Yahoo Tuning Groups Ultimate Backup tuning "double octave" (IE 4/1 period) tuning based on 12TET

--"I would prefer...

--C Eb F Ab Bb D E G A C" -Daniel
That definitely sounds more "major key" than my version...and also sounds very good to my ears; definitely useful, thank you. :-)
I also noticed we have the exact same scale up until D (and, for that note and beyond going upward in the scale, everything is a semitone over my scale)...any reason why/how mathematically you calculated that?

--"Why octave C should sound terribly in your scale? Maybe because it
--fights with neighboring C# when played as a chord?" -Daniel

It seems to clash with the F# in my scale.
However I tried using the C as C Eb F Ab Bb C6...and it worked fine.
I also noticed (building off the above "mini-scale") that

.....C Eb F Ab Bb C6 Eb Ab Bb C7.......
works as well. So, Daniel, what do you think of that one?

And also, just wondering, have you made any other non-single-octave scales in 12TET that you'd recommend as being very symmetric and consonant?

-Michael

--- On Mon, 4/13/09, Daniel Forro <dan.for@tiscali.cz> wrote:

From: Daniel Forro <dan.for@...>
Subject: Re: [tuning] "double octave" (IE 4/1 period) tuning based on 12TET
To: tuning@yahoogroups.com
Date: Monday, April 13, 2009, 9:19 PM

I work a lot with symmetrical scales and chords, so I would prefer

this one:

C Eb F Ab Bb D E G A C

Some detuning on some or all notes (except "root" C) would be also

possible (preferably symmetric, too).

Why octave C should sound terribly in your scale? Maybe because it

fights with neighboring C# when played as a chord?

Daniel Forro

On 14 Apr 2009, at 12:13 PM, djtrancendance wrote:

> I found the below scale strictly by ear. And I figured some of you

> JI buffs would have some ideas for why this works mathematically

> (or not).

> I would also appreciate ideas for what intervals would be best used

> to most efficiently translate into the most pure possible JI form.

> c5 d#5 f5 g#5 a#5 | c#6 d#6 f#6 g#6 a#6 | c7 (4/1 period /"double

> octave")

> Note: you can actually play this entire scale as a huge chord and

> it doesn't sound half bad, at least to my ears.

> ------------ --------- --------- --------- --------

> Side note: I found this scale using plain old 12TET...the only

> weird thing is...that the scale has a "double octave" period (and

> playing the "normal" 2/1 octave note c6, for example, sounds

> terrible in the scale).

> -Michael

🔗Daniel Forro <dan.for@...>

There's no high math in it, just a symmetry, where axis tone is that hidden, not used C in the middle.

Yes, lower 5 tones are the same like in yours, I just copied it, and created symmetry, mirror to it, from upper C downwards. It's easy. I like such toys since my childhood.

Upper notes were not derived by a half tone transposition, if yes, there would be B. It's just intervallic symmetry to lower 5 tones. In number of halftones you will get:

3 2 3 2 (4) 2 3 2 3

where 4 is axis interval. From intervals 2 and 3 it's clear there are anhemitonic pentatonics cells. Lower octave pentatonics is F minor (on C), upper is C major pentatonics (on D).

You can find symmetry also in the missing tones C# F# B, C# is halftone up from C, F# is middle of octave and B is halftone down from C.

I don't see anything special in your last example, as there's no order in it, besides there's no reason to consider it a scale closed in two octaves. It looks just as a repetition of the same notes in the higher octave, and F is missing...

You can create many symmetric scales or chords. For example two scales closed in two octaves, based on diminished chords:

C Db E G Bb D F Ab B C
C D F Ab B Db E G Bb C

I think more interesting are scales closed in different interval from octave(s), as they rotates - each their period, repetition uses different tones. Such scales are good for piano compositions, for example this symmetrical twelve tone row closed in minor seventh over octave:

A Bb C# D# E G Ab B C D F F#

Intervallic structure:

1 3 2 1 3 (1) 3 1 2 3 1

Thanks to 1 3 and 3 1 cells it has Arabian character, but there are also pentatonics cells 2 3 and 3 2, and Lydian subset, and Mixolydian subset, and Japanese hirajoshi, and whole-tone subsets, and diminished chords, and... Because I love tritone relation (half octave) and it's like "burned" into my creative process, right now, two minutes after inventing this scale, I have realized there's another interesting hidden feature: six lower notes are combined from chords A major and Eb major, six upper notes are combined from F minor and B minor chords. A major and B minor triads are mirrored one to the other as well as Eb major second inversion (kvartsextakord) to F minor first inversion (sextakord). That means also there's a lot of tritones inside, because sum of 1, 2 and 3 in different permutations (which all are to find here) gives 6.

Next period will be:

G Ab B C# D F F# A Bb C D# E

Next will be between F - D, next Eb - C (which is the highest note on piano, and as I wanted to finish on it, I constructed scale with this idea).

For sure I will use this one in my nearest work for four hand piano... It gives a lot of possibilities, just to name one more: emphasizing or not emphasizing of the same notes in different octaves (to confuse listeners concerning scale structure), or edge starting notes of periods (which create part of whole tone scale - A G F Eb) etc... In my opinion it's a good example of an ideal connection of numbers and beauty, which is what I always try to find in the music. In my understanding music should have such internal order, organization. To create such works is my small revenge to the entropy :-)

Symmetry doesn't necessarily means consonance, it has nothing common, despite the fact I can create even nice sounding symmetrical chords (try for example F# A E B D, or F# A C E G# B D). Everything depends on intervallic selection. Harmonic series is not symmetric, and it's consonant. But when I prepare symmetrical scales and chords, I don't take care too much about consonance or dissonance. This can be easily added during compositional process by using of latent features of a basic scale, and by selection of intervals.

Of course it's possible also to create non symmetrical scales closed in big interval, where main construction principle is different, for example this rather primitive example of 12 tone assymetric scale combined from diatonics on white keys + pentatonics on black keys:

C D E F G A B Db Eb Gb Ab Bb

It's C Ionian and Gb major pentatonic. More creative would be now to change modes, for example C Dorian and C# minor pentatonics:

C D Eb F G A Bb C# E F# G# B

Or C Locrian plus G major pentatonics:

C Db Eb F Gb Ab Bb B D E G A

Creativity here has no limits... So I wouldn't recommend you any of my former scales, make your own, still there are some more waiting on you :-)

Daniel Forro

On 14 Apr 2009, at 2:47 PM, Michael Sheiman wrote:
>
> --"I would prefer...
> --C Eb F Ab Bb D E G A C" -Daniel
> That definitely sounds more "major key" than my version...and > also sounds very good to my ears; definitely useful, thank you. :-)
> I also noticed we have the exact same scale up until D (and, > for that note and beyond going upward in the scale, everything is a > semitone over my scale)...any reason why/how mathematically you > calculated that?
>
> --"Why octave C should sound terribly in your scale? Maybe because it
> --fights with neighboring C# when played as a chord?" -Daniel
>
> It seems to clash with the F# in my scale.
> However I tried using the C as C Eb F Ab Bb C6...and it worked fine.
> I also noticed (building off the above "mini-scale") that
>
> .....C Eb F Ab Bb C6 Eb Ab Bb C7.......
> works as well. So, Daniel, what do you think of that one?
>
> And also, just wondering, have you made any other non-single-> octave scales in 12TET that you'd recommend as being very symmetric > and consonant?
>
> -Michael

🔗djtrancendance@...

--"It's just intervallic symmetry to lower 5 tones. In
--number of halftones you will get:

--3 2 3 2 (4) 2 3 2 3" -Daniel
Seems obvious looking at it that way, you mirrored the first half so 3 2 3 2 became 2 3 2 3.

--"My scale was: c5 d#5 f5 g#5 a#5 | c#6 d#6 f#6 g#6 a#6 | c7
--AKA 3 2 3 2 3 2 3 2 2 2"

--"It seems there was nothing symmetrical like the pattern you made.
--'(the scale) looks just as a repetition of the same notes (but) F is missing...' "
Actually it's "replaced" with F#(6) and, in the "second octave", c becomes c#(6). Thus two notes are different in each octave.

---(one idea is to...) change modes, for example C Dorian and C# minor ---pentatonics:" C D Eb F G A Bb C# E F# G# B -Daniel
Right, so up until c# it's "c Dorian", but then during/after (that c#) it's "c# Minor".

My only question is, when you do such things, how do you make the area around (G A Bb C# E) symmetrical (and/or "good sounding")...and/or why did you mathematically want to choose C# minor and not, say C# Lydian or C# Major?

-Michael

--- On Tue, 4/14/09, Daniel Forro <dan.for@...> wrote:

From: Daniel Forro <dan.for@...>
Subject: Re: [tuning] "double octave" (IE 4/1 period) tuning based on 12TET
To: tuning@yahoogroups.com
Date: Tuesday, April 14, 2009, 1:58 AM

There's no high math in it, just a symmetry, where axis tone is that

hidden, not used C in the middle.

Yes, lower 5 tones are the same like in yours, I just copied it, and

created symmetry, mirror to it, from upper C downwards. It's easy. I

like such toys since my childhood.

Upper notes were not derived by a half tone transposition, if yes,

there would be B. It's just intervallic symmetry to lower 5 tones. In

number of halftones you will get:

3 2 3 2 (4) 2 3 2 3

where 4 is axis interval. From intervals 2 and 3 it's clear there are

anhemitonic pentatonics cells. Lower octave pentatonics is F minor

(on C), upper is C major pentatonics (on D).

You can find symmetry also in the missing tones C# F# B, C# is

halftone up from C, F# is middle of octave and B is halftone down

from C.

I don't see anything special in your last example, as there's no

order in it, besides there's no reason to consider it a scale closed

in two octaves. It looks just as a repetition of the same notes in

the higher octave, and F is missing...

You can create many symmetric scales or chords. For example two

scales closed in two octaves, based on diminished chords:

C Db E G Bb D F Ab B C

C D F Ab B Db E G Bb C

I think more interesting are scales closed in different interval from

octave(s), as they rotates - each their period, repetition uses

different tones. Such scales are good for piano compositions, for

example this symmetrical twelve tone row closed in minor seventh over

octave:

A Bb C# D# E G Ab B C D F F#

Intervallic structure:

1 3 2 1 3 (1) 3 1 2 3 1

Thanks to 1 3 and 3 1 cells it has Arabian character, but there are

also pentatonics cells 2 3 and 3 2, and Lydian subset, and Mixolydian

subset, and Japanese hirajoshi, and whole-tone subsets, and

diminished chords, and... Because I love tritone relation (half

octave) and it's like "burned" into my creative process, right now,

two minutes after inventing this scale, I have realized there's

another interesting hidden feature: six lower notes are combined from

chords A major and Eb major, six upper notes are combined from F

minor and B minor chords. A major and B minor triads are mirrored one

to the other as well as Eb major second inversion (kvartsextakord) to

F minor first inversion (sextakord). That means also there's a lot of

tritones inside, because sum of 1, 2 and 3 in different permutations

(which all are to find here) gives 6.

Next period will be:

G Ab B C# D F F# A Bb C D# E

Next will be between F - D, next Eb - C (which is the highest note on

piano, and as I wanted to finish on it, I constructed scale with this

idea).

For sure I will use this one in my nearest work for four hand

piano... It gives a lot of possibilities, just to name one more:

emphasizing or not emphasizing of the same notes in different octaves

(to confuse listeners concerning scale structure), or edge starting

notes of periods (which create part of whole tone scale - A G F Eb)

etc... In my opinion it's a good example of an ideal connection of

numbers and beauty, which is what I always try to find in the music.

In my understanding music should have such internal order,

organization. To create such works is my small revenge to the

entropy :-)

Symmetry doesn't necessarily means consonance, it has nothing common,

despite the fact I can create even nice sounding symmetrical chords

(try for example F# A E B D, or F# A C E G# B D). Everything depends

on intervallic selection. Harmonic series is not symmetric, and it's

consonant. But when I prepare symmetrical scales and chords, I don't

take care too much about consonance or dissonance. This can be easily

added during compositional process by using of latent features of a

basic scale, and by selection of intervals.

Of course it's possible also to create non symmetrical scales closed

in big interval, where main construction principle is different, for

example this rather primitive example of 12 tone assymetric scale

combined from diatonics on white keys + pentatonics on black keys:

C D E F G A B Db Eb Gb Ab Bb

It's C Ionian and Gb major pentatonic. More creative would be now to

change modes, for example C Dorian and C# minor pentatonics:

C D Eb F G A Bb C# E F# G# B

Or C Locrian plus G major pentatonics:

C Db Eb F Gb Ab Bb B D E G A

Creativity here has no limits... So I wouldn't recommend you any of

my former scales, make your own, still there are some more waiting on

you :-)

Daniel Forro

On 14 Apr 2009, at 2:47 PM, Michael Sheiman wrote:

> --"I would prefer...

> --C Eb F Ab Bb D E G A C" -Daniel

> That definitely sounds more "major key" than my version...and

> also sounds very good to my ears; definitely useful, thank you. :-)

> I also noticed we have the exact same scale up until D (and,

> for that note and beyond going upward in the scale, everything is a

> semitone over my scale)...any reason why/how mathematically you

> calculated that?

> --"Why octave C should sound terribly in your scale? Maybe because it

> --fights with neighboring C# when played as a chord?" -Daniel

> It seems to clash with the F# in my scale.

> However I tried using the C as C Eb F Ab Bb C6...and it worked fine.

> I also noticed (building off the above "mini-scale" ) that

> .....C Eb F Ab Bb C6 Eb Ab Bb C7.......

> works as well. So, Daniel, what do you think of that one?

> And also, just wondering, have you made any other non-single-

> octave scales in 12TET that you'd recommend as being very symmetric

> and consonant?

> -Michael

🔗Daniel Forro <dan.for@...>

On 14 Apr 2009, at 10:19 PM, djtrancendance@... wrote:

> --"It's just intervallic symmetry to lower 5 tones. In
> --number of halftones you will get:
> --3 2 3 2 (4) 2 3 2 3" -Daniel
> Seems obvious looking at it that way, you mirrored the first > half so 3 2 3 2 became 2 3 2 3.

You've got it.

> --"My scale was: c5 d#5 f5 g#5 a#5 | c#6 d#6 f#6 g#6 a#6 | c7
> --AKA 3 2 3 2 3 2 3 2 > 2 2"
>
> --"It seems there was nothing symmetrical like the pattern you made.

Yes, this is not symmetry.

But in the next sentence I didn't reacted to your original first example, but to your last one:

> > .....C Eb F Ab Bb C6 Eb Ab Bb C7.......
> > works as well. So, Daniel, what do you think of that one?
> >

So why do you again return to your original scale? My description was exact. Same notes, just F is missing in the upper octave. And the highest C7 is start of new period, so it was not necessary to write.

> --'(the scale) looks just as a repetition of the same notes (but) F > is missing...' "
> Actually it's "replaced" with F#(6) and, in the "second octave", > c becomes c#(6). Thus two notes are different in each octave.

Yes, in your original scale. But my reaction was focused to your last example. Read please more carefully :-)
>
> ---(one idea is to...) change modes, for example C Dorian and C# > minor ---pentatonics:" C D Eb F G A Bb C# E F# G# B -Daniel
> Right, so up until c# it's "c Dorian", but then during/after (that > c#) it's "c# Minor".

Not exactly, I said C Dorian followed by C# minor pentatonics.
>
> My only question is, when you do such things, how do you make > the area around (G A Bb C# E) symmetrical (and/or "good > sounding")...and/or why did you mathematically want to choose C# > minor and not, say C# Lydian or C# Major?
>

Please read carefully. I wrote:

> Of course it's possible also to create non symmetrical scales closed
> in big interval, where main construction principle is different, for
> example this rather primitive example of 12 tone assymetric scale
> combined from diatonics on white keys + pentatonics on black keys:

Don't you see clearly written: "non symmetrical scales"? There's no symmetry in all my examples following this.

(And I didn't say that symmetrical means automatically "good sounding". Quite opposite: very often assymmetry is considered to be nice in the art, be it Golden Cut or other principles. I combine and mix assymmetry with symmetry.)

If you want to create 12-tone scales in the similar way as me in those examples, then certain combinations are not possible. There's no mathematics in it. I just use in the upper octave all notes which I didn't use in lower octave. So with C Dorian in lower octave it's not possible to use C# Lydian or C# Major in upper octave, because in such case there will be 7+7=14 notes (not 12), some notes will be used two times (Eb F G Bb C when upper scale will be C# Lydian, Eb F Bb C when C# Major), some will be missing (E F# B in the first case, E B in the second one). Besides the last note B# of both C# scales in upper octave will be identical with the first note of the next period, which I don't want (there's always "bridge" interval in all my scales).

So it's obvious: when there's C Dorian in lower octave (C D Eb F G A Bb), notes missing to chromatics are C# E F# G# B, which is C# minor pentatonics and I use it in the upper octave.

Daniel

"double octave" (IE 4/1 period) tuning based on 12TET

🔗djtrancendance <djtrancendance@...>

🔗Daniel Forro <dan.for@...>

🔗Michael Sheiman <djtrancendance@...>

🔗Daniel Forro <dan.for@...>

🔗djtrancendance@...

🔗Daniel Forro <dan.for@...>

🔗Michael Sheiman <djtrancendance@...>