Kleismic Yarman Temperament

Dear monz, I just contructed a 12-tone scale micro-tempered by a Yarman Kleisma. Only one fifth is down, the rest is up. Here it is:

|
0: 1/1 0.000 unison, perfect prime
1: 99.459 cents 99.459
2: 199.845 cents 199.845
3: 299.304 cents 299.304
4: 399.691 cents 399.691
5: 500.077 cents 500.077
6: 599.536 cents 599.536
7: 699.923 cents 699.923
8: 799.381 cents 799.381
9: 899.768 cents 899.768
10: 1000.155 cents 1000.155
11: 1099.613 cents 1099.613
12: 2/1 1200.000 octave

Hi Ozan,

I can't see the sense of this temperament. It doesn't appear to be a
micro-temperament, or really a temperament at all. What practical
purpose does it serve? A chain of fifths would typically be tempered
so that some number of fifths approximates some higher-limit
consonant interval. Therefore, the 'comma' being tempered out would
not have repeated prime factors higher than 3. Examples of 'commas'
tempered out in the context of chain-of-fifths temperaments include

The syntonic comma, 81:80 or [-4 4 -1>; tempering it out makes four
perfect fifths up octave-equivalent to a pure major third up. If you
want pure major thirds and octaves, temper the fifths narrow by 1/4
of the syntonic comma.

The schisma, 32805:32768 or [-15 8 1>; tempering it out makes eight
perfect fifths up octave-equivalent to a pure major third down. If
you want pure major thirds and octaves, temper the fifths narrow by
1/8 of the schisma.

The Pythagorean comma, 531441:524288 or [-19 12>; tempering it out
makes twelve perfect fifths up octave-equivalent to a unison. If you
want pure octaves, temper the fifths narrow by 1/12 of the
Pythagorean comma (i.e., 12-tone equal temperament).

The septimal comma, 64:63 or [6 -2 0 -1>; tempering it out makes two
perfect fifths up octave-equivalent to a harmonic seventh down. If
you want pure harmonic sevenths and octaves, temper the fifths wide
by 1/2 of the septimal comma.

And so on. But the "Yarman Kleisma", 4000:3993 or [5 -1 3 0 -3>, has
3 factors of 5 and (negative) 3 factors of 11, so it doesn't
correspond to an interval that you would temper out in, or whose
temperament would lead to, a chain-of-fifths scale or tuning.
However, on the tuning-math list, other temperaments which do exploit
this 'comma' have indeed been discussed.

The paper I recently sent you has more on various scales and
temperaments, some of which are single chains of fifths, some of
which are multiple chains of fifths, and some of which aren't based
on chains of fifths at all. It all comes down to which commas are
tempered out. Re-read it again when you have a chance and feel free
to contact me with any questions/comments/criticisms.

Best,
Paul

It is very tight to the 1/7 comma Meantone tuning model,
only with the "wolve" at D#-Bb instead at G#-Ab .
And in this way as ingenious or useless
as the traditional tuning model.

Werner
> -----Urspr�ngliche Nachricht-----
> Von: wallyesterpaulrus [mailto:wallyesterpaulrus@yahoo.com]
> Gesendet: Mittwoch, 23. Februar 2005 20:48
> An: tuning@yahoogroups.com
> Betreff: [tuning] Re: Kleismic Yarman Temperament
>

>
> Hi Ozan,
>
> I can't see the sense of this temperament. It doesn't appear to be a
> micro-temperament, or really a temperament at all. What practical
> purpose does it serve? A chain of fifths would typically be tempered
> so that some number of fifths approximates some higher-limit
> consonant interval. Therefore, the 'comma' being tempered out would
> not have repeated prime factors higher than 3. Examples of 'commas'
> tempered out in the context of chain-of-fifths temperaments include
>
> The syntonic comma, 81:80 or [-4 4 -1>; tempering it out makes four
> perfect fifths up octave-equivalent to a pure major third up. If you
> want pure major thirds and octaves, temper the fifths narrow by 1/4
> of the syntonic comma.
>
> The schisma, 32805:32768 or [-15 8 1>; tempering it out makes eight
> perfect fifths up octave-equivalent to a pure major third down. If
> you want pure major thirds and octaves, temper the fifths narrow by
> 1/8 of the schisma.
>
> The Pythagorean comma, 531441:524288 or [-19 12>; tempering it out
> makes twelve perfect fifths up octave-equivalent to a unison. If you
> want pure octaves, temper the fifths narrow by 1/12 of the
> Pythagorean comma (i.e., 12-tone equal temperament).
>
> The septimal comma, 64:63 or [6 -2 0 -1>; tempering it out makes two
> perfect fifths up octave-equivalent to a harmonic seventh down. If
> you want pure harmonic sevenths and octaves, temper the fifths wide
> by 1/2 of the septimal comma.
>
> And so on. But the "Yarman Kleisma", 4000:3993 or [5 -1 3 0 -3>, has
> 3 factors of 5 and (negative) 3 factors of 11, so it doesn't
> correspond to an interval that you would temper out in, or whose
> temperament would lead to, a chain-of-fifths scale or tuning.
> However, on the tuning-math list, other temperaments which do exploit
> this 'comma' have indeed been discussed.
>
> The paper I recently sent you has more on various scales and
> temperaments, some of which are single chains of fifths, some of
> which are multiple chains of fifths, and some of which aren't based
> on chains of fifths at all. It all comes down to which commas are
> tempered out. Re-read it again when you have a chance and feel free
> to contact me with any questions/comments/criticisms.
>
> Best,
> Paul

--- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...> wrote:

> It is very tight to the 1/7 comma Meantone tuning model,
> only with the "wolve" at D#-Bb instead at G#-Ab .

Yes indeed (or was the wolf between A#-F), but by comma, Werner, you
are referring to the syntonic comma 81:80, which actually makes sense
in this context, because the goal is to have four fifths up sound
more like a pure major third (modulo the octave).

> And in this way as ingenious or useless
> as the traditional tuning model.

In a way, I agree. But in terms of how to specify/describe/derive
this tuning system, the syntonic comma (or some of the other commas)
would make sense as an interval with which to measure the degree of
tempering. The "Yarman Kleisma" wouldn't. However, other types of
tuning systems, not constructed from single chains of fifths, are
indeed based conceptually on distributing the "Yarman Kleisma", and
speaking of degrees of tempering in terms of fractions of the "Yarman
Kleisma" would make sense in that context. Tempering is done for a
purpose -- not just to make all the intervals worse than JI -- and
the specification of the temperament should indicate, or at least not
mislead as to, what that purpose is.

I agree to all, but please weight, I didn't speak about the "purpose of"
or the "idea behind" this tuning model. It was and is clear to me
that it was not created in order to be a traditional tuning.
I only characterised the "result" which is a "temperament"
And indeed, not all intervals of this tuning model are
worse than JI. The 8 major chords between Bb-major and B-major show
major thirds of about 395,7 cents, in contrast to this
the four major thirds F#, C#, Ab and Eb are tuned worse than with ET
and all minor thirds show either a little approach to
10 : 15 frequency ratio or a tight approach to 16 : 19 frequency ratio.
The detuning of the fifth is still in an acceptable range.
So it is in practice a nice alternate tuning to ET.

> -----Urspr�ngliche Nachricht-----
> Von: wallyesterpaulrus [mailto:wallyesterpaulrus@yahoo.com]
> Gesendet: Mittwoch, 23. Februar 2005 21:37
> An: tuning@yahoogroups.com
> Betreff: [tuning] Re: Kleismic Yarman Temperament
>

>
> --- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...> wrote:
>
>> It is very tight to the 1/7 comma Meantone tuning model,
>> only with the "wolve" at D#-Bb instead at G#-Ab .
>
> Yes indeed (or was the wolf between A#-F), but by comma, Werner, you
> are referring to the syntonic comma 81:80, which actually makes sense
> in this context, because the goal is to have four fifths up sound
> more like a pure major third (modulo the octave).

>> And in this way as ingenious or useless
>> as the traditional tuning model.
>
> In a way, I agree. But in terms of how to specify/describe/derive
> this tuning system, the syntonic comma (or some of the other commas)
> would make sense as an interval with which to measure the degree of
> tempering. The "Yarman Kleisma" wouldn't. However, other types of
> tuning systems, not constructed from single chains of fifths, are
> indeed based conceptually on distributing the "Yarman Kleisma", and
> speaking of degrees of tempering in terms of fractions of the "Yarman
> Kleisma" would make sense in that context. Tempering is done for a
> purpose -- not just to make all the intervals worse than JI -- and
> the specification of the temperament should indicate, or at least not
> mislead as to, what that purpose is.

Thank you Werner for your thoughtful comments. So, there is still hope for this accursed temperament?

Sincerely,
Ozan

----- Original Message -----
From: Werner Mohrlok
To: tuning@yahoogroups.com
Sent: 24 Şubat 2005 Perşembe 8:57
Subject: AW: [tuning] Re: Kleismic Yarman Temperament

I agree to all, but please weight, I didn't speak about the "purpose of"
or the "idea behind" this tuning model. It was and is clear to me
that it was not created in order to be a traditional tuning.
I only characterised the "result" which is a "temperament"
And indeed, not all intervals of this tuning model are
worse than JI. The 8 major chords between Bb-major and B-major show
major thirds of about 395,7 cents, in contrast to this
the four major thirds F#, C#, Ab and Eb are tuned worse than with ET
and all minor thirds show either a little approach to
10 : 15 frequency ratio or a tight approach to 16 : 19 frequency ratio.
The detuning of the fifth is still in an acceptable range.
So it is in practice a nice alternate tuning to ET.

Oh Ozan,

wallyestrpaulus will condemn both us, if we
maintain the term "temperament" for your tuning model.
There is no hope...

Werner
> -----Urspr�ngliche Nachricht-----
> Von: Ozan Yarman [mailto:ozanyarman@superonline.com]
> Gesendet: Donnerstag, 24. Februar 2005 09:49
> An: tuning@yahoogroups.com
> Betreff: Re: [tuning] Re: Kleismic Yarman Temperament
>

> Thank you Werner for your thoughtful comments.
> So, there is still hope for this accursed temperament?
>
> Sincerely,
> Ozan

----- Original Message -----
From: Werner Mohrlok
To: tuning@yahoogroups.com
Sent: 24 �ubat 2005 Per�embe 8:57
Subject: AW: [tuning] Re: Kleismic Yarman Temperament

I agree to all, but please weight, I didn't speak about the "purpose of"
or the "idea behind" this tuning model. It was and is clear to me
that it was not created in order to be a traditional tuning.
I only characterised the "result" which is a "temperament"
And indeed, not all intervals of this tuning model are
worse than JI. The 8 major chords between Bb-major and B-major show
major thirds of about 395,7 cents, in contrast to this
the four major thirds F#, C#, Ab and Eb are tuned worse than with ET
and all minor thirds show either a little approach to
10 : 15 frequency ratio or a tight approach to 16 : 19 frequency ratio.
The detuning of the fifth is still in an acceptable range.
So it is in practice a nice alternate tuning to ET.

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--- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...> wrote:

> I agree to all, but please weight, I didn't speak about
the "purpose of"
> or the "idea behind" this tuning model.

That's right, you didn't. I was addressing Ozan, who came up with it
after deriving a small 11-limit ratio: 4000/3993. It is the audible
relevance of describing the detuning of the fifths in terms of this
ratio that I was questioning. It seems that your description, in
terms of a fraction of the syntonic comma, is far more relevant to
the audible qualities of the tuning -- it tells you how much the
various consonances will be detuned.

> It was and is clear to me
> that it was not created in order to be a traditional tuning.
> I only characterised the "result" which is a "temperament"
> And indeed, not all intervals of this tuning model are
> worse than JI.

Which intervals are better than or as good as JI?

> The detuning of the fifth is still in an acceptable range.

You mean the wolf fifth?

> So it is in practice a nice alternate tuning to ET.

It seems I have been misunderstood again. See my last post.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> Thank you Werner for your thoughtful comments. So, there is still
hope for this accursed temperament?
>
> Sincerely,
> Ozan
>
> ----- Original Message -----
> From: Werner Mohrlok
> To: tuning@yahoogroups.com
> Sent: 24 Þubat 2005 Perþembe 8:57
> Subject: AW: [tuning] Re: Kleismic Yarman Temperament
>
>
> I agree to all, but please weight, I didn't speak about
the "purpose of"
> or the "idea behind" this tuning model. It was and is clear to me
> that it was not created in order to be a traditional tuning.
> I only characterised the "result" which is a "temperament"
> And indeed, not all intervals of this tuning model are
> worse than JI. The 8 major chords between Bb-major and B-major
show
> major thirds of about 395,7 cents, in contrast to this
> the four major thirds F#, C#, Ab and Eb are tuned worse than with
ET
> and all minor thirds show either a little approach to
> 10 : 15 frequency ratio or a tight approach to 16 : 19 frequency
ratio.
> The detuning of the fifth is still in an acceptable range.
> So it is in practice a nice alternate tuning to ET.

Surely the tuning can be considered as a variety of meantone
temperament, with 12 notes per octave, in which case it should be
described with the appropriate fraction of a syntonic comma, as you
did.

--- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...> wrote:
> Oh Ozan,
>
> wallyestrpaulus will condemn both us, if we
> maintain the term "temperament" for your tuning model.
> There is no hope...
>
> Werner
> > -----Ursprüngliche Nachricht-----
> > Von: Ozan Yarman [mailto:ozanyarman@s...]
> > Gesendet: Donnerstag, 24. Februar 2005 09:49
> > An: tuning@yahoogroups.com
> > Betreff: Re: [tuning] Re: Kleismic Yarman Temperament
> >
>
> > Thank you Werner for your thoughtful comments.
> > So, there is still hope for this accursed temperament?
> >
> > Sincerely,
> > Ozan
>
> ----- Original Message -----
> From: Werner Mohrlok
> To: tuning@yahoogroups.com
> Sent: 24 Þubat 2005 Perþembe 8:57
> Subject: AW: [tuning] Re: Kleismic Yarman Temperament
>
>
> I agree to all, but please weight, I didn't speak about
the "purpose of"
> or the "idea behind" this tuning model. It was and is clear to
me
> that it was not created in order to be a traditional tuning.
> I only characterised the "result" which is a "temperament"
> And indeed, not all intervals of this tuning model are
> worse than JI. The 8 major chords between Bb-major and B-major
show
> major thirds of about 395,7 cents, in contrast to this
> the four major thirds F#, C#, Ab and Eb are tuned worse than
with ET
> and all minor thirds show either a little approach to
> 10 : 15 frequency ratio or a tight approach to 16 : 19
frequency ratio.
> The detuning of the fifth is still in an acceptable range.
> So it is in practice a nice alternate tuning to ET.
>
>
> You can configure your subscription by sending an empty email to
one
> of these addresses (from the address at which you receive the
list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual
emails.
> tuning-help@yahoogroups.com - receive general help information.
>
>
>
> Yahoo! Groups Sponsor
> ADVERTISEMENT
>
>
>
>
>
> --------------------------------------------------------------------
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>
> a.. To visit your group on the web, go to:
> /tuning/
>
> b.. To unsubscribe from this group, send an email to:
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>
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Service.

I'd condemn neither of you. Part of the problem I'm trying to get at
is in the title of this thread. Whenever I've seen it used, "Kleismic
Temperament" means a temperament in which the Kleisma vanishes. So
shouldn't "Kleismic Yarman Temperament" refer to a temperament in
which the "Yarman Kleisma" vanishes? I think it should.

--- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...> wrote:
> Oh Ozan,
>
> wallyestrpaulus will condemn both us, if we
> maintain the term "temperament" for your tuning model.
> There is no hope...
>
> Werner
> > -----Ursprüngliche Nachricht-----
> > Von: Ozan Yarman [mailto:ozanyarman@s...]
> > Gesendet: Donnerstag, 24. Februar 2005 09:49
> > An: tuning@yahoogroups.com
> > Betreff: Re: [tuning] Re: Kleismic Yarman Temperament
> >
>
> > Thank you Werner for your thoughtful comments.
> > So, there is still hope for this accursed temperament?
> >
> > Sincerely,
> > Ozan
>
> ----- Original Message -----
> From: Werner Mohrlok
> To: tuning@yahoogroups.com
> Sent: 24 Þubat 2005 Perþembe 8:57
> Subject: AW: [tuning] Re: Kleismic Yarman Temperament
>
>
> I agree to all, but please weight, I didn't speak about
the "purpose of"
> or the "idea behind" this tuning model. It was and is clear to
me
> that it was not created in order to be a traditional tuning.
> I only characterised the "result" which is a "temperament"
> And indeed, not all intervals of this tuning model are
> worse than JI. The 8 major chords between Bb-major and B-major
show
> major thirds of about 395,7 cents, in contrast to this
> the four major thirds F#, C#, Ab and Eb are tuned worse than
with ET
> and all minor thirds show either a little approach to
> 10 : 15 frequency ratio or a tight approach to 16 : 19
frequency ratio.
> The detuning of the fifth is still in an acceptable range.
> So it is in practice a nice alternate tuning to ET.
>
>
> You can configure your subscription by sending an empty email to
one
> of these addresses (from the address at which you receive the
list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual
emails.
> tuning-help@yahoogroups.com - receive general help information.
>
>
>
> Yahoo! Groups Sponsor
> ADVERTISEMENT
>
>
>
>
>
> --------------------------------------------------------------------
--------
> --
> Yahoo! Groups Links
>
> a.. To visit your group on the web, go to:
> /tuning/
>
> b.. To unsubscribe from this group, send an email to:
> tuning-unsubscribe@yahoogroups.com
>
> c.. Your use of Yahoo! Groups is subject to the Yahoo! Terms of
Service.

You are right and I agree. I understand your arguments and
I understood them already before. Therefore I apologize
for my inappropriate joke. But as Ozan spoke of "hopes for
an accursed temperament", I was no more able to give a
Grave (serious?) answer.
The background of my first mail was: I possess a list of
many historic and new ideas in tuning models with 12 tones
per octave. By registering this tuning model I awared the
tight approach of the tuning values of the "Kleismic
Temperament" with the "Meantone 1/7 comma tuning model".
That's all.

Best

Werner

> -----Urspr�ngliche Nachricht-----
> Von: wallyesterpaulrus [mailto:wallyesterpaulrus@yahoo.com]
> Gesendet: Donnerstag, 24. Februar 2005 18:40
> An: tuning@yahoogroups.com
> Betreff: [tuning] Re: Kleismic Yarman Temperament
>

>
> I'd condemn neither of you. Part of the problem I'm trying to get at
> is in the title of this thread. Whenever I've seen it used, "Kleismic
> Temperament" means a temperament in which the Kleisma vanishes. So
> shouldn't "Kleismic Yarman Temperament" refer to a temperament in
> which the "Yarman Kleisma" vanishes? I think it should.
>
> --- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...> wrote:
> > Oh Ozan,
> >
> > wallyestrpaulus will condemn both us, if we
> > maintain the term "temperament" for your tuning model.
> > There is no hope...
> >
> > Werner
> > > -----Urspr�ngliche Nachricht-----
> > > Von: Ozan Yarman [mailto:ozanyarman@s...]
> > > Gesendet: Donnerstag, 24. Februar 2005 09:49
> > > An: tuning@yahoogroups.com
> > > Betreff: Re: [tuning] Re: Kleismic Yarman Temperament
> > >
> >
> > > Thank you Werner for your thoughtful comments.
> > > So, there is still hope for this accursed temperament?
> > >
> > > Sincerely,
> > > Ozan
> >