Two new JI chords

How should we name these?

242 460 | 20:23:30

355 347 | 22:27:33

Oz.

.........How should we name these?

242 460 | 20:23:30

355 347 | 22:27:33

Oz.

.....................

Dear ozan , salam, halet che toreh?(How are you?)

in persian music this chord 355 347 | 22:27:33 (belonging to 22-ADO) is
good being used in segah and we can call it (but in 24 ,48,...96 edo)
median triad or neutral triad.

in 96-edo for chords such as below we can have:

337.5 362.5 = lower median triad

362.5 337.5 = upper median triad

and for 242 460 | 20:23:30 we can call it in 96-edo subminor triad.

in 96-edo for chords such as below we can have:

237.5 462.5 = lower subminor triad

262.5 437.5 = upper subminor triad

Best for you

Shaahin mohajeri , Tombak player and microtonalist

My microtonal web site <http://240edo.googlepages.com/>

Shaahin in wikipedia <http://en.wikipedia.org/wiki/Shaahin_Mohajeri>

My farsi page in harmonytalk <http://www.harmonytalk.com/mohajeri>

Irandrumz ensemble <http://irandrumz.googlepages.com/>

*********

www.kayson-ir.com <http://www.kayson-ir.com/>

2288 Iranzamin bldg Iranzamin Ave.

Shahrak Qods, Tehran 14656, Iran
Telephone: (9821) 88072501-9

Fax: (9821) 88072500
Email: shahinm@... <mailto:shahinm@...>

P Please consider the environment before printing this mail note.

--- In tuning@yahoogroups.com, Ozan Yarman <ozanyarman@...> wrote:
>
> How should we name these?
>
> 242 460 | 20:23:30
>
> 355 347 | 22:27:33
>
> Oz.
>

I like the names on the righthand side.

-Carl

For the past year or so, I have been gradually compiling a database of all the 2048 possible scales which can be generated using 12edo, and coding them so that they can be sorted, found, and otherwise manipulated and examined, for their harmonic, compositional and microtonal implications and varieties.

You can find the current work in progress (complete with typos, and other errors;-) at:

http://www.lucytune.com/scales/

Any comments, suggestions, pointers will be appreciated appreciated.

Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

Dear charles
Hi
Many thanks for your Great work , please have a look at:
http://240edo.googlepages.com/amodelforhexatonicscale
to find my classification of hexatonic scales based on m and n,
May be useful.
m and n are 2 great divisions of octave in hexatonic scales . If
m=n=600 cent , we have 6-6 hexatonic scale.

6 is a symbol for 600 cent in 12-EDO or its multiples.But it is also
possible to have m or n with size of 300,400,500,700,800 or 900 cent.
So if considering m or n equal to 3,4,5,7,8 and 9 , we will have:

3-9 hexatonic scale

4-8 hexatonic scale

5-7 hexatonic scale

7-5 hexatonic scale

8-4 hexatonic scale

9-3 hexatonic scale

I have found 448 different hexatonic scales 1n 12-EDO.

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
> For the past year or so, I have been gradually compiling a database
of
> all the 2048 possible scales which can be generated using 12edo,
and
> coding them so that they can be sorted, found, and otherwise
> manipulated and examined, for their harmonic, compositional and
> microtonal implications and varieties.
>
> You can find the current work in progress (complete with typos,
and
> other errors;-) at:
>
> http://www.lucytune.com/scales/
>
> Any comments, suggestions, pointers will be appreciated appreciated.
>
>
>
>
> Charles Lucy
> lucy@...
>
> - Promoting global harmony through LucyTuning -
>
> for information on LucyTuning go to:
> http://www.lucytune.com
>
> For LucyTuned Lullabies go to:
> http://www.lullabies.co.uk
>

Good I am glad at least somebody understands the significance.

So you're looking at all scales which contain six different notes, and seem to found many scale names which escaped me

Thanks for the link.

In the way that I have arranged the FileMaker database, I can isolate all the scales containing only six notes and compare your results.

Even examining just the Messiaen "modes" produces hundreds of possible scales dependent upon the spelling, as he says that he was only considering 12edo.

I recently found his book "Technique of My Musical Language" on the subject in my local library, and one of my musician friends who is a native French speaker tells me that the English translatio to the word mode confuses the whole issue, as "mode" means so many different things in French, and is not directly translatable into English as mode.

It seems that Messiae was referring to methods for grouping intervals to follow particular patterns rather than what we, in English, would understand as modes.

The book lists the patterns quite clearly, and many references that I have found on the net to these "modes" are just plain wrong.

On 23 Oct 2008, at 09:53, acousticsoftombak wrote:

> Dear charles
> Hi
> Many thanks for your Great work , please have a look at:
> http://240edo.googlepages.com/amodelforhexatonicscale
> to find my classification of hexatonic scales based on m and n,
> May be useful.
> m and n are 2 great divisions of octave in hexatonic scales . If
> m=n=600 cent , we have 6-6 hexatonic scale.
>
> 6 is a symbol for 600 cent in 12-EDO or its multiples.But it is also
> possible to have m or n with size of 300,400,500,700,800 or 900 cent.
> So if considering m or n equal to 3,4,5,7,8 and 9 , we will have:
>
> 3-9 hexatonic scale
>
> 4-8 hexatonic scale
>
> 5-7 hexatonic scale
>
> 7-5 hexatonic scale
>
> 8-4 hexatonic scale
>
> 9-3 hexatonic scale
>
> I have found 448 different hexatonic scales 1n 12-EDO.
>
> --- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
> >
> > For the past year or so, I have been gradually compiling a database
> of
> > all the 2048 possible scales which can be generated using 12edo,
> and
> > coding them so that they can be sorted, found, and otherwise
> > manipulated and examined, for their harmonic, compositional and
> > microtonal implications and varieties.
> >
> > You can find the current work in progress (complete with typos,
> and
> > other errors;-) at:
> >
> > http://www.lucytune.com/scales/
> >
> > Any comments, suggestions, pointers will be appreciated appreciated.
> >
> >
> >
> >
> > Charles Lucy
> > lucy@...
> >
> > - Promoting global harmony through LucyTuning -
> >
> > for information on LucyTuning go to:
> > http://www.lucytune.com
> >
> > For LucyTuned Lullabies go to:
> > http://www.lullabies.co.uk
> >
>
>
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

Dear brother Shahin, selam!

Ben iyiyim, sen nasilsin? (I am well, and you?)

I failed to find these chords in SCALA. But we cannot call 20:23:30
(242+460 cents) subminor triad because 6:7:9 (267+435 cents) is the
subminor triad. Likewise, 14:17:21 (336+366 cents) is the supraminor
triad and 18:22:27 (347+355 cents) the neutral triad compared to
22:27:33 (355+347 cents), which is one of the two actual median
triads. Here is a table:

14:16:21 (231+471 cents) ?
20:23:30 (242+460 cents) ?
26:30:39 (248+454 cents) ultraminor triad
6:7:9 (267+435 cents) subminor triad

*

14:17:21 (336+366 cents) supraminor triad
18:22:27 (347+355 cents) neutral triad
22:27:33 (355+347 cents) ?
34:42:51 (366+336 cents) submajor triad

Minor triads reversed:

16:21:24 (471+231 cents) ? (add :28 for Pepper's square)
46:60:69 (460+242 cents) ?
10:13:15 (454+248 cents) ultramajor triad
14:18:21 (435+267 cents) supermajor triad

**************

Here are suggested names for the chords with question marks:

14:16:21 (231+471 cents) Pepper's square minor triad
20:23:30 (242+460 cents) sub-ultraminor triad

18:22:27 (347+355 cents) first neutral (median) triad
22:27:33 (355+347 cents) second neutral (median) triad

16:21:24 (471+231 cents) Pepper's square major triad
46:60:69 (460+242 cents) supra-ultramajor triad

Manuel, can you include these in the next release of Scala with the
suggested names?

Oz.

On Oct 23, 2008, at 8:11 AM, Mohajeri Shahin wrote:

> ………How should we name these?
>
> 242 460 | 20:23:30
>
> 355 347 | 22:27:33
>
> Oz.
> …………………
> Dear ozan , salam, halet che toreh?(How are you?)
> in persian music this chord 355 347 | 22:27:33 (belonging to 22-
> ADO) is good being used in segah and we can call it (but in 24 ,48,
> …96 edo) median triad or neutral triad.
> in 96-edo for chords such as below we can have:
> 337.5 362.5 = lower median triad
> 362.5 337.5 = upper median triad
> and for 242 460 | 20:23:30 we can call it in 96-edo subminor triad.
> in 96-edo for chords such as below we can have:
> 237.5 462.5 = lower subminor triad
> 262.5 437.5 = upper subminor triad
> Best for you
>
>
> Shaahin mohajeri , Tombak player and microtonalist
>
> My microtonal web site
> Shaahin in wikipedia
> My farsi page in harmonytalk
> Irandrumz ensemble
> *********
> www.kayson-ir.com
> 2288 Iranzamin bldg Iranzamin Ave.
> Shahrak Qods, Tehran 14656, Iran
> Telephone: (9821) 88072501-9
> Fax: (9821) 88072500
> Email: shahinm@...
> P Please consider the environment before printing this mail note.
>
>

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
> For the past year or so, I have been gradually compiling a
> database of all the 2048 possible scales which can be generated
> using 12edo, and coding them so that they can be sorted, found,
> and otherwise manipulated and examined, for their harmonic,
> compositional and microtonal implications and varieties.
>
> You can find the current work in progress (complete with typos,
> and other errors;-) at:
>
> http://www.lucytune.com/scales/
>
> Any comments, suggestions, pointers will be appreciated appreciated.

I like what you've done, but I do have a question; in 12-edo, of
course, C# and Db are identical, but some of your scales use sharps
and others use flats (for example, you have one scale shown as "C C#
D E F# A," which if it were ever implemented would probably be
spelled with Gb rather than F#. Yet immediately below it you have one
given as "C D E G Bb B," which if it were ever implemented would
probably be spelled with A# rather than Bb. So I don't understand
your choices. (Of course, if you went to 19-edo, F# and Gb are
different, as are A# and Bb. So if you went beyond 12-edo, the
spellings would make sense, but you'd have a LOT more than 2048
scales!)

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
> For the past year or so, I have been gradually compiling a database
of
> all the 2048 possible scales which can be generated using 12edo,
and
> coding them so that they can be sorted, found, and otherwise
> manipulated and examined, for their harmonic, compositional and
> microtonal implications and varieties.
>
> You can find the current work in progress (complete with typos,
and
> other errors;-) at:
>
> http://www.lucytune.com/scales/
>
> Any comments, suggestions, pointers will be appreciated appreciated.

To a large extent, this is a much more comprehensive chart of what I
was trying to do in Chapter 17 of my book. I'd almost be tempted to
copy it into the new version, but it is obviously too long; I wonder
if
I can assume that your URL will remain valid and that I can simply
refer the reader to your chart as a reference. (I'm not going to
eliminate the present Chapter 17, but I would simply say something
like "For a more comprehensive table, see
http://www.lucytune.com/scales/" at the end of the chapter.)

Yes Bruce. There are an infinite number of possible scales if you are using a "meantone-type" tuning system like LucyTuning.

Sometimes it is possible to identify the spelling for a particular composition from what a known composer wrote,e.g. Verdi for Enigmatic Scale, yet often we have a number of options to choose from.

My general observation is that the shorter the chain of fourths and fifths used, the more "consonant" the scale is likely to sound.

Which (meantone-type) spellings you choose for a 12 edo scale seems to me to depend upon what harmony you wish to use with it, which is why I am also listing the major. minor, aug and dim triads which can be played with each different spellings of 12 edo scales.

<for example, you have one scale shown as "C C#
> D E F# A," which if it were ever implemented would probably be
> spelled with Gb rather than F#.

Using C C# D E F# A makes the following triads available to the player/composer (with reference to a scale having C as the tonic):

A Major, D Major, A minor, F# minor, F# dim

Using C C# D E Gb A can only produce these triads:

A Major, A minor.

Similarly for your other example:

C D E G Bb B
allows:

G Major, C Major, E minor, G minor

yet
C D E G A# B
only allows:

only G Major C Major, and E minor.

I am developing the database beyond 2048 scales, as once I have completed one example for each of the 2048 unique 12 edo scales, I am also exploring alternatives, each of which will provide "different" harmonic potentials.

Have a look at the current work in progress (in FileMaker fp7) linked from:

http://www.lucytune.com/scales/

to get an idea of the direction that I am thinking and working towards.

Yes I realise that there are errors and typos, and I am whittling away at them as I find them during my checking, comparisons, additions, and revisions.

This whole project is becoming a scalar exploration for me, and I am discovering subtle significances about the nature of various scales and the intervals that they generate.

I have been working on the 6 note scales for the past couple of days, and finding many alternative spellings that can be used.

On 24 Oct 2008, at 19:05, Bruce R. Gilson wrote:

> --- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
> >
> > For the past year or so, I have been gradually compiling a
> > database of all the 2048 possible scales which can be generated
> > using 12edo, and coding them so that they can be sorted, found,
> > and otherwise manipulated and examined, for their harmonic,
> > compositional and microtonal implications and varieties.
> >
> > You can find the current work in progress (complete with typos,
> > and other errors;-) at:
> >
> > http://www.lucytune.com/scales/
> >
> > Any comments, suggestions, pointers will be appreciated appreciated.
>
> I like what you've done, but I do have a question; in 12-edo, of
> course, C# and Db are identical, but some of your scales use sharps
> and others use flats (for example, you have one scale shown as "C C#
> D E F# A," which if it were ever implemented would probably be
> spelled with Gb rather than F#. Yet immediately below it you have one
> given as "C D E G Bb B," which if it were ever implemented would
> probably be spelled with A# rather than Bb. So I don't understand
> your choices. (Of course, if you went to 19-edo, F# and Gb are
> different, as are A# and Bb. So if you went beyond 12-edo, the
> spellings would make sense, but you'd have a LOT more than 2048
> scales!)
>
>
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

Yes that link should remain valid, yet the content will develop as I am putting work in progress into that folder for people to use as they wish, and I intend to update the pages and databases as I progress with more scales.

On 24 Oct 2008, at 19:20, Bruce R. Gilson wrote:

> --- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
> >
> > For the past year or so, I have been gradually compiling a database
> of
> > all the 2048 possible scales which can be generated using 12edo,
> and
> > coding them so that they can be sorted, found, and otherwise
> > manipulated and examined, for their harmonic, compositional and
> > microtonal implications and varieties.
> >
> > You can find the current work in progress (complete with typos,
> and
> > other errors;-) at:
> >
> > http://www.lucytune.com/scales/
> >
> > Any comments, suggestions, pointers will be appreciated appreciated.
>
> To a large extent, this is a much more comprehensive chart of what I
> was trying to do in Chapter 17 of my book. I'd almost be tempted to
> copy it into the new version, but it is obviously too long; I wonder
> if
> I can assume that your URL will remain valid and that I can simply
> refer the reader to your chart as a reference. (I'm not going to
> eliminate the present Chapter 17, but I would simply say something
> like "For a more comprehensive table, see
> http://www.lucytune.com/scales/" at the end of the chapter.)
>
>
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
> For the past year or so, I have been gradually compiling a database
of
> all the 2048 possible scales which can be generated using 12edo, and
> coding them so that they can be sorted, found, and otherwise
> manipulated and examined, for their harmonic, compositional and
> microtonal implications and varieties.
>
> You can find the current work in progress (complete with typos, and
> other errors;-) at:
>
> http://www.lucytune.com/scales/
>
> Any comments, suggestions, pointers will be appreciated appreciated.
>

What exactly do you count getting 2048 as a result? Sure not the number
of possible subsets of 12 (which would be 12!, a very much higher
number), and apparently also not the number of subsets up to
translations (which, to my knowledge, yields a much smaller number).
I looked at your website but could not find this information.
--
Hans Straub

If this is just 12-tone et, just give me a nod.

Otherwise, cents?

>
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>

Let 1= used in scale.
Let 0 = not used in scale.

If you make a mantissa of twelve digits from 100000000000

to

111111111111

and convert this from binary to decimal.

2048 for 100000000000

to

4095 for 111111111111

You get a unique different scale for every number from

2048 to 4095

4095-2048 = 2047

Add one as each number represents a unique scale, and you get a result of 2048.

One scale will only contain one note (the tonic) 100000000000

One scale will contain all the notes 111111111111

The scales in between will contain between 2 and 11 notes.

That's how I arrived at 2048 unique 12 edo scales.

On 31 Oct 2008, at 14:35, hstraub64 wrote:

> --- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
> >
> > For the past year or so, I have been gradually compiling a database
> of
> > all the 2048 possible scales which can be generated using 12edo, and
> > coding them so that they can be sorted, found, and otherwise
> > manipulated and examined, for their harmonic, compositional and
> > microtonal implications and varieties.
> >
> > You can find the current work in progress (complete with typos, and
> > other errors;-) at:
> >
> > http://www.lucytune.com/scales/
> >
> > Any comments, suggestions, pointers will be appreciated appreciated.
> >
>
> What exactly do you count getting 2048 as a result? Sure not the > number
> of possible subsets of 12 (which would be 12!, a very much higher
> number), and apparently also not the number of subsets up to
> translations (which, to my knowledge, yields a much smaller number).
> I looked at your website but could not find this information.
> --> Hans Straub
>
>
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

--- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote:
>
>
> If this is just 12-tone et, just give me a nod.
>
> Otherwise, cents?
>

12-tone et, yes. (I haven't checked Charles' notation, though.)
--
Hans Straub

thanks, Hans

On Oct 31, 2008, at 11:10 AM, hstraub64 wrote:

> --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote:
> >
> >
> > If this is just 12-tone et, just give me a nod.
> >
> > Otherwise, cents?
> >
>
> 12-tone et, yes. (I haven't checked Charles' notation, though.)
> -- > Hans Straub
>
>
>

Yes, the scales are initially organised from the twelve 12edo positions, yet my intent is to explore the diverse interpretations of the harmonic potentials beyond the ambiguities of 12edo.

hence a choice of notenames provides greater harmonic precision; which is why I am considering which triads may be generated using which of the millions of possible scales that can be developed from the 2048 edo possibilities.

On 31 Oct 2008, at 14:59, caleb morgan wrote:

>
> If this is just 12-tone et, just give me a nod.
>
> Otherwise, cents?
>
>
>
>
>
>
>
>
>>
>> Change settings via the Web (Yahoo! ID required)
>> Change settings via email: Switch delivery to Daily Digest | Switch >> format to Traditional
>> Visit Your Group | Yahoo! Groups Terms of Use | Unsubscribe
>> RECENT ACTIVITY
>> 8
>> New Members
>> Visit Your Group
>> All-Bran
>> Day 10 Club
>> on Yahoo! Groups
>> Feel better with fiber.
>> Ads on Yahoo!
>> Learn more now.
>> Reach customers
>> searching for you.
>> Moderator Central
>> Yahoo! Groups
>> Join and receive
>> produce updates.
>> .
>>
>
>
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

caleb wrote:

my 2¢

thinking of 12T ET scales in terms of 6 commonly-used scale groups is
a simple way to look at it.

Lydian (group 1)

Lydian #5 (group 2)

Lydian #2 inverts to Lydian #2 #5 (group3)

then 3 symmetrical groups:

Whole Tone

"Hexatonic" (014589)

Octatonic or Octotonic (0134679A)

throw in the (fictional) "blues scale"--really a hybrid

Legless Wonder* sez: Practice all six scales! Get funky with the
seventh! Or embrace the ZoiD!

Or, you could * try * to practice, or conceive of, 2048 "unique"
scales.

Given the rule of seven, this will be achieved when Kurzweil's
"Singularity" happens--i.e., never.

* but I resent it when people help me cross the street.

question: are these scales that need to occupy more than the space of
an octave--say from c1 to c2, it's one scale, from c2 to c3, it's
another, or variations to this effect?

The mind boggles at the number 2048.

1024. 512. 256. 128. 64. 32. 16. 8. 4. 2.

On Oct 31, 2008, at 11:10 AM, Charles Lucy wrote:

> That's how I arrived at 2048 unique 12 edo scales.

2048 is just the starting point of the analysis.

I am now exploring the further reaches.

I could play them all (using midi) and maybe I shall make a short mp3
of each of the millions of possibilities - if I live that long;-)

If the scale repeats in higher/lower octaves, it is the same scale; if
the notes change from octave to octave, the scale changes.

Considered microtonally you can multiply your few "simple" scales by
as many different spellings for each as you may wish to devise.

On 31 Oct 2008, at 15:32, caleb morgan wrote:

>
> caleb wrote:
>
> my 2¢
>
> thinking of 12T ET scales in terms of 6 commonly-used scale groups
> is a simple way to look at it.
>
> Lydian (group 1)
>
> Lydian #5 (group 2)
>
> Lydian #2 inverts to Lydian #2 #5 (group3)
>
> then 3 symmetrical groups:
>
> Whole Tone
>
> "Hexatonic" (014589)
>
> Octatonic or Octotonic (0134679A)
>
> throw in the (fictional) "blues scale"--really a hybrid
>
> Legless Wonder* sez: Practice all six scales! Get funky with the
> seventh! Or embrace the ZoiD!
>
>
> Or, you could * try * to practice, or conceive of, 2048 "unique"
> scales.
>
> Given the rule of seven, this will be achieved when Kurzweil's
> "Singularity" happens--i.e., never.
>
>
> * but I resent it when people help me cross the street.
>
>
> question: are these scales that need to occupy more than the space
> of an octave--say from c1 to c2, it's one scale, from c2 to c3, it's
> another, or variations to this effect?
>
> The mind boggles at the number 2048.
>
> 1024. 512. 256. 128. 64. 32. 16. 8. 4. 2.
>
>
>
>
>
>
> On Oct 31, 2008, at 11:10 AM, Charles Lucy wrote:
>
>> That's how I arrived at 2048 unique 12 edo scales.
>
>
>

Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

caleb wrote: thanks, I understand a little more, now.

On Oct 31, 2008, at 11:50 AM, Charles Lucy wrote:

> 2048 is just the starting point of the analysis.
>
>
> I am now exploring the further reaches.
>
> I could play them all (using midi) and maybe I shall make a short
> mp3 of each of the millions of possibilities - if I live that long;-)
>
> If the scale repeats in higher/lower octaves, it is the same scale;
> if the notes change from octave to octave, the scale changes.
>
> Considered microtonally you can multiply your few "simple" scales by
> as many different spellings for each as you may wish to devise.
>
>
>
>
>
> On 31 Oct 2008, at 15:32, caleb morgan wrote:
>
>>
>> caleb wrote:
>>
>> my 2¢
>>
>> thinking of 12T ET scales in terms of 6 commonly-used scale groups
>> is a simple way to look at it.
>>
>> Lydian (group 1)
>>
>> Lydian #5 (group 2)
>>
>> Lydian #2 inverts to Lydian #2 #5 (group3)
>>
>> then 3 symmetrical groups:
>>
>> Whole Tone
>>
>> "Hexatonic" (014589)
>>
>> Octatonic or Octotonic (0134679A)
>>
>> throw in the (fictional) "blues scale"--really a hybrid
>>
>> Legless Wonder* sez: Practice all six scales! Get funky with the
>> seventh! Or embrace the ZoiD!
>>
>>
>> Or, you could * try * to practice, or conceive of, 2048 "unique"
>> scales.
>>
>> Given the rule of seven, this will be achieved when Kurzweil's
>> "Singularity" happens--i.e., never.
>>
>>
>> * but I resent it when people help me cross the street.
>>
>>
>> question: are these scales that need to occupy more than the space
>> of an octave--say from c1 to c2, it's one scale, from c2 to c3,
>> it's another, or variations to this effect?
>>
>> The mind boggles at the number 2048.
>>
>> 1024. 512. 256. 128. 64. 32. 16. 8. 4. 2.
>>
>>
>>
>>
>>
>>
>> On Oct 31, 2008, at 11:10 AM, Charles Lucy wrote:
>>
>>> That's how I arrived at 2048 unique 12 edo scales.
>>
>>
>
> Charles Lucy
> lucy@...
>
> - Promoting global harmony through LucyTuning -
>
> for information on LucyTuning go to:
> http://www.lucytune.com
>
> For LucyTuned Lullabies go to:
> http://www.lullabies.co.uk
>
>
>
>
>

My definition of the scale would be:

- scale must have at least five steps for the scale limited to one octave range
ex. C Eb F Gb Bb

- scale can be constructed only from intervals 1, 2, 3, 4

- interval twins which sound like triads should be excluded: diminished 33, minor 34, major 43, augmented 44, as they will disturb feeling of scale

- chains of maximally three same intervals 1 or 2 can be used: 111, 222 to avoid musically boring chromatism or whole tone scale

- scales limited to octave and constructed with these rules will have maximally 9 notes
ex. C Db D Eb F F# G Ab Bb

- scale can exceed octave range
ex. C D F F# G# B C# D#, next cycle will start E F# A A#...

- in such wide range scales some notes can be used again in higher octave (including octave itself)
ex. C C# D# E F G A C D Eb F#, next cycle starts G G# A# B C
In composition these octaves, which represents different step number in every cycle, can be emphasized or not

- or can be different and octave repetition is omitted
ex. C D Eb F G A Bb B C# E F# G#, next cycle can start A B C D E F#...
This way is possible to create 12-tone scales which and not use them as dodecaphony series but as a scale, which is to me more interesting than pure dodecaphony

Concerning microtuning I would allow for such scales with so narrow connection to traditional scales using 12-ET maximal detuning about +/- 16 Cents, to avoid quartertones which would disturb this concept.

Daniel Forro

On 1 Nov 2008, at 12:10 AM, Charles Lucy wrote:

> Let 1= used in scale.
>
> Let 0 = not used in scale.
>
> If you make a mantissa of twelve digits from 100000000000
>
> to
>
> 111111111111
>
> and convert this from binary to decimal.
>
> 2048 for 100000000000
>
> to
>
> 4095 for 111111111111
>
> You get a unique different scale for every number from
>
> 2048 to 4095
>
> 4095-2048 = 2047
>
> Add one as each number represents a unique scale, and you get a > result of 2048.
>
> One scale will only contain one note (the tonic) 100000000000
>
> One scale will contain all the notes 111111111111
>
> The scales in between will contain between 2 and 11 notes.
>
> That's how I arrived at 2048 unique 12 edo scales.
>
>
>
>
>
> On 31 Oct 2008, at 14:35, hstraub64 wrote:
>
>> --- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>> >
>> > For the past year or so, I have been gradually compiling a database
>> of
>> > all the 2048 possible scales which can be generated using 12edo, >> and
>> > coding them so that they can be sorted, found, and otherwise
>> > manipulated and examined, for their harmonic, compositional and
>> > microtonal implications and varieties.
>> >
>> > You can find the current work in progress (complete with typos, and
>> > other errors;-) at:
>> >
>> > http://www.lucytune.com/scales/
>> >
>> > Any comments, suggestions, pointers will be appreciated >> appreciated.
>> >
>>
>> What exactly do you count getting 2048 as a result? Sure not the >> number
>> of possible subsets of 12 (which would be 12!, a very much higher
>> number), and apparently also not the number of subsets up to
>> translations (which, to my knowledge, yields a much smaller number).
>> I looked at your website but could not find this information.
>> -->> Hans Straub
>>
>>
>
> Charles Lucy
> lucy@...
>
> - Promoting global harmony through LucyTuning -
>
> for information on LucyTuning go to:
> http://www.lucytune.com
>
> For LucyTuned Lullabies go to:
> http://www.lullabies.co.uk
>
>
>
>
>

I like this very much. If my wife, my )(@#$)*&^# wife weren't hogging the printer, I'd print this out right now.

On Oct 31, 2008, at 12:04 PM, Daniel Forro wrote:

> My definition of the scale would be:
>
> - scale must have at least five steps for the scale limited to one
> octave range
> ex. C Eb F Gb Bb
>
> - scale can be constructed only from intervals 1, 2, 3, 4
>
> - interval twins which sound like triads should be excluded:
> diminished 33, minor 34, major 43, augmented 44, as they will disturb
> feeling of scale
>
> - chains of maximally three same intervals 1 or 2 can be used: 111,
> 222 to avoid musically boring chromatism or whole tone scale
>
> - scales limited to octave and constructed with these rules will have
> maximally 9 notes
> ex. C Db D Eb F F# G Ab Bb
>
> - scale can exceed octave range
> ex. C D F F# G# B C# D#, next cycle will start E F# A A#...
>
> - in such wide range scales some notes can be used again in higher
> octave (including octave itself)
> ex. C C# D# E F G A C D Eb F#, next cycle starts G G# A# B C
> In composition these octaves, which represents different step number
> in every cycle, can be emphasized or not
>
> - or can be different and octave repetition is omitted
> ex. C D Eb F G A Bb B C# E F# G#, next cycle can start A B C D E F#...
> This way is possible to create 12-tone scales which and not use them
> as dodecaphony series but as a scale, which is to me more interesting
> than pure dodecaphony
>
> Concerning microtuning I would allow for such scales with so narrow
> connection to traditional scales using 12-ET maximal detuning about
> +/- 16 Cents, to avoid quartertones which would disturb this concept.
>
> Daniel Forro
>
> On 1 Nov 2008, at 12:10 AM, Charles Lucy wrote:
>
> > Let 1= used in scale.
> >
> > Let 0 = not used in scale.
> >
> > If you make a mantissa of twelve digits from 100000000000
> >
> > to
> >
> > 111111111111
> >
> > and convert this from binary to decimal.
> >
> > 2048 for 100000000000
> >
> > to
> >
> > 4095 for 111111111111
> >
> > You get a unique different scale for every number from
> >
> > 2048 to 4095
> >
> > 4095-2048 = 2047
> >
> > Add one as each number represents a unique scale, and you get a
> > result of 2048.
> >
> > One scale will only contain one note (the tonic) 100000000000
> >
> > One scale will contain all the notes 111111111111
> >
> > The scales in between will contain between 2 and 11 notes.
> >
> > That's how I arrived at 2048 unique 12 edo scales.
> >
> >
> >
> >
> >
> > On 31 Oct 2008, at 14:35, hstraub64 wrote:
> >
> >> --- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
> >> >
> >> > For the past year or so, I have been gradually compiling a > database
> >> of
> >> > all the 2048 possible scales which can be generated using 12edo,
> >> and
> >> > coding them so that they can be sorted, found, and otherwise
> >> > manipulated and examined, for their harmonic, compositional and
> >> > microtonal implications and varieties.
> >> >
> >> > You can find the current work in progress (complete with typos, > and
> >> > other errors;-) at:
> >> >
> >> > http://www.lucytune.com/scales/
> >> >
> >> > Any comments, suggestions, pointers will be appreciated
> >> appreciated.
> >> >
> >>
> >> What exactly do you count getting 2048 as a result? Sure not the
> >> number
> >> of possible subsets of 12 (which would be 12!, a very much higher
> >> number), and apparently also not the number of subsets up to
> >> translations (which, to my knowledge, yields a much smaller > number).
> >> I looked at your website but could not find this information.
> >> --
> >> Hans Straub
> >>
> >>
> >
> > Charles Lucy
> > lucy@...
> >
> > - Promoting global harmony through LucyTuning -
> >
> > for information on LucyTuning go to:
> > http://www.lucytune.com
> >
> > For LucyTuned Lullabies go to:
> > http://www.lullabies.co.uk
> >
> >
> >
> >
> >
>
>
>

P.S.

you wrote that burnin' piece--where the micrograms just keep escalating.

I linked to it.

Hope nobody's stalking you, now.

caleb

On Oct 31, 2008, at 12:04 PM, Daniel Forro wrote:

> My definition of the scale would be:
>
> - scale must have at least five steps for the scale limited to one
> octave range
> ex. C Eb F Gb Bb
>
> - scale can be constructed only from intervals 1, 2, 3, 4
>
> - interval twins which sound like triads should be excluded:
> diminished 33, minor 34, major 43, augmented 44, as they will disturb
> feeling of scale
>
> - chains of maximally three same intervals 1 or 2 can be used: 111,
> 222 to avoid musically boring chromatism or whole tone scale
>
> - scales limited to octave and constructed with these rules will have
> maximally 9 notes
> ex. C Db D Eb F F# G Ab Bb
>
> - scale can exceed octave range
> ex. C D F F# G# B C# D#, next cycle will start E F# A A#...
>
> - in such wide range scales some notes can be used again in higher
> octave (including octave itself)
> ex. C C# D# E F G A C D Eb F#, next cycle starts G G# A# B C
> In composition these octaves, which represents different step number
> in every cycle, can be emphasized or not
>
> - or can be different and octave repetition is omitted
> ex. C D Eb F G A Bb B C# E F# G#, next cycle can start A B C D E F#...
> This way is possible to create 12-tone scales which and not use them
> as dodecaphony series but as a scale, which is to me more interesting
> than pure dodecaphony
>
> Concerning microtuning I would allow for such scales with so narrow
> connection to traditional scales using 12-ET maximal detuning about
> +/- 16 Cents, to avoid quartertones which would disturb this concept.
>
> Daniel Forro
>
> On 1 Nov 2008, at 12:10 AM, Charles Lucy wrote:
>
> > Let 1= used in scale.
> >
> > Let 0 = not used in scale.
> >
> > If you make a mantissa of twelve digits from 100000000000
> >
> > to
> >
> > 111111111111
> >
> > and convert this from binary to decimal.
> >
> > 2048 for 100000000000
> >
> > to
> >
> > 4095 for 111111111111
> >
> > You get a unique different scale for every number from
> >
> > 2048 to 4095
> >
> > 4095-2048 = 2047
> >
> > Add one as each number represents a unique scale, and you get a
> > result of 2048.
> >
> > One scale will only contain one note (the tonic) 100000000000
> >
> > One scale will contain all the notes 111111111111
> >
> > The scales in between will contain between 2 and 11 notes.
> >
> > That's how I arrived at 2048 unique 12 edo scales.
> >
> >
> >
> >
> >
> > On 31 Oct 2008, at 14:35, hstraub64 wrote:
> >
> >> --- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
> >> >
> >> > For the past year or so, I have been gradually compiling a > database
> >> of
> >> > all the 2048 possible scales which can be generated using 12edo,
> >> and
> >> > coding them so that they can be sorted, found, and otherwise
> >> > manipulated and examined, for their harmonic, compositional and
> >> > microtonal implications and varieties.
> >> >
> >> > You can find the current work in progress (complete with typos, > and
> >> > other errors;-) at:
> >> >
> >> > http://www.lucytune.com/scales/
> >> >
> >> > Any comments, suggestions, pointers will be appreciated
> >> appreciated.
> >> >
> >>
> >> What exactly do you count getting 2048 as a result? Sure not the
> >> number
> >> of possible subsets of 12 (which would be 12!, a very much higher
> >> number), and apparently also not the number of subsets up to
> >> translations (which, to my knowledge, yields a much smaller > number).
> >> I looked at your website but could not find this information.
> >> --
> >> Hans Straub
> >>
> >>
> >
> > Charles Lucy
> > lucy@...
> >
> > - Promoting global harmony through LucyTuning -
> >
> > for information on LucyTuning go to:
> > http://www.lucytune.com
> >
> > For LucyTuned Lullabies go to:
> > http://www.lullabies.co.uk
> >
> >
> >
> >
> >
>
>
>

btw, DF, that was a piece of yours I really liked....it was mentioned here on the list

just sayin'

On Oct 31, 2008, at 12:04 PM, Daniel Forro wrote:

> My definition of the scale would be:
>
> - scale must have at least five steps for the scale limited to one
> octave range
> ex. C Eb F Gb Bb
>
> - scale can be constructed only from intervals 1, 2, 3, 4
>
> - interval twins which sound like triads should be excluded:
> diminished 33, minor 34, major 43, augmented 44, as they will disturb
> feeling of scale
>
> - chains of maximally three same intervals 1 or 2 can be used: 111,
> 222 to avoid musically boring chromatism or whole tone scale
>
> - scales limited to octave and constructed with these rules will have
> maximally 9 notes
> ex. C Db D Eb F F# G Ab Bb
>
> - scale can exceed octave range
> ex. C D F F# G# B C# D#, next cycle will start E F# A A#...
>
> - in such wide range scales some notes can be used again in higher
> octave (including octave itself)
> ex. C C# D# E F G A C D Eb F#, next cycle starts G G# A# B C
> In composition these octaves, which represents different step number
> in every cycle, can be emphasized or not
>
> - or can be different and octave repetition is omitted
> ex. C D Eb F G A Bb B C# E F# G#, next cycle can start A B C D E F#...
> This way is possible to create 12-tone scales which and not use them
> as dodecaphony series but as a scale, which is to me more interesting
> than pure dodecaphony
>
> Concerning microtuning I would allow for such scales with so narrow
> connection to traditional scales using 12-ET maximal detuning about
> +/- 16 Cents, to avoid quartertones which would disturb this concept.
>
> Daniel Forro
>
> On 1 Nov 2008, at 12:10 AM, Charles Lucy wrote:
>
> > Let 1= used in scale.
> >
> > Let 0 = not used in scale.
> >
> > If you make a mantissa of twelve digits from 100000000000
> >
> > to
> >
> > 111111111111
> >
> > and convert this from binary to decimal.
> >
> > 2048 for 100000000000
> >
> > to
> >
> > 4095 for 111111111111
> >
> > You get a unique different scale for every number from
> >
> > 2048 to 4095
> >
> > 4095-2048 = 2047
> >
> > Add one as each number represents a unique scale, and you get a
> > result of 2048.
> >
> > One scale will only contain one note (the tonic) 100000000000
> >
> > One scale will contain all the notes 111111111111
> >
> > The scales in between will contain between 2 and 11 notes.
> >
> > That's how I arrived at 2048 unique 12 edo scales.
> >
> >
> >
> >
> >
> > On 31 Oct 2008, at 14:35, hstraub64 wrote:
> >
> >> --- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
> >> >
> >> > For the past year or so, I have been gradually compiling a > database
> >> of
> >> > all the 2048 possible scales which can be generated using 12edo,
> >> and
> >> > coding them so that they can be sorted, found, and otherwise
> >> > manipulated and examined, for their harmonic, compositional and
> >> > microtonal implications and varieties.
> >> >
> >> > You can find the current work in progress (complete with typos, > and
> >> > other errors;-) at:
> >> >
> >> > http://www.lucytune.com/scales/
> >> >
> >> > Any comments, suggestions, pointers will be appreciated
> >> appreciated.
> >> >
> >>
> >> What exactly do you count getting 2048 as a result? Sure not the
> >> number
> >> of possible subsets of 12 (which would be 12!, a very much higher
> >> number), and apparently also not the number of subsets up to
> >> translations (which, to my knowledge, yields a much smaller > number).
> >> I looked at your website but could not find this information.
> >> --
> >> Hans Straub
> >>
> >>
> >
> > Charles Lucy
> > lucy@...
> >
> > - Promoting global harmony through LucyTuning -
> >
> > for information on LucyTuning go to:
> > http://www.lucytune.com
> >
> > For LucyTuned Lullabies go to:
> > http://www.lullabies.co.uk
> >
> >
> >
> >
> >
>
>
>

Thanks for kind words :-)

If you find few free minutes and want to listen some organized noise
sometimes called music, why not to try my contribution to the actual
90th anniversary of Czechoslovakia - first two bulks of "Variations
on Czech national anthem" (right now there's 21 of them, I'm working
on more to reach about 50). Just visit my music pages
www.soundclick.com/forrotronics, or jump in directly:

http://soundclick.com/share?songid=7017967

11 variations, orchestrated. Protestant hymn, three voice canon, four
voice fugato in Phrygian with two voices in inversion, a la Mozart, a
la Smetana (with quotations of themes from Moldau, Tabor, Vyšehrad,
The Bartered Bride and Libussa), a la Dvořák (with motifs from New
World Symphony, Humoresque, Undine/Rusalka), a la Janáček (with
motifs from Sinfonietta, Glagolitic Mass), a la Czech folklore
(quotations of folk songs Bejvávalo, Kočka, Poštovský panáček,
Ovčáci, Ej lásko, Pec, Běží liška, Vyletěla holubička), bossa
nova, a la Africa, a la Japan

and here:

http://soundclick.com/share?songid=7017948

10 variations, recently only as a piano version, arranging in
progress. A la Debussy, a la Schönberg, a la Bartók, a la Messiaen,
Czech variable meter dance "mateník", a la Turkey, a la China,
tango, waltzer, funeral march

More will come later (including reggae, Moravian, csardas, ragtime,
Ars nova, Carlo Gesualdo, salsa, Chopin, Liszt, Skriabin, heavy
metal, Haba, electronic music, gamelan, flamenco, tarantella, Greek
zembetiko, Martinu, minimal music, boogie-woogie...

I'll be happy to hear you send this link to your friends to make
their day more sunny. Nothing more can be done - with establishing
Czechoslovakia, or having selected right this sentimental hackneyed
ditty as a musical symbol of that state. But as a theme to artistic
deformation it's usable, and we have that globalization so I'm trying
to do my best. Good relax between feeding, hugging and changing
diapers of six-week old son Saimon :-)

Daniel Forro

On 1 Nov 2008, at 1:18 AM, caleb morgan wrote:

>
> btw, DF, that was a piece of yours I really liked....it was
> mentioned here on the list
>
> just sayin'
>
>
>
>
>
> On Oct 31, 2008, at 12:04 PM, Daniel Forro wrote:
>
>> My definition of the scale would be:
>>
>> - scale must have at least five steps for the scale limited to one
>> octave range
>> ex. C Eb F Gb Bb
>>
>> - scale can be constructed only from intervals 1, 2, 3, 4
>>
>> - interval twins which sound like triads should be excluded:
>> diminished 33, minor 34, major 43, augmented 44, as they will disturb
>> feeling of scale
>>
>> - chains of maximally three same intervals 1 or 2 can be used: 111,
>> 222 to avoid musically boring chromatism or whole tone scale
>>
>> - scales limited to octave and constructed with these rules will have
>> maximally 9 notes
>> ex. C Db D Eb F F# G Ab Bb
>>
>> - scale can exceed octave range
>> ex. C D F F# G# B C# D#, next cycle will start E F# A A#...
>>
>> - in such wide range scales some notes can be used again in higher
>> octave (including octave itself)
>> ex. C C# D# E F G A C D Eb F#, next cycle starts G G# A# B C
>> In composition these octaves, which represents different step number
>> in every cycle, can be emphasized or not
>>
>> - or can be different and octave repetition is omitted
>> ex. C D Eb F G A Bb B C# E F# G#, next cycle can start A B C D E
>> F#...
>> This way is possible to create 12-tone scales which and not use them
>> as dodecaphony series but as a scale, which is to me more interesting
>> than pure dodecaphony
>>
>> Concerning microtuning I would allow for such scales with so narrow
>> connection to traditional scales using 12-ET maximal detuning about
>> +/- 16 Cents, to avoid quartertones which would disturb this concept.
>>
>> Daniel Forro
>>
>> On 1 Nov 2008, at 12:10 AM, Charles Lucy wrote:
>>
>> > Let 1= used in scale.
>> >
>> > Let 0 = not used in scale.
>> >
>> > If you make a mantissa of twelve digits from 100000000000
>> >
>> > to
>> >
>> > 111111111111
>> >
>> > and convert this from binary to decimal.
>> >
>> > 2048 for 100000000000
>> >
>> > to
>> >
>> > 4095 for 111111111111
>> >
>> > You get a unique different scale for every number from
>> >
>> > 2048 to 4095
>> >
>> > 4095-2048 = 2047
>> >
>> > Add one as each number represents a unique scale, and you get a
>> > result of 2048.
>> >
>> > One scale will only contain one note (the tonic) 100000000000
>> >
>> > One scale will contain all the notes 111111111111
>> >
>> > The scales in between will contain between 2 and 11 notes.
>> >
>> > That's how I arrived at 2048 unique 12 edo scales.
>> >
>> >
>> >
>> >
>> >
>> > On 31 Oct 2008, at 14:35, hstraub64 wrote:
>> >
>> >> --- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>> >> >
>> >> > For the past year or so, I have been gradually compiling a>> database
>> >> of
>> >> > all the 2048 possible scales which can be generated using 12edo,
>> >> and
>> >> > coding them so that they can be sorted, found, and otherwise
>> >> > manipulated and examined, for their harmonic, compositional and
>> >> > microtonal implications and varieties.
>> >> >
>> >> > You can find the current work in progress (complete with
>> typos, and
>> >> > other errors;-) at:
>> >> >
>> >> > http://www.lucytune.com/scales/
>> >> >
>> >> > Any comments, suggestions, pointers will be appreciated
>> >> appreciated.
>> >> >
>> >>
>> >> What exactly do you count getting 2048 as a result? Sure not the
>> >> number
>> >> of possible subsets of 12 (which would be 12!, a very much higher
>> >> number), and apparently also not the number of subsets up to
>> >> translations (which, to my knowledge, yields a much smaller
>> number).
>> >> I looked at your website but could not find this information.
>> >> --
>> >> Hans Straub
>> >>
>> >>
>> >
>> > Charles Lucy
>> > lucy@...
>> >
>> > - Promoting global harmony through LucyTuning -
>> >
>> > for information on LucyTuning go to:
>> > http://www.lucytune.com
>> >
>> > For LucyTuned Lullabies go to:
>> > http://www.lullabies.co.uk
>> >
>> >
>> >
>> >
>> >
>>
>>
>
>
>

Hans wrote:

> What exactly do you count getting 2048 as a result? Sure not
> the number of possible subsets of 12 (which would be 12!, a
> very much higher number),

Not quite 12!. You need to take out rotation and reflections,
which gives you bracelets.

http://en.wikipedia.org/wiki/Bracelet_(combinatorics)

-Carl

I don't see why you're forcing the first note to be on,
though you can get away with it in 12-ET and you're still
getting duplicates under reflection and rotation.

-Carl

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
> Let 1= used in scale.
> Let 0 = not used in scale.
>
> If you make a mantissa of twelve digits from 100000000000
>
> to
>
> 111111111111
>
> and convert this from binary to decimal.
>
> 2048 for 100000000000
>
> to
>
> 4095 for 111111111111
>
> You get a unique different scale for every number from
>
> 2048 to 4095
>
> 4095-2048 = 2047
>
> Add one as each number represents a unique scale, and you get
> a result of 2048.

Thank you for your reassuring confidence Carl.

I am forcing the first note to be on because it is the tonic, which I have arbitrarily chosen to label as "C".

Of course there are repeating patterns and combinations within the twelve positions, yet if one is able to simultaneously hold all twelve notes within the same "breathe" or "thought", one will quickly appreciate that each of the 2048 scales is unique.

Surprisingly, so far (only a couple of hundred scales to go); each of the resulting ScaleCodings, ascending notename patterns, and that the Large and small sequences, also seem to be unique.

I have also included a few other identifying quantities, so that I can "typo and error" check the whole database to produce the "perfect" list.

I shall certainly let you know Carl, if I subsequently discover that you are correct, and that I am wrong.

On 31 Oct 2008, at 17:38, Carl Lumma wrote:

> I don't see why you're forcing the first note to be on,
> though you can get away with it in 12-ET and you're still
> getting duplicates under reflection and rotation.
>
> -Carl
>
> --- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
> >
> > Let 1= used in scale.
> > Let 0 = not used in scale.
> >
> > If you make a mantissa of twelve digits from 100000000000
> >
> > to
> >
> > 111111111111
> >
> > and convert this from binary to decimal.
> >
> > 2048 for 100000000000
> >
> > to
> >
> > 4095 for 111111111111
> >
> > You get a unique different scale for every number from
> >
> > 2048 to 4095
> >
> > 4095-2048 = 2047
> >
> > Add one as each number represents a unique scale, and you get
> > a result of 2048.
>
>
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

Hi Charles,

> I am forcing the first note to be on because it is the tonic,
> which I have arbitrarily chosen to label as "C".

That approach will only work if there is enough symmetry
in the scale. With 12-ET it'll work and you'll still get
dupes. With a linear temperament like LucyTuning it should
still work and you should still have dupes. But with some
JI scales, for example, it wouldn't work.

> Of course there are repeating patterns and combinations within
> the twelve positions, yet if one is able to simultaneously hold
> all twelve notes within the same "breathe" or "thought", one
> will quickly appreciate that each of the 2048 scales is unique.

I think you're saying, if we are talking about absolute
pitches. Well then all 2^12 scales are unique (you can't
force the tonic on).

> Surprisingly, so far (only a couple of hundred scales to go);
> each of the resulting ScaleCodings, ascending notename
> patterns, and that the Large and small sequences, also seem
> to be unique.

It's the L-s sequences that count, and you have to test for
rotations and reflections. What you want to count are the
bracelets of length 12 from alphabet [L s].

If I'm reading the wikipedia page right, it's 1/2 the
number of necklaces plus 48 (in this case). According to
http://www.research.att.com/~njas/sequences/A000031
there are 352 such necklaces. So 352/2 + 48 = 224 unique
12-tone LucyTuned scales. So you're missing a lot of
dupes in your analysis.

-Carl

On Fri, Oct 31, 2008 at 5:53 PM, Carl Lumma <carl@...> wrote:
> Hi Charles,
>
>> I am forcing the first note to be on because it is the tonic,
>> which I have arbitrarily chosen to label as "C".
>
> That approach will only work if there is enough symmetry
> in the scale. With 12-ET it'll work and you'll still get
> dupes. With a linear temperament like LucyTuning it should
> still work and you should still have dupes. But with some
> JI scales, for example, it wouldn't work.
>
>> Of course there are repeating patterns and combinations within
>> the twelve positions, yet if one is able to simultaneously hold
>> all twelve notes within the same "breathe" or "thought", one
>> will quickly appreciate that each of the 2048 scales is unique.
>
> I think you're saying, if we are talking about absolute
> pitches. Well then all 2^12 scales are unique (you can't
> force the tonic on).
>
>> Surprisingly, so far (only a couple of hundred scales to go);
>> each of the resulting ScaleCodings, ascending notename
>> patterns, and that the Large and small sequences, also seem
>> to be unique.
>
> It's the L-s sequences that count, and you have to test for
> rotations and reflections. What you want to count are the
> bracelets of length 12 from alphabet [L s].
>
> If I'm reading the wikipedia page right, it's 1/2 the
> number of necklaces plus 48 (in this case). According to
> http://www.research.att.com/~njas/sequences/A000031
> there are 352 such necklaces. So 352/2 + 48 = 224 unique
> 12-tone LucyTuned scales. So you're missing a lot of
> dupes in your analysis.
>
> -Carl

It really depends on how you want to count things. Charles is
taking the view that a scale is determined by the intervals above the
tonic, so 101011010101 (major) is not the same scale as 101101011010
(minor), though one can be transformed into the other by changing the
starting point. Carl is taking the view that the tonic doesn't count,
only the notes and therefore counts these as one scale. I can see both
points of view on this. Does a difference in tonic makes a difference
in sound? Is D Dorian different from F Lydian? If you answer yes, then
Charles's counting is for you. If you answer no, then you're in Carl's
camp.

David Bowen

Hi Carl;

Again you and I seem to be thinking, writing at cross purposes.

As far as I am concerned there is only one 12 note scale in 12edo. i.e. all twelve notes are played.
There are an infinite number of LucyTuned scales which can be generated from those twelve notes.
Each scale will contain different notes, which will have different notenames and pitches.
The quantity which can be constructed depends upon how many steps around the spiral of fourths and fifth are to be used. i.e multiple sharps and flats may be used.,
and if they fall outside the first octave they will be transposed by octave intervals to fall into the current octave.

To maintain the consistency of my system I will always be using C in the 0 leftmost position, and all other notenames indicate the interval of each of the other eleven notes from C.

Obviously any scale can be transposed to any other key, in which case the note names will change and be derived from the new tonic will occupy the 0 position.
Transpositions will not create a new unique scale in this system.

I agree that patterns will repeat in terms of L and s, between unique scales, yet only for part of the complete twelve note pattern.

If all the notes are the same from the tonic C in 0 position, it will be a duplicate of the original scale, and hence not added as a separate record, or claimed as a new scale.

On 31 Oct 2008, at 22:53, Carl Lumma wrote:

> Hi Charles,
>
> > I am forcing the first note to be on because it is the tonic,
> > which I have arbitrarily chosen to label as "C".
>
> >That approach will only work if there is enough symmetry
> >in the scale. With 12-ET it'll work and you'll still get
> >dupes. With a linear temperament like LucyTuning it should
> >still work and you should still have dupes.
>

> I fail to understand what you mean by symmetry and have addressed > any problems that I foresee with dupes in LucyTuning.
>

Using the system with JI would require the user to position and name the notes by approximations to the nearest LucyTuned note.

> But with some
> JI scales, for example, it wouldn't work.
>
> > Of course there are repeating patterns and combinations within
> > the twelve positions, yet if one is able to simultaneously hold
> > all twelve notes within the same "breathe" or "thought", one
> > will quickly appreciate that each of the 2048 scales is unique.
>
> I think you're saying, if we are talking about absolute
> pitches. Well then all 2^12 scales are unique (you can't
> force the tonic on).
>

>

>
> > Surprisingly, so far (only a couple of hundred scales to go);
> > each of the resulting ScaleCodings, ascending notename
> > patterns, and that the Large and small sequences, also seem
> > to be unique.
>
> It's the L-s sequences that count, and you have to test for
> rotations and reflections. What you want to count are the
> bracelets of length 12 from alphabet [L s].
>
> If I'm reading the wikipedia page right, it's 1/2 the
> number of necklaces plus 48 (in this case). According to
> http://www.research.att.com/~njas/sequences/A000031
> there are 352 such necklaces. So 352/2 + 48 = 224 unique
> 12-tone LucyTuned scales. So you're missing a lot of
> dupes in your analysis.
>
> -Carl
>
>
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

> The restrictions mentioned on this page do not apply, as I can have > multiple negative and positive values for L and s.
>

This page will show a short list of the "close" intervals" expressed as L and s.

The series continues infinitely.

http://www.lucytune.com/new_to_lt/pitch_02.html

>
> If I'm reading the wikipedia page right, it's 1/2 the
> number of necklaces plus 48 (in this case). According to
> http://www.research.att.com/~njas/sequences/A000031
> there are 352 such necklaces. So 352/2 + 48 = 224 unique
> 12-tone LucyTuned scales. So you're missing a lot of
> dupes in your analysis.
>
> -Carl
>
>
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

Clearly expressed David.

Thanks.

On 1 Nov 2008, at 01:51, David Bowen wrote:

> On Fri, Oct 31, 2008 at 5:53 PM, Carl Lumma <carl@...> wrote:
> > Hi Charles,
> >
> >> I am forcing the first note to be on because it is the tonic,
> >> which I have arbitrarily chosen to label as "C".
> >
> > That approach will only work if there is enough symmetry
> > in the scale. With 12-ET it'll work and you'll still get
> > dupes. With a linear temperament like LucyTuning it should
> > still work and you should still have dupes. But with some
> > JI scales, for example, it wouldn't work.
> >
> >> Of course there are repeating patterns and combinations within
> >> the twelve positions, yet if one is able to simultaneously hold
> >> all twelve notes within the same "breathe" or "thought", one
> >> will quickly appreciate that each of the 2048 scales is unique.
> >
> > I think you're saying, if we are talking about absolute
> > pitches. Well then all 2^12 scales are unique (you can't
> > force the tonic on).
> >
> >> Surprisingly, so far (only a couple of hundred scales to go);
> >> each of the resulting ScaleCodings, ascending notename
> >> patterns, and that the Large and small sequences, also seem
> >> to be unique.
> >
> > It's the L-s sequences that count, and you have to test for
> > rotations and reflections. What you want to count are the
> > bracelets of length 12 from alphabet [L s].
> >
> > If I'm reading the wikipedia page right, it's 1/2 the
> > number of necklaces plus 48 (in this case). According to
> > http://www.research.att.com/~njas/sequences/A000031
> > there are 352 such necklaces. So 352/2 + 48 = 224 unique
> > 12-tone LucyTuned scales. So you're missing a lot of
> > dupes in your analysis.
> >
> > -Carl
>
> It really depends on how you want to count things. Charles is
> taking the view that a scale is determined by the intervals above the
> tonic, so 101011010101 (major) is not the same scale as 101101011010
> (minor), though one can be transformed into the other by changing the
> starting point. Carl is taking the view that the tonic doesn't count,
> only the notes and therefore counts these as one scale. I can see both
> points of view on this. Does a difference in tonic makes a difference
> in sound? Is D Dorian different from F Lydian? If you answer yes, then
> Charles's counting is for you. If you answer no, then you're in Carl's
> camp.
>
> David Bowen
>
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

> Does a difference in tonic makes a difference in sound?
> Is D Dorian different from F Lydian? If you answer yes, then
> Charles's counting is for you. If you answer no, then you're
> in Carl's camp.
>
> David Bowen

Hi David,

It's not clear this is Charles' approach -- he seems to be
on the fence. Mode differences only become meaningful if one
specifies a concert pitch -- one is then dealing with
absolute pitches. In scale theory this is hardly ever done,
but it's not invalid if you think pitches matter more than
intervals.

-Carl

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
> Hi Carl;
>
> Again you and I seem to be thinking, writing at cross purposes.
>
> As far as I am concerned there is only one 12 note scale in 12edo.
> i.e. all twelve notes are played.

Yes, of course.

> There are an infinite number of LucyTuned scales which can be
> generated from those twelve notes.

From *which* 12 tones? I think you mean, there are an infinite
number of possible 12-tone LucyTuned scales. That's certainly
true. But there are a limited number that can be made from a
single L and s pair.

Actually I said earlier they were bracelets, but it depends
what you want to do. For my VRWT project, I was just counting
intervals, in which case reflections can be removed. However,
for general scale theory purposes, reflections are significant,
and then you just want plain necklaces.

Our resident expert on the generation of microtonal necklaces
in Paul Hjelmstad. Are you around thees days, Paul?

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Hans wrote:
>
> > What exactly do you count getting 2048 as a result? Sure not
> > the number of possible subsets of 12 (which would be 12!, a
> > very much higher number),
>
> Not quite 12!. You need to take out rotation and reflections,
> which gives you bracelets.
>

The number of all possible subsets of 12EDO is 2^12 = 4096 - that was
what I had meant, I had it wrong with 12! (slightly embarrassing
mistake for a mathematician...). And what Charles is examining are
obviously all possible subsets of 12EDO containing the first note,
which gives 2^11 = 2048.

I know about bracelets - I even know about circle-of-fifth isomorphisms
(multiplication with 7). Guerino Mazzola has done a classification of
all subsets of 12EDO including that.

Gotta have a closer look at what Charles is doing exactly - apparently
it is something like classifying scales not as sets but including a
certain base point. For this, bracelets or even only rotations are not
appropriate. But maybe there is another way of making the task easier...
--
Hans Straub

Yes Hans.

I have now gone through all 2048 possible scales in 12edo, and am adding alternative spellings.

The current total in the database is 2293, for which I have calculated the sequence of intervals, and the scalecoding.

I am beginning to list the triads available using each scale.

My initial spelling choices had been fairly arbitrary, so now I need to continue to explore more possibilities and to also rectify the bugs, typos, and errors.

Obviously I could continue to add more alternative spellings, so I am looking at each scale to find which spelling will produce the shortest chain of fourths and fifths,

on the assumption that that will produce the most (consonant/useful?????) scales.

For the equal interval enthusiasts it might also make sense to define the scales in terms of 88 edo, which will also be useful for the 22 and 44 edo users.

You can find the current state of play at:

http://www.lucytune.com/scales/

Once I have made some more progress on the corrections, I shall export the database of all 2293+ scales into an .xls format from FileMaker to make it more widely accessible.

On 5 Nov 2008, at 15:48, hstraub64 wrote:

> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> >
> > Hans wrote:
> >
> > > What exactly do you count getting 2048 as a result? Sure not
> > > the number of possible subsets of 12 (which would be 12!, a
> > > very much higher number),
> >
> > Not quite 12!. You need to take out rotation and reflections,
> > which gives you bracelets.
> >
>
> The number of all possible subsets of 12EDO is 2^12 = 4096 - that was
> what I had meant, I had it wrong with 12! (slightly embarrassing
> mistake for a mathematician...). And what Charles is examining are
> obviously all possible subsets of 12EDO containing the first note,
> which gives 2^11 = 2048.
>
> I know about bracelets - I even know about circle-of-fifth > isomorphisms
> (multiplication with 7). Guerino Mazzola has done a classification of
> all subsets of 12EDO including that.
>
> Gotta have a closer look at what Charles is doing exactly - apparently
> it is something like classifying scales not as sets but including a
> certain base point. For this, bracelets or even only rotations are not
> appropriate. But maybe there is another way of making the task > easier...
> --> Hans Straub
>
>
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, Charles Lucy <lucy@> wrote:
> >
> > Hi Carl;
> >
> > Again you and I seem to be thinking, writing at cross purposes.
> >
> > As far as I am concerned there is only one 12 note scale in 12edo.
> > i.e. all twelve notes are played.
>
> Yes, of course.
>
> > There are an infinite number of LucyTuned scales which can be
> > generated from those twelve notes.
>
> From *which* 12 tones? I think you mean, there are an infinite
> number of possible 12-tone LucyTuned scales. That's certainly
> true. But there are a limited number that can be made from a
> single L and s pair.
>
> Actually I said earlier they were bracelets, but it depends
> what you want to do. For my VRWT project, I was just counting
> intervals, in which case reflections can be removed. However,
> for general scale theory purposes, reflections are significant,
> and then you just want plain necklaces.
>
> Our resident expert on the generation of microtonal necklaces
> in Paul Hjelmstad. Are you around thees days, Paul?
>
> -Carl

Yes here i stand i can do no other

necklaces lead to Polya theory, and group theory