Canyon Diablo Fall

I present a warts and all piano improvisation of a non-octave tuning I
haven't heard of before - but I'd be surprised if I invented it. I
didn't try very hard to find it, I'll admit.

I divide a perfect fourth into 4 steps of 125 cents.
http://chrisvaisvil.com/?p=3121

what follows is a list of steps over a roughly 2 octave span.

0
125
250
375
500
625
750
875
1000
1125
1250
1375
1500
1625
1750
1875
2000
2125
2250
2375
2500

Looks to me like a non-octave version of negri in 48-EDO. If you keep stacking those 125 cent intervals, you'll get 48-ED32 - the tuning where 5 pure octaves (= 32:1) are divided into 48 equal steps.

The 21-note scale you list here can be viewed as negri[21] with the restriction that each note is only available in a certain octave. What I find interesting is that perfect fourths and major thirds are easily available from most steps, while their complements (perfect fifths and minor sixths) don't exist.

Note that 48-EDO doesn't support negri when using patent vals, but 2\19 and 3\29 are valid generators for negri, and 5\48 lies between them, so I think it's not that far-fetched to speak of 'negri' in 48-EDO. ;)

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> I present a warts and all piano improvisation of a non-octave tuning I
> haven't heard of before - but I'd be surprised if I invented it. I
> didn't try very hard to find it, I'll admit.
>
> I divide a perfect fourth into 4 steps of 125 cents.
> http://chrisvaisvil.com/?p=3121
>
> what follows is a list of steps over a roughly 2 octave span.
>
> 0
> 125
> 250
> 375
> 500
> 625
> 750
> 875
> 1000
> 1125
> 1250
> 1375
> 1500
> 1625
> 1750
> 1875
> 2000
> 2125
> 2250
> 2375
> 2500

Hi Chris,

On 18.03.2013 03:18 Chris Vaisvil wrote:

> I divide a perfect fourth into 4 steps of 125 cents.
I find this a little confusing, the*perfect* fourth isn't 500 cents, but
ca. 498.05,
and in your table, you divided the fourth of 12edo. What was (is) your
intention?
> http://chrisvaisvil.com/?p=3121
Sounds interestring, especially after some rounds (nice "pentatonic" at
7:00).
Thanks for the experience.

Best,
Wolf

Dear Wolf,

are you by any chance a (fellow) native German speaker? If so, I have a suspicion about your confusion.

--- In tuning@yahoogroups.com, Wolf Peuker <wolfpeuker@...> wrote:
> On 18.03.2013 03:18 Chris Vaisvil wrote:
> > I divide a perfect fourth into 4 steps of 125 cents.
> I find this a little confusing, the*perfect* fourth isn't 500 cents, but
> ca. 498.05,
> and in your table, you divided the fourth of 12edo. What was (is) your
> intention?

The German translation for 'perfect fourth' is 'reine Quarte'. However, the adjective 'rein' is ambigous, and besides 'perfect', other possible English translations are 'pure' or 'just', as in 'pure interval' or 'just ratio'. However, in English, 'perfect' just means the interval in questions is perfect (as opposed to diminished or augmented), but it doesn't imply that it is pure / just.

So when Chris wrote 'a perfect fourth', he just refered to an interval that represents 4:3, but not necessarily to a *just* perfect fourth with a ratio of 4:3.

That's at least how I understand it, please correct me if I got something wrong here.

I hope I could help! ;)

- Gedankenwelt

Hi Gedankenwelt94,

Am 19.03.2013 17:04, schrieb gedankenwelt94:
> Dear Wolf,
>
> are you by any chance a (fellow) native German speaker? If so, I have a suspicion about your confusion.
Yes I am :-) And you are absolutely right with your suspicion -
I myself detected the ambiguity, but too late.

>
> The German translation for 'perfect fourth' is 'reine Quarte'. However, the adjective
> 'rein' is ambigous, and besides 'perfect', other possible English translations are
> 'pure' or 'just', as in 'pure interval' or 'just ratio'. However, in English, 'perfect'
> just means the interval in questions is perfect (as opposed to diminished or augmented),
> but it doesn't imply that it is pure / just.

Thanks for this *perfect* clarification ;-)

BTW: this reminds me of the German Wikipedia article "Reine Stimmung"
(with questionable content) that captures every just intonation link...

Best,
Wolf

Hi,

Thank you for the observations regarding this tuning. I had not noticed the
absence the compliment intervals of 5ths and 6ths. That is an interesting
property. I can't say that I'm really aware of the qualifications for Negri
- but now I think I will take a look at the xenharmonic wiki and see how
this fits in.

Again,

Thanks and have a great day!

Chris

On Mon, Mar 18, 2013 at 11:05 AM, gedankenwelt94
<gedankenwelt94@...>wrote:

> **
>
>
> Looks to me like a non-octave version of negri in 48-EDO. If you keep
> stacking those 125 cent intervals, you'll get 48-ED32 - the tuning where 5
> pure octaves (= 32:1) are divided into 48 equal steps.
>
> The 21-note scale you list here can be viewed as negri[21] with the
> restriction that each note is only available in a certain octave. What I
> find interesting is that perfect fourths and major thirds are easily
> available from most steps, while their complements (perfect fifths and
> minor sixths) don't exist.
>
> Note that 48-EDO doesn't support negri when using patent vals, but 2\19
> and 3\29 are valid generators for negri, and 5\48 lies between them, so I
> think it's not that far-fetched to speak of 'negri' in 48-EDO. ;)
>
>
> --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
> >
> > I present a warts and all piano improvisation of a non-octave tuning I
> > haven't heard of before - but I'd be surprised if I invented it. I
> > didn't try very hard to find it, I'll admit.
> >
> > I divide a perfect fourth into 4 steps of 125 cents.
> > http://chrisvaisvil.com/?p=3121
> >
> > what follows is a list of steps over a roughly 2 octave span.
> >
> > 0
> > 125
> > 250
> > 375
> > 500
> > 625
> > 750
> > 875
> > 1000
> > 1125
> > 1250
> > 1375
> > 1500
> > 1625
> > 1750
> > 1875
> > 2000
> > 2125
> > 2250
> > 2375
> > 2500
>
>
>

Hi Wolf,

Thanks for the listen and comments!

Well, yes, indeed I meant the 498 cent fourth but used the 500 cent out of
ignorance. I'm don't possess a lot of tuning knowledge and mostly work on
the composition end of things.

Chris

On Tue, Mar 19, 2013 at 6:46 AM, Wolf Peuker <wolfpeuker@googlemail.com>wrote:

> **
>
>
> Hi Chris,
>
>
> On 18.03.2013 03:18 Chris Vaisvil wrote:
>
> > I divide a perfect fourth into 4 steps of 125 cents.
> I find this a little confusing, the*perfect* fourth isn't 500 cents, but
> ca. 498.05,
> and in your table, you divided the fourth of 12edo. What was (is) your
> intention?
> > http://chrisvaisvil.com/?p=3121
> Sounds interestring, especially after some rounds (nice "pentatonic" at
> 7:00).
> Thanks for the experience.
>
> Best,
> Wolf
>
>
>

--- In tuning@yahoogroups.com, "gedankenwelt94" <gedankenwelt94@...> wrote:
> Note that 48-EDO doesn't support negri when using patent vals, but 2\19 and 3\29 are valid generators for negri, and 5\48 lies between them, so I think it's not that far-fetched to speak of 'negri' in 48-EDO. ;)

Ok, I'm slightly confused now, maybe someone who knows more about regular temperaments can help me.

I assumed negri is only defined for the 7-limit or higher, and that it is required that 49/48 and 225/224 are tempered out:

http://xenharmonic.wikispaces.com/Marvel+temperaments?responseToken=ca7ea7206830efdee25dd4ddb68bf6b2#Negri

But apparently, there's also 5-limit negri, which only tempers out the negri comma, 16875/16384:

https://xenharmonic.wikispaces.com/negri+comma

Now reducing negri to the 5-limit by tempering out 16875/16384 seems like an obvious choice, so this is not too surprising.

However, when I used Graham's temperament finder and entered the commas 16875/16384, 105/104, 144/143 and 325/324 (13-limit), I got the following result:

http://x31eq.com/cgi-bin/rt.cgi?ets=19p_48p&limit=13

...a 13-limit temperament called 'negri 3 dimensions higher' (i.e. based on 5-limit negri) that does not temper out 49/48 or 225/224, and is supported by 48-edo.

So my final question: Is it correct to call this 13-limit temperament 'negri', even though it does not temper out 225/224 (and therefore isn't a marvel temperament)?

Three dimensions below the thirteen limit is the five limit. You have an extension of five limit negri

----------
Graham

------Original message------
From: gedankenwelt94 <gedankenwelt94@...>
To: <tuning@yahoogroups.com>
Date: Thursday, March 21, 2013 5:43:12 PM GMT-0000
Subject: [tuning] Re: Canyon Diablo Fall

--- In tuning@yahoogroups.com, "gedankenwelt94" <gedankenwelt94@...> wrote:
> Note that 48-EDO doesn't support negri when using patent vals, but 2\19 and 3\29 are valid generators for negri, and 5\48 lies between them, so I think it's not that far-fetched to speak of 'negri' in 48-EDO. ;)

Ok, I'm slightly confused now, maybe someone who knows more about regular temperaments can help me.

I assumed negri is only defined for the 7-limit or higher, and that it is required that 49/48 and 225/224 are tempered out:

http://xenharmonic.wikispaces.com/Marvel+temperaments?responseToken=ca7ea7206830efdee25dd4ddb68bf6b2#Negri

But apparently, there's also 5-limit negri, which only tempers out the negri comma, 16875/16384:

https://xenharmonic.wikispaces.com/negri+comma

Now reducing negri to the 5-limit by tempering out 16875/16384 seems like an obvious choice, so this is not too surprising.

However, when I used Graham's temperament finder and entered the commas 16875/16384, 105/104, 144/143 and 325/324 (13-limit), I got the following result:

http://x31eq.com/cgi-bin/rt.cgi?ets=19p_48p&limit=13

...a 13-limit temperament called 'negri 3 dimensions higher' (i.e. based on 5-limit negri) that does not temper out 49/48 or 225/224, and is supported by 48-edo.

So my final question: Is it correct to call this 13-limit temperament 'negri', even though it does not temper out 225/224 (and therefore isn't a marvel temperament)?

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On 3/21/2013 1:43 PM, gedankenwelt94 wrote:
> --- In tuning@yahoogroups.com, "gedankenwelt94"<gedankenwelt94@...>
> wrote:
>> Note that 48-EDO doesn't support negri when using patent vals, but
>> 2\19 and 3\29 are valid generators for negri, and 5\48 lies between
>> them, so I think it's not that far-fetched to speak of 'negri' in
>> 48-EDO. ;)
>
> Ok, I'm slightly confused now, maybe someone who knows more about
> regular temperaments can help me.
>
> I assumed negri is only defined for the 7-limit or higher, and that
> it is required that 49/48 and 225/224 are tempered out:
>
> http://xenharmonic.wikispaces.com/Marvel+temperaments?responseToken=ca7ea7206830efdee25dd4ddb68bf6b2#Negri
>
> But apparently, there's also 5-limit negri, which only tempers out
> the negri comma, 16875/16384:
>
> https://xenharmonic.wikispaces.com/negri+comma
>
> Now reducing negri to the 5-limit by tempering out 16875/16384 seems
> like an obvious choice, so this is not too surprising.

I think you might be right that "negri" was a 7-limit temperament originally, but it looks like it's been used for both 5- and 7-limit temperaments since 2002 and probably earlier. I'm missing a lot of the early history, so I don't know which came first.

> However, when I used Graham's temperament finder and entered the
> commas 16875/16384, 105/104, 144/143 and 325/324 (13-limit), I got
> the following result:
>
> http://x31eq.com/cgi-bin/rt.cgi?ets=19p_48p&limit=13
>
> ...a 13-limit temperament called 'negri 3 dimensions higher' (i.e.
> based on 5-limit negri) that does not temper out 49/48 or 225/224,
> and is supported by 48-edo.
>
> So my final question: Is it correct to call this 13-limit temperament
> 'negri', even though it does not temper out 225/224 (and therefore
> isn't a marvel temperament)?

Graham's script tries to find the best name, but you need to be careful about those "x dimensions higher" names (that means it couldn't find a name for that particular temperament, so it gave it a general name based on the 5-limit negri temperament that it did find).

I don't have a more specific name than "19&48" for this temperament. It looks pretty decent for a 13-limit, but nothing special in the 7-limit list.

Thanks for your answers, Graham and Herman!

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
>
> I think you might be right that "negri" was a 7-limit temperament
> originally, but it looks like it's been used for both 5- and 7-limit
> temperaments since 2002 and probably earlier. I'm missing a lot of the
> early history, so I don't know which came first.

To be honest, I didn't know anything about the history of negri
temperament. I just saw that negri seemed to be defined as a 7-limit
temperament on the marvel temperaments page
<http://xenharmonic.wikispaces.com/Marvel+temperaments> , so I was
confused when I found out that there's also a 5-limit version of negri,
despite not being listed there, while wizzard and other temperaments are
listed as 5-limit temperaments.

About the history, I found out that negri seems to be based on the
10-note maximally even scale in 19-edo:

"Negri ("negripent", "negrisept"):
Origin: 2001, (Paul Erlich?)
Meaning: Named after John Negri's 10-out-of-19 maximally even scale."

(quoted from http://xenharmonic.wikispaces.com/Temperament+names )

If I understand it correctly, "negripent" and "negrisept" (which refered
to 5- and 7-limit negri, resp.) were later combined to "negri".

So, wouldn't it make more sense to list negri on the marvel
temperaments page as a 5-limit temperament (tempering out 16875/16384),
s.th. it is clear that "negri" can also refer to the 5-limit? Maybe
there are good reasons (historical or other) to keep it as it is, but I
find it a little strange and confusing the way it is now.

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
>
> Graham's script tries to find the best name, but you need to be
careful
> about those "x dimensions higher" names (that means it couldn't find a
> name for that particular temperament, so it gave it a general name
based
> on the 5-limit negri temperament that it did find).
>
> I don't have a more specific name than "19&48" for this temperament.
It
> looks pretty decent for a 13-limit, but nothing special in the 7-limit
list.

I'm ok with calling it "an extension of (5-limit) negri", or "19&48". I
was just curious if there is a temperament similar to negri which
describes the tuning generated by 5\48 well, and which is compatible
with 48-edo patent vals. And then I was surprised when I found a
temperament derived from negri, despite not tempering out 49/48 or
225/224. ;)

Best
- Gedankenwelt