Yahoo Tuning Groups Ultimate Backup tuning new version of Tonalsoft Encyclopedia now online

Dear Monz, I notice that there is no mention of a 78-cent tuning in your encyclopedia. Now, I find this to be an entertaining possibility that may deserve mention.

Cordially,
Ozan Yarman

----- Original Message -----
From: monz
To: tuning@yahoogroups.com
Sent: 21 Temmuz 2005 Perşembe 2:45
Subject: [tuning] new version of Tonalsoft Encyclopedia now online

Hello all,

The Tonalsoft Encyclopedia has a new name and a new look:

Tonalsoft Encyclopedia of Microtonal Music Theory

http://tonalsoft.com/enc/

(You'll notice that the links which connect the
Encyclopedia pages with each other are temporarily gone
... not to worry, they'll be back soon.)

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

🔗monz <monz@tonalsoft.com>

Dear Ozan,

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

> Dear Monz, I notice that there is no mention of a
> 78-cent tuning in your encyclopedia. Now, I find this
> to be an entertaining possibility that may deserve mention.

Thanks for that info. I know nothing about any 78-cent
tuning ... if you've described it here before, i missed it.

Converting the Encyclopedia to the new format was a
major effort, which took about 4 times longer than i
thought it would (8 months, instead of my estimated
2 months) ... i'm basically finished with it for the
time being. There's a lot of work to do on Tonescape
to get it ready for the commercial release of version 1.0.

Send me some more info, and i'll make a page for it
when i get the time.

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

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

monz,

You wrote:

> The Tonalsoft Encyclopedia has a new name and a new look:
>
> Tonalsoft Encyclopedia of Microtonal Music Theory
> http://tonalsoft.com/enc/
>

Congratulations! :-)

>
> (You'll notice that the links which connect the
> Encyclopedia pages with each other are temporarily gone
> ... not to worry, they'll be back soon.)

That will be very good, too.

Regards,
Yahya

--
No virus found in this outgoing message.
Checked by AVG Anti-Virus.
Version: 7.0.323 / Virus Database: 267.9.2/53 - Release Date: 20/7/05

🔗Ozan Yarman <ozanyarman@superonline.com>

Dear Monz,

78-cent tuning is derived by equally dividing the fifth (702 cents) into 9 partitions. The results of this tuning are as follows:

78
156
234
312
390
468
546
624
702
780
858
936
1014
1092
1170

etc...

Alternatively, the scale can be created with a generator of 624 cents and a period of 1170 cents.

Note that you can achieve a modest 4:5:6 chord at every degree with such a tuning.

A Farey approximation with an order of 36 based on minimal differences yields the following results:

0: 1/1 0.000 unison, perfect prime
1: 23/22 76.956
2: 35/32 155.140 septimal neutral second
3: 8/7 231.174 septimal whole tone
4: 6/5 315.641 minor third
5: 5/4 386.314 major third
6: 38/29 467.936
7: 37/27 545.479
8: 43/30 623.249
9: 3/2 701.955 perfect fifth
10: 11/7 782.492 undecimal augmented fifth
11: 23/14 859.448
12: 55/32 937.632
13: 61/34 1011.929
14: 62/33 1091.763
15: 57/29 1169.891

The differences between these two scales are as follows:

1: 1: 1.044 cents 1.043595 0.1649 Hertz, 9.8956 cycles/min.
2: 2: 0.860 cents 0.860379 0.1422 Hertz, 8.5348 cycles/min.
3: 3: 2.826 cents 2.825906 0.4885 Hertz, 29.3076 cycles/min.
4: 4: -3.641 cents -3.641287 0.6596 Hertz, 39.5781 cycles/min.
5: 5: 3.686 cents 3.686286 0.6971 Hertz, 41.8251 cycles/min.
6: 6: 0.064 cents 0.064178 0.0127 Hertz, 0.7625 cycles/min.
7: 7: 0.521 cents 0.520963 0.1079 Hertz, 6.4742 cycles/min.
8: 8: 0.751 cents 0.751009 0.1627 Hertz, 9.7625 cycles/min.
9: 9: 0.045 cents 0.044999 0.0102 Hertz, 0.6120 cycles/min.
10: 10: -2.492 cents -2.492035 0.5914 Hertz, 35.4823 cycles/min.
11: 11: -1.448 cents -1.448440 0.3595 Hertz, 21.5672 cycles/min.
12: 12: -1.632 cents -1.631656 0.4236 Hertz, 25.4163 cycles/min.
13: 13: 2.071 cents 2.070604 0.5617 Hertz, 33.7042 cycles/min.
14: 14: 0.237 cents 0.237370 0.0674 Hertz, 4.0440 cycles/min.
15: 15: 0.109 cents 0.109177 0.0324 Hertz, 1.9458 cycles/min.
Mode: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Total absolute difference : 21.4279 cents
Average absolute difference: 1.4285 cents
Root mean square difference: 1.8767 cents
Highest absolute difference: 3.6863 cents
Number of notes different: 15

Cordially,
Ozan

P.S. Good luck on your projects!

----- Original Message -----
From: monz
To: tuning@yahoogroups.com
Sent: 21 Temmuz 2005 Perşembe 7:11
Subject: [tuning] 78-cent tuning (was: new version of Tonalsoft Encyclopedia now online)

Dear Ozan,

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

> Dear Monz, I notice that there is no mention of a
> 78-cent tuning in your encyclopedia. Now, I find this
> to be an entertaining possibility that may deserve mention.

Thanks for that info. I know nothing about any 78-cent
tuning ... if you've described it here before, i missed it.

Send me some more info, and i'll make a page for it
when i get the time.

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

🔗Afmmjr@aol.com

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> Dear Monz,
>
> 78-cent tuning is derived by equally dividing the fifth (702 cents)
into 9 partitions.

This is clearly closely related to the "valentine", or 31&46
temperament. 31edo gives us a generator of 2/31, or 77.4 cents, and
46edo of 3/46, or 78.3 cents. Anything in between can be counted as a
valentine generator, including 78 cents. 9/139 is a poptimal 7-limit
generator, and 17/262 9-limit, but 78/1200 = 13/200 certainly works
also. The notes you gave are the notes of the 16-note valentine MOS
using the 13/200 generator; it becomes a MOS if you assume you are
going to repeat the pattern in octaves.

I think if Monz puts up a page for this it should be in conjunction
with a valentine page.

🔗Ozan Yarman <ozanyarman@superonline.com>

Clearly so Gene.

Cordially,
Ozan
----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 21 Temmuz 2005 Perşembe 22:35
Subject: [tuning] Re: 78-cent tuning (was: new version of Tonalsoft Encyclopedia now online)

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> Dear Monz,
>
> 78-cent tuning is derived by equally dividing the fifth (702 cents)
into 9 partitions.

I think if Monz puts up a page for this it should be in conjunction
with a valentine page.

🔗monz <monz@tonalsoft.com>

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

I disagree. While Robert Valentine was largely interested in MOS
scales in an octave-repeating context, Wendy Carlos (like Ozan) was
interested in true non-octave equal tunings. Since her "Alpha" scale
is 78.0 cents/step, the scale Ozan brought up should be mentioned in
association with Wendy Carlos, not Robert Valentine.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> Clearly so Gene.
>
> Cordially,
> Ozan
> ----- Original Message -----
> From: Gene Ward Smith
> To: tuning@yahoogroups.com
> Sent: 21 Temmuz 2005 Perþembe 22:35
> Subject: [tuning] Re: 78-cent tuning (was: new version of
Tonalsoft Encyclopedia now online)
>
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...>
wrote:
> > Dear Monz,
> >
> > 78-cent tuning is derived by equally dividing the fifth (702
cents)
> into 9 partitions.
>
> This is clearly closely related to the "valentine", or 31&46
> temperament. 31edo gives us a generator of 2/31, or 77.4 cents,
and
> 46edo of 3/46, or 78.3 cents. Anything in between can be counted
as a
> valentine generator, including 78 cents. 9/139 is a poptimal 7-
limit
> generator, and 17/262 9-limit, but 78/1200 = 13/200 certainly
works
> also. The notes you gave are the notes of the 16-note valentine
MOS
> using the 13/200 generator; it becomes a MOS if you assume you are
> going to repeat the pattern in octaves.
>
> I think if Monz puts up a page for this it should be in
conjunction
> with a valentine page.

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

Ozan,

You don't have to get very far through Monz's encyclopedia to come
across this entry:

http://tonalsoft.com/enc/a/alpha.aspx

There it is, a 78-cent (non-octave) equal tuning.

Best,
Paul

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> Dear Monz, I notice that there is no mention of a 78-cent tuning in
your encyclopedia. Now, I find this to be an entertaining possibility
that may deserve mention.
>
> Cordially,
> Ozan Yarman
>
> ----- Original Message -----
> From: monz
> To: tuning@yahoogroups.com
> Sent: 21 Temmuz 2005 Perþembe 2:45
> Subject: [tuning] new version of Tonalsoft Encyclopedia now online
>
>
> Hello all,
>
>
> The Tonalsoft Encyclopedia has a new name and a new look:
>
>
> Tonalsoft Encyclopedia of Microtonal Music Theory
>
> http://tonalsoft.com/enc/
>
>
>
> (You'll notice that the links which connect the
> Encyclopedia pages with each other are temporarily gone
> ... not to worry, they'll be back soon.)
>
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software

🔗Ozan Yarman <ozanyarman@superonline.com>

Ah yes, clumsy me. It was a naive thinking on my part where I imagined I had actually found something interesting that wasn't mentioned before.

Well, thank you for the reminder Paul. It's good to have you back in the tuning list!

Cordially,
Ozan

----- Original Message -----
From: wallyesterpaulrus
To: tuning@yahoogroups.com
Sent: 22 Temmuz 2005 Cuma 23:45
Subject: [tuning] Re: new version of Tonalsoft Encyclopedia now online

Ozan,

You don't have to get very far through Monz's encyclopedia to come
across this entry:

http://tonalsoft.com/enc/a/alpha.aspx

There it is, a 78-cent (non-octave) equal tuning.

Best,
Paul