 1, -2 -1 1 > ... 264 / 175
> .. 48 ... 732.075 .. [ 5 -1, 0 -1 0 > .... 32 / 21
> .. 49 ... 747.170 .. [ -1 0, -2 1 1 > .... 77 / 50
> .. 50 ... 762.264 .. [ 1 -2, 0 1 0 > ..... 14 / 9
> .. 51 ... 777.358 .. [ 5 -2, -2 0 1 > ... 352 / 225
> .. 52 ... 792.453 .. [ 4 -2, -1 2 -1 .... 784 / 495
> .. 53 ... 807.547 .. [ -4 4, -1 -1 1 .... 891 / 560
> .. 54 ... 822.642 .. [ -2 2, 1 -1 0 > .... 45 / 28
> .. 55 ... 837.736 .. [ 2 2, -1 -2 1 > ... 396 / 245
> .. 56 ... 852.830 .. [ 1 2, 0 0 -1 > ..... 18 / 11
> .. 57 ... 867.925 .. [ -2 1, -1 0 1 > .... 33 / 20
> .. 58 ... 883.019 .. [ 0 -1, 1 0 0 > ...... 5 / 3
> .. 59 ... 898.113 .. [ 4 -1, -1 -1 1 .... 176 / 105
> .. 60 ... 913.208 .. [ 3 -1, 0 1 -1 > .... 56 / 33
> .. 61 ... 928.302 .. [ 0 -2, -1 1 1 > .... 77 / 45
> .. 62 ... 943.396 .. [ 2 -4, 1 1 0 > .... 140 / 81
> .. 63 ... 958.491 .. [ -2 5, -1 -1 0 .... 243 / 140
> .. 64 ... 973.585 .. [ 0 3, 1 -1 -1 > ... 135 / 77
> .. 65 ... 988.679 .. [ -3 2, 0 -1 1 > .... 99 / 56
> .. 66 .. 1003.774 .. [ -1 0, 2 -1 0 > .... 25 / 14
> .. 67 .. 1018.868 .. [ 0 2, -1 0 0 > ...... 9 / 5
> .. 68 .. 1033.962 .. [ 2 0, 1 0 -1 > ..... 20 / 11
> .. 69 .. 1049.057 .. [ -1 -1, 0 0 1 > .... 11 / 6
> .. 70 .. 1064.151 .. [ 1 -3, 2 0 0 > ..... 50 / 27
> .. 71 .. 1079.245 .. [ 2 -1, -1 1 0 > .... 28 / 15
> .. 72 .. 1094.340 .. [ 4 -3, 1 1 -1 > ... 560 / 297
> .. 73 .. 1109.434 .. [ 1 -4, 0 1 1 > .... 154 / 81
> .. 74 .. 1124.528 .. [ -5 3, 2 0 -1 > ... 675 / 352
> .. 75 .. 1139.623 .. [ -1 3, 0 -1 0 > .... 27 / 14
> .. 76 .. 1154.717 .. [ 1 1, 2 -1 -1 > ... 150 / 77
> .. 77 .. 1169.811 .. [ 5 1, 0 -2 0 > ..... 96 / 49
> .. 78 .. 1184.906 .. [ -3 0, 2 1 -1 > ... 175 / 88
> (. 79 .. 1200.000 .. [ 1 0, 0 0 0> ........ 2 / 1)
>
>
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>
>

Can you provide the details for Octaid 80? 72 didn't work, because the
super-pythagorean fifth is intolerable to listen to.

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
To: <tuning@yahoogroups.com>
Sent: 22 �ubat 2006 �ar�amba 1:41
Subject: [tuning] Re: Ozan's 159-edo-based tuning

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > It is interesting indeed! However, the octoid just doesn't do
> everything I
> > require from a voluminous temperament or MOS. Can you suggest
> something a
> > little higher at about 80 or so tones?
>
> I could, but in order to make sensible suggestions it would be good to
> hear why Octoid[72] won't work for you. For all I know, Octoid[80],
> with 80 notes to the octave, would.
>

Ozan, don't take this as an attack or anything, I'm just trying to tease out your thinking. Why are these 694.2-cent fifths less offensive than those of 19-equal?

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Petr, the default fifth is exactly 3/2 in my tuning:
>
> 0: 0.000 cents 0.000 0 0 commas C
> 46: 701.955 cents -0.000 0 0 commas G
> 13: 694.245 cents -7.710 -237 D
> 59: 701.955 cents -7.710 -237 A
> 26: 694.245 cents -15.421 -473 E
> 72: 701.955 cents -15.421 -473 B
> 39: 694.245 cents -23.131 -710 F#
> 6: 701.955 cents -23.131 -710 C#
> 52: 701.955 cents -23.131 -710 G#
> 19: 694.245 cents -30.842 -947 D#
> 65: 701.955 cents -30.842 -947 A#
> 32: 694.245 cents -38.552 -1183 E#
> 78: 701.955 cents -38.552 -1183 B#
> 45: 694.245 cents -46.263 -1420 G\
> 12: 701.955 cents -46.263 -1420 D\
> 58: 701.955 cents -46.263 -1420 A\
> 25: 694.245 cents -53.973 -1656 E\
> 71: 701.955 cents -53.973 -1656 B\
> 38: 694.245 cents -61.684 -1893 F#\
> 5: 701.955 cents -61.684 -1893 C#\
> 51: 701.955 cents -61.684 -1893 G#\
> 18: 694.245 cents -69.394 -2130 D#\
> 64: 701.955 cents -69.394 -2130 A#\
> 31: 694.245 cents -77.105 -2366 F\\
> 77: 701.955 cents -77.105 -2366 C\\
> 44: 694.245 cents -84.815 -2603 G\\
> 11: 701.955 cents -84.815 -2603 D\\
> 57: 701.955 cents -84.815 -2603 A\\
> 24: 694.245 cents -92.525 -2840 E\\
> 70: 701.955 cents -92.525 -2840 B\\
> 37: 694.245 cents -100.236 -3076 F)
> 4: 701.955 cents -100.236 -3076 C)
> 50: 701.955 cents -100.236 -3076 G)
> 17: 694.245 cents -107.946 -3313 D)
> 63: 701.955 cents -107.946 -3313 A)
> 30: 694.245 cents -115.657 -3550 Fv
> 76: 701.955 cents -115.657 -3550 Cv
> 43: 694.245 cents -123.367 -3786 Gv
> 10: 701.955 cents -123.367 -3786 Dv
> 56: 701.955 cents -123.367 -3786 Av
> 23: 694.245 cents -131.078 -4023 Ev
> 69: 701.955 cents -131.078 -4023 Bv
> 36: 694.245 cents -138.788 -4259 F^
> 3: 701.955 cents -138.788 -4259 C^
> 49: 701.955 cents -138.788 -4259 G^
> 16: 694.245 cents -146.499 -4496 D^
> 62: 701.955 cents -146.499 -4496 A^
> 29: 694.245 cents -154.209 -4733 F(
> 75: 701.955 cents -154.209 -4733 C(
> 42: 694.245 cents -161.920 -4969 G(
> 9: 701.955 cents -161.920 -4969 D(
> 55: 701.955 cents -161.920 -4969 A(
> 22: 694.245 cents -169.630 -5206 E(
> 68: 701.955 cents -169.630 -5206 B(
> 35: 694.245 cents -177.340 -5443 F//
> 2: 701.955 cents -177.340 -5443 C//
> 48: 701.955 cents -177.340 -5443 G//
> 15: 694.245 cents -185.051 -5679 D//
> 61: 701.955 cents -185.051 -5679 A//
> 28: 694.245 cents -192.761 -5916 E//
> 74: 701.955 cents -192.761 -5916 B//
> 41: 694.245 cents -200.472 -6153 Gb/
> 8: 701.955 cents -200.472 -6153 Db/
> 54: 701.955 cents -200.472 -6153 Ab/
> 21: 694.245 cents -208.182 -6389 Eb/
> 67: 701.955 cents -208.182 -6389 Bb/
> 34: 694.245 cents -215.893 -6626 F/
> 1: 701.955 cents -215.893 -6626 C/
> 47: 701.955 cents -215.893 -6626 G/
> 14: 694.245 cents -223.603 -6863 D/
> 60: 701.955 cents -223.603 -6863 A/
> 27: 694.245 cents -231.314 -7099 Fb
> 73: 701.955 cents -231.314 -7099 Cb
> 40: 694.245 cents -239.024 -7336 Gb
> 7: 701.955 cents -239.024 -7336 Db
> 53: 701.955 cents -239.024 -7336 Ab
> 20: 694.245 cents -246.735 -7572 Eb
> 66: 701.955 cents -246.735 -7572 Bb
> 33: 694.245 cents -254.445 -7809 F
> 79: 701.955 cents -254.445 -7809 C
> Average absolute difference: 129.4185 cents
> Root mean square difference: 149.7660 cents
> Maximum absolute difference: 254.4451 cents
> Maximum formal fifth difference: 7.7105 cents
>
>
> ----- Original Message -----
> From: "Petr Parízek" <p.parizek@...>
> To: <tuning@yahoogroups.com>
> Sent: 21 Þubat 2006 Salý 18:45
> Subject: [tuning] Re: Ozan's 159-edo-based tuning
>
>
> > Hi Ozan.
> >
> > You wrote:
> >
> > > The fifth should have been 3/2. The complication arises from your
> > preference
> > > of 159 equal divisions of the octave, which is a very close
> approximation
> > to
> > > my proposal.
> >
> > Am I right in assuming that the fifth is closer to 3/2 in your tuning than
> > in 159-equal?
> >
> > Petr
> >
> >
>

They are not less offensive, they are very very offensive, but that is the
price I have to pay while retaining all the benefits of 79 tones, unless of
course you can suggest something else as a substitute.

----- Original Message -----
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 22 �ubat 2006 �ar�amba 2:47
Subject: [tuning] Re: Ozan's 159-edo-based tuning

Ozan, don't take this as an attack or anything, I'm just trying to tease out
your thinking. Why are these 694.2-cent fifths less offensive than those of
19-equal?

Oh well, we are all human! Thanx for your encouragement though. Just
remember that I am entitled to making less sense most of the time than not,
given my eccentric disposition and absolute ignorance of the world.

----- Original Message -----
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 22 �ubat 2006 �ar�amba 1:29
Subject: [tuning] Re: Ozan's 159-edo-based tuning

Ozan, I apologize again for my manner. I simply seek mutual edification. Our
past discussions on the topic contained my preliminary reactions, which you
seem to be asking me to rehash, but I prefer to move forward instead of
backwards. The inconsistencies I was referring to were seeming
incompatibilities between your way of thinking and the assumptions behind
the technical machinery that Monz, Gene, and I are used to. Whether you
choose to answer my present set of questions or not, you have my heartfelt
support in every musical endeavor, particularly those which will allow your
rich musical heritage to survive the wave of 12-equal hegemony.

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
>
> Hi Paul (and Oz),
>
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@> wrote:
>
> > --- In tuning@yahoogroups.com, "monz" <monz@> wrote:
> > >
> > > Hi Ozan, Yahya, et al,
> > >
> > >
> > > --- In tuning@yahoogroups.com, "monz" <monz@> wrote:
> > >
> > > > I've made a Tonescape file of your 79-MOS as a subset
> > > > of 159-edo in (2,)5,7,11-space, with 2 as the identity
> > > > interval, and using TM-basis for the 159-edo periodicity-block.
> >
> > Can you state this with more precision and detail, please,
> > for those of us attempting to follow along?
>
>
> TM-basis for 159-edo in 2,5,7,11-space:
>
>
> .. 2,5,7,11-monzo ...... ratio ........ ~cents
> ---------------------------------------------------
>
> .. [-12 -2 1 4 > .. 102487 / 102400 ... 1.470248198
> .. [8 -8 5 -1 > .. 4302592 / 4296875 .. 2.301879062
> .. [-5 3 3 -3 > .... 42875 / 42592 ... 11.46503391
>

How did you arrive at this? Which "val" are you assuming?

And as usual, I think it would make a lot more sense to reduce the pitches (thus making the choice of kernel basis irrelevant) instead of reducing the kernel basis and then constructing an FPB.
>
>
> > > degree ... ~cents .. ------ monzo ------- ....... ratio
> > > ...................... 2 .. 5 .. 7 .. 11
> > >
> > > <snip>
> > > .. 33 ... 498.113 .. [ 9 ..-1 ..-17 ..-1 > ..... 512 / 385
> >
> > I find it pretty humorous that you didn't even get 4/3
> > for 33 steps, one of the few clues Ozan has explicitly
> > given us . . .
>
>
>
> Well, considering that 3 is *not* one of the prime-factors
> in the Tonespace which i used, it's pretty obvious *why*
> i didn't get 4/3.
>
> But OK, yes, you're right ... since Ozan's tuning explicitly
> has a "pure" 3/2 5th, and since i know that his preferred
> version of the tuning uses (4/3)^(1/33) as the generator,
> i guess i should have included prime-factor 3 in the Tonespace.
> I'll do another one for 159-edo which includes 3, and post it.
>
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>

Hi Paul,

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

> > [monz]
> > TM-basis for 159-edo in 2,5,7,11-space:
> >
> >
> > .. 2,5,7,11-monzo ...... ratio ........ ~cents
> > ---------------------------------------------------
> >
> > .. [-12 -2 1 4 > .. 102487 / 102400 ... 1.470248198
> > .. [8 -8 5 -1 > .. 4302592 / 4296875 .. 2.301879062
> > .. [-5 3 3 -3 > .... 42875 / 42592 ... 11.46503391
> >
>
> How did you arrive at this?

I didn't have to do anything myself, Tonescape did it.

> Which "val" are you assuming?

The 2,5,7,11-val is < 159 369 446 550 ] .

> And as usual, I think it would make a lot more sense to
> reduce the pitches (thus making the choice of kernel basis
> irrelevant) instead of reducing the kernel basis and then
> constructing an FPB.

Ah yes, i could tell Tonescape to construct a 79-tone
periodicity-block first, *then* use 159-edo for the tuning.

Why do you say that reducing the number of pitches
makes "the choice of kernel basis irrelevant"?
The choice of kernel basis still determines how
compact the periodicity-block is.

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

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

> Until then, can you give me the cent values for Guiron[77] Gene?

! guiron77.scl
Guiron[77] (118&159 temperament) in 159-et
77
!
22.641509
30.188679
52.830189
60.377358
83.018868
90.566038
113.207547
120.754717
143.396226
150.943396
173.584906
181.132075
203.773585
211.320755
233.962264
256.603774
264.150943
286.792453
294.339623
316.981132
324.528302
347.169811
354.716981
377.358491
384.905660
407.547170
415.094340
437.735849
445.283019
467.924528
490.566038
498.113208
520.754717
528.301887
550.943396
558.490566
581.132075
588.679245
611.320755
618.867925
641.509434
649.056604
671.698113
679.245283
701.886792
709.433962
732.075472
754.716981
762.264151
784.905660
792.452830
815.094340
822.641509
845.283019
852.830189
875.471698
883.018868
905.660377
913.207547
935.849057
943.396226
966.037736
988.679245
996.226415
1018.867925
1026.415094
1049.056604
1056.603774
1079.245283
1086.792453
1109.433962
1116.981132
1139.622642
1147.169811
1169.811321
1177.358491
1200.000000

Here's how I would do Ozan[80]:

! ozan80.scl
Ozan[80] (80&159 temperament) in 159-et
80
!
15.094340
30.188679
45.283019
60.377358
75.471698
90.566038
105.660377
120.754717
135.849057
150.943396
166.037736
181.132075
196.226415
211.320755
226.415094
241.509434
256.603774
271.698113
286.792453
301.886792
316.981132
332.075472
347.169811
362.264151
377.358491
392.452830
407.547170
422.641509
437.735849
452.830189
467.924528
483.018868
498.113208
513.207547
528.301887
543.396226
558.490566
573.584906
588.679245
603.773585
618.867925
633.962264
649.056604
664.150943
679.245283
694.339623
709.433962
724.528302
739.622642
754.716981
769.811321
784.905660
800.000000
815.094340
830.188679
845.283019
860.377358
875.471698
890.566038
905.660377
920.754717
935.849057
950.943396
966.037736
981.132075
996.226415
1011.320755
1026.415094
1041.509434
1056.603774
1071.698113
1086.792453
1101.886792
1116.981132
1132.075472
1147.169811
1162.264151
1177.358491
1192.452830
1200.000000

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

> > .. [-12 -2 1 4 > .. 102487 / 102400 ... 1.470248198
> > .. [8 -8 5 -1 > .. 4302592 / 4296875 .. 2.301879062
> > .. [-5 3 3 -3 > .... 42875 / 42592 ... 11.46503391
> >
>
> How did you arrive at this? Which "val" are you assuming?

Just run the numbers, and you get <159 .. 369 446 550|.

> > But OK, yes, you're right ... since Ozan's tuning explicitly
> > has a "pure" 3/2 5th, and since i know that his preferred
> > version of the tuning uses (4/3)^(1/33) as the generator,
> > i guess i should have included prime-factor 3 in the Tonespace.
> > I'll do another one for 159-edo which includes 3, and post it.

Considering how good the 3 of 159 is, this doesn't make a hell of a
lot of sense.

Gene, thank you for posting these. I see that Guiron doesn't serve my
purposes, but 79 and 80 do. However, I wonder why you prefer to keep the
smaller comma in 80 toward the end instead?

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
To: <tuning@yahoogroups.com>
Sent: 22 �ubat 2006 �ar�amba 3:43
Subject: [tuning] Re: Ozan's 159-edo-based tuning

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> > Until then, can you give me the cent values for Guiron[77] Gene?
>
> ! guiron77.scl
> Guiron[77] (118&159 temperament) in 159-et
> 77
> !
> 22.641509
> 30.188679
> 52.830189
> 60.377358
> 83.018868
> 90.566038
> 113.207547
> 120.754717
> 143.396226
> 150.943396
> 173.584906
> 181.132075
> 203.773585
> 211.320755
> 233.962264
> 256.603774
> 264.150943
> 286.792453
> 294.339623
> 316.981132
> 324.528302
> 347.169811
> 354.716981
> 377.358491
> 384.905660
> 407.547170
> 415.094340
> 437.735849
> 445.283019
> 467.924528
> 490.566038
> 498.113208
> 520.754717
> 528.301887
> 550.943396
> 558.490566
> 581.132075
> 588.679245
> 611.320755
> 618.867925
> 641.509434
> 649.056604
> 671.698113
> 679.245283
> 701.886792
> 709.433962
> 732.075472
> 754.716981
> 762.264151
> 784.905660
> 792.452830
> 815.094340
> 822.641509
> 845.283019
> 852.830189
> 875.471698
> 883.018868
> 905.660377
> 913.207547
> 935.849057
> 943.396226
> 966.037736
> 988.679245
> 996.226415
> 1018.867925
> 1026.415094
> 1049.056604
> 1056.603774
> 1079.245283
> 1086.792453
> 1109.433962
> 1116.981132
> 1139.622642
> 1147.169811
> 1169.811321
> 1177.358491
> 1200.000000
>
> Here's how I would do Ozan[80]:
>
> ! ozan80.scl
> Ozan[80] (80&159 temperament) in 159-et
> 80
> !
> 15.094340
> 30.188679
> 45.283019
> 60.377358
> 75.471698
> 90.566038
> 105.660377
> 120.754717
> 135.849057
> 150.943396
> 166.037736
> 181.132075
> 196.226415
> 211.320755
> 226.415094
> 241.509434
> 256.603774
> 271.698113
> 286.792453
> 301.886792
> 316.981132
> 332.075472
> 347.169811
> 362.264151
> 377.358491
> 392.452830
> 407.547170
> 422.641509
> 437.735849
> 452.830189
> 467.924528
> 483.018868
> 498.113208
> 513.207547
> 528.301887
> 543.396226
> 558.490566
> 573.584906
> 588.679245
> 603.773585
> 618.867925
> 633.962264
> 649.056604
> 664.150943
> 679.245283
> 694.339623
> 709.433962
> 724.528302
> 739.622642
> 754.716981
> 769.811321
> 784.905660
> 800.000000
> 815.094340
> 830.188679
> 845.283019
> 860.377358
> 875.471698
> 890.566038
> 905.660377
> 920.754717
> 935.849057
> 950.943396
> 966.037736
> 981.132075
> 996.226415
> 1011.320755
> 1026.415094
> 1041.509434
> 1056.603774
> 1071.698113
> 1086.792453
> 1101.886792
> 1116.981132
> 1132.075472
> 1147.169811
> 1162.264151
> 1177.358491
> 1192.452830
> 1200.000000
>

Dear Ozan, I have the same question that Carl has:

The key is there; where is the modulation, or, where are the modulations?

Regards,
Haresh.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Gene, thank you for posting these. I see that Guiron doesn't serve my
> purposes, but 79 and 80 do. However, I wonder why you prefer to keep the
> smaller comma in 80 toward the end instead?

I made a guess that you'd prefer it there.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Can you provide the details for Octaid 80? 72 didn't work, because the
> super-pythagorean fifth is intolerable to listen to.

Octoid[80] does not put the meantone fifth and the nearly pure
(schismatic) fifth in the same interval class, so I doubt it is what
you want. Octoid[72] does, however. There are no intolerable
super-pythagorean fifths in the six closed chains of fifths you get in
this way. As I said, these are in fact well-temperaments; two
almost-pure fifths followed by a meantone fifth, and repeat. The minor
thirds are all 300 cents exactly, and the triads differ in that the
ones with the meantone fifths have better major thirds, as they
clearly must, given that the minor thirds are fixed in size.

! octoid80.scl
Octoid[80] in 224-et tuning
80
!
16.071429
32.142857
48.214286
64.285714
80.357143
85.714286
101.785714
117.857143
133.928571
150.000000
166.071429
182.142857
198.214286
214.285714
230.357143
235.714286
251.785714
267.857143
283.928571
300.000000
316.071429
332.142857
348.214286
364.285714
380.357143
385.714286
401.785714
417.857143
433.928571
450.000000
466.071429
482.142857
498.214286
514.285714
530.357143
535.714286
551.785714
567.857143
583.928571
600.000000
616.071429
632.142857
648.214286
664.285714
680.357143
685.714286
701.785714
717.857143
733.928571
750.000000
766.071429
782.142857
798.214286
814.285714
830.357143
835.714286
851.785714
867.857143
883.928571
900.000000
916.071429
932.142857
948.214286
964.285714
980.357143
985.714286
1001.785714
1017.857143
1033.928571
1050.000000
1066.071429
1082.142857
1098.214286
1114.285714
1130.357143
1135.714286
1151.785714
1167.857143
1183.928571
1200.000000

> Gene, thank you for posting these. I see that Guiron doesn't
> serve my purposes, but 79 and 80 do.

Why is that?

-Carl

Ozan,

Did you consider using E101 for your tuning? It has the benefit that the
best third is notated as E\.

Manuel

Dear Manuel, I'm afraid it won't do. Perde segah of ~390 cents has to be a
natural E to begin with.

Ozan

----- Original Message -----
From: <coul@hccnet.nl>
To: <tuning@yahoogroups.com>
Sent: 22 �ubat 2006 �ar�amba 19:20
Subject: [tuning] Re: Ozan's 159-edo-based tuning

> Ozan,
>
> Did you consider using E101 for your tuning? It has the benefit that the
> best third is notated as E\.
>
> Manuel
>
>

If you can only have 79 tones on your instrument, what does it matter whether they're from a superset which has 171, 217, 224, 270, 311, or even an infinite number of tones per octave? It seems that only the number of tones on the instrument which has to conform to practical constraints, not the number of notes in the superset -- right? Just curious (the MOS scales in my paper are *not* drawn from any equal-tempered supersets).

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Such is the problem I encountered myself with 7-limit consonances in
> 200-edo. If one chooses to deal with such high numbers, surely better
> options exist within that nominal region. Gene suggested 313 as a universal
> tuning if I'm not mistaken. The problem is, you cannot go much higher than
> 80 or so tones with a Qanun, or for any other practical instrument of Maqam
> Music for that matter.
>
> Cordially,
> Ozan
>
> ----- Original Message -----
> From: "Petr Parízek" <p.parizek@...>
> To: <tuning@yahoogroups.com>
> Sent: 21 Þubat 2006 Salý 22:34
> Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning
>
>
> > Hi Ozan.
> >
> > > As for 200-edo. I am very pleased with it since it has an excellent 1/4
> > > Pyth-comma tempered fifth next to a just fifth. But is it good enough to
> > be
> > > called universal?
> >
> > Well, speaking for myself at least, what more could I wish? The only case
> > where I might blame 200-EDO may be perhaps if I found a 3 cent detuning to
> > be too much (I mean when approximating 7/4). Indeed, I confess, in some
> > situations, I really do.
> >
> > Petr
> >
>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> >
> > Petr, the default fifth is exactly 3/2 in my tuning:
>
> OK, I misstated; but then your tuning is not based on an equal
> division of the fourth into 33 parts.
>
So what is it?

By all means, it IS a 33 equal division of the pure fourth carried to the
79th tone that is completed to the octave whereby the resultant scale is
rotated to yield an exact pure fourth as well as fifth.

----- Original Message -----
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 22 �ubat 2006 �ar�amba 21:30
Subject: [tuning] Re: Ozan's 159-edo-based tuning

> --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
> >
> > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> > >
> > > Petr, the default fifth is exactly 3/2 in my tuning:
> >
> > OK, I misstated; but then your tuning is not based on an equal
> > division of the fourth into 33 parts.
> >
> So what is it?
>
>

> (like I could find 19-EDO, 22, 31, 50, or 53 while trying to find a good
> tuning for common tonal music),

22-equal is absolutely terrible for common tonal music. The comma problems, which I've discussed before, turn into comma disasters. I've been playing in 22-equal for over 10 years and any attempt at common-practice tonality quickly degenerates into a comedy. Blackwood's and other composers' attempts to do this sound to me like a perversion, and give 22 a bad name, given 22-equal's many wonderful non-common-practice resources.

I wholeheartedly agree with you Paul.

----- Original Message -----
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 22 �ubat 2006 �ar�amba 22:14
Subject: [tuning] Re: Ozan's 159-edo-based tuning

>
> > (like I could find 19-EDO, 22, 31, 50, or 53 while trying to find a good
> > tuning for common tonal music),
>
> 22-equal is absolutely terrible for common tonal music. The comma
problems, which I've discussed before, turn into comma disasters. I've been
playing in 22-equal for over 10 years and any attempt at common-practice
tonality quickly degenerates into a comedy. Blackwood's and other composers'
attempts to do this sound to me like a perversion, and give 22 a bad name,
given 22-equal's many wonderful non-common-practice resources.
>
>
>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> I found no faults with SCALA e79 notation for 79 MOS 159-tET beforehand. Or
> do you believe that I take everything for granted before putting them to
> good use?

Absolutely not what I believe, given what I wrote below. You continue to misintepret the spirit of my inquiries, which is to open up mutual understanding.

Also, this post was not primarily directed toward you, but toward Manuel and Gene.

> ----- Original Message -----
> From: "wallyesterpaulrus" <wallyesterpaulrus@...>
> To: <tuning@yahoogroups.com>
> Sent: 22 Þubat 2006 Çarþamba 0:57
> Subject: [tuning] Re: Ozan's 159-edo-based tuning
>
>
> I agree with Gene that the current version of Scala does not produce
> sensible results when using e31 with 103-equal, e79 with 159-equal, etc. Of
> course you may have your own reasons for liking or disliking what it's
> doing, but one should not take the SCALA output for granted. For but one
> thing, the result will be sensitive to the choice of starting note, usually
> taken as C.
>
> -- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> >
> > Dear monz,
> >
> > Thanks very much for the praises. I have uploaded to pictures of my Qanun
> > to:
> >
> > http://www.ozanyarman.com/anonymous/
> >
> > Sorry for the bad quality. My webcam can do no better and the Qanun just
> > won't fit in my flatbed scanner!
> >
> > A score is very easy to prepare with a frequency analyzer program.
> > Unfortunately Solo Explorer by Gailius Raskinis detected polyphony and
> could
> > not transcribe the piece.
> >
> > The unalterated notes used are these according to SCALA e79:
> >
> > A B( C# D Fb F G A B( C# D E( F# G A B( C# D
> >
> > Fb equates to E buselik, not E segah, hence the characteristic of the
> > Buselik Maqam, whose tonic is lower D. However, I finished on lower A
> > Ashiran with a Hijaz flavor.
> >
> > Cordially,
> > Oz.
>

Sorry about that! It's becoming a habit of mine these day. My apologies.

----- Original Message -----
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 22 �ubat 2006 �ar�amba 22:29
Subject: [tuning] Re: Ozan's 159-edo-based tuning

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> I found no faults with SCALA e79 notation for 79 MOS 159-tET beforehand.
Or
> do you believe that I take everything for granted before putting them to
> good use?

Absolutely not what I believe, given what I wrote below. You continue to
misintepret the spirit of my inquiries, which is to open up mutual
understanding.

Also, this post was not primarily directed toward you, but toward Manuel and
Gene.

Certainly not.

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
To: <tuning@yahoogroups.com>
Sent: 22 �ubat 2006 �ar�amba 9:07
Subject: [tuning] Re: Ozan's 159-edo-based tuning

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > Gene, thank you for posting these. I see that Guiron doesn't serve my
> > purposes, but 79 and 80 do. However, I wonder why you prefer to keep the
> > smaller comma in 80 toward the end instead?
>
> I made a guess that you'd prefer it there.
>
>
>

I have given ample explanations why, have I not?

----- Original Message -----
From: "Carl Lumma" <clumma@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 22 �ubat 2006 �ar�amba 12:38
Subject: [tuning] Re: Ozan's 159-edo-based tuning

> > Gene, thank you for posting these. I see that Guiron doesn't
> > serve my purposes, but 79 and 80 do.
>
> Why is that?
>
> -Carl
>

It certainly matters how you place those tones and how much of them you are
able to handle before one is constrained by the instrument in question. I
find 79 MOS 159-tET to be a very good choice with its three sizes of fifths,
adequate approximation of 3,5,7,11,13 limit intervals, and a myriad of
transposition capabilities. Besides, the notation is just right for Maqam
Music.

What other subset would you suggest that appeals to me then?

----- Original Message -----
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 22 �ubat 2006 �ar�amba 21:07
Subject: [tuning] Re: Ozan's 159-edo-based tuning

If you can only have 79 tones on your instrument, what does it matter
whether they're from a superset which has 171, 217, 224, 270, 311, or even
an infinite number of tones per octave? It seems that only the number of
tones on the instrument which has to conform to practical constraints, not
the number of notes in the superset -- right? Just curious (the MOS scales
in my paper are *not* drawn from any equal-tempered supersets).

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> I have given ample explanations why, have I not?

Evidently not. Guiron provides a great multitude of nearly pure
fifths, but does not do very well with 112/75, which tempers to the
meantone fifth; this has a complexity of 44 generators. Is that why not?

I can easily enough find temperaments in which the complexity of the
fifth and meantone fifth are both low; in fact I have.

Now how about a 13-limit version, since Gene gave the 13-limit TM
basis for the 2D temperament that gives you this MOS scale? 13-limit
would be a step closer to the much higher-prime-limit ratios Ozan
said he was interested in approximating with this scale (a while
back).

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
>
> --- In tuning@yahoogroups.com, "monz" <monz@> wrote:
>
> > But OK, yes, you're right ... since Ozan's tuning explicitly
> > has a "pure" 3/2 5th, and since i know that his preferred
> > version of the tuning uses (4/3)^(1/33) as the generator,
> > i guess i should have included prime-factor 3 in the Tonespace.
> > I'll do another one for 159-edo which includes 3, and post it.
>
>
> Lo and behold ...
>
>
> Ozan Yarman - 79-MOS 159-edo, in (2,)3,5,7,11-space
> ===================================================
>
>
> TM-basis unison-vectors:
>
> . 2,3,5,7,11-monzo ..... ratio .........~cents
> -------------------------------------------------
>
> .. [-3 2 -1 2 -1 > ... 441 / 440 .... 3.930158439
> .. [-7 -1 1 1 1 > .... 385 / 384 .... 4.502561833
> .. [5 -7 -1 3 0 > .. 10976 / 10935 .. 6.478999485
> .. [-2 -2 4 1 -2 > .. 4375 / 4356 ... 7.534875468
>
>
>
> The 79-MOS 159-edo tuning in 2,3,5,7,11-space:
>
> degree .. ~cents ... 2,3,5,7,11-monzo ..... ratio
> ----------------------------------------------------
>
> ... 0 ..... 0.000 .. [ 0 0, 0 0 0 > ....... 1 / 1
> ... 1 .... 15.094 .. [ 4 0, -2 -1 1 > ... 176 / 175
> ... 2 .... 30.189 .. [ 3 0, -1 1 -1 > .... 56 / 55
> ... 3 .... 45.283 .. [ 0 -1, -2 1 1 > .... 77 / 75
> ... 4 .... 60.377 .. [ 2 -3, 0 1 0 > ..... 28 / 27
> ... 5 .... 75.472 .. [ 6 -3, -2 0 1 > ... 704 / 675
> ... 6 .... 90.566 .. [ 0 4, 0 -1 -1 > .... 81 / 77
> ... 7 ... 105.660 .. [ -3 3, -1 -1 1 .... 297 / 280
> ... 8 ... 120.755 .. [ -1 1, 1 -1 0 > .... 15 / 14
> ... 9 ... 135.849 .. [ 3 1, -1 -2 1 > ... 264 / 245
> .. 10 ... 150.943 .. [ 2 1, 0 0 -1 > ..... 12 / 11
> .. 11 ... 166.038 .. [ -1 0, -1 0 1 > .... 11 / 10
> .. 12 ... 181.132 .. [ 1 -2, 1 0 0 > ..... 10 / 9
> .. 13 ... 196.226 .. [ 2 0, -2 1 0 > ..... 28 / 25
> .. 14 ... 211.321 .. [ 4 -2, 0 1 -1 > ... 112 / 99
> .. 15 ... 226.415 .. [ 1 -3, -1 1 1 > ... 154 / 135
> .. 16 ... 241.509 .. [ -2 2, 2 -2 0 > ... 225 / 196
> .. 17 ... 256.604 .. [ -1 4, -1 -1 0 ..... 81 / 70
> .. 18 ... 271.698 .. [ 1 2, 1 -1 -1 > .... 90 / 77
> .. 19 ... 286.792 .. [ -2 1, 0 -1 1 > .... 33 / 28
> .. 20 ... 301.887 .. [ -3 1, 1 1 -1 > ... 105 / 88
> .. 21 ... 316.981 .. [ 1 1, -1 0 0 > ...... 6 / 5
> .. 22 ... 332.075 .. [ 3 -1, 1 0 -1 > .... 40 / 33
> .. 23 ... 347.170 .. [ 0 -2, 0 0 1 > ..... 11 / 9
> .. 24 ... 362.264 .. [ -1 -2, 1 2 -1 .... 245 / 198
> .. 25 ... 377.358 .. [ 3 -2, -1 1 0 > .... 56 / 45
> .. 26 ... 392.453 .. [ 5 -4, 1 1 -1 > .. 1120 / 891
> .. 27 ... 407.547 .. [ -3 2, 1 -2 1 > ... 495 / 392
> .. 28 ... 422.642 .. [ -4 2, 2 0 -1 > ... 225 / 176
> .. 29 ... 437.736 .. [ 0 2, 0 -1 0 > ...... 9 / 7
> .. 30 ... 452.830 .. [ 2 0, 2 -1 -1 > ... 100 / 77
> .. 31 ... 467.925 .. [ -4 1, 0 1 0 > ..... 21 / 16
> .. 32 ... 483.019 .. [ 0 1, -2 0 1 > ..... 33 / 25
> .. 33 ... 498.113 .. [ 2 -1, 0 0 0 > ...... 4 / 3
> .. 34 ... 513.208 .. [ 6 -1, -2 -1 1 .... 704 / 525
> .. 35 ... 528.302 .. [ -2 -2, 0 2 0 > .... 49 / 36
> .. 36 ... 543.396 .. [ 2 -2, -2 1 1 > ... 308 / 225
> .. 37 ... 558.491 .. [ -1 3, 1 -2 0 > ... 135 / 98
> .. 38 ... 573.585 .. [ 0 5, -2 -1 0 > ... 243 / 175
> .. 39 ... 588.679 .. [ -5 2, 1 0 0 > ..... 45 / 32
> .. 40 ... 603.774 .. [ -1 2, -1 -1 1 ..... 99 / 70
> .. 41 ... 618.868 .. [ 1 0, 1 -1 0 > ..... 10 / 7
> .. 42 ... 633.962 .. [ 2 2, -2 0 0 > ..... 36 / 25
> .. 43 ... 649.057 .. [ -3 -1, 1 1 0 > .... 35 / 24
> .. 44 ... 664.151 .. [ 1 -1, -1 0 1 > .... 22 / 15
> .. 45 ... 679.245 .. [ 3 -3, 1 0 0 > ..... 40 / 27
> .. 46 ... 701.887 .. [ -1 1, 0 0 0 > ...... 3 / 2
> .. 47 ... 716.981 .. [ 3 1, -2 -1 1 > ... 264 / 175
> .. 48 ... 732.075 .. [ 5 -1, 0 -1 0 > .... 32 / 21
> .. 49 ... 747.170 .. [ -1 0, -2 1 1 > .... 77 / 50
> .. 50 ... 762.264 .. [ 1 -2, 0 1 0 > ..... 14 / 9
> .. 51 ... 777.358 .. [ 5 -2, -2 0 1 > ... 352 / 225
> .. 52 ... 792.453 .. [ 4 -2, -1 2 -1 .... 784 / 495
> .. 53 ... 807.547 .. [ -4 4, -1 -1 1 .... 891 / 560
> .. 54 ... 822.642 .. [ -2 2, 1 -1 0 > .... 45 / 28
> .. 55 ... 837.736 .. [ 2 2, -1 -2 1 > ... 396 / 245
> .. 56 ... 852.830 .. [ 1 2, 0 0 -1 > ..... 18 / 11
> .. 57 ... 867.925 .. [ -2 1, -1 0 1 > .... 33 / 20
> .. 58 ... 883.019 .. [ 0 -1, 1 0 0 > ...... 5 / 3
> .. 59 ... 898.113 .. [ 4 -1, -1 -1 1 .... 176 / 105
> .. 60 ... 913.208 .. [ 3 -1, 0 1 -1 > .... 56 / 33
> .. 61 ... 928.302 .. [ 0 -2, -1 1 1 > .... 77 / 45
> .. 62 ... 943.396 .. [ 2 -4, 1 1 0 > .... 140 / 81
> .. 63 ... 958.491 .. [ -2 5, -1 -1 0 .... 243 / 140
> .. 64 ... 973.585 .. [ 0 3, 1 -1 -1 > ... 135 / 77
> .. 65 ... 988.679 .. [ -3 2, 0 -1 1 > .... 99 / 56
> .. 66 .. 1003.774 .. [ -1 0, 2 -1 0 > .... 25 / 14
> .. 67 .. 1018.868 .. [ 0 2, -1 0 0 > ...... 9 / 5
> .. 68 .. 1033.962 .. [ 2 0, 1 0 -1 > ..... 20 / 11
> .. 69 .. 1049.057 .. [ -1 -1, 0 0 1 > .... 11 / 6
> .. 70 .. 1064.151 .. [ 1 -3, 2 0 0 > ..... 50 / 27
> .. 71 .. 1079.245 .. [ 2 -1, -1 1 0 > .... 28 / 15
> .. 72 .. 1094.340 .. [ 4 -3, 1 1 -1 > ... 560 / 297
> .. 73 .. 1109.434 .. [ 1 -4, 0 1 1 > .... 154 / 81
> .. 74 .. 1124.528 .. [ -5 3, 2 0 -1 > ... 675 / 352
> .. 75 .. 1139.623 .. [ -1 3, 0 -1 0 > .... 27 / 14
> .. 76 .. 1154.717 .. [ 1 1, 2 -1 -1 > ... 150 / 77
> .. 77 .. 1169.811 .. [ 5 1, 0 -2 0 > ..... 96 / 49
> .. 78 .. 1184.906 .. [ -3 0, 2 1 -1 > ... 175 / 88
> (. 79 .. 1200.000 .. [ 1 0, 0 0 0> ........ 2 / 1)
>
>
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@...> wrote:
>
> Now how about a 13-limit version, since Gene gave the
> 13-limit TM basis for the 2D temperament that gives you
> this MOS scale? 13-limit would be a step closer to the
> much higher-prime-limit ratios Ozan said he was interested
> in approximating with this scale (a while back).

Sure -- just point me to the numbers, and i'll whip one up.
(did Gene post it here, or on tuning-math?)

So this will only be a 2D Lattice? I hope so, because
2D temperaments are my favorite viewing in Tonescape,
since we have the "Closed Curved" geometry which warps
it into a helix when the 3rd dimension is used.

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

> > I have given ample explanations why, have I not?

You apparently desire three kinds of fifths as well as
good higher-limit approximations.

What, in a perfect world, would these three sizes of
fifth be?

One of the fifths in your 79-tone scale seems to be over
your stated maximum tolerable size of 708 cents.

And you haven't said which higher-limit intervals are
absolutely essential, and how many of them (in how
many modes they) should appear.

-Carl

> > > I have given ample explanations why, have I not?
>
> You apparently desire three kinds of fifths as well as
> good higher-limit approximations.
>
> What, in a perfect world, would these three sizes of
> fifth be?

696, 702, 708 cents or so.

>
> One of the fifths in your 79-tone scale seems to be over
> your stated maximum tolerable size of 708 cents.
>

In an ideal world. Still, it's not so horrible.

> And you haven't said which higher-limit intervals are
> absolutely essential, and how many of them (in how
> many modes they) should appear.
>

One may need to go as high as 17 at minumum.

> -Carl
>
>

Oz.

> > What, in a perfect world, would these three sizes of
> > fifth be?
>
> 696, 702, 708 cents or so.

Alright, Gene, what have you got for that in 80 tones
or less? Guiron doesn't do it.

-Carl

I would like very much to suggest something else that would offend
you less, so I'm taking my time in asking you many pertinent
questions first. With the right information, the tuning-math folks
can run an efficient computer search for alternative systems that
could save months of human labor time.

I'm still quite unclear as to why a decent fifth, similar to that of
79-equal, wouldn't make more sense as an interval by which to
generate the spine or circle of fifths, rather than alternating a
nearly pure fifth with a "very very offensive one". The alternation
does not in any way allow the system to function more flexibly, only
less flexibly, unless I'm missing something. Isn't a fifth the most
common interval by which a scale is modulated? If you have a
mode/scale/key with some pure fifths in it, and you modulate by a
fifth, why should most of the formerly pure fifths now become "very
very offensive"? In my very limited understanding of your system and
its motivations, this confuses me, since I thought modulation was of
major importance to you.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> They are not less offensive, they are very very offensive, but that
is the
> price I have to pay while retaining all the benefits of 79 tones,
unless of
> course you can suggest something else as a substitute.
>
> ----- Original Message -----
> From: "wallyesterpaulrus" <wallyesterpaulrus@...>
> To: <tuning@yahoogroups.com>
> Sent: 22 Þubat 2006 Çarþamba 2:47
> Subject: [tuning] Re: Ozan's 159-edo-based tuning
>
>
> Ozan, don't take this as an attack or anything, I'm just trying to
tease out
> your thinking. Why are these 694.2-cent fifths less offensive than
those of
> 19-equal?
>

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
>
> Hi Paul,
>
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@> wrote:
>
> > > [monz]
> > > TM-basis for 159-edo in 2,5,7,11-space:
> > >
> > >
> > > .. 2,5,7,11-monzo ...... ratio ........ ~cents
> > > ---------------------------------------------------
> > >
> > > .. [-12 -2 1 4 > .. 102487 / 102400 ... 1.470248198
> > > .. [8 -8 5 -1 > .. 4302592 / 4296875 .. 2.301879062
> > > .. [-5 3 3 -3 > .... 42875 / 42592 ... 11.46503391
> > >
> >
> > How did you arrive at this?
>
>
> I didn't have to do anything myself, Tonescape did it.

So you're selling us a product which has a mind of its own?

> > Which "val" are you assuming?
>
> The 2,5,7,11-val is < 159 369 446 550 ] .

Did you consider any other possibilities? And it's been quite a few
days since I asked why you (initially) omitted prime 3 -- if you're
never going to answer me, oh well, I'll drop that question.

> > And as usual, I think it would make a lot more sense to
> > reduce the pitches (thus making the choice of kernel basis
> > irrelevant) instead of reducing the kernel basis and then
> > constructing an FPB.
>
>
>
> Ah yes, i could tell Tonescape to construct a 79-tone
> periodicity-block first, *then* use 159-edo for the tuning.

Not what I meant, but worth considering.

> Why do you say that reducing the number of pitches
> makes "the choice of kernel basis irrelevant"?

No, I meant Tenney-reducing the pitches (or better yet, Kees-reducing
them), rather than Tenney-reducing the kernel basis.

> The choice of kernel basis still determines how
> compact the periodicity-block is.

Not at all true, if you reduce the pitches. Then the choice of kernel
basis becomes irrelevant -- any valid kernel basis yields the same
final result. Which, BTW, is more compact than any Fokker periodicity
block arising from any valid kernel basis.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@> wrote:
>
> > > .. [-12 -2 1 4 > .. 102487 / 102400 ... 1.470248198
> > > .. [8 -8 5 -1 > .. 4302592 / 4296875 .. 2.301879062
> > > .. [-5 3 3 -3 > .... 42875 / 42592 ... 11.46503391
> > >
> >
> > How did you arrive at this? Which "val" are you assuming?
>
> Just run the numbers, and you get <159 .. 369 446 550|.

What do you mean, "just run the numbers"?

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> It certainly matters how you place those tones

No doubt!

> and how much of them you are
> able to handle before one is constrained by the instrument in
>question.

I don't think you understood my question, which was about some
constraint that appears to lie well beyond the instrument itself.
Would you re-read it then?

> I
> find 79 MOS 159-tET to be a very good choice with its three sizes
of fifths,
> adequate approximation of 3,5,7,11,13 limit intervals, and a myriad
of
> transposition capabilities. Besides, the notation is just right for
Maqam
> Music.
>
> What other subset would you suggest that appeals to me then?

In the context of this particular discussion/thread/post, I would
simply ask what you think of a 79-tone MOS that does *not* arise as a
subset of any EDO. If there aren't more than 79 tones per octave on
the instrument, what could it matter if the superset from which the
tones are chosen form 159-equal, or any equal tuning at all for that
matter? 'Cause you'll never have an opportunity to use more than 79
of them anyway, so you'll never become aware of the closure, or lack
thereof, of the "universe set" of 159 or >159 pitches. Gene has
determined a 13-limit kernel basis (IIRC) for the 2D temperament
which yields your 79-note MOS (or an 80-note MOS with one extra
note). If this turns out to correspond to your desires, why not use
the TOP or Kees tuning for this temperament, rather than drawing the
notes from an EDO?

> ----- Original Message -----
> From: "wallyesterpaulrus" <wallyesterpaulrus@...>
> To: <tuning@yahoogroups.com>
> Sent: 22 Þubat 2006 Çarþamba 21:07
> Subject: [tuning] Re: Ozan's 159-edo-based tuning
>
>
> If you can only have 79 tones on your instrument, what does it
matter
> whether they're from a superset which has 171, 217, 224, 270, 311,
or even
> an infinite number of tones per octave? It seems that only the
number of
> tones on the instrument which has to conform to practical
constraints, not
> the number of notes in the superset -- right? Just curious (the MOS
scales
> in my paper are *not* drawn from any equal-tempered supersets).
>

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

> > What, in a perfect world, would these three sizes of
> > fifth be?
>
> 696, 702, 708 cents or so.

224-et seems like a good choice then.

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

> > Just run the numbers, and you get <159 .. 369 446 550|.
>
> What do you mean, "just run the numbers"?

Solve the linear equations you can derive from the commas, or do what
I did and take wedge products.

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@> wrote:
> >
> > Now how about a 13-limit version, since Gene gave the
> > 13-limit TM basis for the 2D temperament that gives you
> > this MOS scale? 13-limit would be a step closer to the
> > much higher-prime-limit ratios Ozan said he was interested
> > in approximating with this scale (a while back).
>
>
>
> Sure -- just point me to the numbers, and i'll whip one up.
> (did Gene post it here, or on tuning-math?)

Here, and you replied that this was just was you were looking for (so
I know you saw the numbers already), but didn't proceed any further.

> So this will only be a 2D Lattice?

No, but it's a 2D temperament, while ETs are 1D temperaments, in
terms of the number of independent generators you need to generate
it. The generators aren't what your lattices are based on, though.

> I hope so, because
> 2D temperaments are my favorite viewing in Tonescape,
> since we have the "Closed Curved" geometry which warps
> it into a helix when the 3rd dimension is used.

I'm glad you adopted this suggestion of mine for displaying meantone
tunings, and this all makes sense for most 2D temperaments of the 5-
limit. But any of these 2D temperaments you're referring to derived
from the 7-limit (as more than half the 2D temperaments in my "Middle
Path" paper are) or any higher limit?

Hi Paul,

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@...> wrote:
>
> --- In tuning@yahoogroups.com, "monz" <monz@> wrote:
>
> > > > TM-basis for 159-edo in 2,5,7,11-space:
> > > >
> > > >
> > > > .. 2,5,7,11-monzo ...... ratio ........ ~cents
> > > > ---------------------------------------------------
> > > >
> > > > .. [-12 -2 1 4 > .. 102487 / 102400 ... 1.470248198
> > > > .. [8 -8 5 -1 > .. 4302592 / 4296875 .. 2.301879062
> > > > .. [-5 3 3 -3 > .... 42875 / 42592 ... 11.46503391
> > > >
> > >
> > > How did you arrive at this?
> >
> >
> > I didn't have to do anything myself, Tonescape did it.
>
> So you're selling us a product which has a mind of its own?

Almost! ;-)

Seriously -- the whole idea behind Tonescape's tuning
capabilities is that the user doesn't have to fuss with
all the mathematical stuff (unless he/she wants to).
The computer handles all of that. If you have the
"TM-basis" box checked, Tonescape does all the calculating
for you.

If you want don't want TM-basis and would prefer to
pick your own unison-vectors, you simply uncheck the
box, and Tonescape provides a big list of possibilities.

> > > Which "val" are you assuming?
> >
> > The 2,5,7,11-val is < 159 369 446 550 ] .
>
> Did you consider any other possibilities?

As i said, Tonescape did it automatically. It normally
doesn't say anything about a val unless the tuning
you're trying to develop has torsion.

We'll eventually add in features that let you pick
vals, similar to the way you can choose your own
unison-vector basis. I know these are essentially
the same process ... Tonescape just doesn't offer
val notation yet.

> And it's been quite a few days since I asked why
> you (initially) omitted prime 3 -- if you're
> never going to answer me, oh well, I'll drop that question.

I thought you already had the answer to that: in the
post which started this thread, Ozan said that his
tuning gives good approximations to 5,7, and 11, and
he didn't mention 3 except for the fact that 4/3 is
the interval to be divided. To which i can only respond:
duh! My bad.

> > > And as usual, I think it would make a lot more sense to
> > > reduce the pitches (thus making the choice of kernel basis
> > > irrelevant) instead of reducing the kernel basis and then
> > > constructing an FPB.
> >
> >
> >
> > Ah yes, i could tell Tonescape to construct a 79-tone
> > periodicity-block first, *then* use 159-edo for the tuning.
>
> Not what I meant, but worth considering.

Then can you please elaborate on what you did mean?
It seems i'm not understanding you well here.

> > Why do you say that reducing the number of pitches
> > makes "the choice of kernel basis irrelevant"?
>
> No, I meant Tenney-reducing the pitches (or better
> yet, Kees-reducing them), rather than Tenney-reducing
> the kernel basis.
>
> > The choice of kernel basis still determines how
> > compact the periodicity-block is.
>
> Not at all true, if you reduce the pitches. Then the
> choice of kernel basis becomes irrelevant -- any valid
> kernel basis yields the same final result. Which, BTW,
> is more compact than any Fokker periodicity block
> arising from any valid kernel basis.

OK, now i have to confess my ignorance. I've spent a
lot of time in the past year working on Tonescape and
only skimming past many posts on these lists. What does
it mean to Tenney- (or Kees-) reduce the pitches?

It seems that this can apply directly to how Tonescape
works, so i definitely want to learn more.

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

Hi Paul,

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@...> wrote:
>
> --- In tuning@yahoogroups.com, "monz" <monz@> wrote:
> >
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> > <wallyesterpaulrus@> wrote:
> > >
> > > Now how about a 13-limit version, since Gene gave the
> > > 13-limit TM basis for the 2D temperament that gives you
> > > this MOS scale? 13-limit would be a step closer to the
> > > much higher-prime-limit ratios Ozan said he was interested
> > > in approximating with this scale (a while back).
> >
> >
> >
> > Sure -- just point me to the numbers, and i'll whip one up.
> > (did Gene post it here, or on tuning-math?)
>
> Here, and you replied that this was just was you were
> looking for (so I know you saw the numbers already), but
> didn't proceed any further.

Hmm ... OK, i'll have to search then later, when i have time.

Are you talking about this? ...

/tuning/topicId_64170.html#64412

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> > > Correspondng linear temperaments do not seem
> > > distinguished. In the 7-limit we have <<33 54 95 9 58 69||,
> > > with commas 10976/10935 and the 5-limit comma |3 -18 11>
>
> The mapping is such that 33 generators gives a fourth,
> 54 generators a minor sixth, and 95 generators an
> approximate 16/7 interval, which defines everything else
> in the 7-limit. It sends the small (six and a half cent)
> interval, or comma, 10976/10935 to the unison. That is,
> such an interval is "tempered out". Also tempered out is
> 2^3 5^11/3^18, of size 14.26 cents.
>
> The "ozan" temperament, 80&159, gets more interesting
> in higher prime limits. In the 11-limit, we get 4000/3993
> and 3025/3024 as commas; in the 13-limit 325/324 and
> 364/363; and so forth.

> > So this will only be a 2D Lattice?
>
> No, but it's a 2D temperament, while ETs are 1D temperaments,
> in terms of the number of independent generators you need
> to generate it. The generators aren't what your lattices
> are based on, though.

Just to clarify: i used the "usual" prime-factors as
generators in the Lattice of Ozan's tuning which i posted.
But Tonescape can use anything you'd like as generators.

> > I hope so, because
> > 2D temperaments are my favorite viewing in Tonescape,
> > since we have the "Closed Curved" geometry which warps
> > it into a helix when the 3rd dimension is used.
>
> I'm glad you adopted this suggestion of mine for displaying
> meantone tunings, and this all makes sense for most 2D
> temperaments of the 5-limit. But any of these 2D temperaments
> you're referring to derived from the 7-limit (as more than
> half the 2D temperaments in my "Middle Path" paper are) or
> any higher limit?

If you give me details of one example (cents values of
generators and the ratios they're supposed to represent),
i'll make a Tonescape file of it and post the pretty pictures.

Tonescape will do "Geometry|Closed Curved" for any temperament.
However, when the un-closed Lattice has more than 2 dimensions,
the closed version doesn't convey much meaningful visual
information, IMO -- it just looks like a cluttered mess,
altho you can still see the symmetry in the form.

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

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@> wrote:
>
> > > Just run the numbers, and you get <159 .. 369 446 550|.
> >
> > What do you mean, "just run the numbers"?
>
> Solve the linear equations you can derive from the commas, or do what
> I did and take wedge products.

Gene, you're obviously not reading very carefully. Monz gave the
commas. I asked where he got them. He said from the val. I asked where
he got that. You're answering for him, "from the commas". Geez! Can't
you see that you're just leading me around a logical circle?

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
>
> Hi Paul,
>
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@> wrote:
> >
> > --- In tuning@yahoogroups.com, "monz" <monz@> wrote:
> >
> > > > > TM-basis for 159-edo in 2,5,7,11-space:
> > > > >
> > > > >
> > > > > .. 2,5,7,11-monzo ...... ratio ........ ~cents
> > > > > ---------------------------------------------------
> > > > >
> > > > > .. [-12 -2 1 4 > .. 102487 / 102400 ... 1.470248198
> > > > > .. [8 -8 5 -1 > .. 4302592 / 4296875 .. 2.301879062
> > > > > .. [-5 3 3 -3 > .... 42875 / 42592 ... 11.46503391
> > > > >
> > > >
> > > > How did you arrive at this?
> > >
> > >
> > > I didn't have to do anything myself, Tonescape did it.
> >
> > So you're selling us a product which has a mind of its own?
>
>
>
> Almost! ;-)
>
> Seriously -- the whole idea behind Tonescape's tuning
> capabilities is that the user doesn't have to fuss with
> all the mathematical stuff (unless he/she wants to).
> The computer handles all of that. If you have the
> "TM-basis" box checked, Tonescape does all the calculating
> for you.

But why can't you tell me how? Am I just supposed to accept
this "black box"?

> If you want don't want TM-basis and would prefer to
> pick your own unison-vectors, you simply uncheck the
> box, and Tonescape provides a big list of possibilities.

Oh? But what about the "val"?

> > > > Which "val" are you assuming?
> > >
> > > The 2,5,7,11-val is < 159 369 446 550 ] .
> >
> > Did you consider any other possibilities?
>
>
> As i said, Tonescape did it automatically. It normally
> doesn't say anything about a val unless the tuning
> you're trying to develop has torsion.
>
> We'll eventually add in features that let you pick
> vals, similar to the way you can choose your own
> unison-vector basis.

Aha. But why the current "black box", and what is it doing?

> > > > And as usual, I think it would make a lot more sense to
> > > > reduce the pitches (thus making the choice of kernel basis
> > > > irrelevant) instead of reducing the kernel basis and then
> > > > constructing an FPB.
> > >
> > >
> > >
> > > Ah yes, i could tell Tonescape to construct a 79-tone
> > > periodicity-block first, *then* use 159-edo for the tuning.
> >
> > Not what I meant, but worth considering.
>
> Then can you please elaborate on what you did mean?

Do the same kind of reduction you did to the kernel basis, only do it
to the pitch ratios instead.

> It seems i'm not understanding you well here.

I tried to explain below.

> > > Why do you say that reducing the number of pitches
> > > makes "the choice of kernel basis irrelevant"?
> >
> > No, I meant Tenney-reducing the pitches (or better
> > yet, Kees-reducing them), rather than Tenney-reducing
> > the kernel basis.
> >
> > > The choice of kernel basis still determines how
> > > compact the periodicity-block is.
> >
> > Not at all true, if you reduce the pitches. Then the
> > choice of kernel basis becomes irrelevant -- any valid
> > kernel basis yields the same final result. Which, BTW,
> > is more compact than any Fokker periodicity block
> > arising from any valid kernel basis.
>
>
> OK, now i have to confess my ignorance. I've spent a
> lot of time in the past year working on Tonescape and
> only skimming past many posts on these lists. What does
> it mean to Tenney- (or Kees-) reduce the pitches?

One way of saying it is that it means to find the simplest ratio for
each pitch that you can obtain by starting with the pitch's ratio in
the Fokker periodicity block, periodicity strip, or periodicity sheet
(whichever vanishing commas you use to define that) and transposing
it by any number/combination of vanishing commas. The result will be
the same no matter which Fokker periodicity block, strip, or sheet
you start with. Gene does this a whole lot on the tuning-math list.

> It seems that this can apply directly to how Tonescape
> works,

You better believe it!

> so i definitely want to learn more.

I suggest posting your questions on this to the tuning-math list.

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
>
> Hi Paul,
>
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@> wrote:
> >
> > --- In tuning@yahoogroups.com, "monz" <monz@> wrote:
> > >
> > > --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> > > <wallyesterpaulrus@> wrote:
> > > >
> > > > Now how about a 13-limit version, since Gene gave the
> > > > 13-limit TM basis for the 2D temperament that gives you
> > > > this MOS scale? 13-limit would be a step closer to the
> > > > much higher-prime-limit ratios Ozan said he was interested
> > > > in approximating with this scale (a while back).
> > >
> > >
> > >
> > > Sure -- just point me to the numbers, and i'll whip one up.
> > > (did Gene post it here, or on tuning-math?)
> >
> > Here, and you replied that this was just was you were
> > looking for (so I know you saw the numbers already), but
> > didn't proceed any further.
>
>
> Hmm ... OK, i'll have to search then later, when i have time.
>
> Are you talking about this? ...
>
>
> /tuning/topicId_64170.html#64412

Yes, at the bottom.

> --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@>
> wrote:
> >
> > > > Correspondng linear temperaments do not seem
> > > > distinguished. In the 7-limit we have <<33 54 95 9 58 69||,
> > > > with commas 10976/10935 and the 5-limit comma |3 -18 11>
> >
> > The mapping is such that 33 generators gives a fourth,
> > 54 generators a minor sixth, and 95 generators an
> > approximate 16/7 interval, which defines everything else
> > in the 7-limit. It sends the small (six and a half cent)
> > interval, or comma, 10976/10935 to the unison. That is,
> > such an interval is "tempered out". Also tempered out is
> > 2^3 5^11/3^18, of size 14.26 cents.
> >
> > The "ozan" temperament, 80&159, gets more interesting
> > in higher prime limits. In the 11-limit, we get 4000/3993
> > and 3025/3024 as commas; in the 13-limit 325/324 and
> > 364/363; and so forth.
>
>
>
> > > So this will only be a 2D Lattice?
> >
> > No, but it's a 2D temperament, while ETs are 1D temperaments,
> > in terms of the number of independent generators you need
> > to generate it. The generators aren't what your lattices
> > are based on, though.
>
>
>
> Just to clarify: i used the "usual" prime-factors as
> generators in the Lattice of Ozan's tuning which i posted.
> But Tonescape can use anything you'd like as generators.

Don't confuse "generators" with "rungs". Ozan's tuning is 2D in terms
of generators but clearly you needed more than two directions of
rungs to make an 11-limit harmonic lattice of it.

> > > I hope so, because
> > > 2D temperaments are my favorite viewing in Tonescape,
> > > since we have the "Closed Curved" geometry which warps
> > > it into a helix when the 3rd dimension is used.
> >
> > I'm glad you adopted this suggestion of mine for displaying
> > meantone tunings, and this all makes sense for most 2D
> > temperaments of the 5-limit. But any of these 2D temperaments
> > you're referring to derived from the 7-limit (as more than
> > half the 2D temperaments in my "Middle Path" paper are) or
> > any higher limit?
>
>
>
> If you give me details of one example (cents values of
> generators

Why are cents values relevant when dealing with temperament in the
abstract? Surely your meantone helix doesn't depend on any cents
values . . . (?)

> and the ratios they're supposed to represent),
> i'll make a Tonescape file of it and post the pretty pictures.

How about 7-limit meantone, as in my paper? The generators can be
said to represent 2:1 and 3:2. Since you asked, in the TOP tuning
(just one of many possibilities), these generators are 1201.7 and
697.57 cents -- exactly the same as they are in the TOP tuning for 5-
limit meantone.

But generators of 2D temperaments are often ambiguous between
different ratio-interpretations, but this never mattered to you
before, so I don't know why you now need ratio-interpretations for
the generators all of a sudden. Can't you simply take the
specification of the original JI lattice, plus the set of vanishing
commas, as input? For example, to get meantone, I'd start with the 5-
limit lattice, and temper out 81:80. Does this work for you?

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > > What, in a perfect world, would these three sizes of
> > > fifth be?
> >
> > 696, 702, 708 cents or so.
>
> Alright, Gene, what have you got for that in 80 tones
> or less? Guiron doesn't do it.

The 80-note MOS 12&224[80] does. It has 76 sensibly JI fifths, 72 very
nice 696.4 meantone fifths, and 64 sharp fifths of size 707.1 cents.
Thus the fifth situation is very well in hand; I hope Ozan take a look
at it.

Hi Paul (and Gene)

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@...> wrote:
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@>
> wrote:
> >
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> > <wallyesterpaulrus@> wrote:
> >
> > > > Just run the numbers, and you get <159 .. 369 446 550|.
> > >
> > > What do you mean, "just run the numbers"?
> >
> > Solve the linear equations you can derive from the commas,
> > or do what I did and take wedge products.
>
> Gene, you're obviously not reading very carefully. Monz gave
> the commas. I asked where he got them. He said from the val.
> I asked where he got that. You're answering for him, "from
> the commas". Geez! Can't you see that you're just leading
> me around a logical circle?

I already explained that Tonescape used the TM-basis
for 159-edo in 2,5,7,11-space. Doing TM-reduction on
the kernel for this tuning yields the val Gene posted
above, and the unison-vectors ("commas") which i posted
earlier.

It would be tough for me to provide you with a more
detailed explanation than that ... Chris and i figured
out how to do it based on Gene's posts here and on
tuning-math, and after Chris coded it into Tonescape,
i moved on to other important things, like creating
the so-necessary Help menu files (which i'm working
on right now) to teach people how to use the damn thing.
:)

I do recall that it's a process which uses Hermite
reduction first, and then something else after that
... i think was "LL reduction" ...?

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

> > > > What, in a perfect world, would these three sizes of
> > > > fifth be?
> > >
> > > 696, 702, 708 cents or so.
> >
> > Alright, Gene, what have you got for that in 80 tones
> > or less? Guiron doesn't do it.
>
> The 80-note MOS 12&224[80] does. It has 76 sensibly JI fifths,
> 72 very nice 696.4 meantone fifths, and 64 sharp fifths of size
> 707.1 cents. Thus the fifth situation is very well in hand; I
> hope Ozan take a look at it.

That's great. Have you posted a Scala file?

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > The 80-note MOS 12&224[80] does. It has 76 sensibly JI fifths,
> > 72 very nice 696.4 meantone fifths, and 64 sharp fifths of size
> > 707.1 cents. Thus the fifth situation is very well in hand; I
> > hope Ozan take a look at it.
>
> That's great. Have you posted a Scala file?

It's toof1.scl. I wonder what could be done with it musically.

Hi Paul,

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@...> wrote:
>
> --- In tuning@yahoogroups.com, "monz" <monz@> wrote:
> >
> > > > So this will only be a 2D Lattice?
> > >
> > > No, but it's a 2D temperament, while ETs are 1D temperaments,
> > > in terms of the number of independent generators you need
> > > to generate it. The generators aren't what your lattices
> > > are based on, though.
> >
> >
> > Just to clarify: i used the "usual" prime-factors as
> > generators in the Lattice of Ozan's tuning which i posted.
> > But Tonescape can use anything you'd like as generators.
>
> Don't confuse "generators" with "rungs".

Yikes! ... what the heck is a "rung" in tuning theory?

I presume there's a new Encyclopedia page waiting to
be created about this ...?

> Ozan's tuning is 2D in terms of generators

To clarify: "2D in terms of generators" means:

1st dimension = the ~15-cent step which makes almost
the whole tuning; and

2nd dimension = the ~22 cent step which "completes
the octave" as Ozan puts it.

Yes?

If this is not correct, then please elaborate on what
"2D in terms of generators" refers to.

> but clearly you needed more than two directions
> of rungs to make an 11-limit harmonic lattice of it.

Please elaborate on this a bit. I have no idea what
you mean.

> > > > I hope so, because
> > > > 2D temperaments are my favorite viewing in Tonescape,
> > > > since we have the "Closed Curved" geometry which warps
> > > > it into a helix when the 3rd dimension is used.
> > >
> > > I'm glad you adopted this suggestion of mine for displaying
> > > meantone tunings, and this all makes sense for most 2D
> > > temperaments of the 5-limit. But any of these 2D temperaments
> > > you're referring to derived from the 7-limit (as more than
> > > half the 2D temperaments in my "Middle Path" paper are) or
> > > any higher limit?
> >
> >
> > If you give me details of one example (cents values of
> > generators
>
> Why are cents values relevant when dealing with temperament
> in the abstract? Surely your meantone helix doesn't depend
> on any cents values . . . (?)

I have more to say on this "abstract" aspect, below.

> > and the ratios they're supposed to represent),
> > i'll make a Tonescape file of it and post the pretty pictures.
>
> How about 7-limit meantone, as in my paper? The generators
> can be said to represent 2:1 and 3:2. Since you asked, in
> the TOP tuning (just one of many possibilities), these
> generators are 1201.7 and 697.57 cents -- exactly the same
> as they are in the TOP tuning for 5-limit meantone.

Hmm ... so you call it "7-limit" because it gives good
approximations of ratios-of-7 (as well as ratios-of-5)
... but it's really constructed as a "linear temperament"
(i know, we don't like that term anymore ...) -- that is,
the generator representing 2:1 is considered to be the
"identity interval", and the generator representing 3:2
is iterated to build up the tuning, exactly as in
pythagorean and "ordinary" (non-TOP) meantones.

To create a Tonescape Lattice of this tuning, i'd say
that we want to make it 4D, since the tuning is intended
to represent prime-factors 3, 5, and 7 (and 2) -- or,
more accurately, the ratios 3:2, 5:4, and 7:4
(and the identity-interval 2:1).

> But generators of 2D temperaments are often ambiguous
> between different ratio-interpretations, but this never
> mattered to you before, so I don't know why you now need
> ratio-interpretations for the generators all of a sudden.
> Can't you simply take the specification of the original
> JI lattice, plus the set of vanishing commas, as input?
> For example, to get meantone, I'd start with the 5-
> limit lattice, and temper out 81:80. Does this work
> for you?

Sure, that's exactly how Tonescape works.

But a tuning in Tonescape can never be abstract, because
the purpose of Tonescape is not just to work out theoretical
concepts, but to enable the user to compose music. You have
to nail down exactly what frequencies the pitches represent
before you can create music.

When you use this method to create meantone in Tonescape,
the default result is 1/4-comma meantone. Then if you desire
a different flavor of meantone, you just go into the
Tuning Editor and change the fraction-of-a-comma.

Using "the specification of the original JI lattice,
plus the set of vanishing commas, as input" already
implies a set of ratio approximations.

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

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

> I suggest posting your questions on this to the tuning-math list.

OK, will do.

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

> > > The 80-note MOS 12&224[80] does. It has 76 sensibly JI fifths,
> > > 72 very nice 696.4 meantone fifths, and 64 sharp fifths of size
> > > 707.1 cents. Thus the fifth situation is very well in hand; I
> > > hope Ozan take a look at it.
> >
> > That's great. Have you posted a Scala file?
>
> It's toof1.scl. I wonder what could be done with it musically.

Humph, that's not in the current version (52) of the scale
archive.

-Carl

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

> > > That's great. Have you posted a Scala file?
> >
> > It's toof1.scl. I wonder what could be done with it musically.
>
> Humph, that's not in the current version (52) of the scale
> archive.

You asked if I posted it, which I did here:

/tuning/topicId_64578.html#64578

Hi Paul,

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

> How about 7-limit meantone, as in my paper? The generators
> can be said to represent 2:1 and 3:2. Since you asked, in
> the TOP tuning (just one of many possibilities), these
> generators are 1201.7 and 697.57 cents -- exactly the same
> as they are in the TOP tuning for 5-limit meantone.

Hmm ... this is a very interesting tuning. I notice that
this TOP meantone forms a nearly-closed system at 31 tones,
but that if you continue it past that, you get an
adaptive-JI system.

Anyway, i made a Tonescape Lattice of the 31-tone version,
in pseudo-2,3,5,7-space:

/tuning/files/monz/erlich_7-limit-TOP-meantone_31-tone-chain.gif

For the notation, i used 1,200,000-edo, so that you can
consider it to be cents with the last three digits representing
those which come after the decimal point.

I didn't use any mathematical formula to calculate the
shape of the block -- i just added each pitch manually,
trying to keep all the pitches as close as possible to
the origin.

I was so intrigued by this that i already started composing
a piece in it (it's so easy in Tonescape [shameless plug])
... let's hope that i finish it, which is something i haven't
done for quite some time.

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

> > > > That's great. Have you posted a Scala file?
> > >
> > > It's toof1.scl. I wonder what could be done with it musically.
> >
> > Humph, that's not in the current version (52) of the scale
> > archive.
>
> You asked if I posted it, which I did here:
>
> /tuning/topicId_64578.html#64578

Aha! So let's compare:

toof1
72 696.429
76 701.786
64 707.143

ozan[79]
33 694.340
46 701.887
32 709.434

On the left is the number of occurrances in the modes of
the scale of the given fifth (size shown on the right).
So not only are toof1's fifths closer to Ozan's stated
targets, there's more of them.

What do you think, Ozan? And will it be possible for you
to add one more note to your qanun?

-Carl

> -- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> >
> > Dear monz,
> >
> > Thanks very much for the praises. I have uploaded to pictures
> > of my Qanun to:
> >
> > http://www.ozanyarman.com/anonymous/

I see this instrument looks as beautiful as it sounds.

-Carl

I'm afraid neither Guiron77 nor Octoid80 serve my purposes. The chain of
fifths are not right, and neither is the notation thus.

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
To: <tuning@yahoogroups.com>
Sent: 22 �ubat 2006 �ar�amba 9:17
Subject: [tuning] Re: Ozan's 159-edo-based tuning

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > Can you provide the details for Octaid 80? 72 didn't work, because the
> > super-pythagorean fifth is intolerable to listen to.
>
> Octoid[80] does not put the meantone fifth and the nearly pure
> (schismatic) fifth in the same interval class, so I doubt it is what
> you want. Octoid[72] does, however. There are no intolerable
> super-pythagorean fifths in the six closed chains of fifths you get in
> this way. As I said, these are in fact well-temperaments; two
> almost-pure fifths followed by a meantone fifth, and repeat. The minor
> thirds are all 300 cents exactly, and the triads differ in that the
> ones with the meantone fifths have better major thirds, as they
> clearly must, given that the minor thirds are fixed in size.
>
> ! octoid80.scl
> Octoid[80] in 224-et tuning
> 80
> !
> 16.071429
> 32.142857
> 48.214286
> 64.285714
> 80.357143
> 85.714286
> 101.785714
> 117.857143
> 133.928571
> 150.000000
> 166.071429
> 182.142857
> 198.214286
> 214.285714
> 230.357143
> 235.714286
> 251.785714
> 267.857143
> 283.928571
> 300.000000
> 316.071429
> 332.142857
> 348.214286
> 364.285714
> 380.357143
> 385.714286
> 401.785714
> 417.857143
> 433.928571
> 450.000000
> 466.071429
> 482.142857
> 498.214286
> 514.285714
> 530.357143
> 535.714286
> 551.785714
> 567.857143
> 583.928571
> 600.000000
> 616.071429
> 632.142857
> 648.214286
> 664.285714
> 680.357143
> 685.714286
> 701.785714
> 717.857143
> 733.928571
> 750.000000
> 766.071429
> 782.142857
> 798.214286
> 814.285714
> 830.357143
> 835.714286
> 851.785714
> 867.857143
> 883.928571
> 900.000000
> 916.071429
> 932.142857
> 948.214286
> 964.285714
> 980.357143
> 985.714286
> 1001.785714
> 1017.857143
> 1033.928571
> 1050.000000
> 1066.071429
> 1082.142857
> 1098.214286
> 1114.285714
> 1130.357143
> 1135.714286
> 1151.785714
> 1167.857143
> 1183.928571
> 1200.000000
>

Perhaps as high a prime-limit as 17 will yield interesting results too.

----- Original Message -----
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 22 �ubat 2006 �ar�amba 23:48
Subject: [tuning] Re: Ozan's 79-MOS 159-edo tuning in 2,3,5,7,11-space

> Now how about a 13-limit version, since Gene gave the 13-limit TM
> basis for the 2D temperament that gives you this MOS scale? 13-limit
> would be a step closer to the much higher-prime-limit ratios Ozan
> said he was interested in approximating with this scale (a while
> back).
>
>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> I'm afraid neither Guiron77 nor Octoid80 serve my purposes. The chain of
> fifths are not right, and neither is the notation thus.

I don't see why you would worry about notation at this point. What do
you want in chains of fifths?

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Perhaps as high a prime-limit as 17 will yield interesting results too.

The patent val for 159 gives the best tuning through the 17-limit;
here aren TM bases:

c7: {1029/1024, 10976/10935, 15625/15552}
c11: {385/384, 441/440, 4000/3993, 10976/10935}
c13: {325/324, 364/363, 385/384, 625/624, 10976/10935}
c17: {273/272, 325/324, 364/363, 375/374, 385/384, 3773/3757}

In the 13 and 17 limits particularly, the most complex comma is
clearly cheesier than the rest, which suggests the characteristic
temperament, meaning the one obtained by tossing the most complex
comma, should be interesting. These are

7 limit: <<3 -24 -1 -45 -10 65|| guiron, the 118&159 temperament

11, 13 and 17 limits: <<18 15 -6 9 42 54 ... || tritikleismic, the
72&87 temperament.

Here I give only the octave equivalent part of the wedgie; the
temperament has a period of 1/3 octave and a hanson-type generator of
a minor third, tempering out 15625/15552. It's a good way of getting
to the 11-limit, but not such a good way of getting to meantone
fifths, which have a rather high complexity--54, the same as 17/16.

Hi Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> >
> > Perhaps as high a prime-limit as 17 will yield
> > interesting results too.
>
> The patent val for 159 gives the best tuning through
> the 17-limit;

I want to put "patent val" into the Encyclopedia.
Should it be described on the "val" page, or have
its own separate page? Can you please write up a
definition for me? Thanks.

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

Hi Gene,

Another request for an Encyclopedia defintion ...

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:

> The patent val for 159 gives the best tuning through the
> 17-limit; here aren TM bases:
>
> c7: {1029/1024, 10976/10935, 15625/15552}
> c11: {385/384, 441/440, 4000/3993, 10976/10935}
> c13: {325/324, 364/363, 385/384, 625/624, 10976/10935}
> c17: {273/272, 325/324, 364/363, 375/374, 385/384, 3773/3757}
>
> In the 13 and 17 limits particularly, the most complex
> comma is clearly cheesier than the rest, which suggests
> the characteristic temperament, meaning the one obtained
> by tossing the most complex comma, should be interesting.
> These are
>
> 7 limit: <<3 -24 -1 -45 -10 65|| guiron, the
> 118&159 temperament
>
> 11, 13 and 17 limits: <<18 15 -6 9 42 54 ... ||
> tritikleismic, the 72&87 temperament.

Becausae of some big gaps in my reading the tuning lists
over the last couple of years, i never fully grasped this
the meaning of this "a&b temperament" type of notation.
Definition, please. Thanks.

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

Given my satisfaction for the moment with 79 MOS 159-tET (generator,
notation and approximation-wise), and the myriad of explanations I have
already given, I do not know what prevents you from settling with what I
demonstrated to work already.

As for the horribly low fifth, the intonation of my instrument or minute
tuning calibrations does help change it by a few cents, whereby I can
acquire a 2/7 comma fifth at certain degrees if I so desire.

Moreover, I need alternating fifths for transition from Rast to Suz-i
Dilara, or Buselik to Nishabur. Otherwise the chain of fifths is broken.

Oz.

----- Original Message -----
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 23 �ubat 2006 Per�embe 0:23
Subject: [tuning] Re: Ozan's 159-edo-based tuning

I would like very much to suggest something else that would offend
you less, so I'm taking my time in asking you many pertinent
questions first. With the right information, the tuning-math folks
can run an efficient computer search for alternative systems that
could save months of human labor time.

I'm still quite unclear as to why a decent fifth, similar to that of
79-equal, wouldn't make more sense as an interval by which to
generate the spine or circle of fifths, rather than alternating a
nearly pure fifth with a "very very offensive one". The alternation
does not in any way allow the system to function more flexibly, only
less flexibly, unless I'm missing something. Isn't a fifth the most
common interval by which a scale is modulated? If you have a
mode/scale/key with some pure fifths in it, and you modulate by a
fifth, why should most of the formerly pure fifths now become "very
very offensive"? In my very limited understanding of your system and
its motivations, this confuses me, since I thought modulation was of
major importance to you.

[PA]
I don't think you understood my question, which was about some
constraint that appears to lie well beyond the instrument itself.
Would you re-read it then?

[OZ]
Would you be kind enough to rephrase and ask me again?

>
> What other subset would you suggest that appeals to me then?

[PA]
In the context of this particular discussion/thread/post, I would
simply ask what you think of a 79-tone MOS that does *not* arise as a
subset of any EDO. If there aren't more than 79 tones per octave on
the instrument, what could it matter if the superset from which the
tones are chosen form 159-equal, or any equal tuning at all for that
matter? 'Cause you'll never have an opportunity to use more than 79
of them anyway, so you'll never become aware of the closure, or lack
thereof, of the "universe set" of 159 or >159 pitches. Gene has
determined a 13-limit kernel basis (IIRC) for the 2D temperament
which yields your 79-note MOS (or an 80-note MOS with one extra
note). If this turns out to correspond to your desires, why not use
the TOP or Kees tuning for this temperament, rather than drawing the
notes from an EDO?

[OZ]
How many times do I need to repeat that I do not derive my tuning from any
EDO, but from the equal division of the pure fourth? It was Gene himself who
pointed out months ago the similarity of my tuning to 79 MOS 159, a
definition which I accepted at the cost of being misunderstood.

So, if you think you are able to suggest something better, why not provide
me the TOP or Kees tuning that I dare not comprehend?

Oz.

Indeed! Can we obtain a 80 or so tone MOS out of it?

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
To: <tuning@yahoogroups.com>
Sent: 23 �ubat 2006 Per�embe 1:28
Subject: [tuning] Re: Ozan's 159-edo-based tuning

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> > > What, in a perfect world, would these three sizes of
> > > fifth be?
> >
> > 696, 702, 708 cents or so.
>
> 224-et seems like a good choice then.
>
>

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

> I want to put "patent val" into the Encyclopedia.
> Should it be described on the "val" page, or have
> its own separate page? Can you please write up a
> definition for me? Thanks.

It's the same as "standard val", a term I am abandoning because of
numerous objections.

For any positive integer n and prime limit p, the patent val for n and
p is defined to be the following:

<n round(n log2(3)) round(n log2(5)) ... round(n log2(p)|

Here "round" means the function rounding to the nearest integer, also
called the nint function, and written round(x), nint(x), [x] or ||x||
for a real number x.

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

> Becausae of some big gaps in my reading the tuning lists
> over the last couple of years, i never fully grasped this
> the meaning of this "a&b temperament" type of notation.
> Definition, please. Thanks.

I have a precise definition for this, but other people are more loose
about it. In my usage, a&b, for positive integers a and b and prime
limit p, is the temperament defined by the wedgie for the patent vals
for a and b in the prime limit p.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Given my satisfaction for the moment with 79 MOS 159-tET (generator,
> notation and approximation-wise), and the myriad of explanations I have
> already given, I do not know what prevents you from settling with what I
> demonstrated to work already.

No one understands why you prefer it, so the questions keep coming.

Neither do I understand why nobody understands my continuing explanations.

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
To: <tuning@yahoogroups.com>
Sent: 24 �ubat 2006 Cuma 0:33
Subject: [tuning] Re: Ozan's 159-edo-based tuning

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > Given my satisfaction for the moment with 79 MOS 159-tET (generator,
> > notation and approximation-wise), and the myriad of explanations I have
> > already given, I do not know what prevents you from settling with what I
> > demonstrated to work already.
>
> No one understands why you prefer it, so the questions keep coming.
>
>
>
>

An 80-note MOS out of 224 sounds intriguing. Can we have the cent values or
the step numbers please?

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
To: <tuning@yahoogroups.com>
Sent: 23 �ubat 2006 Per�embe 5:32
Subject: [tuning] Re: Ozan's 159-edo-based tuning

> --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
> >
> > > > What, in a perfect world, would these three sizes of
> > > > fifth be?
> > >
> > > 696, 702, 708 cents or so.
> >
> > Alright, Gene, what have you got for that in 80 tones
> > or less? Guiron doesn't do it.
>
> The 80-note MOS 12&224[80] does. It has 76 sensibly JI fifths, 72 very
> nice 696.4 meantone fifths, and 64 sharp fifths of size 707.1 cents.
> Thus the fifth situation is very well in hand; I hope Ozan take a look
> at it.
>
>
>

I am not sure I liked it.

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
To: <tuning@yahoogroups.com>
Sent: 23 �ubat 2006 Per�embe 7:02
Subject: [tuning] Re: Ozan's 159-edo-based tuning

> --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
> >
> > > The 80-note MOS 12&224[80] does. It has 76 sensibly JI fifths,
> > > 72 very nice 696.4 meantone fifths, and 64 sharp fifths of size
> > > 707.1 cents. Thus the fifth situation is very well in hand; I
> > > hope Ozan take a look at it.
> >
> > That's great. Have you posted a Scala file?
>
> It's toof1.scl. I wonder what could be done with it musically.
>
>

I'm not sure if this appeals to me Carl, despite the fifths. The scale is
very irregular for my requirements and 5-limit consonances are problematic.

----- Original Message -----
From: "Carl Lumma" <clumma@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 23 �ubat 2006 Per�embe 11:59
Subject: [tuning] Re: Ozan's 159-edo-based tuning

> > > > > That's great. Have you posted a Scala file?
> > > >
> > > > It's toof1.scl. I wonder what could be done with it musically.
> > >
> > > Humph, that's not in the current version (52) of the scale
> > > archive.
> >
> > You asked if I posted it, which I did here:
> >
> > /tuning/topicId_64578.html#64578
>
> Aha! So let's compare:
>
> toof1
> 72 696.429
> 76 701.786
> 64 707.143
>
> ozan[79]
> 33 694.340
> 46 701.887
> 32 709.434
>
> On the left is the number of occurrances in the modes of
> the scale of the given fifth (size shown on the right).
> So not only are toof1's fifths closer to Ozan's stated
> targets, there's more of them.
>
> What do you think, Ozan? And will it be possible for you
> to add one more note to your qanun?
>
> -Carl
>
>

Notation has everything to do with my purposes. I'm trying to revolutionize
Maqam Music transcription, remember?

I desire that a diatonical scale can be meantone/well and pythagorean at
every degree.

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
To: <tuning@yahoogroups.com>
Sent: 23 �ubat 2006 Per�embe 19:28
Subject: [tuning] Re: Ozan's 159-edo-based tuning

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > I'm afraid neither Guiron77 nor Octoid80 serve my purposes. The chain of
> > fifths are not right, and neither is the notation thus.
>
> I don't see why you would worry about notation at this point. What do
> you want in chains of fifths?
>
>
>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> An 80-note MOS out of 224 sounds intriguing. Can we have the cent
values or
> the step numbers please?

The scale "toof1" which we've been discussing seems like the most
plausible candidate for now. Another was Octoid[80], which you didn't
like. You should have both scales in terms of cents already.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> I'm not sure if this appeals to me Carl, despite the fifths. The
scale is
> very irregular for my requirements and 5-limit consonances are
problematic.

The scale is very irregular in terms of step size, but *any* scale
with a lot of three different kinds of fifth is going to be, because
the differences between the fifths are small. The 5-limit consonances
are not a problem so far as I can see. For one thing, we've got lots
of copies of the diatonic scale in there, and as well as a lot of
nearly pure fifths, a lot of nearly pure major thirds.

Toof1 has 44 nearly pure major triads and 44 nearly pure minor triads.
It also has 8 otonal and 8 utonal tetrads to close accuracy, and of
course less closely tuned versions as well. Your scale has 25 of each
kind of triad in its best tuning, and the accuracy while very good
(the same as 53) isn't as close as 224. Nor does it have any near-pure
tetrads to boast of. I would say toof1 clearly has it beat in the
5-limit consonances department.

I cannot even get a decent Rast scale on C!

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
To: <tuning@yahoogroups.com>
Sent: 24 �ubat 2006 Cuma 1:19
Subject: [tuning] Re: Ozan's 159-edo-based tuning

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > I'm not sure if this appeals to me Carl, despite the fifths. The
> scale is
> > very irregular for my requirements and 5-limit consonances are
> problematic.
>
> The scale is very irregular in terms of step size, but *any* scale
> with a lot of three different kinds of fifth is going to be, because
> the differences between the fifths are small. The 5-limit consonances
> are not a problem so far as I can see. For one thing, we've got lots
> of copies of the diatonic scale in there, and as well as a lot of
> nearly pure fifths, a lot of nearly pure major thirds.
>
> Toof1 has 44 nearly pure major triads and 44 nearly pure minor triads.
> It also has 8 otonal and 8 utonal tetrads to close accuracy, and of
> course less closely tuned versions as well. Your scale has 25 of each
> kind of triad in its best tuning, and the accuracy while very good
> (the same as 53) isn't as close as 224. Nor does it have any near-pure
> tetrads to boast of. I would say toof1 clearly has it beat in the
> 5-limit consonances department.
>
>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> I'm not sure if this appeals to me Carl, despite the fifths. The
scale is
> very irregular for my requirements and 5-limit consonances are
problematic.

One way of thinking about it is that it's a sort of adaptive version
of 12-et. There are twelve note-groups, each consisting of six or
seven alternative notes. By choosing your alternative, you can get a
huge number of different 12-note scales out of toof1; subscales of
these are probably, most of the time, what you'd be looking for.
Certainly, you can find sensibly just 5-limit harmony in abudence.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> I cannot even get a decent Rast scale on C!

If Rast is the same as a diatonic scale, then you certainly can. It
has them in vast abundence. I think perhaps it would be better if we
moved 1/1 somewhere else, as you seem to not like where it is.

What about 13/12, 12/11 and 11/10?

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
To: <tuning@yahoogroups.com>
Sent: 24 �ubat 2006 Cuma 1:55
Subject: [tuning] Re: Ozan's 159-edo-based tuning

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > I cannot even get a decent Rast scale on C!
>
> If Rast is the same as a diatonic scale, then you certainly can. It
> has them in vast abundence. I think perhaps it would be better if we
> moved 1/1 somewhere else, as you seem to not like where it is.
>
>
>
>

> Neither do I understand why nobody understands my continuing
> explanations.

You haven't given a complete statement of your criteria in
precise terms. We now know that you require three types of
fifth and what sizes they should be. We know you want
higher-limit approximations but not precisely what will work
and what would be unacceptable. Now we see you have
restrictions on how a chain of fifths will produce a third.
Can you state it in a precise manner?

-Carl

> > > > > > That's great. Have you posted a Scala file?
> > > > >
> > > > > It's toof1.scl.
//
> > > You asked if I posted it, which I did here:
> > >
> > > /tuning/topicId_64578.html#64578
> >
> > Aha! So let's compare:
> >
> > toof1
> > 72 696.429
> > 76 701.786
> > 64 707.143
> >
> > ozan[79]
> > 33 694.340
> > 46 701.887
> > 32 709.434
> >
> > On the left is the number of occurrances in the modes of
> > the scale of the given fifth (size shown on the right).
> > So not only are toof1's fifths closer to Ozan's stated
> > targets, there's more of them.
> >
> > What do you think, Ozan? And will it be possible for you
> > to add one more note to your qanun?
>
> I'm not sure if this appeals to me Carl, despite the fifths.
> The scale is very irregular for my requirements and 5-limit
> consonances are problematic.

In what way are they problematic?

-Carl

I thought I had made precise statements on how both the Rast and the Suz-i
Dilara scales must be achieved via an unbroken chain of fifths. I have
specified already the desirable sizes and tried to show to the best of my
ability how these have to alterate on several degrees. I have also made
precise statements concerning how I desired high prime limit approximations
by giving several Maqam scales. I have repeated myself to the extent that I
don't know what else to say anymore.

----- Original Message -----
From: "Carl Lumma" <clumma@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 24 �ubat 2006 Cuma 2:07
Subject: [tuning] Re: Ozan's 159-edo-based tuning

> > Neither do I understand why nobody understands my continuing
> > explanations.
>
> You haven't given a complete statement of your criteria in
> precise terms. We now know that you require three types of
> fifth and what sizes they should be. We know you want
> higher-limit approximations but not precisely what will work
> and what would be unacceptable. Now we see you have
> restrictions on how a chain of fifths will produce a third.
> Can you state it in a precise manner?
>
> -Carl
>
>

If Gene can start 1/1 on a more convenient degree, I may re-evaluate the
scale once more.

----- Original Message -----
From: "Carl Lumma" <clumma@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 24 �ubat 2006 Cuma 2:09
Subject: [tuning] Re: Ozan's 159-edo-based tuning

> > > > > > > That's great. Have you posted a Scala file?
> > > > > >
> > > > > > It's toof1.scl.
> //
> > > > You asked if I posted it, which I did here:
> > > >
> > > > /tuning/topicId_64578.html#64578
> > >
> > > Aha! So let's compare:
> > >
> > > toof1
> > > 72 696.429
> > > 76 701.786
> > > 64 707.143
> > >
> > > ozan[79]
> > > 33 694.340
> > > 46 701.887
> > > 32 709.434
> > >
> > > On the left is the number of occurrances in the modes of
> > > the scale of the given fifth (size shown on the right).
> > > So not only are toof1's fifths closer to Ozan's stated
> > > targets, there's more of them.
> > >
> > > What do you think, Ozan? And will it be possible for you
> > > to add one more note to your qanun?
> >
> > I'm not sure if this appeals to me Carl, despite the fifths.
> > The scale is very irregular for my requirements and 5-limit
> > consonances are problematic.
>
> In what way are they problematic?
>
> -Carl
>
>