Two non-octave scales, two views on one temperament

Hi there.

Although I can't play non-octave scales in real-time at the moment, maybe someone of you will find these two useful. So in case you want to play around with them sooner than I can, here they are:

! xid1.scl
!
Semisixth in two octaves
16
!
73.18474
258.10077
443.01679
627.93282
701.11756
886.03359
1070.94962
1144.13436
1329.05038
1513.96641
1587.15115
1772.06718
1956.98321
2030.16795
2215.08397
4/1

! xid2.scl
!
Semitenth in two octaves
16
!
129.05038
258.10077
387.15115
627.93282
756.98321
886.03359
1015.08397
1144.13436
1384.91603
1513.96641
1643.01679
1772.06718
1901.11756
2141.89923
2270.94962
4/1

Petr

I like your semitenth especially since it has

0. 387. 757. 1385. 1772. 2271. 2400. 2529.

DanN

Hi Dan.

>I like your semitenth especially since it has
>
> 0. 387. 757. 1385. 1772. 2271. 2400. 2529.

Thanks, that's interesting. What does this particular selection of pitches mean? Or why have you singled out these ones and not others?

Anyway, I think I still like the two-octave semisixth more as it maps a full 2:3:5:8, though not a 2/1.

Petr

Hey, Petr,

It's just a chord (though perhaps not a scale) I like: augmented triads
stacked first a tritone apart, then a 4th, then a 3rd, etc. And one can tune
on the violin to Gb-D-Ab-E (though, like I say, that chord may not function
as a very lovely scale in general)..

DanN

On Thu, Jul 7, 2011 at 12:27 PM, Petr Parízek <petrparizek2000@...>wrote:

> **
>
>
> Hi Dan.
>
>
> >I like your semitenth especially since it has
> >
> > 0. 387. 757. 1385. 1772. 2271. 2400. 2529.
>
> Thanks, that's interesting. What does this particular selection of pitches
> mean? Or why have you singled out these ones and not others?
>
> Anyway, I think I still like the two-octave semisixth more as it maps a
> full
> 2:3:5:8, though not a 2/1.
>
> Petr
>

Hi Petr,

I copied the tunings and probably will try them. What is a semisixth?
I searched on the xenwiki and didn't find the term.

Thanks,

Chris

2011/7/5 Petr Pařízek <petrparizek2000@...>

> **
>
>
> Hi there.
>
> Although I can't play non-octave scales in real-time at the moment, maybe
> someone of you will find these two useful. So in case you want to play
> around with them sooner than I can, here they are:
>
> ! xid1.scl
> !
> Semisixth in two octaves
> 16
> !
> 73.18474
> 258.10077
> 443.01679
> 627.93282
> 701.11756
> 886.03359
> 1070.94962
> 1144.13436
> 1329.05038
> 1513.96641
> 1587.15115
> 1772.06718
> 1956.98321
> 2030.16795
> 2215.08397
> 4/1
>
> ! xid2.scl
> !
> Semitenth in two octaves
> 16
> !
> 129.05038
> 258.10077
> 387.15115
> 627.93282
> 756.98321
> 886.03359
> 1015.08397
> 1144.13436
> 1384.91603
> 1513.96641
> 1643.01679
> 1772.06718
> 1901.11756
> 2141.89923
> 2270.94962
> 4/1
>
> Petr
>
>
>

"Although I can't play non-octave scales in real-time at the moment, maybe
someone of you will find these two useful. So in case you want to play
around with them sooner than I can..."

Why can't you, Petr? Just taking a moment to plug Fife (
http://dwnielsen.net ) in case it's helpful. I need someone to try it out on
another (Windows) machine and tell me if it works for them (although I
understand if you don't want to play tester).

DanN

On Thu, Jul 7, 2011 at 5:46 PM, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Hi Petr,
>
> I copied the tunings and probably will try them. What is a semisixth?
> I searched on the xenwiki and didn't find the term.

Semisixth is called "sensi" on the xenwiki. The generator is a
supermajor third. In this case he's making the period out to be two
octaves instead of one. The idea is that two supermajor thirds gets
you to a major sixth.

-Mike

Hi Petr

I tried both tunings last night but unfortunately they didn't click with me.
I'm not sure why though.

Chris

On Thu, Jul 7, 2011 at 8:30 PM, Daniel Nielsen <nielsed@...> wrote:

> **
>
>
> "Although I can't play non-octave scales in real-time at the moment,
> maybe
>
> someone of you will find these two useful. So in case you want to play
> around with them sooner than I can..."
>
> Why can't you, Petr? Just taking a moment to plug Fife (
> http://dwnielsen.net ) in case it's helpful. I need someone to try it out
> on another (Windows) machine and tell me if it works for them (although I
> understand if you don't want to play tester).
>
> DanN
>
> _
>

Oops, I meant 0. 387. 757. 1385. 1772. -->2142.<-- 2400. 2529.

(steps 0 3 5 9 12 14 16)

On Tue, Jul 5, 2011 at 10:24 PM, Daniel Nielsen <nielsed@...> wrote:

> I like your semitenth especially since it has
>
> 0. 387. 757. 1385. 1772. 2271. 2400. 2529.
>
> DanN
>

Chris wrote:

> Hi Petr
>
> I tried both tunings last night but unfortunately they didn't click with > me.
> I'm not sure why though.

Try playing around with triads, there's quite a lot of 2:3:5:8 approximations in the semisixth version or 1:3:4:5 in the semitenth version.

Petr

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
> I tried both tunings last night but unfortunately they didn't click >with me.
> I'm not sure why though.

It is a bit misleading to call these "scales". Even though it may be technically correct to refer to these as scales, "scale" has certain unspoken connotations. These are more like "purpose-built interval arrays", or something along those lines, and in an academic environment would qualify as "pre-compositional material". But they originate as (Petr's) post-compositional materials, that is, the "scales" are derived from the true pre-compositional structures Petr had in mind- (efficiently) spelling out the tempering-out a specific comma for example.

Oh, Chris- when you tried these "scales", did you use your guitar as your MIDI controller?

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@> wrote:
> > I tried both tunings last night but unfortunately they didn't click >with me.
> > I'm not sure why though.
>
> It is a bit misleading to call these "scales". Even though it may be technically correct to refer to these as scales, "scale" has certain unspoken connotations. These are more like "purpose-built interval arrays", or something along those lines, and in an academic environment would qualify as "pre-compositional material". But they originate as (Petr's) post-compositional materials, that is, the "scales" are derived from the true pre-compositional structures Petr had in mind- (efficiently) spelling out the tempering-out a specific comma for example.
>

Lobawad wrote:

> It is a bit misleading to call these "scales". Even though it may be > technically correct to refer to these as scales,
> "scale" has certain unspoken connotations. These are more like > "purpose-built interval arrays", or something
> along those lines, and in an academic environment would qualify as > "pre-compositional material". But they
> originate as (Petr's) post-compositional materials, that is, the "scales" > are derived from the true
> pre-compositional structures Petr had in mind- (efficiently) spelling out > the tempering-out a specific comma
> for example.

To be more precise, first I had the comma, [2 9 -7], and I tempered it out using the individual multiplication by approximately:
6/10*6/10*6/10*6*6/10*6/10*6/10*6/10*6 (either this way or it was backwards, I've forgotten now)
I'm saying "approximately" because the steps were not 6/1 and 1/10 but each of them was divided by the 16th root of 78732/78125 (which means one becomes narrower and the other becomes wider).
This gave me 16 pitches, the last of which was 0 cents. If I strip this one out and sort the result in ascending order, I get 16 equal divisions of 60/1 without actually having the 60/1 there.
Then, I reduced all the pitches into a range of 4/1 and used this 4/1 as the equivalence interval.

Okay, this was semisixth.
Semitenth is similar, except that the generagor is the octave complement of the previous one.

Once I find a way to play this, I'll make something out of it.

Petr

I used my 88 key fake piano mid controller. I did try quite a number of
chords. Perhaps I'll go back and try these tunings again - though I wish
someone would tell me what a semisixth and semitenth are.

Chris

On Sun, Jul 10, 2011 at 4:40 AM, lobawad <lobawad@...> wrote:

> **
>
>
> Oh, Chris- when you tried these "scales", did you use your guitar as your
> MIDI controller?
>
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
> >
> >
> >
> > --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@> wrote:
> > > I tried both tunings last night but unfortunately they didn't click
> >with me.
> > > I'm not sure why though.
> >
> > It is a bit misleading to call these "scales". Even though it may be
> technically correct to refer to these as scales, "scale" has certain
> unspoken connotations. These are more like "purpose-built interval arrays",
> or something along those lines, and in an academic environment would qualify
> as "pre-compositional material". But they originate as (Petr's)
> post-compositional materials, that is, the "scales" are derived from the
> true pre-compositional structures Petr had in mind- (efficiently) spelling
> out the tempering-out a specific comma for example.
> >
>

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> I used my 88 key fake piano mid controller. I did try quite a number of
> chords. Perhaps I'll go back and try these tunings again - though I wish
> someone would tell me what a semisixth and semitenth are.

A semisixth is an approximate sqrt(5/3); equating that with 9/7 tempers out 245/243. A semitenth is an approximate sqrt(5/2), equating that with 11/7 tempers out 245/242.

thank you!

On Sun, Jul 10, 2011 at 8:34 PM, genewardsmith
<genewardsmith@sbcglobal.net>wrote:

> **
>
>
>
>
> --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
> >
> > I used my 88 key fake piano mid controller. I did try quite a number of
> > chords. Perhaps I'll go back and try these tunings again - though I wish
> > someone would tell me what a semisixth and semitenth are.
>
> A semisixth is an approximate sqrt(5/3); equating that with 9/7 tempers out
> 245/243. A semitenth is an approximate sqrt(5/2), equating that with 11/7
> tempers out 245/242.
>
>
>

Chris wrote:

> I used my 88 key fake piano mid controller.

What synth or WS are you controlling with that?

> I did try quite a number of
> chords. Perhaps I'll go back and try these tunings again - though I wish
> someone would tell me what a semisixth and semitenth are.

Semisixth, AFAIK, is a name of a particular temperament rather than an interval. But in theory, the interval in question could be called like that as well. Let's put it straight in the 5-limit so that you could understand my point:
If you have a step of ~443 cents, then two of them make a nice major sixth (that's why "semisixth"). But also (and this is an the goal in 5-limit semisixth tempering) 7 of them make a very good fifth plus 2 octaves, and 9 of them make a very good major third plus 3 octaves. This particular temperament is called "semisixth" or "semisixths" (or "sensipent") and is understood to have a one-octave period in most cases. In my version, I used a two-octave period, which offers more harmonic possibilities with less tones and also gives me a MOS within the entire interval sequence leading to the comma pump.

Semitenth is rather a piece of my modified terminology, not a well-known term which I would have read somewhere out there. If you have a step of ~757 cents, then two of them make a nice minor tenth (that's why semitenth). Although the tempering is just the opposite of semisixth (i.e. using -7 and -9 generators for the desired approximations), I called it "semitenth" because a two-octave period makes it a different scale.

If you use Scala, you can load the first scale and type "show location 2:3:5" or load the second scale and type "show location 3:4:5". This should tell you which scale degrees approximate the target chords.

Hope this helps.

Petr

Thanks for the explanation of semisixth, etc. Petr.

I used pianoteq - that is pretty much my default unless I have my guitar
synth out.

On Mon, Jul 11, 2011 at 11:21 AM, Petr Parízek <petrparizek2000@...>wrote:

> **
>
>
> Chris wrote:
>
> > I used my 88 key fake piano mid controller.
>
> What synth or WS are you controlling with that?
>
>
> > I did try quite a number of
> > chords. Perhaps I'll go back and try these tunings again - though I wish
> > someone would tell me what a semisixth and semitenth are.
>
> Semisixth, AFAIK, is a name of a particular temperament rather than an
> interval. But in theory, the interval in question could be called like that
>
> as well. Let's put it straight in the 5-limit so that you could understand
> my point:
>